Astronomy

By Agnes M. Clerke, A. Fowler, and J. Ellard Gore

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Title: Astronomy

Author: Agnes M. Clerke
A. Fowler
J. Ellard Gore

Release date: December 21, 2025 [eBook #77516]

Language: English

Original publication: New York: D. Appleton and Company, 1898

Credits: Richard Tonsing and the Online Distributed Proofreading Team at https://www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.)

*** START OF THE PROJECT GUTENBERG EBOOK ASTRONOMY ***

_THE
CONCISE
KNOWLEDGE
LIBRARY_

ASTRONOMY

[Illustration:

Photograph of the Moon taken at Paris by MM. Loewy and Puiseux with
the great Coudé Equatorial, February 14, 1894.
]

THE CONCISE KNOWLEDGE LIBRARY

ASTRONOMY

❧

AGNES M. CLERKE

AUTHOR OF A POPULAR HISTORY OF ASTRONOMY DURING THE NINETEENTH CENTURY

A. FOWLER, A.R.C.S., F.R.A.S.

DEMONSTRATOR TO THE ROYAL COLLEGE OF SCIENCE

J. ELLARD GORE, F.R.A.S., M.R.I.A.

AUTHOR OF THE SCENERY OF THE HEAVENS, THE WORLDS OF SPACE, ETC.

[Illustration: Black-and-white publisher’s emblem with a tree above a
shield featuring stylized letters, flanked by scrolls reading ‘Inter
Folia Fructus.’]

NEW YORK
D. APPLETON AND COMPANY
1898

_Authorized Edition._

PREFACE

This work aims to present in concise form a popular synopsis of
Astronomical Knowledge to date.

In Section I., Miss Agnes M. Clerke, author of “A Popular History of
Astronomy during the Nineteenth Century,” gives a brief historical
sketch of the science from Hipparchus to the present time. In Section
II., an attempt is made by Mr. A. Fowler, A.R.C.S., F.R.A.S.,
Demonstrator of Astronomical Physics to the Royal College of Science, to
briefly outline the general principles of spherical and gravitational
Astronomy, and to describe the instrumental means now at the command of
observers in the various branches of Astronomical research. The author
begs to record his indebtedness to Loomis’ “Treatise on Astronomy,” and
Young’s “General Astronomy,” which have been frequently consulted,
especially for memorial data; to Mr. W. Shackleton, for assistance in
proof-reading; and to Mr. C. P. Butter, for valuable help in preparing
the diagrams. Section III., contributed by Miss Agnes M. Clerke, deals
with the Solar System; and Section IV., written by Mr. J. Ellard Gore,
F.R.A.S., M.R.I.A., treats of the Sidereal Heavens.

The work is illustrated by a large number of diagrams and other
illustrations, prepared expressly for its pages, as well as by a number
of photographic and other reproductions of photographs and drawings made
by distinguished astronomers in Europe and America. In this connexion
numerous acknowledgments are due.

The Editor begs to express his sense of indebtedness to the following
astronomers and publishers, for kind permission to reproduce original
photographs and drawings from their works:

To M. Loewy, Director de l’Observatoire, Paris, for permission to
reproduce the photograph of the Moon, which forms the frontispiece of
this volume; to Professor Edward S. Holden, Director of the Lick
Observatory, for permission to reproduce drawings and photographs of the
Observatory at Nice, p. 2; the Thirty-six Inch Reflector of Lick
Observatory, p. 40; the Meridian Circle of the Paris Observatory, p.
203; the Spectroscope adapted to the eye end of the Lick Telescope, p.
221; and Jupiter showing the Red Spot, p. 322; to Dr. Isaac Roberts, for
permission to reproduce his photograph of the photographic telescope
used by him, p. 196; to Messrs. Trichnor & Co., of Berlin, for
permission to reproduce two illustrations of Donati’s Comet, pp. 228 and
363; and one of Sun-spots and Magnetic Variations, p. 246—all from
Langley’s “New Astronomy”; to Messrs. Witherby & Co., for permission to
reproduce the photograph of a Sun-spot by Janssen, p. 243; the
photograph of Jupiter, p. 328; the photographs of Swift’s Comet, pp. 374
and 375, Brooks’ Comet, p. 381, and the Milky Way, p. 557, from
_Knowledge_; to Messrs. Taylor & Francis, for the diagram of curves
showing the development of Sun-spots, p. 257; to Professor George E.
Hale, of Kenwood Observatory, Chicago, for his illustrations of Eruptive
Prominences photographed at Kenwood, March 24th, 1896, pp. 264 and 265,
reproduced from the _Astrophysical Journal_; to the Council of the Royal
Society, for the illustration of the Eclipsed Sun, p. 267, reproduced
from “Philosophical Transactions”; to Professor Barnard, for the
photographs of the Corona, reproduced on p. 269; and the drawings of the
Transit of Jupiter’s Satellite, on p. 330, reproduced from the _Monthly
Notices_ of the Royal Astronomical Society; the Eye of Mars, p. 302; and
of Saturn and his Rings, p. 335; to the editor of the _Astronomische
Nachrichten_, for the map of Mercury, by Schiaparelli, reproduced on p.
276; to the editor of _Nature_, for the drawing of Venus by Mascari, on
p. 280; to Messrs. George Philip & Son, for the map of the Moon, given
on p. 291, from Fowler’s “Telescopic Astronomy”; to Messrs. Longman,
Green & Co., for the Chart of Mars, p. 300, and the diagram of the
Apparent Orbit of the Companion of Sirius, p. 439, from Proctor’s “Old
and New Astronomy”; to Professor W. W. Payne of Goodsell Observatory,
for the use of the drawing of the Oases of Mars, p. 304, from “Popular
Astronomy”; and the photograph of Holmes’ Comet, p. 378, from the same
work; to Messrs. A. & C. Black, for the illustrations of the Great Comet
of September, 1882, p. 361, reproduced from Miss Clerke’s “History of
Astronomy”; to Messrs. Crosby, Lockwood & Co., for permission to
reproduce the illustration of the Nebula in Andromeda 31 Messier, p.
398, from the frontispiece of Mr. J. E. Gore’s “Visible Universe”; and
also for the same authority, regarding the diagrams, showing the Stars
visible in the Northern Hemisphere, p. 401; the Stars visible in the
Southern Hemisphere, p. 403; the drawing showing the position of the
Solar Apex, according to different computers, p. 429; and the
photographs of the Spiral Nebula 51 Messier, p. 533; and the Milky Way
in Sagittarius, p. 555, all from the same work; to Messrs. A. D. Innes &
Co., for the use of the diagram, Apparent Orbit of Zeta Herculis, p.
436; Triple Stars, p. 451; and for permission to reproduce the
photographs, 37 Messier, p. 505; the star cluster, Omega Centauri, p.
512; the Nebulæ of Orion, p. 521; and the Magellanic Clouds, p. 537,
from “The Worlds of Space”; and to Messrs. Sutton & Co., for the use of
the diagram of the Apparent Orbit of 70 Ophiuchi, p. 443; the
photographs of the Double Cluster of Perseus, p. 503; the Star Cluster
in Gemini, p. 504; the Star Cluster in Hercules, p. 507; and the drawing
of the Trifid Nebula, Sagittarius, p. 525, from “The Scenery of the
Heavens”; and the drawing of the Temporary Star of 1572, p. 481, from
“Planetary and Stellar Studies,” both published by them.

A. H. M.

CONTENTS

SECTION I.—HISTORY By Agnes M. Clerke.
Chap. Page
I. FROM HIPPARCHUS TO LAPLACE 3
II. A CENTURY OF PROGRESS 21

SECTION II.—GEOMETRICAL ASTRONOMY AND ASTRONOMICAL INSTRUMENTS.
By A. Fowler, A.R.C.S., F.R.A.S.

I. THE EARTH AND ITS ROTATION 41
II. THE EARTH’S REVOLUTION ROUND THE SUN 55
III. HOW THE POSITIONS OF THE HEAVENLY BODIES ARE DEFINED 65
IV. THE EARTH’S ORBIT 72
V. MEAN SOLAR TIME 78
VI. THE MOVEMENTS OF THE MOON 87
VII. MOVEMENTS OF PLANETS, SATELLITES, AND COMETS 98
VIII. ECLIPSES AND OCCULTATIONS 110
IX. HOW TO FIND OUR SITUATION ON THE EARTH 122
X. THE EXACT SIZE AND SHAPE OF THE EARTH 129
XI. THE DISTANCES AND DIMENSIONS OF THE HEAVENLY BODIES 139
XII. THE MASSES OF CELESTIAL BODIES 151
XIII. GRAVITATIONAL EFFECTS OF SUN AND MOON UPON THE EARTH 162
XIV. INSTRUMENTAL MEASUREMENT OF ANGLES AND TIME 171
XV. TELESCOPES 176
XVI. INSTRUMENTS OF PRECISION 198
XVII. ASTROPHYSICAL INSTRUMENTS 211

SECTION III.—THE SOLAR SYSTEM.
By Agnes M. Clerke.

I. THE SOLAR SYSTEM AS A WHOLE 229
II. THE SUN 237
III. THE SUN’S SURROUNDINGS 253
IV. THE INTERIOR PLANETS 273
V. THE EARTH AND MOON 283
VI. THE PLANET MARS 297
VII. THE ASTEROIDS 310
VIII. THE PLANET JUPITER 318
IX. THE SATURNIAN SYSTEM 333
X. URANUS AND NEPTUNE 343
XI. FAMOUS COMETS 352
XII. NATURE AND ORIGIN OF COMETS 368
XIII. METEORITES AND SHOOTING STARS 385

SECTION IV.—THE SIDEREAL HEAVENS.
By J. E. Gore, F.R.A.S.

I. THE STARS AND CONSTELLATIONS 399
II. DOUBLE, MULTIPLE, AND COLOURED STARS 410
III. THE DISTANCES AND MOTIONS OF THE STARS 417
IV. BINARY STARS 431
V. VARIABLE AND TEMPORARY STARS 458
VI. CLUSTERS AND NEBULÆ 497
VII. THE CONSTRUCTION OF THE HEAVENS 538

LIST OF ILLUSTRATIONS

_Frontispiece to Volume_—PHOTOGRAPH OF THE MOON.

SECTION I.—HISTORY.
_Page_
_Frontispiece_—THE OBSERVATORY AT NICE 2

SECTION II.—GEOMETRICAL ASTRONOMY.

_Frontispiece_—THE LICK REFRACTOR OF THIRTY-SIX INCHES
APERTURE 40
_Fig._
1.— ROUGH MEASUREMENT OF EARTH’S DIAMETER 43
2.— HORIZONS AT TWO PLACES ON THE EARTH 44
3.— FOUCAULT’S PENDULUM EXPERIMENT 49
4.— SUN’S RAYS—DAY AND NIGHT 52
5.— ATMOSPHERIC REFRACTION 54
6.— APPARENT PATHS OF SUN AT EQUINOXES AND SOLSTICES 56
7.— ABERRATIONAL ORBIT OF A STAR 58
8.— THE SUN’S ALTITUDE IN SUMMER AND WINTER 62
9.— THE SUN’S ALTITUDE AT THE EQUINOXES 63
10.— THE MIDNIGHT SUN 64
11.— ALTITUDE AND AZIMUTH 66
12.— RIGHT ASCENSION, DECLINATION, ETC. 69
13.— ELLIPTIC FORM OF EARTH’S ORBIT 72
14.— THE ELLIPSE 73
15.— HOW TO DRAW AN ELLIPSE 74
16.— ILLUSTRATING KEPLER’S SECOND LAW 76
17.— EFFECT OF OBLIQUITY OF ECLIPTIC UPON THE EQUATION OF TIME 81
18.— THE MOON’S PHASES 90
19.— THE LUNAR MONTH 91
20.— THE MOON’S ROTATION 93
21.— THE MOON’S NODES 94
22.— POSITION OF ECLIPTIC AT SUNSET AT VERNAL EQUINOX 96
23.— MOVEMENT OF AN INTERIOR PLANET 99
24.— MORNING AND EVENING STARS 100
25.— MOVEMENT OF AN EXTERIOR PLANET 103
26.— APPARENT PATHS OF CERES, PALLAS, JUNO, AND VESTA, IN 1896 104
27.— OPPOSITION OF MARS 105
28.— ELEMENTS OF AN ELLIPTIC ORBIT 107
29.— THE EARTH’S SHADOW 110
30.— THE LUNAR ECLIPTIC LIMIT 112
31.— ECLIPSES OF THE SUN 114
32.— DURATION OF A SOLAR ECLIPSE 115
33.— TRACK OF ECLIPSE OF APRIL 16, 1893 117
34.— DETERMINATION OF LATITUDE 124
35.— ANCIENT MODE OF MEASURING LATITUDE 125
36.— TRIANGULATION 132
37.— MOVEMENTS OF THE EARTH’S POLE, 1890–95 138
38.— PARALLAX OF A HEAVENLY BODY 140
39.— DIAMETER OF A HEAVENLY BODY 142
40.— MEASUREMENT OF THE MOON’S DISTANCE 143
41.— RELATIVE DISTANCE OF VENUS 145
42.— THE PARALLAX OF MARS 147
43.— THE TRANSIT OF VENUS 148
44.— THE MOON’S CURVILINEAR PATH 155
45.— THE TIDES 163
46.— NUTATION 169
47.— SECTION OF READING MICROSCOPE 172
48.— THE READING MICROSCOPE 173
49.— THE ACHROMATIC OBJECT-GLASS 177
50.— THE NEWTONIAN REFLECTOR 179
51.— THE CASSEGRAIN REFLECTOR 181
52.— THE PHOTOGRAPHIC TELESCOPE 196
53.— THE MERIDIAN CIRCLE OF THE PARIS OBSERVATORY 203
54.— THE MICROMETER APPLIED TO A BINARY STAR 208
55.— THE SPECTROSCOPE ADAPTED TO THE EYE END OF THE LICK
TELESCOPE 221

SECTION III.—THE SOLAR SYSTEM.

_Frontispiece_—DONATI’S COMET 228

1.— PHOTOGRAPH OF A SUN-SPOT 243
2.— SUN-SPOTS AND MAGNETIC VARIATIONS 246
3.— CURVES SHOWING THE DEVELOPMENT OF SUN-SPOTS 257
4.— ERUPTIVE PROMINENCE 264
5.— THE SAME, 18 MINUTES LATER 265
6.— THE ECLIPSED SUN 267
7.— THE CORONA OF JANUARY 1, 1889 269
8.— MAP OF MERCURY 276
9.— VENUS, FROM A DRAWING BY MASCARI 280
10.— MAP OF THE MOON 291
11.— PHOTOGRAPH OF THE TOTALLY ECLIPSED MOON 296
12.— CHART OF MARS 300
13.— THE “EYE OF MARS” 302
14.— THE OASES OF MARS 304
15.— JUPITER, SHOWING THE RED SPOT 322
16.— PHOTOGRAPH OF JUPITER 328
17.— TRANSIT OF JUPITER’S FIRST SATELLITE 330
18.— SATURN AND HIS RINGS 335
19.— GREAT COMET OF SEPTEMBER, 1882 361
20.— DONATI’S COMET 363
21.— PHOTOGRAPH OF SWIFT’S COMET 374
22.— THE SAME, 24 HOURS LATER 375
23.— PHOTOGRAPH OF HOLMES’ COMET 378
24.— PHOTOGRAPH OF BROOKS’ COMET 381

SECTION IV.—THE SIDEREAL HEAVENS.

_Frontispiece_—NEBULA IN ANDROMEDA 31 MESSIER 398

1.— STARS VISIBLE IN THE NORTHERN HEMISPHERE 401
2.— STARS VISIBLE IN THE SOUTHERN HEMISPHERE 403
3.— DIAGRAM SHOWING “SOLAR APEX” AS ROUNDLY COMPUTED 429
4.— APPARENT ORBIT OF ZETA HERCULIS 436
5.— APPARENT ORBIT OF THE COMPANION OF SIRIUS 439
6.— APPARENT ORBIT OF 70 OPHIUCHI 443
7.— TRIPLE STARS 451
8.— THE TEMPORARY STAR OF 1572 481
9.— THE DOUBLE STAR CLUSTER IN PERSEUS 503
10.— STAR CLUSTER IN GEMINI 504
11.— 37 MESSIER 505
12.— STAR CLUSTER IN HERCULES 507
13.— THE STAR CLUSTER, OMEGA CENTAURI 512
14.— THE ORION NEBULÆ 521
15.— THE NEBULA ROUND ETA ARGUS 523
16.— THE TRIFID NEBULA, SAGITTARIUS 525
17.— SPIRAL NEBULA, 51 MESSIER 533
18.— MAGELLANIC CLOUDS 537
19.— PHOTOGRAPH OF MILKY WAY, SAGITTARIUS 555
20.— THE MILKY WAY 557

ASTRONOMY

[Illustration:

THE OBSERVATORY AT NICE.

[_See page 192_
]

SECTION I.—HISTORY.

BY AGNES M. CLERKE.

CHAPTER I.
FROM HIPPARCHUS TO LAPLACE.

In the year 134 B.C., a temporary star blazed out in the constellation
Scorpio. It was observed by a man of extraordinary genius, and furnished
the incentive to one of his most memorable works. This was the
construction, on essentially modern principles, of a catalogue of 1,080
stars. Hipparchus thus, with deliberation and singular prescience,
furnished a standard by which future changes in the heavens might be
detected. He was a native of Rhodes, but belonged to the school of
Alexandria; and at Alexandria, after three centuries, he found an able
and ambitious successor.

Claudius Ptolemæus was one of the many “inheritors of unfulfilled
renown.” He combined, completed, and preserved what his predecessors,
eminent or obscure, had done. Gathering materials from all quarters, and
adding much of his own, he reared an astronomical edifice so imposing,
coherent, and substantial, that the lapse of fourteen centuries left it
virtually unassailed, and, to a superficial judgment, unassailable.
Fitly, then, this monument of industry and ingenuity kept the title
bestowed upon it by the Arabs of “Almagest,” signifying “the Greatest.”
It bears, nevertheless, perennial witness to the possibility of
satisfying the human mind with the truth of appearances, apart from the
truth of things. For although the Almagest embodies a large amount of
real knowledge, that knowledge is throughout falsely interpreted. The
Ptolemaic system was constructed on the principle of “saving the
phenomena”—that is, of providing expedients geometrically valid, even if
physically inadmissible, by which to represent the apparent movements of
the heavenly bodies. That they might, to a great extent, be apparent
only, was obvious to the cultivated Greek mind. The rotation of the
earth on an axis was a familiar Pythagorean doctrine; it was adopted by
Plato, and Aristarchus of Samos went to the length of ranking our green
world as a planet revolving yearly round the sun. The idea, however, was
too recondite for vulgar apprehension; it was tainted with a suspicion
of impiety, and its development would, besides, have proved extremely
embarrassing to the nascent science of that age. So Hipparchus chose the
prudent alternative of treating astronomy from the purely mathematical
standpoint; he submitted to the restrictions imposed by the hypothesis
of equable circular motion; and, with wonderful skill, fitted the
Apollonian eccentrics and epicycles to expound celestial wanderings.
Ptolemy inevitably followed suit. He set some five dozen spheres in
motion, while leaving the earth at rest; and at rest it remained until,
in long meditations by the foggy shores of the Baltic, a grave-browed
ecclesiastic elaborated certain cogent arguments in favour of its
motion.

During the interval between Ptolemy and Copernicus, astronomy kept in
the Alexandrian groove. Early in the eighth century, the seat of
learning having been transferred to Baghdad, the charge of its
crystalline machinery devolved upon Arabs and Jews, men of fine
technical acquirements, but small originative power, men of the kind
described in the “Vicar of Wakefield,” who, “had they been bred
cobblers, would all their lives have only mended shoes, but never made
them.” Not but that they executed the necessary repairs with uncommon
ingenuity, modifying the cumbrous structure given into their keeping to
suit the fresh inequalities brought to light by their patient
watchfulness. But their improvements consisted in adding to already
intolerable complications—in piling orb on orb, in devising
“trepidations” and oscillations, of which nature took small heed; so
that the better they observed, the worse their system became.

The science was diligently cultivated. Al-Mamûm, son and successor of
“good Harûn-al-Raschid,” founded at Baghdad a school of astronomy, of
which Albategnius, called “the Ptolemy of the Arabs,” was the brightest
ornament. He discovered, early in the tenth century, the movement of the
“sun’s apogee”—that slow revolution of the longer axis of the earth’s
orbit, regarded by astronomical glacialists as a factor in the
production of recurring Ice Ages. The Persian grandee, Al-Sûfi (903–986)
belonged to the same group. His “Description of the Stars” was a revised
edition, not a simple reprint, of the Alexandrian list, and has the
value derived from personal consultation with the skies. Thus, Algol,
now purely white, is recorded in it as a decidedly red star. About a
century later, Aboul Wefa detected the moon’s “variation,” independently
noted, after five centuries, by Tycho Brahé. Then the Tartars had their
turn. Nasir Eddin (1201–1274) was a native of Khorassan; but his love of
learning drew him to the city of the Khalifs, where he assembled a band
of experts for the construction of new planetary tables, the old ones
having lapsed into hopeless disaccord with the heavens. Last came Ulugh
Beigh, grandson of the furious Tamerlane. He founded at Samarcand a kind
of astronomical Solomon’s House, built a grand observatory, and worked
in it assiduously. His vigorous and ennobling reign of forty years was
terminated by one of those domestic catastrophes which ordinarily fix
the chronology of Eastern dynasties. He was murdered by his son in 1447,
and the sands of the desert thereupon closed, so to speak, over his
civilising efforts. His star catalogue, edited by Francis Baily in 1843,
is the outcome of fresh observations made in the old way. A Tartar
prince, he ranks as an Arab astronomer.

Mohammedan science had already fulfilled its appointed task. A torch,
still alight, had been handed on from East to West. Its extinction would
have been a calamity. A total break in the cultivation of astronomy, for
instance, would have cost ages to repair. The Ptolemaic system, it is
true, disguised rather than revealed nature; yet it constituted a
regulated body of knowledge, only looked at from a wrong point of view.
An unbiassed spectator had merely to shift his position and open his
eyes, in order to perceive the simplicity of the real celestial
mechanism. No better illustration could be adduced of Bacon’s aphorism
that “truth emerges more easily from error than from confusion.”

It was from the Moors in Spain that Christian Europe took its first
lessons in antique science. The Alphonsine Tables were due to Oriental
industry. They were compiled at Toledo about 1270 by an assemblage of
Arab experts directed by Hassan, the Jew delegate of Alfonso X. of
Castile. But they caught Western attention, and drew Western
intelligence towards the abstruse art they exemplified. Thus a little
treatise on the Sphere composed about 1230, by John Holywood, a
Yorkshireman, known to cosmopolitan fame as Johannes de Sacrobosco,
obtained astonishing popularity; at least sixty-five Latin editions of
it appearing between 1472 and 1647, besides French, Italian, German, and
Spanish versions, and endless commentaries. With the revival of
classical learning, the Almagest, previously known in blundering Latin
translations from the Arabic, came to be read in the original Greek, and
thus re-emergent, roused fresh enthusiasm. Inspired by the afflatus,
George Purbach (1423–1461) and his brilliant pupil, Johannes Müller of
Königsberg in Franconia (Regiomontanus), successively professors of
mathematics at Vienna, applied themselves to burnishing up the ancient
epicyclical apparatus; while in Italy, the seductive opinions of the
Pythagorean school gained ground, as evidence came to light, that there
had been astronomers before Ptolemy no less than kings before Agamemnon.
The orthodox doctrine naturally continued to be taught at the
universities; but some of the professors held esoteric opinions of a
different cast, which they freely imparted to privileged disciples. The
earth’s rotation was spoken of as a matter of common knowledge by
Lionardo da Vinci; it was inculcated in rhyme, before the close of the
fifteenth century, by Girolamo Tagliavia, a Calabrese poet; it was
debated by scholars and pedants; on all sides influences wrought to
shatter the integrity of Ptolemaic convictions.

True progress, however, consists less in destruction than in
re-organisation. And this demands powers of a high order. They were
brought into play just at the right moment. Nicholas Copernicus was born
at Thorn on the Vistula, February 19, 1473. At the age of twenty-three,
having exhausted the teaching resources of the university of Cracow, he
crossed the Alps in quest of instruction in Greek and mathematics.
Towards the close of 1496, then, he was enrolled as a student at
Bologna, and shortly afterwards became the pupil, assistant, and friend
of the Ferrarese astronomer, Domenico Maria Novara. Here, beyond
reasonable doubt, Copernicus adopted Copernican opinions. The question,
_An terra moveatur?_ was incessantly mooted at Bologna; advanced
thinkers replied in the affirmative; Novara himself most likely took his
intellectual beliefs from Plato and Aristarchus, while looking to
Ptolemy for his daily bread. The transalpine scholar, at any rate,
brought back with him to Poland in 1505, an unalterable persuasion that
the heliocentric system belonged to the reality of things. He devoted
eighteen years of his abode within the cathedral precincts of
Frauenburg—from 1512 to 1530—to demonstrating its detailed conformity
with the phenomena of the heavens; but allowed only a sketch of his
results to be published. It was only at the earnest request of the
Bishop of Culm that he finally delivered up to him the manuscript of “De
Revolutionibus Orbium Coelestium,” the first printed copy of which was
laid on his deathbed, May 24, 1543.

The immediate effect was small. The new system of astronomy was admired,
but not adopted. It indeed contradicted the evidence of the senses, and
failed to compel assent from the understanding. For its author had not
completely broken with tradition. He unfortunately retained the false
supposition of equable circular motion, and thus greatly marred the
simplicity of his scheme of the heavens. Orbs still kept rolling upon
orbs, Mercury alone demanding a combination of seven to bear him over
his course. But if seven, it might have been asked, why not seven times
seven? The principle of representing appearances by transcendental means
remained the same as before. Ignorance of the laws of motion raised
other formidable objections. A whirling earth, it was thought, should
leave behind all detached objects; absolute repose was taken to be the
condition _sine quâ non_ of stability. Then the seeming immobility of
the stars implied for them a remoteness so extravagant, according to
prevalent ideas, that even Kepler admitted it to be “a big pill to
swallow.” Copernicus was fully aware that the earth’s orbital revolution
must occasion stellar perspective displacements; indeed, he staked the
truth of his theory upon future measurements of annual parallax.
Nevertheless, four centuries passed before they were successfully
executed.

Tycho Brahé was the last great mediæval observer. Like Hipparchus, he
was summoned by a star—the marvellous “new star” of 1572; and, having
obtained from Frederick II. of Denmark the grant of an islet in the
Sound, he built upon it a mansion “royal, rich and wide,” erected
magnificent instruments, and used them, not only with consummate skill,
but also with a certain princely pomp, donning robes of state before
admitting the bright “populace of heaven” to audience. His stormy
temper, however, led to disputes with the young King Christian IV.; he
forsook Uraniborg, and died at Prague in 1601. Curiously enough, the
very accuracy of his observations led him astray from speculative truth.
For it enabled him to perceive the incompatibility of many facts with
Copernican expedients for harmonising them, and intensified the
difficulty raised to Copernican views by the absence of stellar
parallax. So he devised a system of his own, in which the planets
revolved round the sun, but the sun round the earth. It scarcely
survived its contriver.

The invention of the telescope created descriptive astronomy. Without
it, the mechanism of the solar system could have been laid bare, and the
law of force regulating its action discovered; and in point of fact,
Kepler’s achievements owed nothing, and Newton’s very little, to the
optician’s art. Inquiries, on the other hand, into the nature of the
heavenly bodies were wholly inspired by it; it disclosed the amazing
multitude of the stars, and opened endless vistas of research. No one
could at first have divined the momentous character of the accident by
which Hans Lippershey, a spectacle-maker at Middleburg in Holland, hit
upon an arrangement of lenses serving virtually to abridge distance. It
happened in 1608; and Galileo Galilei (1564–1642), hearing of it shortly
afterwards at Venice, prepared on the hint a “glazed optic tube,” and
viewed with it, early in 1610, the satellites of Jupiter, the mountains
of the moon, the star streams of the Milky Way, and in 1611, the phases
of Venus, the spots on the sun, and the strange appendages of Saturn.
Thus, amid a tumult of applause, the telescopic revelation of the
heavens began. It was brilliantly illustrative, although not
demonstrative, of Copernican theory; and Galileo drove his own vivid
conviction on the subject home to general apprehension by the literary
skill with which he treated it in his famous “Dialogues” (1632). He most
substantially promoted the new views, however, by his recognition of the
laws of motion, and of force as the cause of motion. The problem of the
heavens, stript thereby of metaphysical obscurities, was laid bare to
the reason as one of pure mechanics; the planets came to be treated as
ordinary projectiles, and distinct reasoning about the nature of their
paths was rendered possible. Newton’s great task was thus prepared and
defined by Galileo.

Kepler’s (1573–1630) three generalisations formed a still more
indispensable prelude to its accomplishment. Their immediate effect was
to sweep away the Copernican remnants of Ptolemaic lumber, and to
disclose the harmonious plan upon which our system is ordered. But it
was a geometrical plan only. Kepler indeed divined the influence of a
central power, which he surmised to be of a magnetic nature; and he
aspired towards the establishment of a truly physical astronomy. Yet he
was far from perceiving the full implications of the laws he had
himself, after half a lifetime of trial and failure, at last
triumphantly discovered. These laws are:

(I.) The planets travel in ellipses of which the sun occupies one focus.

(II.) They travel at rates varying in such a manner that the “radius
vector”—or imaginary line joining each to the sun—describes equal areas
in equal times.

(III.) The cubes of their mean distances from the sun are proportional
to the squares of their periods of revolution.

Now these are precisely the conditions under which planetary circulation
should proceed if governed by a force emanating from the sun, and
decreasing as the square of the distance from him increased. Moreover,
Hooke, Halley, and Wren separately got so far as to perceive that it
could be explained on this principle. But Isaac Newton alone could
demonstrate what they divined, and even his supreme faculties were
dangerously strained by the laborious process. This was not all. He
showed that the earth exerts on the moon just the same kind of pull that
the sun exerts on the planets; a pull identical with the familiar
“attraction of gravitation,” by which the globe we inhabit holds
integrally together, retains its oceans in their beds, and bears with it
through space its “cloud of all-sustaining air.” Its domestic affairs
are thus guided by the same unchanging rule that dominates its foreign
relations.

The publication in 1687 of Newton’s “Principia” marked an unprecedented
advance in knowledge. The advance consisted in unification. A science of
celestial physics, capable of indefinite future expansion, was founded
on the sure basis of terrestrial experience. Canons of interpretation,
derived from immediate perception, were proved applicable to the
phenomena of the heavens. The line drawn in antique philosophy between
the “corruptible” things under our feet and the “incorruptible” over our
heads was forever rubbed out. Sublunary and empyreal regions were thrown
together into one vast domain.

Although Newton’s law is, in itself, of extreme simplicity, its actual
workings are highly intricate. Because dependent upon a universal and
unintermittent influence, they are self-modifying, so that each
consequence becomes a cause, and to each cause is attached an endless
train of effects. They can be dealt with only with the aid of the
infinitesimal calculus, and then, not directly, but by successive and
tedious approximations, or by arts and devices of almost superhuman
ingenuity. Hence Newton’s laurels would have remained comparatively
barren had he not found successors in a group of men of extraordinary
ability. What he had begun, Clairaut, D’Alembert, Euler, Lagrange, and
Laplace carried on by showing the adequacy of a single law to account
for every traceable deviation from undisturbed elliptical motion. In the
course of a long and arduous campaign, they carried every position that
they attacked. Over and over again, the principle of gravitation seemed
to be compromised; over and over again, it was vindicated by these
intrepid champions.

This process of gradual verification began in 1747, when Clairaut and
D’Alembert sent to the Paris Academy of Sciences, on the same day, the
first satisfactory solutions of the “Problem of three Bodies.” The
motions of the moon, nevertheless, did not at once fall in with the
general theory; they were rendered amenable only after years of anxious
toil. Barely the initial difficulties had been overcome when Euler, in
1753, published his “Theory of the Moon,” from which Tobias Mayer of
Göttingen constructed lunar tables. Now tables are the test of theories.
Every row of figures they contain is a prediction, by the fulfilment, or
non-fulfilment of which the underlying scheme must stand or fall.
Through such comparisons, mathematical astronomers find out the
shortcomings of their methods, or the insufficiency of their hypotheses,
and are incited to refine the first, and correct the second. Demands for
the application of the nicer criteria thus afforded suggest
observational improvements, which seldom fail to bring to light minor
discrepancies with theory, impelling to fresh efforts for their
abolition. Such alternations of advance along the abstract and the
practical lines result in a continual diminution in the _scale_ of
error, although not in its annihilation; absolute exactitude being, as
it were, an asymptote, continually approached, but touched only at
infinity—that is, never, under subsisting conditions. Even now the
length of the moons tether is four or five miles. To that extent, she
may go astray from her computed path, not without occasioning
disquietude to the responsible authorities.

So far as could be ascertained in the eighteenth century, her subjection
to known law was completed by the dispersal of the mystery surrounding a
slight, continuous acceleration of her orbital velocity detected by
Halley in 1693. It had been in progress since the earliest recorded
eclipse in 721 B.C., if not longer; there was no sign of its cessation
or reversal, and the grave question arose, Was the principle of
universal attraction, elsewhere unreservedly obeyed, here fatally
complicated by the action of a resisting medium involving the eventual
collapse of the earth-moon system? Laplace gave the answer, November 19,
1787, by proving the observed quickening of pace to be a necessary and
simple consequence of a secular diminution in the ellipticity of the
earths orbit. This, however, will not go on for ever in the same
direction; after many ages the tide of change will turn, and a complete
restoration to the _status quo ante_ will ensue.

Another master-stroke of Laplace’s genius was his explanation, also in
1787, of the “long inequality” of Jupiter and Saturn. He demonstrated
its strictly gravitational origin in the mutual disturbance of the two
giant planets, rendered up to a certain point cumulative by the
approximate commensurability of their periods. While Jupiter performs
five circuits Saturn accomplishes nearly two, and the perturbation set
up at their conjunction is hence both intensified and balked of
compensation for 918 years.

The epoch of trial and confirmation immediately following the
publication of the “Principia” lasted then a full century. During its
course, difficulties had arisen only to be overcome; suggested
qualifications of the single and simple law of gravity had proved
unnecessary; at its close, recalcitrance had everywhere been overcome,
and there was victory all along the line. And not only were the workings
of the planetary system exhibited as depending upon an elementary
principle, but they were further shown to be perfectly equilibrated. It
contained within itself, so far as could be ascertained, no seeds of
decay; its destruction could only come from without. This remarkable
conclusion was established in a series of splendid treatises by Lagrange
and Laplace. The special adaptation to permanence of the solar mechanism
was demonstrated in them. Ruinous disturbances were shown to be excluded
by the overwhelming disparity of mass between the central body and its
attendants, no less than by the regularity and harmony of their
movements and distribution. Thus only slight oscillatory changes can
occur. Millions of years will elapse without producing any fundamental
alteration. The machine is so beautifully adjusted as to right itself
automatically through the mutual action of its various parts. And it is
the force which perturbs that eventually restores.

The astronomical acquisitions of the century were embodied in Laplace’s
“Mécanique Céleste,” published 1799–1805. This “Almagest of the
eighteenth century,” as it has been termed, is in a rare degree
comprehensive and complete. It leaves nothing enigmatical. Every
question propounded in it receives an answer, if not definitive, at
least highly authoritative; and the range of these questions is very
wide. All the phenomena which the Greeks and Arabs had rightly observed,
but wrongly interpreted, are not merely “saved” by geometrical
artifices, but derived as a connected whole from one physical cause,
absolutely prescribing that they should be thus, and no otherwise. The
work is a record of unmixed triumphs. It seems as if the author, for
want of more worlds to conquer, had laid down the sword of the calculus
to take up the pen of the chronicler. With grave exultation, he proceeds
from point to point, recounting the events of the campaign,
commemorating the battles won by the brilliant staff of mathematical
heroes to which he himself belonged, and expatiating in the broad
subjugated plain. He scarcely looked beyond. There was indeed at that
time no “beyond” where his methods of investigation were applicable. The
“Mécanique Céleste” hints at no unsatisfied ambitions; it is a book of
the _teres atque rotundus_ sort—a world in itself well arranged and
compact, to which outlying perplexities are allowed no access. Nor
should this be counted a defect. As a monument to one of the greatest
periods in the history of science, its fitting character was that of an
ordered collection of acquired certainties.

The countrymen of Newton took no part in the striking series of
operations by which the intricate consequences of the law of gravity
were deduced and shown to correspond with reality. During the whole of
the eighteenth century, they stood aside from the race towards
verification. Their effacement was due to no lack of ability, but to a
mistaken choice of means. Newton’s synthetic method was a veritable Bow
of Ulysses. It was too tough to be bent by other hands than his own.
Thus, no sequel could be given to the “Principia.” There was no
possibility of following up the line of demonstration pursued in it.
Newton himself would have vainly attempted to carry it much further. In
order to advance, it was necessary, as Dr. Whewell remarked, to begin
afresh. This, British mathematicians were unwilling to do. The easy and
flexible analytical method brought to perfection on the continent
remained strange to them. With inadequate strength, they persisted in
wielding the cumbrous weapon of a giant—in using main force, so to
speak, where skill and agility were required. Our insularity in this
respect lasted until about 1816, when, by the joint efforts of the
younger Herschel, Charles Babbage, and George Peacock (afterwards Dean
of Ely), mathematical studies were revolutionised at the University of
Cambridge.

The neglect in England of theoretical research was, however, partly
compensated by the steady progress of practical astronomy. For a century
and a half after its foundation in 1675, the Royal Observatory at
Greenwich continued to be the main—almost the only source of information
regarding the places of the heavenly bodies. Thence were obtained the
data necessary for the correction of theory, since there alone the
visible positions of the sun, moon, and planets were systematically
determined. _Actual_, compared with _predicted_, movements gave
so-called “tabular errors”; and tabular errors indicated theoretical
shortcomings, the rectification of which led gradually, but surely,
towards a higher plane of knowledge.

John Flamsteed (1646–1719), the first astronomer-royal, was, in
Professor De Morgan’s phrase, “Tycho Brahé with a telescope.” By his
diligence and insight he set on foot modern astronomy of precision. The
“British Catalogue” of nearly 3,000 stars, was, in its day, an unique
and most valuable work. His lunar observations were indispensable to
Newton’s calculations, which, indeed, through the insufficient supply of
them, now and again came to a halt; he constructed new solar tables, and
kept watch over the careers of planets and comets. His completion, in
1689, of a seven-foot mural quadrant, constituted a marked advance in
the art of instrument-making. It was firmly fixed in the meridian, so
that the distances from the zenith of the heavenly bodies at the moment
of culmination could be read off on the limb, the time being
simultaneously noted by a clock. Their positions in the sky relative to
a set of forty otherwise known stars were thus completely determined,
and they were determined essentially after the manner still in use.

On Flamsteed’s death in 1719, Edmund Halley (1656–1742) succeeded to his
place. An expedition to St. Helena in 1677, for the purpose of observing
stars invisible in these latitudes, got him the name of the “southern
Tycho.” They were the very first so situated to be located on the sphere
(except those few that came within Ptolemy’s range), and a list of them,
to the number of 341, was appended to the “British Catalogue.” The
purpose to which Halley devoted most sustained attention was, unluckily,
that in which he was least successful. Early in life he formed the
design of observing the moon through an entire revolution of its nodes,
so as to bring lunar tables to the perfection required for solving the
prize-problem of longitudes. But the _contumax sidus_—his opprobrious
term for our satellite—proved more than a match for him. The eighteen
years’ watch was kept, notwithstanding that the watcher had reached the
age of sixty-five before he was able to set about it; but in vain;
nothing came of it. Halley’s varied performances were, nevertheless, so
considerable as to warrant Lalande in describing him as “the greatest of
English astronomers”; and he ranked next to Newton among contemporary
English men of science.

His cometary labours alone sufficed to perpetuate his name. He initiated
the computation, on Newtonian principles, of the orbits traversed by
such bodies—then a most toilsome process; and, among twenty-four, found
three so much alike as to suggest the identity of the great comets of
1531, 1607, and 1682. A renewed apparition might then be expected in
1758, and he appealed to “candid posterity to acknowledge that this was
first discovered by an Englishman.” The prediction roused widespread
interest, and as the epoch for its fulfilment drew near, Clairaut
undertook the formidable task of determining to what extent it might be
postponed by the retarding influence of Jupiter and Saturn. Many times
he despaired of its execution, even with the efficient aid of Lalande
and Madame Lepaute, the wife of a Paris clock-maker; and at last, after
months of wearisome calculation, having succeeded in forming the
differential equations representing the comet’s disturbed motion, he
threw down the paper on which they were written, with the exclamation,
“Now, integrate them who can!” Eventually this, too, was done; and the
comet, caught sight of on Christmas Day, 1758, by Palitzsch, a rustic
star-gazer in Saxony, passed the sun within the month’s “law” permitted
to it by the French geometer. This signal triumph laid the sure
foundation of cometary astronomy.

In 1679, Halley drew attention to the importance of transits of Venus
for measuring the sun’s distance; and developed later a method
extensively used in observing the eighteenth century pair of transits in
1761 and 1769. But the accuracy actually attained in determining the
instants of contact between the limbs of the sun and planet fell far
short of what he had anticipated as attainable. The “black drop”
interposed its pernicious effects, and occasioned wide discrepancies.
The margin of uncertainty regarding the value of the great unit was,
none the less, diminished, although it still remained uncomfortably
wide; while the public interest excited by such rare events, the
adventurous character of the expeditions sent to the uttermost parts of
the earth for their utilisation, and the combined efforts of various
nations towards the same end, served to popularise astronomy, and to
give it something of that cosmopolitan stamp now borne by it.

Besides the discovery of the secular acceleration of the moon’s motion,
that of the long inequality of Jupiter and Saturn was due to Halley; he
ascertained, in 1718, the proper movements of Sirius, Aldebaran, and
Arcturus, thereby virtually demonstrating the non-existence of “fixed”
stars; he associated auroræ with terrestrial magnetism; noted the
globular star clusters in Hercules and Centaur; and divined nebulæ to be
composed of “a lucid medium shining with its own proper lustre,” and
filling “spaces immensely great.” Yet, in spite of the comprehensiveness
of his genius, his administration at Greenwich was a failure. He was a
better astronomer than astronomer-royal.

James Bradley (1693–1762), who came after him, gave a narrower scope to
his abilities, yet was of unsurpassed sagacity in connecting effects
with their causes. Robert Hooke (1635–1703) had observed, in 1669,
annual displacements of γ Draconis, a star nearly crossing the zenith of
London, which he took for results of parallax; and Flamsteed, in 1694,
had similarly interpreted a similar affection of the pole-star. They had
both been misled by an “aberration,” due to the progressive transmission
of light combined with the advance of the earth in its orbit. Bradley
determined to sift the matter thoroughly, and observed Hooke’s star
continuously from 1725 until 1728, first at Kew with Molyneux, then at
Wanstead in Essex. It evidently described a small ellipse in the sky
with a period of one year; yet its place in the ellipse was not what it
should have been on the parallactic hypothesis; so he remained for some
time in the dark about it. During a water-party on the Thames, however,
in September 1728, he noticed that the slant of the pennant varied with
changes in the boat’s course, the wind remaining steady throughout. This
gave him the clue he wanted; and his discovery of the “aberration of
light” was communicated to the Royal Society in the month of January
following. That of the nutation of the earth’s axis followed in 1748.
Both, setting aside their importance in themselves, were indispensable
as preliminaries to accuracy in fixing the places of the heavenly
bodies. For they are vital elements in the process of “reduction,” by
which the ore of truth contained in observations is extricated from the
dross of casual circumstances. The raw material, collected by timing
transits and reading circles, must be so refined and purified that the
facts contained in it become mutually comparable. Before Bradley’s time
allowance was indeed roughly made for refraction in our atmosphere, and
for the precession of the equinoxes; and, in the case of the moon, for
parallax; but the effects of aberration and nutation had remained mixed
up with a mass of disguising errors. Their elimination constituted an
inestimable improvement.

In the immediate art of observation Bradley was a master. He did not
live to possess an achromatic telescope; neither astronomical circles
nor equatorial mountings were at his disposal. His leading instrument
was an eight-foot quadrant, by John Bird, certainly of admirable
workmanship; although of a type long since, and for good reasons,
superseded. He amassed with it, nevertheless, a treasure of high-class
observations. The bulk of them remained in manuscript until 1798, so
that it was reserved for this century to turn them to account; but their
value has only developed with the efflux of years. Those relating to the
moon and planets, reduced by Sir George Airy, lent efficient aid towards
perfecting the theories of those bodies. Those of 3,222 stars formed
into a catalogue by Bessel were published in 1818 with the proud, but
not unmerited title of “Fundamenta Astronomiæ.” The same original data,
again in 1886 reduced with the utmost nicety of care by Dr. Auwers of
Berlin, afforded a splendid accession to knowledge of stellar proper
motions. Acquaintance with Bradley’s stars now extends over 144 years;
and the amount and direction of their progress across the sphere during
that long interval have, for the most part, become defined with
tolerable certainty.

Nathaniel Bliss (1700–1764), the fourth astronomer-royal, filled the
post only two years. Yet the observations made under his care form a
sequel to Bradley’s well worth having. The reign of his successor, Nevil
Maskelyne (1732–1811), extended over forty-six years. His determinations
of the sun, moon, and planets, were in great demand abroad for the
correction of tables, and as criteria of theories; while, of the stars,
he paid attention only to thirty-six, catalogued as reference-points in
1790. Their proper motions served Herschel for his second investigation,
in 1805, of the sun’s translation through space. By the close of the
century, Maskelyne’s instruments had lapsed into decrepitude; and only
the stimulus supplied by Pond’s strictures roused him to order one of
Troughton’s improved circles. But he died before it was mounted, and its
employment fell to the share of his critic, John Pond (1767–1836), the
sixth astronomer-royal. Maskelyne’s most enduring title to fame is his
foundation, in 1767, of the “Nautical Almanac.”

English observers were ably seconded by English artists. Graham, Sisson,
Cary, Bird, Ramsden, had, from the beginning to the end of the
eighteenth century, no foreign competitors of note. Their quadrants and
sectors were distinguished both for stability and for refinement of
execution. The mechanical skill displayed in their construction was no
less necessary for the promotion of practical astronomy than the
subtlety of eye and hand needed to employ them to the best advantage.
Bradley’s work was conditioned by the performances of Graham and Bird.
Without Graham’s sector he could not have discovered the aberration of
light; without Bird’s quadrant the perennial worth of his Greenwich
observations would have been impaired, if not destroyed. Observatories
all over the continent were furnished in the latter half of the
eighteenth century with instruments of English make; the art of
accurately dividing circular limbs was invented in England, and nowhere
else successfully practised. The innovation of substituting entire
circles for quadrants was effectively introduced by Ramsden; and Piazzi
came from Palermo in 1788 for the purpose of securing from him a
five-foot altazimuth, at that date the finest sky-measuring machine in
the world. Edward Troughton (1753–1835) ably carried on the tradition of
his predecessors, and brought the altazimuth, transit circle, and
equatorial up to the modern standard of efficiency. But they were no
longer in exclusive demand. The foundation, in 1804, of Reichenbach’s
Institute at Munich finally abolished the British monopoly in supplying
astronomers with their exquisite and ingenious tools.

The improvement of refracting telescopes ran a somewhat similar course.
The essential step of combining flint and crown glass, so as to bring
differently-coloured rays to one focus, was taken in 1733 by Chester
More Hall, a gentleman of fortune in Essex; but he published nothing,
and the re-invention of the “achromatic” lens was left to John Dollond
(1706–1761) a Spitalfields weaver. “I obtained,” he wrote in 1758, “a
perfect theory for making object-glasses, to the apertures of which I
could scarcely conceive any limits.” The excise duty on glass, however,
which was repealed only in 1845, drew these limits very narrowly in this
country; and it was through the extraordinary perseverance of a Swiss
artisan named Guinand, in overcoming the difficulties connected with
glass-making, and the genius of Joseph Fraunhofer (1787–1826) in
moulding the material thus placed at his disposal, that refractors began
at Munich to rise towards their present power and perfection.

The history of the reflecting telescope is British throughout. It was
invented by Newton, made practically effective by John Hadley
(1682–1744), and brought very near to theoretical perfection by James
Short of Edinburgh (1710–1768); yet it is remarkable that not a single
observation of lasting interest was made with any of his instruments, a
few of which have survived, and are regarded with admiration to this
day. The career of reflectors as engines of discovery began, but did not
end, with William Herschel.

CHAPTER II.
A CENTURY OF PROGRESS.

On March 13, 1781, an event occurred without precedent in the history of
astronomy. A new member of the sun’s immediate retinue was disclosed. A
hard-worked music-teacher at Bath performed this startling—indeed,
according to antique notions—impossible feat; and the name of Herschel
became known _urbi et orbi_. It was far from being by chance that the
“new planet swam into his ken.” The Octagon Chapel organist was no
ordinary lucky amateur. He had, some time previously, made two notable
resolutions. The first was to push the improvement of telescopes to the
furthest verge of what was possible; the second, to leave no corner of
the starry heavens unexplored. And he applied himself with marvellous
energy, in despite of accumulated professional engagements, to carry
them into execution. He thus rapidly grew to be an adept in the art of
constructing specula, and a master in the art of using them.

Two lines of effort, accordingly, converged, in his case, towards
celestial discoveries. With all his diligence in “reviewing” the
heavens, he could not have distinguished at sight Uranus from a fixed
star, but for the uncommon excellence of his seven-foot reflector; nor
would the reflector, had it been used in the ordinary erratic fashion of
casual stargazers, been at all likely to have encountered the little
bluish disc of the remote orb then slowly wending its way through the
constellation of the Twins. The direct, and a momentous result of the
discovery was to secure for astronomy the undivided powers of the
extraordinary man who had made it. George III. attached him to his
Court, delivered him from the drudgery of teaching, and gave him the
means of carrying out his grand designs.

Their fulfilment involved the construction of great light-gathering
machines. Herschel ardently desired to see as far and as much as the
conditions of mortality permitted; he was the first to connect depth of
penetration into space with extent of reflective surface; and he
accordingly strained every nerve to secure the means by which to compass
the end he had mainly in view. Nor was he content with mere size. His
mirrors were as remarkable for beauty of figure as for breadth of
aperture. They bore, on proper occasions, enormously high magnifying
powers, and the precise roundness of the star-images formed by them
excited the incredulous wonder of contemporaries. The quality of some of
his largest instruments was guaranteed by the heavens themselves. Their
approval was signified to the seven-foot reflector through the detection
with it of Uranus; the “large twenty-foot,” with a speculum of eighteen
inches, revealed in January 1787, two Uranian moons, Oberon and Titania;
and the monster forty-foot, through the tube of which George III.
promenaded with the Archbishop of Canterbury, brought into view, within
three weeks of its completion, Enceladus and Mimas, the innermost and
hardest to observe of Saturn’s numerous family of satellites.

The forty-foot was “Herschel’s furthest”; he fully recognised that with
it he had touched the line which divides failure from success. If,
indeed, he had not overpassed it; for the subsequent career of the great
telescope hardly bore out the promise of its start. It was an unwieldy
engine, demanding vastly more time and labour to bring into play than
the twenty-foot; and Herschel took such account of minutes as few men do
of hours or days. His fiftieth birthday had in fact gone by before his
optical ambition was satisfied; while his appetite for exploration was
only whetted by what he had already accomplished. He estimated, however,
that a “review of the heavens” with the forty-foot would have occupied
800 years; hence it was used only on special occasions. The Orion nebula
was the last celestial object upon which, January 19, 1811, “its broad,
bright eye” rested; and it was then, with due honour, placed on the
retired list.

Two years before his death, which occurred August 25, 1822, the elder
Herschel initiated his son into the secrets of speculum-building. The
pupil was worthy of the master. John Herschel (1792–1871) aimed only at
producing generally available instruments, and his success was easy and
unqualified. His eighteen-inch mirrors seem to have been all but
faultless. They certainly afforded him better views of the nebulæ than
had been obtained by his father. Thus he first saw the “Dumb-bell” in
its true oval shape; and his remarks upon annular lines of structure in
elliptical nebulæ prove that features unmistakably imprinted upon Dr.
Roberts’ photographs had been antecedently visible to him, and probably
to him alone.

The next stride in the enlargement of reflectors was made by an Irish
nobleman, the third Earl of Rosse (1800–1867). His leviathan telescope,
six feet in aperture, and fifty-four in length, has, in point of actual
size, never been surpassed. Distinguished rather for light-grasp than
for precise definition, it found its appropriate field in the nebular
realms of the sphere; and the discovery of spiral nebulæ, with which it
made its début, was one of high and wide significance.

William Lassell (1800–1881) of Starfield, near Liverpool, set the
example, in 1840, of mounting reflectors equatorially, so as to enable
them, by the application of clock-work, to follow automatically the
diurnal movement of the heavens. His specula were of almost unrivalled
perfection in form and finish. One twenty-four inches in diameter, now
at Greenwich, left a splendid record. With it Lassell detected, October
10, 1846, the satellite of Neptune; September 18, 1848, simultaneously
with W. C. Bond of Cambridge, U.S., Hyperion, the seventh in order of
distance and last in order of discovery of Saturn’s eight moons; and
October 24, 1851, Ariel and Umbriel, the inner pair of Uranian
satellites, of which Sir William Herschel had possibly, although not
very probably, caught transient glimpses. He erected a similar
instrument of fourfold capacity at Malta in 1861, registered with its
aid 600 new nebulæ, and delineated the complex structure of many others,
previously less well seen.

The four-foot reflector built in 1870 by Thomas Grubb of Dublin for the
Melbourne Observatory disappointed expectation. An apparatus so delicate
that the abrasion of 1/20,000th of an inch makes all the difference
between good and bad definition, is ill-fitted to endure the
rough-and-tumble experiences of an ocean-voyage; and that it in some way
“suffered a sea-change” is scarcely doubtful. It was the last great
telescope of its kind, metallic specula, having, in the seventies, been
superseded by mirrors made of glass upon which a thin layer of silver
has been chemically deposited. These have many advantages over their
predecessors. They are considerably more reflective; they are more
easily constructed; their shape is less liable to injury; their
brilliancy, although more evanescent, can be readily restored. They have
the drawback, however, of being extremely sensitive to changes of
temperature. A three-foot mirror of this description by Calver, was
employed by Dr. Common at Ealing with surprising success, early in 1883,
for the purpose of photographing the Orion nebula. It was mounted at the
Lick Observatory, California, in 1896. Dr. Common has since himself
constructed a similar instrument of five feet aperture, which is the
most potent light-collector ever yet turned to the skies. It is curious
to learn that the silver spread over its surface weighs less than one of
the “fourpenny bits” some time ago withdrawn from circulation; the
reflecting film is in fact only 1/280,000 inch thick.

Reflectors are perfectly, and _naturally_, achromatic, rays of all
colours being thrown back at the same angle, and consequently meeting at
the same focus. This gives additional brilliancy to the images formed by
them, compared with those given by object-glasses, the colour-correction
of which has hitherto been so imperfect that much light has to be
“thrown away” as worse than useless. New kinds and combinations of
optical glass have, however, of late been invented, by which this grave
defect may be cured. Reflecting telescopes, on the other hand, are less
manageable, and suffer more from distortion through change of position.
Their cheapness recommends them to amateurs; but they should, on
principle, be reserved for special departments of work, such as nebular
photography and the chemical delineation of stellar and nebular spectra.

The growth of refractors, like that of reflectors, has obtained from
time to time the sanction of unexpected disclosures. Thus a superb
fifteen-inch, turned out at Munich in 1847, for Harvard College,
Cambridge, U.S., showed Hyperion to Bond, September 16, 1848, and on
November 15, 1850, surprised him with a view of Saturn’s dusky ring.
This telescope was surpassed, after fifteen years, through the energy
and genius of Alvan Clark, the famous self-taught American optician,
originally a portrait-painter at Cambridgeport, Massachusetts. Before it
had left the workshop, an eighteen-inch achromatic, now the leading
instrument at the Dearborn Observatory, Evanston, Illinois, won maiden
honours by disclosing to Alvan G. Clark, one of the maker’s sons,
January 31, 1862, the dim companion of Sirius, which, before being seen,
had made itself _felt_ by gravitational disturbances of its radiant
primary. The Washington twenty-six-inch, by the same firm, was rendered
illustrious by Professor Hall’s discovery, in 1877, of a pair of Martian
moons; the Lick thirty-six-inch, by bringing within the range of
Professor Barnard’s keen eyesight, September 9, 1892, Jupiter’s tiny
“fifth satellite.” The diploma performance of the Yerkes forty-inch,
mounted in 1896 at the Chicago University Observatory, is yet to come.
Meanwhile, several very perfect refractors, up to thirty-two inches of
aperture, have been built on this side of the Atlantic by Sir Howard
Grubb of Dublin, and the MM. Henry of Paris; and a twenty-five-inch,
finished so long ago as 1868, and at the cost of his life through the
labours which it entailed, by Thomas Cooke of York, after having lain
for upwards of a score of years choked by the fog and smoke of
Gateshead, has recently begun a promising career at Cambridge, under the
care of Mr. Frank Newall, son of the original owner.

And now we cannot but ask ourselves, has the _ne plus ultra_ in
telescopic magnitude been attained? There is no reason to suppose that
it has, provided that due allowance be made for inexorable conditions.
Climate is one of these. The largest instruments are those most readily
crippled by atmospheric hindrances. The greater their powers, the fewer
are the nights on which they are likely to be available. If they are to
“shine in use,” and not “rust unburnished,” they must then be erected in
exceptionally favourable localities, such as the summit of Mount
Hamilton (the site of the Lick Observatory), or the Harvard College
southern station at Arequipa in Peru. In South Africa, too, but “up
country”—not in the Cape peninsula—splendid facilities for astronomical
observation are to be found.

From Professor Keeler’s report it can readily be gathered, and he indeed
explicitly states, that the Yerkes forty-inch marks the limit of useful
size in equatorials. For the character of the star-images formed by it
slightly change their character when it is directed to different parts
of the sky; and this implies that its lenses become, as it moves,
infinitesimally deformed through the effects of their own weight. No
larger instrument, accordingly, can safely be permitted to swing in
mid-air. The huge light-concentrating machines of the future will lie in
wait for the objects to be observed, instead of pursuing them. They will
either be supported horizontally, or mounted in the “Coudé” fashion
invented by M. Loewy. In either case, the necessary movement will be
performed vicariously by a plane mirror.

Thus, the optical and mechanical outlook is decidedly better than the
atmospheric. The question, How to build giant telescopes? is more easily
answered than the question, Where to place them when built? The ultimate
barrier to seeing indefinitely far into space is the rigid circumstance
that we live on an air-girt globe. The prospects of astronomy are deeply
involved in the forecast of its hampering effects. The dependence of
those prospects upon telescopic improvements became obvious when
Herschel took the whole contents of the sphere “for his province.” These
are indefinitely numerous, indefinitely far-off, indefinitely faint. The
task of their correlation undertaken by Herschel, and inherited from him
by modern astronomers, can at no time be more than approximately
fulfilled; but for each successive approximation more light is needed.
Those who would investigate the universe can never get enough of that
too scarce commodity.

Until Herschel conceived the novel idea of a comprehensive science of
the stars, they had been chiefly regarded as convenient sky-marks, by
which to track the wanderings of our nearer neighbours in space. When it
was perceived that the sky-marks were not fixed, it became necessary to
determine their movements; and this was very roughly done for
fifty-seven stars by Tobias Mayer of Göttingen, in 1757; and more
accurately for thirty-six by Maskelyne, a third of a century later. But
if the stars were travelling, the sun could not be supposed to stand
still; and the possibility of laying down his line of march through
space, by extricating a common element from the confused network of
mutually-crossing stellar paths, occurred to Mayer, and was actually
realised by Herschel in 1783. His inquiry, with the scanty materials
then at command, was a wonderful stroke of audacity, which very nearly
hit the mark; yet few believed in his result until it was confirmed by
Argelander in 1837.

The various attempts made, prior to 1782, to measure the parallaxes of
some of the brighter stars were instigated by the wish to find a
demonstrative argument in favour of the Copernican theory of our system.
They had no reference to sidereal structure. Herschel, however, took up
the subject simply for the purpose of fixing the scale of that vast
edifice. Before sounding the skies, he sought to ascertain the length of
his fathom-line. He never ascertained it. To the end of his life, he
could only make plausible assumptions as to the distances of the stars.
Their real parallaxes were insensible with his instrumental means. But
he fortunately chose for his experiments Galileo’s “double-star method.”
This consisted in determining the relative positions of two close stars,
one of which, taken to be indefinitely remote, was designed to serve as
a standard of reference for the perspective shiftings of the other. It
was thus that Herschel’s attention was directed to double stars. He
found them to be astonishingly numerous—far more numerous than could
have been anticipated by the doctrine of probabilities. In January,
1782, he presented to the Royal Society a catalogue of 269 star-pairs,
and he had collected 434 more by December, 1784. From their abundance
alone, the Rev. John Michell inferred their character of binary systems;
and Herschel, after twenty years of observation, was able, in 1802, to
announce the fact of their mutual revolutions. Thus was taken the second
great step towards the unification of the Cosmos. Newton proved that
terrestrial gravity dominates the solar system; Herschel showed that a
law of attraction, presumably (and assuredly) identical in its mode of
operation, extends through sidereal space.

One cannot reflect without amazement that the special life-task set
himself by this struggling musician—originally a penniless deserter from
the Hanoverian Guard—was nothing less than to search out the
“construction of the heavens.” He did not accomplish it, for that was
impossible; but he never relinquished, and, in grappling with it, laid
deep and sure the foundations of sidereal science. No one before him had
thought of approaching the subject otherwise than by way of speculation;
he alone had the boldness to attack it experimentally. Having invented
for the purpose an ingenious method of “star-gauging,” based upon the
hypothesis that the stars are, on an average, scattered evenly through
space, he concluded in 1784, from its application, that the Milky Way is
the visual projection of a disc-shaped stellar aggregation, within which
our sun is somewhat excentrically placed. The progress, however, of his
telescopic studies convinced him that the continued action of a
“clustering power” had long ago drawn the stars into many separate
allotments, and annulled the original uniformity of their distribution.
So the disc theory was given up, and the Milky Way came to be regarded
as a collection of genuine clusters, arranged into an irregular ring
encircling the solar system. This view, implicitly held by the elder
Herschel from 1802, was explicitly stated by his son in 1847. The
results that Herschel expected from star-gauging may, in the future, be
derived from the more elaborate process of star-gauging by magnitudes,
photographically executed; and the sky-charting work, rapidly
progressing in all parts of the world, will at least supply ample
materials for sounding the star-depths.

These are stored besides with the curious objects called “nebulæ.” They
were little noticed until Herschel, on March 4, 1774, made

“That marvellous round of milky light
Below Orion,”

the subject of his earliest recorded observation. Except, indeed, as
impediments to comet-hunting. Thus, Messier, one of the keenest
sportsmen in that line who have ever scanned the sphere, tried to
eliminate by enumerating them, and drew up in 1771 a list of 45 such
misleading objects, enlarged in 1781 to 103. And Lacaille, during an
expedition to the Cape in 1752–1755, picked up 42 more. So far this
department of knowledge had been cultivated when Herschel began to
“sweep the heavens.” To _sweep_ them, be it remembered. Not merely to
gaze at hap-hazard, or to look out for show specimens, but to gather in
the celestial harvest methodically, zone by zone, so as to “leave no
spot of the heavens unvisited.” The fruits were proportioned to his
diligence. The nebulæ discovered by him amounted, in 1802, to 2,500. And
he did not merely discover; he investigated them as well. He separated
them into classes, noted the mode of their distribution, and searched
out their relationships. To begin with, he believed them to be of a
purely stellar nature—to be, in fact, independent galaxies. Miss Burney
was informed by him in 1786 that he had “discovered fifteen hundred
universes.” A few years later, however, he reasoned out for himself the
gaseous nature of a great many nebulæ, such as that in Orion, and those
of the “planetary” sort; and published in 1811 a complete theory,
strikingly illustrated with examples taken from his telescopic
experiences, of stellar development out of nebulous stuff. The
supposition that they included the revelation of “exterior universes”
was thus rendered, to say the least, superfluous; yet it was not
perhaps, even by him, wholly abandoned. It was, moreover, revived in
consequence of the performances of the great Rosse reflector, from 1845
onwards, in resolving apparent nebulæ into “bee-like swarms” of stars.
Meanwhile Sir John Herschel’s examination of those wonders of the
southern heavens, the Magellanic Clouds, had virtually decided nebular
standing. For they contain within a limited compass, as Dr. Whewell
argued in 1853, “stars, clusters of stars, nebulæ, regular and
irregular, and nebulous streaks and patches. These, then, are different
kinds of things in themselves, not merely different to us.” That stars
and nebulæ co-exist in every part of the heavens, has since been fully
established; while the laws respectively governing their distribution
over the sphere are related in such a manner as to leave no doubt that
these two classes of sidereal objects unite to form the grand galactic
whole. Hence, to all reasonable apprehension, “island universes” have
vanished into the inane.

Sir John Herschel accomplished the unparalleled feat of sweeping the
heavens from pole to pole. Having, within eight years from 1825, revised
his father’s work at Slough, he conceived the noble idea of rounding it
off in the southern hemisphere; and, in 1833–4, transported his
instruments from Slough to Feldhausen near Cape Town. During the four
years of his residence there, he not only executed his proposed survey,
registering 1,790 nebulæ—300 of them for the first time—and discovering
and measuring 2,100 double stars, but carried out a number of special
researches. He catalogued the miscellaneous contents of the Magellanic
Clouds—systems _sui generis_, as he justly termed them—made a detailed
and laborious study of the Argo nebula, applied pretty extensively the
paternal method of star-gauging, observed Halley’s comet at its second
predicted return, measured the sun’s heat-emissions, carefully watched
the spot-maximum of 1837, and finally, struck with a sudden rise in
magnitude of η Argûs, brought to general knowledge that star’s
extraordinary character. These varied results were embodied in a
monumental volume, published in 1847.

One of the greatest triumphs of modern science has been the
establishment of an “Astronomy of the Invisible.” It was primarily due
to Bessel’s inquiries into the disturbed proper motions of the
“Dog-stars,” Sirius and Procyon. They convinced him that each of these
brilliant orbs is attended by a massive satellite, round which it
revolves as it advances, its path in the sky being thus not straight but
wavy. Telescopic verification of his forecast was, nevertheless, delayed
until 1862 in the case of Sirius, until 1896 as regards Procyon. The
earliest, and still the most memorable result in this line is the
discovery of Neptune. Bessel knew that the thing was to be done, and in
1840 planned the doing of it. But his powers began, soon afterwards, to
be crippled by deadly illness, to which he succumbed, March 17, 1846.
_Uno avulso, non deficit alter._ Adams and Leverrier separately
undertook the enterprise he had relinquished, and each with perfect
success. It was a formidable one. The _direct_ problem of perturbations
taxes the highest mathematical resources; the _inverse_ problem is not
only more arduous, but was then untried. Laplace and Lagrange had shown
how to determine the perturbations produced by a known disturbing body;
it was left for Adams and Leverrier to find an unknown body through its
disturbing effects. Irregularities in the movements of Uranus betrayed
the presence of Neptune, and by the powerful analysis brought to bear
upon them, were made to serve as an index to his actual place in the
heavens at a given epoch. This was done by Adams in September, 1845; but
his calculations, deposited at the Royal Observatory in the hope that
they would incite to a telescopic search for the new planet, remained
there buried in a drawer. Sir George Airy had no faith in them, and he
unaccountably received no reply to a test-question addressed to their
author. In the following June, however, he was roused by the
intelligence of Leverrier’s advance towards the goal already attained by
Adams, to arrange an exploratory campaign with the Cambridge
“Northumberland equatorial.” But here again, disbelief—reinforced by the
absence of a detailed star-map—stepped in to retard proceedings
conducted by Professor Challis in so leisurely a fashion that the object
“wanted” was found before he had sifted his observations, September 23,
1846, by Galle of Berlin, acting under Leverrier’s precise directions.
It proved on inquiry to have been twice observed at Cambridge during the
previous couple of months.

Gravitational astronomy won its crowning distinction by the discovery of
Neptune. It afforded the first instance of a body made known as an
unseen power previously to being visually detected. Many stellar
systems, however, have since then been ascertained to include members
which can only be _felt_, owing to their partial, if not total
obscurity. Again, the spectroscope tells of the existence of others
entirely beyond the range of direct vision with the most powerful
optical appliances; not because they do not shine (although this is
sometimes also the case), but because they revolve so close to their
primaries as to form with them single and indissoluble telescopic
objects.

The spectroscope and the photographic camera have been mentioned as aids
to astronomy. Their adoption has profoundly modified the science,
widening its borders, inviting it to undertake novel tasks, endowing it
with previously undreamt-of powers. Realms of knowledge deemed
inaccessible to human faculties have, as if at the touch of a magician’s
wand, been thrown open; and of the many paths leading into the interior,
only a few have yet been pursued, and that for a short distance. The
prospects of exploration are hence unlimited, and of bewildering
variety.

Spectrum analysis is essentially a chemical method. It depends upon the
principle firmly established in 1859 by Kirchhoff and Bunsen, two
professors at the university of Heidelberg, that different kinds of
glowing vapour give out distinctive rays of variously coloured light,
commonly called “lines,” simply because, for the purpose of getting rid
of overlapping images, and for convenience of measurement, they are
transmitted through a narrow slit. Thus, the presence of a familiar, and
almost ubiquitous deep-yellow line, named by Fraunhofer “D,” and shown
by a moderately powerful apparatus to be double, _infallibly_ testifies
to the presence of sodium; iron, rendered gaseous by heat, gives out
several thousand lines ranging from end to end of the spectrum, not one
of which is common to any other substance; hydrogen shows a radiant
sequence exclusively its own; and so of all the remaining elements. To
apply this mode of detection, the light from the source to be studied
must be analysed, or dispersed into its various component colours
through the unequal action upon them of a prism, or train of prisms.
Dispersion can also be effected by “diffraction”; and since the spectrum
thus produced is “normal,” or dependent wholly upon wave-length, it is
always employed where a high degree of exactitude is aimed at. The
coloured fringes of shadows originate in this way, through the
interference of ethereal undulations; while the rainbow is a prismatic
phenomenon, drops of water performing the refractive office of actual
prisms.

The rainbow exemplifies too—although less perfectly than the electric
light—what is called a “continuous spectrum.” Its tints merge one into
the other insensibly, without any sensible dark interruption. Now,
incandescent liquids and solids of every kind and quality give
rainbow-like spectra; they emit light which _rolls out_ into an unbroken
band of colour. Hence there is nothing characteristic about them. They
are to the chemical enquirer absolutely uncommunicative. Vapours and
gases alone can be induced to show the _badge_ of their particular
nature.

Celestial spectrum analysis began with the sun. The solar spectrum is
furrowed transversely by a multitude of fine dark lines, known as
“Fraunhofer lines,” because Fraunhofer brought them within scientific
cognisance by carefully mapping and measuring them. Their significance
remained a standing puzzle until Kirchhoff, in 1859, furnished the key
to it, by demonstrating the correlation of radiation and absorption. In
other words, vapours and gases have the faculty of arresting those
precise rays of light which they are in a condition to emit. Hence, the
ignited, although relatively cool vaporous envelope of a white-hot body
like the sun, or the carbons of the electric arc, acts predominantly as
an intercepting medium, stopping more than it sends out of its peculiar
rays. There results a continuous spectrum crossed by dark lines of the
same chemical significance as if they were bright. They would, in fact,
show as bright if the brilliant background, upon which they are seen
projected, could be withdrawn. The interpretation, upon this principle,
of the Fraunhofer lines, proved the sun to be surrounded by hydrogen in
vast quantities, by incandescent sodium, magnesium, iron, calcium, and a
number of other metals. Spectrum analysis in this way assumed a double
aspect. The hieroglyphics of coloured light were rendered legible,
whether positively or negatively written. And the spectra of the
heavenly bodies are actually found to be inscribed, some in one way,
some in the other; not unfrequently, in both combined.

The new and marvellous power of investigation thus acquired was in 1864
applied to the stars by Dr. Huggins and his coadjutor, Professor W. A.
Miller. They ascertained the presence in the atmospheres of Aldebaran
and Betelgeuse, of nine or ten terrestrial elements, thereby setting on
foot the science of stellar chemistry. Moreover, on August 29, in the
same year, Dr. Huggins made the signal discovery of gaseous nebulæ.
Admitting the dim rays of a “planetary” in Draco through the slit of his
spectroscope, he perceived it to be composed of three bright green
lines, one of them Fraunhofer’s “F”—an emanation of hydrogen. This one
observation verified after seventy-three years Herschel’s inference of
the existence in the heavens of a “fiery haze,” destined, according to
his long forecast of creative processes, eventually to “subside into
stars.”

By the discovery of celestial spectrum analysis, a third stadium of
progress towards the unification of the sciences was reached. The first
step was taken with the demonstration that the force retaining the
planets in their orbits is no other than that which causes rivers to
flow, and apples to fall upon the earth. The extension of the same law
to the stellar universe through the discovery of binary stars, showing
that matter, wherever existing, possesses at least one unchanging
quality, constituted the second. It was now learned that the sun and
stars were composed of the identical _species_ of matter scattered in
the dust of the earth, dug up from its bowels, condensed to make its
oceans, entering into the very framework of our own bodies. An universal
chemistry was established, based upon the relations of light to material
molecules, and of material molecules to the ether filling space; and, as
an inevitable consequence, the new branch of knowledge, termed
“astrophysics,” made its ardently welcomed advent. By it astronomy has
entered into close alliance with the rest of the sciences. No laboratory
experiment is any longer indifferent to her; and laboratory experiments,
on the other hand, derive from the connexion vastly augmented
importance. The youth of learning seems renewed. Secrets of nature,
formerly believed to lie beyond the scope of investigation, have been
penetrated; _nil desperandum_ is the motto which astro-physicists have
earned the title to adopt as their own.

The old art of direct observation has, during the latter half of the
present century, developed in sundry novel directions. By the use of
auxiliary appliances, the telescope has gained a wonderful increase of
subtlety and power. Modern astronomical work may be divided into four
classes:—telescopic, spectroscopic, photographic, and spectrographic or
spectrophotographic. Daguerre’s invention was almost immediately tried
with the sun and moon; J. W. Draper and the two Bonds in America,
Foucault and Fizeau in France, and Warren de la Rue in this country,
being among the pioneers of celestial photography. But it was not until
after the introduction of the collodion process that really useful
results were obtained. With the regular employment at Kew, from 1858
onwards, of De la Rue’s “photoheliograph,” began the daily
selfregistration of sun-spots, suggested by Sir John Herschel in 1847;
and pictures of the eclipsed sun, obtained with the same instrument at
Rivabellosa in Spain, July 18, 1860, terminated a prolonged dispute as
to the nature of the red prominences by exhibiting them as undeniably
solar appendages. Lunar photography was meanwhile successfully
prosecuted, and Henry Draper’s picture, of September 3, 1863, remained
unsurpassed for a quarter of a century. Star-prints were first secured
at Harvard College, under the direction of W. C. Bond in 1850; and his
son, G. P. Bond, made, in 1857, a most promising start with double-star
measurements on sensitive plates, his subject being the well-known pair
in the Tail of the Great Bear. The competence of the new method to meet
the stringent requirements of exact astronomy was still more decisively
shown in 1866 by Dr. Gould’s determination from his plates of nearly
fifty stars in the Pleiades. Their comparison with Bessel’s places for
the same objects proved that the lapse of a score of years had made no
sensible difference in the configuration of that immemorial cluster; and
Professor Jacoby’s recent measures of Rutherfurd’s photographs, taken in
1872 and 1874, enforced the same conclusion. To the “collodion period”
also belongs the earliest spectrograph, taken by Dr. Huggins in 1863;
but the analysed light of Sirius left an uncharacteristic, although a
strong impression. No lines were visible in it; a “virgin page” was
presented. Before prosecuting the subject, fresh developments had to be
awaited.

The invention of gelatine dry plates was the decisive event in the
history of celestial photography. Dr. Huggins turned it to account with
marked success for depicting the spectrum of Vega, December 21, 1876,
and was able, three years later, to exhibit to the Royal Society
photographs of the spectra of six white, or Sirian stars, stamped with
the ultra-violet series of hydrogen lines, then for the first time
recognised, whether on the earth, or in the sky. The uses of the camera
have since then multiplied at a prodigious rate. Its versatility appears
unbounded. There are very few departments of astronomy left in which the
eye has the advantage over it. A volume might be written on its
successes; its comparative failures would scarcely fill a page. Its
extraordinary power of penetrating space would have amazed and delighted
William Herschel. This is due to the indefinitely prolonged exposures
rendered practicable by the employment of dry plates; and these
exposures can be interrupted and resumed at pleasure. Three-night
photographs are now quite commonly taken, following the example given by
Dr. Roberts in 1889. Now every additional minute of exposure brings
intelligence from further and further sky-depths, owing to the happy
faculty of sensitive plates for accumulating impressions. The eye sees
at once, or not at all; the chemical retina sees by degrees, storing up
insensible effects until they become sensible, and this without
definable limit. This is its most essential prerogative. For the
portrayal of nebulæ and comets, it is inestimable; and by its means the
boundaries of the sidereal system may be laid down before the twentieth
century is far on its way. A picture of the great comet of 1882,
standing out from a richly spangled background, taken at the Cape
Observatory under Dr. Gill’s direction, was the object-lesson by which
the advantages of photographic star-charting were effectually learnt.
They have been practically illustrated in the _Cape Durchmusterung_, a
southern continuation, by photographic means, of Argelander’s
corresponding telescopic work at Bonn; and are being turned to account
on a magnified scale, in the International Survey of the heavens, now in
progress at seventeen observatories scattered over the face of the
globe. Special problems have, meanwhile, been investigated with striking
success, by the chemical method, and its fresh applications are
innumerable. Hitherto, performance has usually outrun promise; but
promise has now so quickened its pace as to make the issue of the race
dubious. We can only be sure that the future will be full of surprises.

ASTRONOMY

[Illustration:

THE LICK REFRACTOR OF THIRTY-SIX INCHES APERTURE.
]

SECTION II.—GEOMETRICAL ASTRONOMY AND ASTRONOMICAL INSTRUMENTS.

BY A. FOWLER, A.R.C.S., F.R.A.S.

CHAPTER I.
THE EARTH AND ITS ROTATION.

It is a common remark that we are creatures of circumstances, and in no
sense is this truer than in its application to the conditions under
which we view the heavenly bodies. At the commencement of a study of
astronomy it is accordingly important to first ascertain as far as
possible the nature of the earth on which we are situated, and to
determine in what way our observations are affected by our local
conditions.

THE HORIZON.—When we look at the sky we see a vast hemispherical vault
of which we seem to occupy the centre. If we are at sea, the water and
sky appear to meet at a certain distance, in whatever direction we look.
Where these meet we have what is called the visible horizon. On land,
the horizon is usually broken up by terrestrial objects, such as hills,
buildings, or vegetation, but otherwise the appearances are the same as
at sea.

SHAPE OF THE EARTH.—When we observe the horizon, whether from land or
sea, our eyes are at a certain elevation above the level of the ground
or water, as the case may be, and the higher we are situated, the
greater is the distance of the visible horizon, although the circular
outline is retained. No matter where we may be, the same appearances are
noted, and we are thus led to infer that the earth is a globe, as no
other shape could appear circular from all points of view.

There are other considerations which lead to the same conclusion with
regard to the shape of the earth. One of the most familiar proofs that
the earth cannot be flat is found in the aspects of a ship putting out
to sea or coming into port, when observed from a somewhat elevated
position on shore. A ship does not become visible in its entirety, as it
would if diminishing distance were the only cause affecting its
visibility; the masts are seen first, and then the lower parts of the
vessel gradually make their appearance. This finds a simple explanation
in the curvature of the surface of the sea, and as similar appearances
can be seen in all parts of the world, a globular form is indicated.

The fact that one may continue to travel westward and yet return to the
point of starting, is quite in harmony with the supposition that the
earth is globular, but it does not furnish a proof. This facility would
evidently be equally afforded by a cylindrical earth, or even by a flat
earth of which the Pole occupied the centre.

Still another indication of the rotundity of the earth is given by the
phenomena of an eclipse of the moon. On these occasions, as will appear
later, the moon passes through the shadow of the earth, and as this
shadow is always circular, nothing but a spherical, or nearly spherical,
body can be in question.

SIZE OF THE EARTH ROUGHLY MEASURED.—Granting then that the earth is
spherical, a measurement of its curvature will enable us to determine
its size. To do this it is necessary to measure the distance of the
visible horizon from the eye at a known elevation. Then it can be shown
that if the height of the eye is only a small fraction of the diameter
of the earth, the diameter is as many times larger than the distance of
the horizon as that distance is greater than the height of the eye.
Thus, to an observer whose eye is 5 feet above sea level, the horizon is
2¾ miles distant, while from the top of a lighthouse 66 feet high the
sky would appear to meet the sea at a distance of 10 miles. One way in
which an approximate measurement may be made is illustrated in Fig. 1.
Three posts are placed in line, with their tops at the same height above
the surface of some calm stretch of water such as is afforded by a
canal. A telescope fixed to the first post, so that its centre is at the
top, is directed to the upper end of the third post, and it is seen to
sight the middle one at some distance from the top. When the posts are a
mile apart, the line joining the two extremes turns out to be 8 inches
below the top of the middle one.

[Illustration:

FIG. 1.—_Rough Measurement of Earth’s Diameter._
]

In our diagram this 8 inches is represented by the distance _b d_, and
if we imagine an arc of a circle _d e_ concentric with the surface of
the water, the part which it intersects on the end post, namely _a e_,
will also be 8 inches. This means that to an eye at _a_, 8 inches above
the surface represented by _d e_, the visible horizon at _d_ would be a
mile distant. Applying the proportion named above, it results that the
earth is 7,920 miles in diameter.

Owing to various causes, this method only furnishes a rough indication
of the dimensions of our globe; but, if we had no other evidence, the
result would suffice to explain that the irregularities of the earth’s
surface, though seeming so large to us who dwell upon it, are not
inconsistent with the idea that the surface forms part of a sphere. The
highest mountains with which we are acquainted do not exceed 5½ miles in
height, and this is only ¹⁄₁₄₀₀th part of the earth’s diameter. On a
globe 14 inches in diameter, representing the earth, the highest
mountains would be less than a hundredth of an inch on the same scale;
so that, taking the earth generally, it is practically a smooth globe.

DIFFERENT HORIZONS AT DIFFERENT PLACES.—So far then we have learned that
the earth is a globe about 8,000 miles in diameter. This enables us to
understand that persons in different parts of the earth will see the sky
in different ways. At any given place we can see only what is above our
horizon, and it results from the spherical form of the earth that no two
observers have precisely the same horizon. If we consider a section of
the earth, such as is shown in Fig. 2, an observer at the point _a_ will
have a horizon represented in section by the line _b c_, while the
horizon of an observer at _d_ will be represented be _e f_. It is clear
then that an external distant object, such as the sun or a star, which
may appear on the horizon in the direction _a b_, as seen from the point
_a_, will be at a considerable angle above the horizon when seen from
the point _d_.

[Illustration:

FIG. 2.—_Horizons at Two Places on the Earth._
]

SENSIBLE AND RATIONAL HORIZON.—Having this conception of the horizon as
a thing terrestrial, we may consider its astronomical relationships a
little further. If we imagine the plane of the horizon prolonged until
it cuts the distant sphere on which the stars and other celestial bodies
seem to lie, it will meet that sphere in what is called the _sensible
horizon_. A parallel plane passing through the centre of the earth is
called the _rational horizon_, but as the starry sphere is at an almost
infinite distance, the rational and sensible horizons coalesce into one
celestial horizon.

Closely associated with the horizon is the point vertically overhead
which is called the _zenith_, and the point vertically below which is
called the _nadir_. As the plane of the horizon is tangential to the
earth’s surface at the point of observation, the zenith is simply the
prolongation into space of the line joining the centre of the earth with
the place of observation; at the point _a_ in Fig. 2, for example, the
zenith is in the direction _o a z_.

The zenith as thus defined, however, is not the astronomical zenith, but
what is called the geocentric zenith. As will appear later, the earth is
not truly spherical, so that the direction of gravity does not pass
exactly through the earth’s centre, and the astronomical zenith is
overhead in the direction of gravity.

DIURNAL MOTION OF THE HEAVENS.—In the day-time, when the sky is clear,
we see the sun; at night, we sometimes see the moon, always some stars,
and occasionally a comet. If we continue our observations, even for a
few hours, we begin to recognise that the heavenly bodies have an
apparent movement towards the west, very similar to the daily motion of
the sun, with which everyone must have been familiar from childhood.

Continuing such observations, it is found that the great majority of the
stars do not appear to change their positions relatively to each other,
although their apparent places in the sky are different at different
times. These have consequently been called the “fixed stars,” but in the
light of our present knowledge, the name is not to be taken too
strictly. On account of this seeming fixity, the stars have been divided
from very remote times into _constellations_, or groups, which enable us
to name and identify individual members of the starry host. Other bright
objects having the appearance of stars, when they are viewed merely by
the naked eye, may be seen to change their positions with regard to the
stars in that part of the sky in which they appear. These are the
_planets_—the “wandering stars” of the ancients, to whom five were
known, namely, Mercury, Venus, Mars, Jupiter, and Saturn.

Comets also are seen to share in the general westward movement of the
heavenly bodies, but, in addition, they have another movement relative
to the stars situated in the same part of the sky.

If we closely observe the stars in Europe, we shall find some of them
rising due east, and setting due west; others, again, will be found to
rise in the north-east, and to travel nearly overhead; still others will
be seen to rise south of east, attain only a small elevation above the
horizon, and pass from our view as far south of west as they rise south
of east. One point in the heavens appears stationary, and all the stars
seem to traverse their daily courses round this as a centre. This
stationary point is the north _celestial pole_. It is marked by no star,
but a fairly conspicuous star is at present only about a degree and a
half removed from it The name given to this star is the Pole Star, or
Polaris. As seen from London, stars within 51½° from the celestial pole
never set, and such stars are said to be _circumpolar_.

When our place of observation is changed from one of middle latitude to
one very near the Equator, these appearances are modified. We still see
the stars rising and setting daily, but there will be _two_ points which
do not seem to move, one on the northern and the other on the southern
horizon. One of these stationary points is identical with that seen from
higher latitudes, and the other, which is called the _south celestial
pole_, is diametrically opposite to it What is more, stars which were
not visible at all at our first place of observation will be seen in the
south. All the stars will rise and set, and will alike be above the
horizon for twelve hours.

If we could see the stars from the North Pole, the Pole Star, which is
on the horizon of places at the Equator, would be found overhead, and
all the stars visible to us would be ever above the horizon. Not only
this, not one of the glittering stars which adorns the southern heavens
would ever be seen at all.

In place of the rising and setting of stars, which lends such a great
interest to their observation in other parts of the world, as seen from
the poles the stars will simply travel round and round in circles
parallel to the horizon.

To produce the apparent daily revolution of the heavens, and the changes
in the appearances observed at different places, one of two causes must
be at work; either the celestial bodies themselves must be performing a
daily majestic movement from east to west round a motionless earth, or
the earth itself must be whirling round from west to east, and so
changing the situation of the observer’s horizon with regard to external
bodies. In the early days of astronomical observations this observed
revolution of the heavens was thought to be real, but, with our present
knowledge, we are no longer justified in regarding the earth as
occupying a place of any such importance as that of the centre of the
universe. By the earth’s rotation, an observer, unless situated exactly
at the North or South Pole, is carried round in a circle, and his
horizon is gradually swept round so that on one side stars are setting
and on the other side rising. The appearances at different places find a
simple and sufficient explanation in the varying inclination of the
observer’s horizon to the earth’s axis of rotation as the place of
observation is changed.

A very simple experiment will assist one to comprehend the varying
position of the horizon in different latitudes, and its effect upon the
apparent diurnal movement of the heavens. Through the middle of an
orange pass a knitting-needle, so that the two together may be taken to
represent the earth and its axis. A circular piece of thin card pushed
on to the needle at one end will represent the polar horizon, and, if
the orange be rotated, it will be at once realised that such movement
produces no change in the plane of this horizon, although different
points on the visible horizon will be successively brought in line with
different groups of stars or other external bodies.

Another piece of card should next be fixed on the orange by means of a
pin at a point corresponding to the Equator. Again spinning the model
earth on its axis, this horizon will be seen to constantly change its
plane with regard to outside objects, and in a manner which perfectly
accounts for the apparent movement of the heavens as observed from a
point on the Equator.

A third piece of card touching the surface of the orange at an
intermediate place will have an oblique movement, and as referred to
this plane, the stars appear to traverse their daily rounds in oblique
circles.

EXPERIMENTAL PROOFS OF ROTATION.—Not only does a supposed rotation of
the earth accord perfectly with all that we can glean from observations
of the heavens, but actual demonstrations of the reality of this
movement are forthcoming. Sir Isaac Newton suggested one experimental
method of setting the matter at rest. The further a thing is removed
from the centre of the earth, the greater is the circle which it
describes in a day, and the greater, consequently, the speed with which
it must travel. Thus the top of a high tower moves more quickly than its
base, and the surface of a mine than the bottom of the shaft. A stone
let fall from the top of a tower thus starts with a greater forward
velocity than that of objects at the base, and when it reaches the
earth’s surface, it will be a little east of the point where a
plumb-line let down from its starting-point reaches the surface. This
experiment has been tried, but there are so many disturbing causes
affecting the movement of the falling stone that the results are not
very satisfactory, although generally confirming the earths rotation
from west to east. Evidently this method would fail at the Pole, and
would be most effective at the Equator.

A much more beautiful and perfect proof is furnished by the celebrated
Foucault’s pendulum experiment. Again fancying ourselves at the North
Pole, let us imagine a long and heavy pendulum, suspended in such a
manner that the plane in which it swings is not affected by the earth’s
rotation. The trace of such a pendulum on a bed of sand placed beneath
it would remain in a constant position if the earth were at rest. As the
earth rotates, the bed of sand is twisted round, and the path of the
pendulum apparently changes. The experiment was first actually carried
out by Foucault in 1851, at the Pantheon in Paris, and it created a
widespread interest. Since then, pendulums have been erected in various
parts of the world, and all agree in essential results. The experiment
can be seen in actual operation in the science section of the South
Kensington Museum. The pendulum bob is a very heavy one, and before
commencing the experiment, it is held out of the vertical by a loose
band, which is fixed to the wall by a piece of string. On burning the
string, the band falls off, and the pendulum starts its swing with
little or no movement out of a plane. The pendulum bob is suspended by a
long piano wire which is attached to a bracket carrying a conical pivot.
The pivot rests on an agate plate at the end of a beam, and the weight
of the bracket is compensated by an adjustable weight (Fig. 3). When
swinging, the pendulum has a constant tendency to remain in one plane,
and the turning of the beam beneath the pivot has no effect on the
absolute direction of the plane of swing. Beneath the pendulum is a
table divided into degrees, and the hourly apparent movement of the
plane of swing at Kensington is observed to be nearly 12°.

[Illustration:

FIG. 3.—_Foucault’s Pendulum Experiment._
]

If the experiment could be performed at the North Pole, the pendulum
plane would apparently rotate from east to west, making a complete
rotation once a day. At the South Pole the direction of movement would
be reversed, but the rate would be the same as at the North Pole. The
experiment, however, fails altogether at the Equator, while at places
between the Poles and Equator the rate of movement varies with the
latitude.

A more compact piece of apparatus for demonstrating the earth’s rotation
is the gyroscope, which we also owe to Foucault’s ingenuity. The
principle is exactly the same as in the case of the pendulum. A heavy
disc is set in very rapid rotation, and is suspended in such a way that
its points of support may be turned round without disturbing its plane
of rotation. The results obtained with this instrument substantiate
those derived from pendulums.

These experimental proofs of the rotation of the earth further teach us
the same fact that we learn from observations of the stars, namely, that
the earth makes a complete turn on its axis once a day.

LATITUDE AND LONGITUDE.—Having thus arrived at the conclusion that the
earth is a globe turning on an axis once in twenty-four hours, the
_North and South Poles_ may be defined as the points where the axis of
rotation meets the surface, while the _Equator_ is the circle passing
through places midway between the Poles. Imaginary circles passing round
the earth through the Poles are called _meridians_, while circles
parallel to the Equator are called _parallels_. These conceptions enable
us to define very precisely the situation of any particular place upon
the terrestrial sphere. We measure its angular distance from the
Equator, as seen from the centre of the earth, and call this its
_latitude_; London, for instance, is 51½° north of the Equator, and this
is abbreviated to lat. 51½°N. All places on the same parallel have the
same latitude, so that another measurement is required to designate the
exact location of any one place. For this purpose the meridian passing
through some place is agreed upon as a start-point, and we can then say
that the place in question is so many degrees east or west; such a
measurement represents the _longitude_ of the place. At present there is
no universal agreement as to the initial meridian, but in all British
maps the meridian passing through the centre of the transit instrument
at the Royal Observatory, Greenwich, is taken as the start-point.
Longitudes are reckoned up to 180° E. and 180° W. New York, for example,
is in long. 73° 58′ W., and Berlin in long. 13° 24′ E.

THE CARDINAL POINTS.—For general convenience in expressing the situation
of an object, it is usual to say that it is towards the north, south,
south-west, etc., as the case may be. A north or south line at any
place, or a _meridian line_, as it is called, is in the direction of the
terrestrial meridian passing through the place. The north point of the
horizon is thus the point in which the meridian line meets the horizon
towards the North Pole. The opposite point is south; while the east and
west points lie in the directions at right angles. There are various
ways in which a meridian line may be drawn. One of the simplest is to
erect a vertical rod and to observe when its shadow thrown by the sun is
shortest; at that moment the shadow marks the direction of north and
south. This method is not very exact, as it is so difficult to tell when
the shadow is shortest. A more accurate result may be obtained by
drawing a circle round the stick as centre, and noting the points on
this circle reached by the end of the shadow before and after noon; the
point midway between these, marks the position of the shadow when
shortest. By taking the average result of observations made with more
than one circle, a good approximation can be obtained.

For a somewhat rough determination of the direction of the cardinal
points, a watch showing the correct time may be utilised. Directing the
hour hand to the sun, the south point will lie midway between that and
XII. In the case of a watch having a dial marked up to XXIV., and
reading XII. at mid-day, the latter figure would always point to the
south when the hand indicating the hour was directed towards the sun.
This will be easily understood if it be remembered that the sun is in
the south at intervals of (approximately) twenty-four hours.

[Illustration:

FIG. 4.—_Day and Night._
]

DAY AND NIGHT.—The succession of days and nights by which our daily
arrangements are regulated is at once explained by the fact that the
earth is round, and turns on its axis once a day. At any particular
instant of time the sun can only shine on that half of the earth which
is turned towards it. At all places included in the illuminated part the
sun will be above the horizon, and it will be day. One half of the earth
will be turned away from the sun, and to all places in that part it will
be night. Under the conditions represented in Fig. 4, to a person
situated at the point P it will be midnight; he will, however, be
carried by the earth’s rotation along the circle P Q R; when he arrives
at a point on _a b_, the sun will be rising to him, and his day will
commence. On reaching the point R the sun will be on the spectator’s
meridian, and it will be noon. After another interval he will arrive at
the boundary of light and shade, and his night will commence.

ATMOSPHERIC REFRACTION.—In common with other substances through which
light can pass, the atmosphere by which the earth is surrounded has the
effect of bending rays of light out of their courses, and on account of
this we do not see the heavenly bodies in their true positions. If the
air were of uniform density the effect of this refraction would be as
illustrated to the left in Fig. 5. The light from a star S will reach
the observer at O after striking the atmospheric shell at _a_ and being
refracted along the line _a_ O; consequently the observer will see it in
the direction O S′, and not in the direction O S, which it would have if
the air were absent. As a matter of fact, the atmosphere becomes less
dense in passing upwards, so that the rays of light are subjected to a
succession of small deviations; two such refractions are illustrated at
the right of Fig. 5. When a star is overhead there is no refraction, and
the greatest displacements of a star’s positions are produced on the
horizon, where the light has to pass through a great thickness of
atmosphere.

Refraction always makes the heavenly bodies appear higher in the sky
than they otherwise would be, and some very curious effects can be
traced to it. Thus the sun becomes visible on account of refraction some
time before it has actually risen, and remains visible for a little
while after it has really descended below the horizon. The amount of
refraction varies with the temperature and pressure of the air, but the
average amounts for different elevations above the horizon are as
follows:

TABLE OF MEAN
REFRACTIONS.
┌───────────┬───────────┐
│ Altitude. │Refraction.│
├───────────┼───────────┤
│ 0°│ 34′ 54″│
│ 2°│ 18′ 9″│
│ 4°│ 11′ 39″│
│ 6°│ 8′ 23″│
│ 8°│ 6′ 29″│
│ 10°│ 5′ 15″│
│ 12°│ 4′ 23″│
│ 14°│ 3′ 45″│
│ 16°│ 3′ 17″│
│ 18°│ 2′ 54″│
│ 20°│ 2′ 35″│
│ 25°│ 2′ 2″│
│ 30°│ 1′ 38″│
│ 40°│ 1′ 8″│
│ 50°│ 0′ 48″│
│ 60°│ 0′ 33″│
│ 70°│ 0′ 21″│
│ 90°│ 0′ 0″│
└───────────┴───────────┘

Refraction is responsible, among other things, for the curiously
distorted appearances of the sun and moon, when they are very near the
horizon.

TWILIGHT.—The atmosphere, or rather the solid and liquid particles which
it always contains, has the property of reflecting light, and hence it
does not suddenly become dark when the sun has set. Even until the sun
has descended 18° below the horizon, the upper parts of the air continue
to reflect his beams, and this is the origin of _twilight_. In the
tropics the sun sets almost vertically, so that it gets below the
twilight limit comparatively quickly, and this explains the short
twilight which is remarked by all who have visited a tropical country.
In our own country the sun has an apparent oblique motion, and a
relatively long period elapses before twilight ends. The increase in the
duration of twilight is, indeed, very noticeable in merely travelling
from London to the north of Scotland in summer-time.

[Illustration:

FIG. 5.—_Atmospheric Refraction._
]

Within the Arctic Circle, at places where the sun itself is never
visible for months together, its reflected beams in the form of twilight
may be seen for months.

CHAPTER II.
THE EARTH’S REVOLUTION ROUND THE SUN.

APPARENT MOVEMENTS OF THE SUN.—During any day on which we may observe
the sun, it will be seen to rise at a certain place on the horizon,
gradually ascend into the heavens to a certain point, then as steadily
sink towards the west until it disappears at some point on the western
horizon. If we watch the sun about the 20th of March, we shall find it
to rise due east, and set due west; it will be above the horizon for
exactly twelve hours, and below for the same length of time. When this
happens, we have the _vernal_ or _spring equinox_, as the nights are
then equal in all parts of the world. From this time to the third week
in June, we shall find the sun to rise more and more to the north of
east, and to set gradually further north of west. This is accompanied by
a daily increase in the apparent height of the sun at noon, and by
increasing length of day and reduction of night. For some days before
the 21st of June the change of the sun’s place of rising and setting is
very slow, and after this day the places of rising and setting begin to
recede to the south. We then have the _summer solstice_, so-called
because the sun seems to stand still, in so far as its northward travel
is concerned. The point of rising or setting of the sun goes on moving
nearer to the south point of the horizon, until about September 22, we
again have the sun above the horizon for twelve hours, and below the
horizon for an equal period; this is the _autumnal equinox_. The
southward movement is continued until December 21, after which the
rising begins to take place further towards the north. When furthest
south, we have the _winter solstice_ in the Northern Hemisphere, the sun
being above the horizon for only a short time, and reaching only a small
altitude at noon. From December 21 to March 20, the sun rises further to
the north, at first very gradually, and afterwards more rapidly. These
varying amounts of sunshine correspond to the short days of winter, and
the long days of summer. A diagrammatic representation of the apparent
path of the sun at the solstices and equinoxes for some place, such as
London, is given in Fig. 6.

[Illustration:

FIG. 6.—_Apparent Paths of Sun at Equinoxes and Solstices._
]

It is clear, then, that our relations to the sun are very different from
our relation to the stars, inasmuch as the apparent position of the sun,
as projected upon the sky, is constantly changing, but returns to
similar conditions at the end of a year. If our place of observation is
changed, the apparent diurnal movement of the sun is affected in the
same way as that of the stars.

To explain these annual changes of the sun, with regard to an observer’s
horizon, it is only necessary to suppose that the sun marches northwards
towards the celestial pole from the winter to the summer of the Northern
Hemisphere, and southwards from summer to winter. It is not to be
imagined, however, that this apparent movement towards or from the north
celestial pole is necessarily a real movement of the sun; we shall, in
fact, very shortly see that it is only an apparent movement due to the
changing situation of the earth with respect to the sun.

THE ECLIPTIC.—A very small amount of actual observation, without the aid
of instruments, suffices to show that the changes in the sun’s relation
to any observers horizon at different parts of the year are associated
with a change in its situation among the stars. If we direct our gaze
towards the south at midnight, we are looking towards that part of space
which is directly opposite to the sun, as will be evident from Fig. 4,
and if the sun’s apparent movement were only in a polar direction, we
should always see the same stars in the same part of the sky at the same
hour. Such, however, is not the case. The stars are found more and more
towards the west at the same hour as the year advances. Sirius, for
instance, is due south about midnight on December 31; but at the end of
January it will pass through the south point shortly before ten P.M.
Similar changes are noted in the case of all the stars, and they
indicate either an easterly movement of the sun among the stars, or a
westerly motion of the stars with regard to the sun. If it were possible
to see the stars in the immediate neighbourhood of the sun, this
relative motion could be directly observed; but under the actual
circumstances, the apparent track of the sun amongst the stars must be
determined indirectly. When we make observations at midnight, we know
that the sun is opposite to stars which are due south at that moment;
and the height which it reaches above the horizon at noon indicates its
angular distance from the celestial pole. It is thus possible to trace
the sun’s apparent path on a map of the stars, or upon a celestial
globe; this is called the _ecliptic_, and it is found to be a great
circle of the celestial sphere—that is, it is a circle contained in a
plane which passes through the centre of the sphere.

The observed movement of the sun among the stars might be produced
either by a revolution of the sun round the earth in a year, or by a
revolution of the earth round the sun in the same period, the stars
being supposed at rest at a greater distance than the sun. There are
many phenomena which indicate that it is the earth which moves round the
sun, but the most direct proof is found in what is known to astronomers
as the aberration of light.

ABERRATION AS A PROOF OF THE EARTH’S REVOLUTION.—While engaged on an
observation having for its object the determination of the distance of a
star, Dr. Bradley made a discovery of very great interest and importance
to astronomers. What he found practically amounts to this, that in order
to see a star exactly at the centre of the field of view of a telescope
we must direct the optical axis of the instrument at a small angle to
the line joining the earth and star, irrespective of other deviations,
such as that produced by refraction. The direction of this displacement
is constantly changing throughout the year, but it is common to all the
stars, and the fact that the original apparent position is regained at
the end of a year at once associates aberration with a revolution of the
earth round the sun.

[Illustration:

FIG. 7.—_Aberrational Orbit of a Star._
]

In Fig. 7 we have a perspective view of the earth’s orbit with the sun
at S. A star _s_ would appear in the direction A _s_ when seen from the
earth, supposed at rest at the point A; actually it is seen at _a_,
ahead of its place, and in the course of a year it describes the
_aberrational orbit_, _a b c d_, these points corresponding to positions
A B C D of the earth in its annual path.

As a result of aberration, then, each star appears to revolve once a
year in a small elliptic path about its average position. The breadths
of these ellipses vary according to their angular distances from the
ecliptic, but all have precisely the same length of about 41″. Half the
length of the ellipses, which amounts to 20″.5, is accordingly called
the _constant_ of _aberration_.

The fact that the earth’s velocity in its orbit forms a sensible
fraction of the velocity of light is the cause of aberration. If we let
an object fall down the middle of a tube which is at rest, it will fall
to the bottom without touching the side if the tube be held vertically.
When the tube has a forward movement, however, it must be inclined at an
angle in order that the falling body may pass clear to the bottom, and
the greater the speed of the tube the more it must be inclined. So it is
with light which comes from a star and traverses the tube of a telescope
situated on a moving earth; the tube must be inclined to the actual path
of the light rays.

Other proofs that it is the earth which moves round the sun are
furnished by the parallaxes of the stars, and by spectroscopic measures
of the earth’s velocity.

APPROXIMATE SCALE OF EARTH’S ORBIT.—A very beautiful application of the
constant of aberration is in the measurement of the distance of the
earth from the sun. We have only to bear in mind that the apparent size
of the sun does not change very much, in order to realise that the path
of the earth must be very nearly a circle; if the distance changed very
much there would be a correspondingly great change in the sun’s apparent
diameter. Now the constant of aberration is a measure of the relative
velocity of the earth in its orbit and the velocity of light. There are
several ways of determining the velocity of light, and it is known to be
very nearly 186,300 miles per second. In a right-angled triangle having
one angle equal to the constant of aberration, the side opposite to this
angle would represent the velocity of the earth, if the longer side
represented that of light. In such a triangle the proportion between
these sides would be nearly as 1 to 10,000. That is, the velocity of
light is about 10,000 times that of the earth in its orbit. The earth’s
velocity is thus found to be about 18½ miles per second, so that the
distance which it traverses in a year is found by a simple
multiplication. In this way the circumference of the earth’s orbit is
obtained, and it is easily deduced that the radius of the orbit, which
is nothing more than the sun’s distance, is not far from 93,000,000
miles.

THE ZODIAC.—The space about 8° above and below the ecliptic constitutes
what is called the _zodiac_. The zodiac is of very great antiquity, and
marks out the region traversed by the sun and all the planets known to
the ancients. It is divided into twelve parts of 30° each, called signs
of the zodiac, from the supposed outlines of animals, etc., marked out
by the stars. The names of these signs are probably familiar to everyone
from the well-known rhyme:

“_The Ram, the Bull, the Heavenly Twins,
And next the Crab the Lion shines,
The Virgin, and the Scales,
The Scorpion, Archer, and the Goat,
The man that bears the Watering-Pot,
And Fish with glittering tails._”

The astronomical names and symbols corresponding to these are as
follows:—

♈︎ Aries, The Ram.
♉︎ Taurus, The Bull.
♊︎ Gemini, The Twins.
♋︎ Cancer, The Crab.
♌︎ Leo, The Lion.
♍︎ Virgo, The Virgin.
♎︎ Libra, The Balance.
♏︎ Scorpio, The Scorpion.
♐︎ Sagittarius, The Archer.
♑︎ Capricornus, The Goat.
♒︎ Aquarius, The Water-Bearer.
♓︎ Pisces, The Fishes.

The sun enters the sign Aries at the vernal equinox in March, and the
others in successive months. On account of the precession of the
equinoxes (see p. 69), however, the sun no longer enters the
_constellation_ Aries at the vernal equinox, but it is still said to
enter the _sign_ Aries.

INCLINATION OF THE EARTH’S AXIS.—The revolution of the earth round the
sun provides us with a very satisfactory explanation of the apparent
easterly movement of the sun among the stars. There is, however, another
very important point. We have seen that during a year the sun has a
movement towards and from the Pole, as well as an easterly movement. The
plane of the earth’s orbit, therefore, cannot be coincident with the
plane of the Equator; if it were, the sun would have the same apparent
movement every day—it would always rise due east, and set due west, in
all parts of the earth. The ecliptic, moreover, would be coincident with
the celestial equator. When the ecliptic is determined by observations
in the way already explained (p. 57), it is found to intersect the
celestial equator in two points, and the plane containing it is inclined
at an angle of very nearly 23½° to the equatorial plane. This
inclination of the Equator to the ecliptic, or “obliquity of the
ecliptic,” indicates that the earth’s axis of rotation is inclined to
the plane in which the revolution round the sun is performed, the actual
inclination being about r66½°.

Further, the axis of rotation must remain parallel to itself during the
revolution of the earth. Otherwise, the situation of the celestial pole
would be seen to change, and the Pole Star would no longer serve to show
us which way lies north.

It is precisely this inclination of the earth’s axis which brings about
the varying lengths of days and nights which we associate with different
seasons.

THE SEASONS.—Let us in the first place contrast the conditions in summer
with those which obtain in winter. Imagine that we can view the sun and
earth from a very distant point lying in the plane of the ecliptic, and
situated so that a line joining it with the sun is perpendicular to the
line joining the sun and earth in summer or winter.

[Illustration:

FIG. 8.—_The Sun’s Altitude in Summer and Winter._
]

The sun will thus appear in some position represented by O in Fig. 8; in
the summer of the Northern Hemisphere the earth will be in the position
S, and in winter in the position W, since it travels half way round its
orbit in six months’ time. An observer situated at London will be 38½°
from the North Pole, and he is represented by the point A in our
diagram. The horizon at noon of such an observer is represented by the
line H R, tangential to the surface of the sphere at the point A. At
noon, then, the altitude of the sun is equal to the angle O A H. When it
is winter in the Northern Hemisphere, the earth’s axis is inclined away
from the sun, and our observer at London is so situated that at noon his
horizon is the line H′ R′, while the sun’s altitude is the angle O A′
R′, which is no less than 47° smaller than in summer. People who dwell
in the Southern Hemisphere enjoy the long days of summer at the time
when our own days are shortest, and _vice versâ_, and the reason for
this is clearly that when the position of the earth’s axis presents the
greatest part of the Northern Hemisphere towards the sun, the greater
part of the southern half of our globe is turned away from the sun.

At the equinoxes, which occur very nearly midway between the solstices,
the earth’s axis is directed neither towards nor away from the great
source of light and heat, so that both hemispheres are presented to the
sun under exactly the same conditions. This state of affairs is shown
diagrammatically in Fig. 9. The sun’s altitude at noon at the
commencement of spring is equal to that at the beginning of autumn, and
depends only upon the observer’s latitude. The half of our globe which
is then flooded with the sun’s rays comprises both the North and South
Poles, and it is evident that as the earth turns round, every place upon
it, whether in Arctic or equatorial regions, receives the benefit of
twelve hours sunshine, and at the same time has a night of twelve hours
duration.

[Illustration:

FIG. 9.—_The Sun’s Altitude at the Equinoxes._
]

THE MIDNIGHT SUN.—The facilities which are now offered for foreign
travel have induced many people to pay a visit to the north of Norway,
one of the objects in view frequently being to witness the so-called
“midnight sun.” It seems somewhat paradoxical to speak of night when the
sun is above the horizon, but it simply means that in high latitudes the
sun may be seen over the northern horizon when it is midnight at places
further south which have the same longitude. We have seen that in our
own country there are certain stars which never set, and when we get to
the Pole itself, all the stars which are there visible will present this
peculiarity.

In order to see the sun at midnight, then, what we have to do is to
travel towards the Pole until we reach a latitude where the sun itself
becomes circumpolar. At the Pole this would be the state of things
during the whole of the northern summer, when the sun is north of the
Equator, and since the sun never travels northward more than 23½°, it
can only be circumpolar at places within that angular distance from the
Pole, that is, within the Arctic Circle.

[Illustration:

FIG. 10.—_The Midnight Sun._
]

Let A in Fig. 10 be such a place, the sun being to the left. At noon the
horizon of A is represented by H R, and the sun will appear in the south
at a certain altitude, S A H. At midnight the earth’s rotation will
change the observers position to A′ and his horizon to H′ R′, but it
will not have taken him out of sunshine. The sun will then appear due
north, but, except at the Pole, its altitude, S A′ H′, will be lower
than at noon. At a place situated on the Arctic circle, latitude 66½°,
the midnight sun would only be visible for one night at the summer
solstice, were it not that refraction causes it to appear above the
horizon when it is geometrically more than its own apparent diameter
below.

At Tromsö the midnight sun is visible from May 19 to July 22, and at the
North Cape from May 12 to July 29.

Nature, however, exacts compensation for this lavish share of summer
sunshine in high latitudes, and there is a correspondingly number of
dreary days in winter when the sun does not rise at all.

CHAPTER III.
HOW THE POSITIONS OF THE HEAVENLY BODIES ARE DEFINED.

TWO MEASUREMENTS REQUISITE.—In order to make a more precise study of the
movements of the heavenly bodies, it is essential that we should have
some very definite means of specifying their positions upon the
celestial sphere. To define the position of any object, at least two
measurements are required. If, for example, one wishes to draw attention
to a particular letter on the page of a book, it is only necessary to
say that it is so many lines from the top, and a certain number of
letters from the end of the particular line on which it lies. In the
same way, latitude and longitude sufficiently indicate the situation of
a place on the surface of the earth, and similar measures can be
employed to indicate the places of the heavenly bodies.

ALTITUDE AND AZIMUTH.—The horizon and zenith at any place—being in a
constant position with reference to the earth—may be utilised for
indicating the positions of external bodies. We may say, for instance,
that at noon on June 24, the sun, as seen from London, is 62° above the
horizon, or 28° from the zenith. Technically, the former is called the
_altitude_ of the sun, being the angular distance above the horizon,
while the latter measure is called the _zenith distance_.

[Illustration:

FIG. 11.—_Altitude and Azimuth._
]

We may next note that an object, besides having a certain altitude, is a
certain number of degrees from the north, south, east, or west points,
measured horizontally; if we reckon from the north point through E, S,
and W, from 0° to 360°, such a horizontal measurement is called
_azimuth_; if reckoned north or south of the east or west points it is
called the _amplitude_ of the body. Fig. 11 illustrates these terms. In
this diagram the observer is placed at O, N S and E W respectively
representing a north and south, and an east and west line in the
horizon; the point Z is the zenith, and S a heavenly body. A vertical
circle drawn from Z through S will meet the horizon at a point A. The
azimuth of S is thus the angle N O A, and its amplitude is the angle E O
A, while the altitude of S is simply the angle A O S. Measurements of
altitude and azimuth are made by means of an instrument called the
altazimuth, an account of which will be found on page 202.

DECLINATION.—Altitude and azimuth only specify the position of a star
for a particular place at a particular time. A better system is
evidently one which is independent of the observer’s situation on the
earth. Of the two measurements required, one is readily decided upon; we
can say that the sun, or star, or other heavenly body is a certain
number of degrees from the north celestial pole; or, what is just as
good, we can state the number of degrees north or south of the celestial
equator, which lies midway between the poles. The former measurement
gives what is called the _north polar distance_ of the star, and the
latter its _declination_.

RIGHT ASCENSION.—Just as the latitude of a place on the earth does not
tell whether it is in Europe or North America, so declination alone
fails to locate a heavenly body. We must have some measurement
equivalent to terrestrial longitude, and it is therefore necessary in
the first instance to select a start-point, which shall do for stars
what Greenwich does for our geographical maps. By universal consent the
fundamental point for the stars is a point situated on the celestial
equator where it is crossed by that part of the ecliptic occupied by the
sun at the vernal equinox. This zero mark is called the _First Point of
Aries_, and is frequently denoted by the symbol ♈︎ identical with that
employed for the corresponding sign of the zodiac.

The location of this reference point being thus determined, the _right
ascension_ of a celestial body may be defined as its angular distance
from the First Point of Aries, as measured along the celestial equator.
Like terrestrial longitude, it may be stated in degrees, but it is more
usually expressed in hours, minutes, and seconds of time, for the reason
that in general the measurement of a right ascension consists of an
observation of the time at which the body in question comes to a certain
position.

The right ascensions and declinations of stars are best determined when
they are on the meridian of the place of observation, and such
measurements are made by means of a transit instrument. When a star is
on the meridian, its declination is estimated by the angle at which the
instrument is inclined to the celestial equator when directed to the
star. The fact that the earth is turning on its axis furnishes us with a
simple method of finding the right ascensions of the heavenly bodies.
Imagine a plane passing through the observers position on the earth and
through the earth’s axis. This, prolonged indefinitely, cuts the
celestial sphere in his meridian, and it is evident that on account of
the earth’s rotation it will turn completely round every twenty-four
hours. It may therefore be regarded as the hour-hand of a clock, which
is provided with figures ranging from I. to XXIV. When this gigantic
clock hand sweeps past the First Point of Aries, all stars then seen in
the plane—that is, all stars which are on the meridian—will have zero
right ascension. After a complete rotation it will again sweep through
the First Point of Aries.

USE OF STAR TIME.—Meanwhile, suppose we have a clock regulated so that
it marks twenty-four hours between these two meridian passages of the
First Point of Aries. Evidently, then, the time by this clock at which
any object in the sky is seen on the meridian will depend upon its
angular distance from the celestial meridian passing through the First
Point of Aries. As the earth is rotating through 360° in twenty-four
hours, reckoned by our clock, the meridian plane will travel at the rate
of 15° per hour, so that, for example, a star 60° from the celestial
meridian passing through the First Point of Aries, will appear to cross
the observer’s meridian at IV. hours by the clock. A clock so regulated
to keep time with the stars is called a sidereal clock, and the sidereal
time at which a celestial body crosses the meridian, or “souths,” is the
right ascension of that object. Such a time measurement can be converted
into angular measure by allowing 15° per hour, 15′ per minute, and 15″
per second of time.

CELESTIAL LATITUDE AND LONGITUDE.—In some astronomical questions it is
often convenient to adopt a different system of co-ordinates to indicate
the situation of a celestial body. Just as the earth’s equatorial plane
serves as a basis for the measurement of declination, the earth’s plane
of revolution—that is, the plane of the ecliptic—is used as the term of
reference for _celestial latitude_, which may be defined as the angular
distance of an object above or below the plane of the ecliptic.
_Celestial longitude_ is the angular distance from the First Point of
Aries measured along the ecliptic.

A diagram such as that in Fig. 12 may assist the comprehension of these
co-ordinates. Here the observer is supposed to be situated at the point
O, at the centre of the celestial sphere. To him the north and south
celestial poles will appear in some such positions as N and S, and the
celestial equator will be represented by a great circle at right angles
to the line joining these two points. The apparent path of the sun—the
ecliptic—will be indicated by another great circle, which is inclined to
the Equator; and the poles of the ecliptic will be represented by P and
P′.

The Equator crosses the ecliptic at the First Point of Aries, marked ♈︎.
Considering now a star which the observer sees in the direction of the
line O S, its position would be reckoned as follows in the two systems:—

Right Ascension = Angle ♈︎ O R }
Declination = „ S O R }

Celestial Longitude = Angle ♈︎ O L }
„ Latitude = „ S O L }

Either pair of co-ordinates can, by a mathematical process, be expressed
in terms of the other.

[Illustration:

FIG. 12.—_Right Ascension, Declination, Celestial Latitude, and
Celestial Longitude._
]

PRECESSION OF THE EQUINOXES.—It is not too early to remark that the
First Point of Aries is not absolutely a fixed point on the celestial
equator. This is on account of the precession of the equinoxes, which
consists of a backward movement of the First Point, due to a change in
the position of the earth’s equator. As a point common to the ecliptic
and equator, it is conveniently retained as the starting-point of right
ascensions and celestial longitudes, but in consequence of precession,
these co-ordinates are subject to a constant change. The amount of
precession for a point on the Equator is 50″·2 per annum, and this
movement requires 25,800 years for a complete revolution.

GEOCENTRIC AND HELIOCENTRIC POSITIONS.—When observing objects at a very
great distance, they will appear in the same direction to a spectator on
the earth as they would if he could by some means be transferred so as
to be able to see them from the sun. If, for instance, one sees the Peak
of Teneriffe from a distant ship, its apparent direction will be very
slightly affected by a change of a mile in the ship’s position. But a
similar change of place would produce a greater difference of direction
when a nearer body was under observation. If an object is relatively
near to the sun and earth, its direction, and, therefore, its apparent
position on the celestial sphere, will be different, as seen from the
earth and sun. Such will be the case with planets and other bodies which
lie in our immediate neighbourhood, speaking astronomically. Hence, it
is often convenient to distinguish between the _geocentric_ position of
a celestial body—referring it to the position it would occupy if it
could be seen from the centre of the earth—and the _heliocentric_
position, representing it as it would appear to an observer occupying
the centre of the sun. We thus have geocentric and heliocentric
latitudes and longitudes of the nearer heavenly bodies.

STAR CATALOGUES.—The problem of constructing catalogues showing the
positions of the stars is one of considerable practical value, as well
as one of great scientific importance. In the first instance, such
catalogues were of necessity compiled from data acquired by naked eye
observations, so that the ancient catalogues comprise only a small
number of stars.

As far back as 295 B.C., the positions of stars were determined by
Timocharis with sufficient accuracy to lead Hipparchus to his great
discovery of the precession of the equinoxes about 170 years later. From
observations at Rhodes, Hipparchus drew up a catalogue of 1,022 stars,
giving their latitudes and longitudes; this is preserved for us in
Ptolemy’s “Almagest,” where the positions are corrected for precession,
and reduced to the epoch 150 A.D. The next catalogue of importance was
due to the industry of Tycho Brahé (1546–1601), who gave the positions
of 1,005 stars with greater accuracy than had been previously obtained;
indeed, notwithstanding his want of optical aid, it has been estimated
that the probable errors of his measures were not more than 24″ and 25″
in right ascension and declination respectively. The last of the naked
eye catalogues is that of Hevelius, giving the positions of 1,553 stars.

Coming to more recent times, in which the employment of telescopes has
vastly increased the power of accurate observation, there are the
catalogues of Flamsteed, Halley, Lacaille, Lalande, Argelander, the
British Association, and catalogues of the stars in particular parts of
the sky which have been published by all the leading national
observatories. Eighteen observatories are now taking part in the
construction of an international star catalogue by means of photography,
and this is intended to record with great accuracy the positions of
nearly 3,000,000 stars. A modern star catalogue usually places the stars
in the order of their right ascensions, and, in addition to the two
co-ordinates, furnishes the necessary data for determining the exact
situations of the stars at any particular time.

CHAPTER IV.
THE EARTH’S ORBIT.

EXACT SHAPE OF THE ORBIT.—It will be clear that if we made our annual
journey in a circle we should always be at the same distance from the
sun, and the apparent size of that luminary would never vary. This,
however, is not the case. Exact measurements, which are best made by
means of the transit instrument, indicate variations which, though not
perceptible to the unassisted eye, establish a want of circularity. The
observations bearing on this point consist of a measurement of the time
required for the sun to cross the meridian—the larger its apparent
diameter, the longer it will obviously be in passing the meridian. An
observation of the sidereal time at which the centre of the sun passes
the meridian determines the right ascension, and from this one can
calculate the sun’s longitude.

[Illustration:

FIG. 13.—_Elliptic Form of Earth’s Orbit._
]

If such observations be made at intervals during a year, we can utilise
them for determining the shape of the earths orbit independently of a
knowledge of the actual size. In Fig. 13 let us suppose the sun to be
situated at the point S; from S we draw a line, S A, representing the
line joining the earth and sun at the vernal equinox when the sun’s
longitude is zero. If our observations include a measure of the sun’s
diameter on that day, let S A be drawn on some convenient scale. To plot
the observations for other days, we must draw S F, S E, etc., at angles
A S F, A S E, etc., equal to the sun’s longitude, and make the lengths
inversely proportional to the apparent diameters, on the same scale as S
A. The other observations can be plotted in the same way, and the earths
orbit is then found to be an ellipse with the sun in one of its foci.
Actually, the earth’s orbit is much more nearly circular than is shown
in Fig. 13, and in illustration of this the following numerical data may
be given:—

1896. Jan. 1 Greatest apparent diameter of sun = 32′ 35″·2 in long. 281°
July 3 Least „ „ „ = 31′ 30″·6 „ 102°
March 29 Mean „ „ „ = 32′ 4″ „ 9°
Oct. 5 „ „ „ „ = 32′ 4″ „ 193°

It thus appears that in 1896 we were nearest to the sun on January 1, as
on that day the sun’s apparent diameter was greatest, while we were
furthest removed on July 3.

[Illustration:

FIG. 14.—_The Ellipse._
]

The ellipse is a curve of such importance in astronomy that an
understanding of some of its properties is essential for further
progress. This beautiful closed curve lies in one plane, and its figure
is such that the sum of the distances of any point upon it from two
fixed points within the curve is constant. These two fixed points, F F′
(Fig. 14), are called the foci of the ellipse, and we have, for example,
the sum of the lengths P F and P F′, equal to the sum of P′ F and P′ F′.
The line A B passing through the foci is the greatest distance across
the ellipse, and is called the major axis; at right angles to this is
the minor axis C D.

Following our definition of the ellipse, we see that as B is a point
upon its circumference, B F + B F′ must be equal to the sum of the
distances of any point P from the foci. But since B F is of the same
length as A F′, the sum of the distances of the point B from the foci,
and therefore of all other points, is equal to the major axis. Hence the
average or mean distance of the focus F from all points on the ellipse
is half the length of the major axis. It follows also that C F is equal
to the semi-major axis O B.

At the point O, where the axes intercept each other, we have the centre
of the ellipse, and the ratio between the distance from the centre to
either of the foci and the semi-major axis, _i.e._, (O F)/(O B) is
called the eccentricity of the ellipse. Thus, in an ellipse of
eccentricity 0·5, the foci would lie midway between the centre of the
ellipse and the extremities of the major axis. The eccentricity is
always less than unity; if it become unity, the two foci merge together,
and the curve becomes a circle.

[Illustration:

FIG. 15.—_How to draw an Ellipse._
]

To draw an ellipse, two pins may be stuck into a piece of paper at the
points intended as foci. A loop of thread is then made and thrown over
the pins. A pencil placed inside the loop, so as to stretch it, and
traced completely round, will outline an ellipse. The size and shape of
the ellipse may be varied by changing the length of the thread and the
distance between the pins. Such, then, is the curve in which our earth
performs its annual journey round the sun, the sun being relatively
fixed in one of the foci.

APHELION AND PERIHELION.—When the earth is in that part of its orbit
where it makes its nearest approach to the sun, it is said to be in
_perihelion_; when at the point furthest removed from the sun it is in
_aphelion_. The line joining these two points is obviously the major
axis of the earth’s orbit, and when this is imagined to be prolonged
indefinitely into space it is called the _line of apsides_, or _apse
line_. When the earth is in perihelion, the sun’s apparent diameter will
be the greatest possible, and when in aphelion it will be at a minimum.
A knowledge of these limiting values of the apparent solar diameter
enables us to determine the eccentricity of the orbit of the earth. The
sun’s apparent diameter when the earth is in perihelion amounts to 32′
35″·2, and to 31′ 30″·6, when the earth is in aphelion, from which it
results that the value of e is 0·0167.

UNEQUAL SPEED OF THE EARTH.—The observations by which we are enabled to
determine the true form of the earth’s orbit are not quite exhausted of
their usefulness; we can utilise them still further for studying the
varying rate of the earth’s motion. If the earth moved through equal
angles every day, the apparent movement of the sun would always be
uniform, and in that case the sun’s daily increase of longitude would be
constant.

The following figures, however, prove that this uniformity does not
exist:—

1896. Sun’s daily motion in longitude.
Jan. 1 1° 1′ 8″·5
Mar. 29 1° 0′ 6″·7
July 3 0° 57′ 12″·1

Facts such as these led Kepler in 1609 to the discovery of his famous
second law of planetary motion, namely, that the radius vector (the line
joining the sun and earth in the case of the earth’s orbit) describes
equal areas in equal times. For the sake of clearness, imagine the
earth’s orbit to be represented by the elongated ellipse in Fig. 16,
with the sun in the focus _S_. When the earth is near perihelion, it
will move over a certain distance, _a b_, in a given time; some time
afterwards it will be in another part of the orbit, and in the same
interval as before it will traverse the distance _c d_; again, in
another equal interval of time, it will move from the point _e_ to the
point _f_. The law tells that the areas _S a b_, _S c d_, and _S e f_,
are equal so long as equal times are in question; in different parts of
its path, then, the earth’s rate of motion must vary, _c d_, for
example, being smaller than _a b_. It will be seen that the motion is
most rapid when the earth is in perihelion, and least rapid when in
aphelion.

[Illustration:

FIG. 16.—_Illustrating Kepler’s Second Law._
]

CHANGES IN THE EARTH’S ORBIT.—Owing to disturbances caused by the
proximity of other bodies, the earth’s orbit is not always of the same
shape. The eccentricity is steadily diminishing, and in about 24,000
years the orbit will be very nearly a circle; it will afterwards become
more elliptical again, until in another 40,000 years or so the
eccentricity will be about 0·02. So far as our knowledge goes, the
eccentricity will never exceed 0·07.

The direction of the major axis of the earth’s orbit, that is, the line
of apsides, moves forward at the rate of about 11″ per annum, so that at
this speed a whole revolution will be made in a period of 108,000 years.

On account of precession, the equinox moves backwards along the orbit at
the rate of 50″·2 per annum, so that the movement of the apse line with
regard to the equinox is 61′ in a year; or, in other words, the
perihelion point of the earth’s orbit makes a complete revolution with
respect to the equinoctial point in a little over 20,000 years. The
earth at present passes through perihelion in our northern winter, but
owing to this motion of the apse line it will in 10,000 years time be at
aphelion in winter. Northern winters will then be somewhat colder than
at present. The plane of the orbit itself is subject to changes, with
the result that the obliquity of the ecliptic is variable in amount. In
the course of ages the obliquity may oscillate between the limits 24°
35′ 58″ and 21° 58′ 36″. The mean value during 1896 was 23° 27′ 9″·9.

THE EARTH’S REAL PATH.—In this and preceding chapters, we have had
occasion to consider various features of the earth’s orbit, but it must
now be pointed out that what we call the orbit of the earth is not quite
the same thing as the earth’s actual path in space. The earth, as we
know, is accompanied by the moon, and these two bodies are bound
together in such a way that it is really the centre of gravity of the
earth and moon which describes an elliptic orbit round the sun; the moon
is so small in relation to the earth that the centre of gravity of the
two companions lies within the earth’s surface, but, nevertheless, an
oscillatory displacement of the earth’s centre in space is produced by
the moon’s monthly circuit round the earth. We judge of the earth’s
movement by the apparent movement of the sun, and we actually find a
monthly inequality in the sun’s apparent motion. A very good
illustration of this may be found in the varying celestial latitude of
the sun. It will be clear that if the earth always moved in the plane of
the ecliptic, the sun’s latitude would always be zero. If, on the other
hand, the earth has a motion round the common centre of gravity, it will
be above the ecliptic when the moon is below, and _vice versâ_; the sun
will, therefore, not always appear to be in the ecliptic, and its
latitude will depend upon that of the moon. The following figures from
the “Nautical Almanac” will illustrate this point:

Sun’s apparent latitude. Moon’s latitude.
1896, April 1 0″·70 S. 5° 9′ S.
„ 10 0″·01 N. 1° 41′ N.
„ 16 0″·39 N. 5° 6′ N.
„ 22 0″·07 S. 0° 48′ N.
„ 29 0″·74 S. 5° 1′ S.

The displacement in right ascension amounts to a little over 6″, and is,
therefore, large enough to be directly measurable.

On account of this association with her satellite, the earth’s centre
moves some hundreds of miles above and below the plane of the ecliptic.

The so-called “perturbations,” or disturbing effects of the other
planets, also cause the earth to depart more or less from the plane of
the ecliptic and from a geometrical elliptic path. Nevertheless, these
disturbances can be calculated and allowed for, so that when we speak of
the earth’s orbit we really mean the path which the centre of gravity of
the earth and moon would traverse if subject only to the influence of
the sun.

CHAPTER V.
MEAN SOLAR TIME.

SUN-DIAL TIME.—The changing directions of shadows thrown by the sun have
been utilised from very remote periods for the measurement of time, the
instrument usually employed being a sun-dial. On account of the varying
declination of the sun, it is necessary to employ as a time-measurer the
shadow of a line which lies parallel to the earth’s axis, that is, if we
wish the same hour marks to be permanently useful. Such a rod must lie
in the plane of the meridian, and be inclined to the horizon at an angle
equal to the latitude of the place. If the shadow be received on a
horizontal dial, hours may be marked upon it corresponding to the
duration of the longest day at the place where it is set up. Sometimes,
as on old churches, one sees a vertical sun-dial, the rod, or _style_,
as it is called, being still parallel to the earth’s axis, but as a dial
facing the south is only serviceable for twelve hours, another on the
north wall is necessary for times before six in the morning and after
six in the evening. As indicated by the sun-dial, it will always be noon
when the sun is on the meridian, that is, when it is due south.

The time indicated by sun-dials is distinguished astronomically as
_apparent time_, and an _apparent solar day_ is the time which elapses
between two successive southings of the sun. It is longer than the
sidereal day, for the reason that the sun moves eastward among the
stars.

NECESSITY FOR MEAN TIME.—The varying speed of the earth in its orbit, or
what comes to the same thing, the variable rate of the sun’s apparent
eastward movement, prepares us for the discovery that the intervals
between successive noons as indicated by sun-dials are unequal. That is,
the apparent solar day is not of uniform length, and our clocks could
not be regulated to indicate noon at the same moments as the sun-dial
unless they were rated afresh every day. All our daily actions are
regulated by the sun, and our time-keepers must also be controlled by
its movement if they are to be as convenient as is necessary for
purposes of everyday life. Our clocks and watches are therefore
regulated to measure twenty-four hours in the time corresponding to the
average duration of the apparent solar day throughout a year. In other
words, they are controlled by the movements of an imaginary sun, called
the _mean sun_, which is supposed to come to the meridian after equal
intervals, and in order that it may do this while having a uniform
motion, it must of necessity move along the celestial equator. In this
way the time shown by our clocks and watches never departs very greatly
from that shown by sun-dials, the maximum discrepancy being little more
than a quarter of an hour. A _mean solar day_ is thus the average length
of the apparent solar days throughout a year.

THE EQUATION OF TIME.—The difference between apparent and mean solar
time is called the _equation of time_, and a knowledge of its amount
enables us to determine mean time from an observation of apparent time.

One of the causes of this difference we have already seen to be the
varying speed of the earth in its orbital movement; this produces a
correspondingly irregular motion of the sun amongst the stars, and in
consequence the true sun comes to the meridian after unequal intervals.
Neglecting for a moment another cause of the varying length of the day,
the relation of the apparent and mean solar days would be somewhat as
follows:—Let us suppose that when the earth is at perihelion, we set our
clocks to the same time as the sun-dial. In the interval which elapses
before noon next day the true sun will have moved faster than the mean
sun, because the earth, which produces the apparent eastward movement of
the sun, is then travelling at its greatest speed. Consequently, our
meridian will overtake the mean sun before it comes up to the true sun,
and mean noon will occur before apparent noon; the difference will be
the equation of time for the day, and it must evidently be added to
apparent time in order to give mean time. This will go on for a certain
period, when, in consequence of the reduced rate of the earth’s orbital
velocity, the suns eastward motion will be less than that of the mean
sun, and the two will again come to the meridian at the same time when
the earth reaches its aphelion point; clocks and sun-dials would then
give identical times. After aphelion passage, the earth is moving
slowly, and the apparent eastward velocity of the true sun will be less
than that of the mean; our meridian will therefore come to the true sun
before it overtakes the mean sun, so that apparent noon will precede
mean noon, and the equation of time will have to be subtracted from
apparent time to give mean time. The two suns would again come together
when the earth reached perihelion, and the equation of time, so far as
this cause was concerned, would vanish. As the earth’s orbit is only
slightly elliptical, the equation of time due to this cause alone would
never amount to more than seven minutes.

This, however, is by no means the whole cause of the equation of time; a
still greater source of variation is the obliquity of the ecliptic. To
investigate the part played by this inclination of the fundamental
planes, let us now suppose that the true sun has a uniform angular
motion in the ecliptic, while the mean sun moves uniformly along the
Equator. Both these fictitious suns would have the same rate of movement
along their respective paths, since they come back to the same places
after the lapse of a year. If, then, these two suns start together at
the equinox, both would indicate noon at that time, and there would be
no equation of time. The “ecliptic sun” would then be moving at an angle
of 23½° to the Equator, as along _a b_ in Fig. 17. If the distance _a b_
represents the average daily movement of the “ecliptic” sun, and _d c_
the equal movement of the mean sun, it is clear that our meridian will
overtake the true sun at _b_ before the mean sun at _c_, so that
apparent noon will precede mean noon, and the equation of time must be
subtracted from apparent time to give mean time. The difference becomes
greater up to a certain limit, and then since both suns will traverse
90° in the same time, they will pass the meridian together at the
solstice.

[Illustration:

FIG. 17.—_Effect of Obliquity of Ecliptic upon the Equation of Time._
]

In the next quarter of a revolution, from solstice to equinox the
difference is similar, but in the opposite direction, and the same
applies to successive quadrants described throughout the year.

The net amount of the equation of time at any moment is thus the added
effects due to two causes.

In 1896 the greatest and least values of the equation of time at
Greenwich mean noon were as follows:—

M. S.
Feb. 11 14 27 to be added to apparent time.
April 14 0 7 „ „ „
May 13 3 50 to be subtracted from apparent time.
June 13 0 6 „ „ „
July 25 6 17 to be added to apparent time.
August 31 0 0 „ „ „
Nov. 2 16 20 to be subtracted from apparent time.
Dec. 24 0 7 to be added to apparent time.

A somewhat notable effect, owing its origin to the equation of time, is
seen in the times of sunrise and sunset given in our almanacs. On
November 8, for example, the sun rises at Greenwich at 6h. 58m., and
sets at 4h. 31m., thus apparently making the afternoon about half an
hour longer than the morning. As reckoned by the sun-dial, however, the
morning and afternoon would differ only by a few seconds, and the
peculiarity noted arises simply from the fact that our clocks keep time
with the mean, and not with the true sun.

DETERMINATION OF TIME.—Although the sun-dial may be used to indicate the
time of day with sufficient accuracy for some purposes, its use is
limited by the fact that it can only be employed when the sun is visible
at the place of observation. Other modes of measuring the flow of time
have, therefore, long been adopted. In early days, the rate at which a
candle burned, or at which water or sand escaped through a small
aperture, was employed as a time-measurer. Coming to more recent times,
clocks and watches serve a similar purpose, but from what has already
been stated, it is evidently necessary to regulate them according to the
results of astronomical observations.

The most precise determinations of time are made by means of a transit
instrument, that is, an instrument by which the exact moment at which a
celestial body passes the meridian can be observed. The positions of
certain fundamental stars called “clock stars” have been determined with
great accuracy, and it is therefore known to within a very small
fraction of a second at what sidereal time one of these stars will pass
the meridian. If the sidereal clock does not indicate this time when the
star is observed on the meridian, its error can be noted and corrected.
In this way the sidereal time is ascertained, and its equivalent in mean
solar time is only a matter of simple calculation.

Another method is to observe, by means of a sextant, or an altazimuth,
the time, by a clock, at which the sun or a star has a certain altitude
before noon, and the time at which it has the same altitude after noon.
Midway between these times marks the time at which the body passed the
meridian; the true sidereal time of passage is furnished by the known
right ascension, and the corresponding mean time can therefore be
calculated.

At sea, time is most frequently determined by observing the altitude of
the sun in the morning or evening, when it is nearly in an east or west
direction. The time by the chronometer corresponding to a certain
altitude of the sun is noted, and by spherical trigonometry the apparent
solar time is deduced; mean solar time is then obtained by correcting
for the equation of time. The nearer the sun is to due east or west, the
more accurate are the results obtained by this method.

TIME AT DIFFERENT PLACES.—In all these methods of finding the time,
_local time_ is alone determined, whether it be sidereal or solar. When
solar time is in question, we have seen that mean noon is determined by
the passage of the mean sun across the meridian. All places on the same
meridian will thus have equal times; but at places on different
meridians, the local times will be different. When it is noon at
Greenwich, it will be something before noon at places to the west of
Greenwich (for the reason that the sun has not yet crossed their
meridians), while at places to the cast it will be afternoon, because
the sun has already passed the meridian. As the earth rotates through
360° in a day, it will turn 15° in an hour, or 1° in four minutes. Hence
at places 15° east of Greenwich the time will be an hour in advance of
Greenwich time, while at places 15° west it will be an hour earlier. For
places in other longitudes, the difference of time is in the same
proportion. The following are the local times at several places when it
is noon at Greenwich:—

A.M. P.M.
Dublin 11.35 Paris 0.9
New York 7.4 Berlin 0.54
Toronto 6.42 Calcutta 5.53
Vancouver 3.38 Melbourne 9.40

Throughout the whole of England and Scotland, Greenwich mean time is
exclusively employed in preference to local times. This has the very
practical advantage of uniformity; and as in no case does local time
differ more than half an hour from Greenwich time, there is little
inconvenience in regard to the beginning and end of day.

Until recently, the time systems of other countries have been mainly
based on the times corresponding to their various national
observatories. At present, what is called “zone time,” in which the
hours alone differ from Greenwich time, has been adopted in several
European states, as well as in other parts of the world.

The present state of time reckoning on this much improved plan is
indicated by the following table:—

_Country._ │ _Standard time._
───────────────────────────────┼───────────────────────────────────────
England │
Belgium │Greenwich time.
Holland │
───────────────────────────────┼───────────────────────────────────────
Denmark │
Germany │Mid-European time, 1 hour fast on
Italy │ Greenwich.
Switzerland │
Norway and Sweden │
───────────────────────────────┼───────────────────────────────────────
Colony of Natal │2 hours fast on Greenwich.
───────────────────────────────┼───────────────────────────────────────
United States │4, 5, 6, 7, or 8 hours slow on
Canada │ Greenwich, according to longitude.
───────────────────────────────┼───────────────────────────────────────
Japan │9 hours fast on Greenwich.
───────────────────────────────┼───────────────────────────────────────
Western Australia │8 „ „ „
───────────────────────────────┼───────────────────────────────────────
South Australia │9 „ „ „
───────────────────────────────┼───────────────────────────────────────
Victoria, New South Wales, │10 „ „ „
Queensland, and Tasmania │
───────────────────────────────┴───────────────────────────────────────

TELEGRAPHING TIME.—An important part of the work of the chief national
observatories is the determination of correct time, and its
communication to the public at large. Railways have especially created a
demand for a uniform and accurate system of time reckoning, and to meet
this need there is usually an organised service providing an automatic
distribution of time-signals by means of the electric telegraph. The
transmission of such time-signals was first established on a large scale
in connection with Greenwich Observatory, and at the present time
signals are sent to the General Post Office, whence they are distributed
automatically to post offices and subscribers throughout the kingdom. In
addition, signals are sent direct to Westminster for the regulation of
the great clock on the Houses of Parliament, and time-balls are dropped
at certain hours at Greenwich and Deal, in order that navigators may
have the opportunity of rectifying their chronometers.

THE YEAR.—The day is too small an interval of time to be conveniently
employed as a unit for chronological purposes, so that at present the
count of time by days is practically limited to the number of days in a
month. A greater unit, but still too small, is supplied by the month,
and the necessity for a more serviceable unit early led to the adoption
of the length of the year. This is at once a natural division of time,
corresponding to the recurrence of the seasons, and sufficiently answers
all requirements for measuring extended intervals.

If we determine the exact time required by the sun to pass from one
fixed point in the heavens to the same point again, we shall find the
time in which the earth makes a complete revolution round the sun, that
is, the time in which a line joining the earth and sun sweeps through an
angle of 360°. This interval, which is called the _sidereal year_,
amounts to 365 days 6 hours 9 minutes 9 seconds of mean solar time. It
will be clear, however, that the most useful year is that which will
give us the same day of the month at the same season in all years. If
there were no precession of the equinoxes, this would be of the same
length as the sidereal year, but on account of precession the passage of
the sun from the vernal equinox to the same equinox again occupies less
than a sidereal year. In fact, this equinoctial, or _tropical year_
amounts to 365 days 5 hours 48 minutes 46 seconds; that is, about 20
minutes less than the sidereal year. This is the year which is always
understood, unless it is otherwise stated. If our calendars were
regulated according to the sidereal year, the same day of the month
would in time run through all possible changes of seasons, the 25th of
December, for instance, occurring at one time in winter, and gradually
changing through spring, summer, and autumn.

THE CALENDAR.—The earlier calendars with which history acquaints us were
mainly based on the lunar month of about 29½ days, twelve of which made
up a lunar year of 354 days. The calendar year was thus more than 11
days shorter than the actual year, and in order to bring the dates into
agreement with the seasons, arbitrary intercalations were occasionally
made by the authorities.

In the year 45 B.C. a great reform was introduced by Julius Cæsar; 365¼
days was adopted as the length of the year, and it was prescribed that
ordinary years should be reckoned as consisting of 365 days, while every
fourth year divisible by 4 without remainder should be a _leap year_ of
366 days. Matters were so much simplified by this arrangement that the
Julian calendar remained unaltered until 1582, and is even now retained
throughout Russia.

The tropical year, as we have seen, is less than 365¼ days, so that the
Julian calendar does not quite keep course with the seasons. Although
the difference is only 11¼ minutes, it amounts to an entire day in 128
years, so that if the vernal equinox occurred on the 21st of March at
one time it would occur on the 20th after 128 years. If, then, it be
desired to bring the existing dates of any particular year into
agreement with dates at a previous period, as regards the seasons, a
correction in addition to that ordained by Cæsar must be introduced. In
the time of Pope Gregory, in the year 1582, the vernal equinox fell on
the 11th of March, and the necessity of a new calendar came to be
recognised. The astronomer Clavius, with the authority of the Pope,
devised our present “Gregorian” calendar. This arrangement, first of
all, altered the actual date of the equinox from the 10th to the 21st of
March, that is, to the day on which it occurred in the year of the great
Council of the Church at Nicæa, 325 A.D. To bring about this alteration
it was necessary to drop 10 days from the calendar, and it was therefore
decided that the day following the 4th of October, 1582, should be
called the 15th instead of the 5th. To prevent subsequent changes in the
date of the equinox the Julian rule for leap year was slightly modified.
If the date number of a year is divisible by 4 without remainder it is
still to be a leap year, unless it be a century year, in which case it
must be divisible by 400 without remainder if it is to be called a leap
year.

It was not until 1752 that the Gregorian calendar was adopted in
England, and as 1700 was a leap year according to the Julian rule the
old style date was 11 days behind the Gregorian date. An Act of
Parliament decreed that the day following September 2, 1752, should be
called the 14th. The Act was carefully planned so as to prevent
injustice in the collection of rents and the like, but it was only
accepted after considerable opposition.

It has lately been pointed out that if we wish to make the day of the
year correspond with the seasons for all time, a modification of the
Gregorian calendar must be adopted. By the Gregorian rule, three leap
years are omitted every four centuries; but Mr. W. T. Lynn has drawn
attention to the fact that if one were dropped every 128 years instead,
the calendar would be sensibly perfect, and the seasons would always
commence on the same dates.

CHAPTER VI.
THE MOVEMENTS OF THE MOON.

THE MOON’S REVOLUTION.—Apart from the changes in the appearance of the
moon due to the ever-varying phases, the first fact which strikes the
attentive observer is that the moon has an eastward movement among the
stars, and that this motion is much more rapid than that of the sun.
Indeed, the moon gains a whole revolution upon the sun in a period of
about 29½ days, this being the interval between two successive new or
full moons. As referred to the stars, however, it is found that the moon
and any particular star which cross the meridian together at a certain
time will again do so after the lapse of only 27⅓ days. Besides this
eastward movement among the stars, the moon moves towards and away from
the Pole; the full moon, for instance, is sometimes seen high in the
heavens at midnight, and at other times very low. Indeed, the moon’s
apparent movements resemble in a very general way those of the sun, but
they cannot be attributed to a revolution of the earth round the moon,
as those of the sun are to a real movement of the earth round the sun.
We have seen that there are direct proofs of the earth’s revolution
round the sun, and a revolution round the moon, even in a smaller orbit,
would not be consistent with the observed movements of the greater
luminary. Being convinced of the reality of the moon’s movements around
the earth, we can next proceed to investigate the circumstances of its
varied motions.

Just as we learn the conditions of the earth’s movements by observations
of the sun’s apparent movements which are their natural consequence, we
can determine the moon’s motions by studying its varying situations with
regard to the much more distant stars. We can measure the moon’s right
ascension and declination at different times with the transit
instrument, and, if desired, we can mark out the apparent path on our
star charts or celestial globes. In this way it is found that the moon
moves in a plane which is inclined at 5° 9′ to the plane of the
ecliptic. As to the shape of the orbit, we have only to observe the
changes in the moon’s apparent size; when it is nearest to us it will
appear largest, and when furthest removed its apparent diameter will be
least. Actual observations show that, like the orbit of the earth, the
moon’s orbit is an ellipse, with the earth in one focus. Owing to
various causes, the orbit is somewhat variable in shape, and its
eccentricity ranges from 0·07 to 0·045. When the moon is at the point of
its orbit nearest to the earth, it is said to be in _perigee_; and when
at the most distant part of its orbit, in _apogee_.

The earth’s orbit, as we shall see by and by, is very small as compared
with stellar distances, and the moon’s apparent movement, with regard to
the stars, is not affected by the revolution of the earth and moon round
the sun; consequently the interval between its passing a star and
overtaking the same star again is a measure of the time in which the
moon’s movement round the earth is performed—this is 27 days, 7 hours,
43 minutes, and is called the moon’s _sidereal period_. The direction of
the moon’s motion is opposite to that of the hands of a clock, a
movement which is said to be _direct_ (motion in the reverse direction
would be _retrograde_).

PHASES.—Two circumstances lead us to suppose that the light of the moon
is borrowed from the vast store thrown out into space by the sun. First,
the fact that it puts on _phases_, for if it were a body shining by its
own light we should always see a full moon. Second, the fact that the
phase we see depends absolutely on the moon’s situation with regard to
the sun and earth.

There is every reason to suppose that the moon is a dark globular body,
so that the sun can only illuminate that hemisphere which is turned
towards it. At new moon the illuminated part is turned directly away
from us, and we are thus led to infer that when new the moon lies
directly between the earth and sun. At full moon, on the contrary, the
whole of the illuminated part is presented to us, and we therefore
conclude that at this time the earth lies between the sun and moon. On
account of the inclination of the moon’s orbit to that of the earth, the
sun, earth, and moon do not always come exactly in a straight line at
new or full moon; when they do, the interesting phenomena of solar and
lunar eclipses occur. (Chapter VIII.)

A diagram will help to elucidate the production of the moon’s
intermediate phases. Supposing the sun’s rays to proceed from the left,
the earth being at O, the moon will be at A when new. Proceeding towards
B, a small portion of the illuminated side will be turned towards us,
and the moon will be a crescent. On reaching the point C, exactly half
of the sunlit hemisphere will be visible to us, and we have the moon’s
_first quarter_. Passing to the point D we see more than half of the
bright part of our satellite, and it appears gibbous in form, until it
reaches E, where it becomes full. Similar phases occur in inverse order
during the movement along the other part of the orbit.

[Illustration:

FIG. 18.—_The Moon’s Phases._
]

Such would be the conditions as to the phases of the moon, if the earth
were at rest.

THE MONTH.—If the earth were fixed in space with regard to the sun, the
moon’s phases would be repeated in the time corresponding to its period
of revolution round the earth. This is 27 days 7 hours 43 minutes, and
measures the length of a sidereal month.

It is much more useful, however, to refer the month to the phases
actually observed. If in Fig. 19 we have the sun, earth, and moon
represented at a full moon by S, E, and M respectively, the next full
moon will not occur until the three bodies occupy the positions S, E′,
and M′, the earth having travelled about 30° along its orbit. Between
two full moons, then, the moon must make a complete revolution round the
earth, and through an additional angle, A E′ M′, which will be equal to
the earth’s angular motion in the interval. This movement of the moon
occupies 29 days 12 hours 44 minutes, and is the duration of a _lunar
month_. It also determines the _synodic period_ of our satellite, a term
which, taken generally, signifies the period in which a planet or
satellite recovers the same position with respect to the sun when
observed from the earth.

[Illustration:

FIG. 19.—_The Lunar Month._
]

A calendar month, of which there are twelve in a year, must of necessity
consist of a whole number of days, and the average duration of such a
month is longer than that of a lunar month.

A remarkable relation exists between the synodic month and the length of
the year. In 19 Julian years of 365¼ days there are almost exactly 235
synodic months, so that after the completion of this period full moons
again occur on the same days of the month. The discovery of this cycle
is usually ascribed to Meton, a Greek astronomer, 433 B.C. It is
accordingly known as the _Metonic Cycle_, and is still used in the
calculation of the moveable festival of Easter.[1]

ROTATION AND LIBRATIONS.—Even observations made without instrumental
assistance show that the surface of our satellite always presents the
same face to us, and without further inquiry one might suppose that it
had no axial movement corresponding to that of its primary. If there
were no rotation, however, we should in turn see all parts of the moon,
and the observed circumstances indicate that it must rotate on an axis,
in the same direction as that of its orbital movement, and in the same
time. In Fig. 20 let E represent the earth, and _a b c_ the part of the
moon which is turned towards us when it is at M. When the moon arrives
at M′, observations show us that the same part is presented to our view,
so that the part corresponding to that we saw in position M is
represented by _a′ b′ c′_. Now, if the moon had not rotated in the
interval, the line joining _a_ and _c_ would have retained the same
direction, and would have been in the position _d e_; the part _c′ e_
would thus have been carried out of sight, while another part which was
not seen when the moon was at M would have come into view. In order that
we may see the same part of the moon in two different positions, M and
M′, the dividing-line _a c_ between the visible and invisible portions
must turn through an angle equal to that between the lines _d e_ and _a′
c′_; and since this angle is equal to that described by the moon in the
same time, the period of the moon’s rotation on its axis must be equal
to that of its revolution round the earth.

On account of the elliptical form of its orbit, the angular movement of
the moon is not quite uniform; like the earth, it is subject to the law
of areas. Hence, as the rotation is equable, the foregoing explanation
does not strictly hold. In fact, this varying velocity results in a
_libration in longitude_, which means that we sometimes see a little
more of the western edge and sometimes of the eastern edge. There is
also a _libration in latitude_ on account of the fact that the moon’s
axis is inclined to the plane of its orbit, so that at different times
we see more of the North or South Pole, as the case may be; in this
respect the moon behaves to the earth somewhat as the earth does to the
sun in regard to the seasons, but the inclination is not so great.

[Illustration:

FIG. 20.—_The Moon’s Rotation._
]

The moon is so near to us that the portion of it which we see depends to
a slight extent upon our terrestrial location. When the moon is rising
we see a little more of its western edge than will be seen by an
observer to the east of us, where the moon is in the south, and more
than we ourselves shall see when it has come to our own meridian. Just
before the time of setting we get to see a little beyond the eastern
edge. This is called the _diurnal libration_, and never amounts to more
than a degree.

Thanks to these librations, we are enabled to make telescopic
observations of 9 per cent. of the moon’s surface which would not
otherwise be open to our investigations.

CHANGES OF THE MOON’S ORBIT.—The moon’s orbit is by no means to be
regarded as a hard and fast geometrical figure. Indeed, it is subject to
such great distortions in consequence of “perturbations” that the
computation of the moon’s position at any future time is one of great
complexity. One of the most easily recognised changes in the orbit is
the revolution of its _nodes_, that is, of the points where it crosses
the plane of the ecliptic.

[Illustration:

FIG. 21.—_The Moon’s Nodes._
]

The latter being a plane of indefinite extent, to which the moon’s orbit
is inclined at 5° 9′, the moon will be alternately above and below the
ecliptic for about half its period of revolution. The point where it
passes from south to north of the ecliptic, A in Fig. 21, is the
_ascending node_, and the corresponding point on its southward path is
the _descending node_ of the orbit. Connecting these two points is the
line of nodes (A B), and by observations of the points where the moon’s
path intersects the ecliptic at different times it is found that the
line of nodes _regredes_ or moves backwards. The rate of this revolution
of the moon’s nodes is very irregular, but a whole revolution is made in
18·6 years.

This retrogression of the moon’s nodes may be well illustrated by the
following heliocentric longitudes of the ascending node as given in
recent “Nautical Almanacs”:

1892 January 1 53° 51′·56.
1893 „ 34° 28′·69.
1894 „ 15° 19′·00.
1895 „ 355° 49′·31.
1896 „ 336° 29′·61.

The line of apsides of the moon’s orbit joins the perigee and apogee;
the direction of this line in space changes in a very variable manner,
but in the long run it makes a complete revolution in 8·9 years.

When the sun is passing through the moon’s line of apsides it
temporarily increases the eccentricity of the orbit; when at right
angles to this line, the orbit becomes more nearly circular. This
disturbance of the moon has accordingly a period equal to that required
for two successive passages of the sun over the apse line of the moon’s
orbit.

Such are a few of the movements which come within the province of the
_lunar theory_, a fuller treatment of which is beyond our scope.

THE HARVEST MOON.—The full moon which occurs nearest to the autumnal
equinox is called the _harvest moon_, for the reason that it rises very
nearly at the same hour for several nights together, and so gives us a
greater share of moonlight, by which harvest operations may be extended.
At that time the sun will be at the autumnal equinoctial point, and when
it is setting in the west, the vernal equinoctial point, and the moon
with it, must be rising due east. The part of the ecliptic then above
the horizon will extend from the east to the west point, but will lie
wholly below the celestial equator (Fig. 22). As the moon’s path is very
slightly inclined to the ecliptic, its movement will thus make only a
small angle with the horizon, and for several nights together it will
rise at nearly the same time.

In March, when the sun is near the vernal equinox, the full moon will be
near the autumnal equinoctial point; when the sun is setting, the moon
will be rising as before, but in this case the part of the ecliptic
which is above the horizon lies wholly above the celestial equator. The
ecliptic is thus inclined at an angle to the horizon greater by 47° than
when the vernal equinox is rising in autumn; the moons path being near
the ecliptic, its movement during a day will at this time carry it a
long way below the Equator, and it will rise much later the following
day.

[Illustration:

FIG. 22.—_Position of Ecliptic at Sunset at Vernal Equinox_ (E A W)
_and Autumnal Equinox_ (E B W).
]

In the Southern Hemisphere, the conditions are reversed, the harvest
moon occurring at our vernal equinox, which, however, is the
commencement of the southern autumn quarter.

The phenomena of the harvest moon recur, but are not so marked, in the
month of October, and it is then called the hunter’s moon.

It is important to bear in mind that this rising of the moon at nearly
the same hour for several days occurs every month, but as the risings
then occur either in daylight or after midnight, and the moon is not
full, no special attention is drawn to them.

Again, since the phenomenon of the harvest moon depends upon the small
inclination of the path of the full moon to the horizon when it is at
the equinoctial point, the circumstances will be modified by the
latitude of the place of observation. At the Equator, for example, there
will be no harvest moon, as there the ecliptic is always greatly
inclined to the horizon; in fact, it will be inclined at the same angle
in spring as in autumn.

The moon’s path being inclined to the ecliptic, the conditions as to the
harvest moon will depend to a small extent upon the position of the
moon’s nodes, which, as we have seen, revolve in a period of a little
less than 19 years. At times, then, the moon’s path will be inclined 5°
more, and 9 years afterwards 5° less, than is the plane of ecliptic, and
under the latter conditions the harvest moon will be most pronounced.

HIGH AND LOW MOONS.—At the time of full moon, the moon is in the
opposite part of the heavens to that occupied by the sun, sometimes
being 5° above and other times 5° below. Manifestly, then, if the sun be
high in the heavens at mid-day, it will be only a little below the
northern horizon at midnight, and the moon, consequently, will be only a
small distance above the southern horizon. In summer, then, quite apart
from the fact that the nights are shorter, there is less moonlight. In
winter, on the other hand, the sun descends far below the northern
horizon at midnight, and the full moon has a high elevation in the
southern part of the sky. By this happy arrangement, the full moon is
longest above the horizon when its light is of greatest benefit to
mankind.

CHAPTER VII.
MOVEMENTS OF PLANETS, SATELLITES, AND COMETS.

APPARENT MOVEMENTS OF PLANETS.—It has already been pointed out that like
the sun and moon, the planets also have an apparent movement with
respect to the more distant stars. Mercury and Venus are never seen very
far from the sun, while other planets, among which are Mars, Jupiter,
and Saturn, may be seen in the part of the heavens opposite to the sun.

One point, and that a very important one, which we notice from our
observations is that the planets never depart very far from the
ecliptic, so that the planes in which they perform their movements are
nearly coincident with the plane in which our own annual journey round
the sun is performed. The apparent movements of the planets are such
that it is quite impossible to regard these bodies as circulating in
regular orbits round the earth itself. If they revolve round any other
body it is manifest that their apparent or geocentric motions will be
compounded of the real movements of the planets and that of the earth.
It is not necessary here to trace the steps by which it has been
determined that the planets revolve in regular orbits around the sun.
Suffice it to say that their observed movements are simply and
sufficiently explained by supposing that, like the earth, which may now
be regarded as a planet, they travel in elliptic orbits with the sun at
one of the foci. Besides this revolution, the planets have a rotatory
motion about their axes, but this question cannot be studied apart from
the telescopic features, and will therefore be treated in Section III.
of the present work.

The circumstance that the planets Mercury and Venus are never seen long
after sunset or before sunrise, indicates that their orbits must lie
between us and the sun. Hence, they are distinguished as the _interior
planets_, while those outside the earth’s orbit are called the _exterior
planets_.

MOVEMENTS OF INTERIOR PLANETS.—Let us consider briefly the conditions
under which we observe the interior planets. If such a planet be
represented by M in Fig. 23, while the earth is represented by E
traversing a larger orbit, the planet is said to be in _inferior
conjunction_ with the sun, when it lies directly between the sun and
earth. The actual movements of the planets being direct—that is,
anticlockwise—the planet at M has an apparent westerly motion as seen by
an observer situated on the earth, and from this we gather that it moves
more rapidly than the earth. For simplicity let us regard the earth as
being at rest at the point E. Then, as the planet reaches the position
M′, where it is as far as possible to the west of the sun, it is said to
be at its _greatest western elongation_. Proceeding in its orbit, the
planet’s apparent movement is direct, and it eventually comes in line
with the sun on the further side as seen from the earth; it is then said
to be in _superior conjunction_. From this point the planet moves to the
east of the sun until it comes to the point M, after which the motion
becomes retrograde, and the planet proceeds to inferior conjunction
again. When at its greatest distance to the east of the sun, as at M‴,
the planet is said to be at its _greatest eastern elongation_. Taking
the term _elongation_ in general, it may be regarded as a measure of the
angular distance of a planet from the sun as observed from the earth.

[Illustration:

FIG. 23.—_Movement of an Interior Planet._
]

If the orbits of the planets were perfect circles, the greatest
elongation distances of an interior planet would always be the same;
sometimes, however, we are nearer to the sun than at the other times,
and the apparent separation of the planet from the sun would seem
greater than at other times, even if there were no other cause at work.
The variations of the elongation distances are greater than can be
accounted for by our own varying distance, and are naturally attributed
to the elliptical form of the orbits of the interior planets themselves.
Mercury, for example, sometimes only departs 18° from the sun, while at
other times it reaches as far as 28° east or west.

When we take account of the fact that the earth has also a movement
along its orbit, it will be seen that the same conditions hold good with
regard to elongations and conjunctions, except that the intervals
between them will be longer.

[Illustration:

FIG. 24.—_Morning and Evening Stars._
]

MORNING AND EVENING STARS.—From superior to inferior conjunction an
interior planet is to the east of the sun. It then rises after the sun,
and sets after the sun, so that it is visible for a short time in the
early evening; in other words, it is an _evening star_ during this part
of its path. Between inferior and superior conjunctions, the planet is
conversely a _morning star_. This is illustrated in Fig. 24, where the
position of an observer towards whom the sun is rising is shown at A. An
interior planet at P is above the horizon at sunrise, but will be below
at sunset, the observer having been carried to A′ by the earths
rotation; it will thus be a morning star. When the planet occupies the
position P′ it is below the horizon at sunrise, but will remain in sight
after the sun has set in the evening, the observer then having been
transferred to A′ by the earth’s rotation.

PHASES OF INTERIOR PLANETS.—From the conditions which have been stated
with regard to the movements of the interior planets, one is not
surprised to find that telescopic examination reveals that these bodies
put on phases similar to those of the moon. At superior conjunction the
planets exhibit a fully illuminated disc, at greatest elongations they
appear as a half moon, while at inferior conjunction their dark sides
alone are presented to us. The apparent sizes of the planets, as
measured with the aid of a telescope, are also found to vary according
to their positions; when at inferior conjunction, the planet is much
nearer to us than at other times, and it consequently appears larger.
The apparent brightness of an interior planet also varies. At superior
conjunction the whole of the disc is illuminated, but the planet is then
so far removed from us that its light is very feeble. On the other hand,
at inferior conjunction, when it is nearest to us, the dark side of the
planet is turned towards us. The greatest brightness thus occurs at some
intermediate point. In the case of Venus this is between the greatest
elongations and inferior conjunction, when it is 40° from the sun. It is
then bright enough to be seen with the naked eye in full sunshine, and
has sometimes, on such occasions, been erroneously regarded by ignorant
persons as the Star of Bethlehem.

TRANSIT OF VENUS.—If an inferior conjunction occurs when the planet is
very near to a node—this term having the same significance as in the
case of the moon (p. 94)—the planet, whether it be Mercury or Venus,
will be seen projected as a dark spot upon the bright disc of the sun.
Such an occurrence is called a _transit of Venus_ or of Mercury, as the
case may be. Just as we do not get an eclipse of the sun every month, so
we do not get a transit of Venus every time the earth and that planet
have the same heliocentric longitude, and for the same reason, namely,
that the plane of the orbit is inclined to the ecliptic. As we shall see
in another chapter, a transit of Venus has a most important application
in the determination of one of the fundamental constants of
astronomy—the sun’s distance. The conditions as to the recurrence of
transits are of great interest. In the case of Venus, the _synodic_
period is 584 days, this being the time which elapses between two
successive inferior conjunctions. Five synodic periods are thus very
nearly equal to eight years, and 152 synodic revolutions are even more
nearly equal to 243 years. As seen from the earth, the sun crosses the
nodes of the orbit of Venus on June 5 and December 7, and since there
can be no transit when the planet is more than 4½° from the node, the
transits will all occur about these dates. A transit will be followed by
another after the lapse of 8 years, if the planet is not too far from
the node; but there can be no other transit with the planet at the same
node until 243 years have elapsed. There are, however, transits
occurring at similar intervals when the planet is at the other node. The
following dates on which transits have occurred, or will occur, will
illustrate the foregoing statements:—

8 years│December 7, 1631,│243 years.│——————————
„ │December 4, 1639,│ „ │243 years.
8 years│December 9, 1874,│ „ │ „
„ │December 6, 1882,│——————————│ „
8 years│June 5, 1761, │243 years.│——————————
„ │June 3, 1769, │ „ │243 years.
8 years│June 8, 2004, │ „ │ „
„ │June 6, 2012, │——————————│ „

[Illustration:

FIG. 25.—_Movement of an Exterior Planet._
]

MOVEMENTS OF EXTERIOR PLANETS.—The exterior planets are at once
recognised as such by their occasional appearance in the part of the sky
opposite to that of the sun. They are then said to be in _opposition_.
When in the same line as the sun, and on the remote side of it, as at P′
in Fig. 25, the planet is in _conjunction_. The apparent movements of
such a planet are very complex. Neglecting for a moment the earth’s
motion, it is evident that the apparent rate of movement of the planet
with reference to the stars will vary very considerably according as the
planet is near opposition or near conjunction, the movement appearing to
be most rapid when the planet is nearest to us. Upon this unequal rate
of motion is superposed a varying direction of motion produced by the
changing position of the earth. When the planet is at P, and the earth
at E, both are moving in the same direction, but as the earth has the
greater angular velocity, the apparent motion of the planet will be
retrograde, that is, the planet will appear to go backwards in its path.
If the earth be near the point E′, its orbital movement will be directed
away from the planet, and will scarcely affect its apparent position;
accordingly, about this time the planet has a direct movement in the
heavens. Between these two points the direction of the apparent movement
of the planet has changed, so that at some intermediate position it
would seem to have suspended its wanderings; here we have a _stationary
point_. For a certain time, before and after conjunction, the linear
directions of movements of the earth and planet will be opposed to each
other, and on this account the _direct_ apparent motion of the planet
will be accelerated. Presently, as the earth gains on the planet,
another stationary point will be reached, and with the approach to
opposition the planet will again retrograde.

If both orbits were in the same plane, these apparent movements would
all be backwards and forwards along a great circle of the celestial
sphere coincident with the ecliptic, the eastward movement
predominating. The planes in which the planets perform their revolutions
are, however, inclined to the ecliptic, and the result is that they
appear to us to travel in loops, some of which are illustrated in Fig.
26.

[Illustration:

FIG. 26.—_Apparent Paths of Ceres, Pallas, Juno and Vesta, in 1896._
]

From the fact that we are constantly within the orbit of an outer
planet, it is evident that we must always see more than half of the
planetary hemisphere on which the sun is shining. Consequently, an
exterior planet never puts on a crescent phase, or presents the
appearance of a half moon. The nearer the planet the greater will be the
dark area which it is possible for us to observe. In the case of Mars,
for example, we sometimes see it gibbous like the moon about three days
from full, but in the more distant planets this gibbosity is scarcely
perceptible. The greatest phase of an exterior planet occurs when it is
at _quadrature_, that is, when a line joining the earth and sun is
perpendicular to one joining the earth with the planet.

FAVOURABLE AND UNFAVOURABLE OPPOSITIONS.—A little consideration of Fig.
25 will make it perfectly clear that an exterior planet is very much
nearer to us at a time of opposition than at a conjunction. We are, in
fact, then, nearer to the planet by the diameter of the earth’s orbit, a
matter of some 186 millions of miles. Accordingly, the planets, more
especially our neighbour Mars, are best studied in the telescope about a
time of opposition. Now, if we had to deal with circular orbits, the
distance of a planet at opposition would remain constant, and we should
see the planet equally well at all oppositions. It is found, however,
that this is not the case, and the ellipticity of the orbits of the
earth and planets supplies a simple and sufficient explanation. Sir
Robert Ball illustrates this in the case of Mars by a diagram similar to
Fig. 27. It will be seen that, when the opposition occurs in August, the
earth is much nearer to Mars than when it happens at other times. The
least favourable oppositions are those which occur in February, the
planet then being nearly twice as far removed from us as at the nearest
approach during an August opposition.

[Illustration:

FIG. 27.—_Opposition of Mars._
]

As regards the more distant planets, the diameter of the earth’s orbit
and the variations of opposition distance are of less importance, since
they form a much smaller proportion of the distances of those planets
from the sun.

ELEMENTS OF A PLANETARY ORBIT.—A complete study of the apparent
movements of the planets with which we are acquainted shows that their
real movements are performed round the sun in ellipses, the sun being
placed at a focus. Each orbit, like that of the earth, has its
perihelion and aphelion points, and its apse line; not being coincident
with the ecliptic, it will have a line of nodes, and an ascending and
descending node. Each planet will further have a particular inclination
to the ecliptic, and a period of revolution peculiar to itself.
Consequently, to systematise our knowledge of any particular orbit,
certain conventions are adopted, and the seven things we must know, in
order that we may specify the size of the orbit, its position in space,
and the situation of the planet in its orbit, are as follows:—

_a_ = Semi axis major of elliptic orbit.

_e_ = Eccentricity.

_i_ = Inclination to ecliptic.

Ω = Longitude of ascending node.

π = Longitude of perihelion.

P = Period of revolution. (_u_, the mean daily motion, sometimes
replaces P.)

E = The epoch, giving the longitude of the planet at some particular
time.[2]

The first two quantities indicate the size and shape of the orbit, the
next three its position with regard to the ecliptic, and the last two
are required to determine the situation of the planet in its orbit. Some
of the elements are illustrated in Fig. 28.

[Illustration:

FIG. 28.—_Elements of an Elliptic Orbit._
]

DETERMINATION OF A PLANET’S PERIOD.—Observations enable us to determine
the synodic period of a planet, and knowing that the earth’s period is a
year, it is a simple matter to determine that of the planet. In the case
of an exterior planet, the interval from opposition to opposition
furnishes the best means of determining the synodic period. The exact
moment of an opposition cannot usually be directly observed, and what
one actually does is to measure the R.A. and declination of the sun on
several days about the time of opposition, as also those of the planet;
then, by reducing these co-ordinates to celestial longitude and
latitude, it is not difficult to determine at what moment the longitudes
differed by 180°, that is, the moment at which opposition took place.
The problem of finding the planet’s sidereal period, then, amounts to
this: at what rate must the planet be moving in order that the earth may
make a complete revolution, and move, in addition, through the same
angle as the planet? In other words, what must be the period of the
planet in order that the earth may gain a whole revolution in the
interval corresponding to the synodic period? The daily movement of the
planet will be 360°/P, and that of the earth 360°/365¼, if P denote the
number of days in the planet’s sidereal period. The earth’s gain per day
will thus be the difference between these two quantities, and since a
whole revolution is gained in the synodic period, the gain per day can
be expressed as 360°/S, where S represents the synodic period; thus we
get

360°/365¼ − 360°/P = 360°/S
or
1/365¼ − 1/P = 1/S

The synodic period of Mars is 780 days, and the application of the
foregoing formula leads us to 687 days as the time of its revolution
round the sun.

A single determination of a synodic period does not give precise
results, for the reason that the orbits of the planets are elliptical,
and the intervals consequently dependent upon whether the planet is near
perihelion, or far removed from it when an opposition is observed. It
is, therefore, necessary to determine the time of opposition at long
intervals, and so reduce the errors in measuring the length of a single
period.

MOVEMENTS OF SATELLITES.—Telescopic observations show that some of the
planets are accompanied by _satellites_, which revolve round their
primaries as the moon revolves round the earth. The apparent movements
of these bodies, with regard to the planets, are very similar to those
of the interior planets with regard to the sun, having similar points of
greatest eastern and western elongations. The facts which have been
collected show that each satellite, like our own moon, moves in an
elliptical orbit, with the planet in one of its foci. With one
exception, the satellites attending the planets of our system have a
direct movement; those of Uranus, however, have apparently a movement in
the same direction as the hands of a watch, but this can be regarded as
direct, if we consider the plane of the orbit to be inclined more than
90° to the plane of the ecliptic.

THE ORBITS OF COMETS.—Another class of bodies which circulate round the
sun now claims our attention. These are the _comets_, some of which are
never seen without the aid of telescopes, while others have been
brilliant enough to excite a widespread wonder and interest. They
usually have a very rapid movement relatively to the stars; and to learn
something as to their real motions, we commence by measuring their right
ascensions and declinations as frequently as possible. When such
observations are plotted, they give us the geocentric movement of a
comet, which generally seems very irregular, and gives one the idea that
it is subject to no law. Unlike the planets, comets do not usually keep
near the ecliptic, but move in planes inclined at all angles to it.
Their rates of apparent movement also change very rapidly.

When the effect of the earth’s movement upon that of a comet is
eliminated, it is found that the movement of the comet is performed
either in an ellipse, a parabola, or an hyperbola, the sun in each case
occupying one of the foci.

From our definition of the eccentricity of an ellipse, it will be seen
that, when the eccentricity is zero, we have a circle. When the
eccentricity becomes unity, the ellipse becomes a parabola, so that the
latter curve may be regarded as part of an ellipse, of which the foci
are at an infinite distance apart. In the case of the hyperbola, the
eccentricity is greater than unity.

Comets which move round the sun in ellipses are called _periodic
comets_, for the reason that they return regularly into the sun’s
neighbourhood. Those which traverse parabolic or hyperbolic paths will
pass once round the sun and continue to journey into the depths of
interstellar space until their movements are changed by the proximity of
other bodies into the neighbourhood of which their wanderings may take
them.

When a new comet is observed, one of the things which astronomers
endeavour to do is to determine its orbit, so that its path may be
predicted with sufficient accuracy to enable it to be picked up readily
with a telescope when it becomes so feeble that it is no longer visible
to the naked eye. In the first instance, the motion is assumed to be
parabolic, and any deviation from such an orbit forms the subject of a
rigorous calculation by means of which the precise form is determined.

CHAPTER VIII.
ECLIPSES AND OCCULTATIONS.

ECLIPSES OF THE MOON.—As the various members of the solar system shine
only by virtue of the light which they receive from the sun, they will
cease to be visible if by any means they are deprived of the sun’s rays.
Each planet or satellite must evidently cast a shadow which is turned
directly away from the sun, and any other body passing wholly or
partially within such a shadow will be proportionately debarred from
receiving the direct light of the sun.

[Illustration:

FIG. 29.—_The Earth’s Shadow._
]

Were the sun a mere point of light these shadows would be parts of
cones, the apex always being at the sun, and they would be prolonged
indefinitely into space. As a matter of fact, every individual point
upon the sun’s disc is competent to cast a conical shadow, and the net
result is that only a relatively small space behind a planet or
satellite is really in total darkness. This will be readily understood
from Fig. 29, in which S is the sun, and E the earth. The total shadow
now becomes a cone, with the apex turned directly away from the sun, but
round this there is a region of partial shadow which is only illuminated
by portions of the sun. If we imagine a section of the shadow across the
line _a b_, we should find a central disc of total darkness called the
_umbra_, and surrounding this a ring of half shadow called the
_penumbra_.

From the known dimensions of the sun and earth, and the distance between
them, it is easy to calculate the size of the earth’s shadow-cone, and
its length is found to be greater than the distance of the moon. The
axis of this shadow will, of course, always be in the plane of the
ecliptic. If, then, at the time of opposition, the moon is sufficiently
near the plane of the ecliptic, it will pass through the shadow, and we
shall have the phenomena of a _lunar eclipse_. When the moon is wholly
immersed in the umbra, the eclipse is total, and if it further passes
quite symmetrically through the shadow, the eclipse is said to be
central. This would always be the state of affairs if the moon performed
its monthly journey in the plane of the ecliptic, and a total eclipse
would occur every month. The moon’s orbit, however, is inclined to the
ecliptic, so that for a central eclipse, the moon must be simultaneously
at opposition and at a node. If the moon be near the node when at
opposition, a total eclipse may occur, but it cannot be central, and the
duration of the total obscuration will be reduced. Still further from
the node, the moon will be above or below the ecliptic, and will be only
partially involved in the shadow-cone; such an eclipse is called a
partial one. Beyond a certain distance from the node, the inclination of
the moon’s orbit will take the moon entirely out of the umbral shadow,
and no eclipse will be possible.

The circumstances of an eclipse of the moon thus vary very considerably,
and there is still another reason why we may expect them to be
different. We have seen that the earth’s distance from the sun changes
throughout the year, and, in consequence, its shadow will be of varying
length, and the diameter of the shadow at any specified distance will
not be constant. The moon, again, is not always at the same distance
from the earth, and it will, therefore, pass through varying depths of
shadow in different eclipses, and with different velocities.

The breadth of the earth’s umbral shadow at the point where the moon
passes through it is, on the average, about three times the moon’s
diameter, and the time taken for the moon to traverse this distance is
about two hours. The duration of totality in a central eclipse may,
therefore, amount to two hours, while an additional two hours may be
occupied by the partial phases.

[Illustration:

FIG. 30.—_The Lunar Ecliptic Limit._
]

THE LUNAR ECLIPTIC LIMIT.—The greatest distance of the moon from a node
at which a partial eclipse is possible, is called the _lunar ecliptic
limit_, and is very easily calculated. In Fig. 30, let E N represent a
part of the ecliptic, N being the node of the moon’s orbit, and E the
centre of the earth’s shadow. As the orbit of the moon is inclined about
5° 9′ to the ecliptic, it may be represented by the line N M, inclined
at an angle to N E. If E A be the radius of the earth’s shadow, which,
on the average, is about three-quarters of a degree, and M A the moon’s
apparent semi-diameter (about a quarter a degree), it is clear that the
point beyond which no eclipse is possible is that in which the line M E,
perpendicular to N M, is equal to the sum of the semi-diameters. All the
quantities for solving the triangle N E M are thus known, and it can be
readily calculated that N M, the greatest distance of the moon from the
node at which an eclipse would be possible, under average conditions is
about 11°.

Taking into account the varying distances between the sun, earth, and
moon, it is found that an eclipse must always occur if the moon is
within 9° of the node, and may occur if it be 12° from the node. These
figures refer to the passage of the moon through the umbra, as the
effect of its entrance into the penumbra is too slight to be observed.

The entrance of the moon into the earth’s shadow is a definite
phenomenon, which is independent of the observer’s position on the
earth, and the phases of the eclipse are seen at exactly the same moment
from all places where the moon is above the horizon. The computation of
the circumstances at a given place is accordingly a simple one.

When a lunar eclipse is not total at any of its phases, it is usual to
specify its _magnitude_ by the ratio of the greatest measurement of the
obscured part to the moon’s diameter. Thus the magnitude of the partial
eclipse of February 28th, 1896, is given in the “Nautical Almanac” as
0·870, the moon’s diameter being taken as unity.

The conditions of lunar eclipses which have been stated have reference
to the moon’s passage through the earth’s geometrical shadow, but the
actual conditions are greatly modified by the fact that the earth is
surrounded by an atmosphere which refracts the suns light so much that
the moon is seldom quite obscured during totality. The commencement of
the total phase is also rendered difficult of observation by the
somewhat indefinite boundary between the umbra and penumbra.

ECLIPSES OF THE SUN.—If the moon performed its revolution in the plane
of the ecliptic, it is evident that it must always come between us and
the sun once in each month. This it does not do, but occasionally it
happens to be in the ecliptic when in conjunction, and the moon is then
seen to be projected upon the sun. In other words, there is an eclipse
of the sun. Let us consider the circumstances, in the first instance, to
an observer placed at the centre of the earth. If the centres of the
moon and sun appear in the same straight line, the eclipse will be
_total_ or _annular_, according as the moon or sun has the greater
apparent diameter. Both these forms of eclipses are possible, on account
of the varying apparent diameters of the sun and moon consequent upon
their variable distances from the earth. If the moon appear the larger
it will evidently cover up the whole of the sun, but when it is the
smaller, a ring of sunlight will be visible round the dark holy of the
moon, and the eclipse will be an annular one. These conditions are
illustrated in Fig. 31, _a_ and _b_ representing a total and an annular
eclipse respectively. If the moon and sun be not quite in the same
straight line, the moon may still be seen partially projected on the
sun’s disc, in which case there will be a _partial eclipse_ of the sun,
as in Fig. 31, _c_.

[Illustration:

FIG. 31.—_Eclipses of the Sun._ (_a_) _Total Eclipse_, (_b_) _Annular
Eclipse_, (_c_) _Partial Eclipse._
]

In a total eclipse there are four so-called _contacts_: the first when
the moon is seen to encroach upon the sun’s disc, the second when the
advancing edge of the moon reaches the opposite limb, the third when the
following edge of the moon first touches the sun’s boundary, and the
fourth when the projected moon finally passes off the sun. The interval
between the second and third contacts marks the duration of totality. As
referred to our supposed observer at the centre of the earth, the
duration evidently depends upon the apparent rate of the moon’s eastward
movement as compared with that of the sun, as well as upon the
differences of the apparent diameters of the two bodies.

The production of eclipses of the sun may also be considered as arising
from the immersion of an observer in the shadow of the moon. This shadow
has its axis turned from the sun, but is so short that it does not
always reach the earth. If an observer comes near the axis of the
conical shadow, and within the apex, the eclipse will be total; if he is
in the axis, but outside the apex, the eclipse will be annular.

[Illustration:

FIG. 32.—_Duration of a Solar Eclipse._
]

The whole of the shadow of the moon is so small that only a few places
on the earth’s surface can be simultaneously immersed in it, and when we
come to discuss the conditions of an eclipse with regard to a particular
observer, the problem becomes a complicated one. At some places the
eclipse may be total, at others it will be only partial, while at others
no eclipse will occur at all. These differences are due to the fact that
the sun is scarcely appreciably displaced by the change of locality,
while the apparent position of the moon may be affected to the extent of
nearly a degree. Again, the observer situated on the earth’s surface has
a movement of his own, produced by the earth’s rotation, and his rate of
motion depends upon the latitude in which he is situated. The effect of
this movement upon the conditions of the eclipse are very pronounced.
Suppose for a moment that the sun, moon, and earth, are fixed along the
same straight line S M E in Fig. 32, a terrestrial observer at _a_ on
the earth’s Equator would see an eclipse at noon; if he were not in
rotation, and the three bodies remained at rest, the eclipse would be a
perpetual one. He is, however, carried onward by the earth’s rotation,
and even if the moon were at rest, it would appear to him to pass over
the sun in the reverse direction. This retardation of the moon will be
less in amount for observers away from the Equator, and also for
observers to whom the sun is not on the meridian when eclipsed. The
effect of rotation on an observer at _b_ (Fig. 32), for example, is to
move him almost in the direction of the line joining the moon and sun,
and the backward tendency of the moon due to rotation is very slight. On
account of the earth’s rotation, then, the duration of a solar eclipse
is lengthened, the greatest increase occurring at those places where the
sun is on the meridian at the time of eclipse.

There is another source of gain of duration of an eclipse to the
observer who sees the phenomenon about noon. The moon’s apparent
diameter is then augmented by a greater amount than at other places,
because the observer is then nearest to the moon; while the sun’s
apparent diameter is not appreciably affected. The greater the
difference in the apparent diameters of the sun and moon, the longer
will totality last.

These and other circumstances have all to be taken into account in
computing the conditions under which an eclipse will be seen at any
given place.

According to an eminent authority, Professor Young, the greatest
possible diameter of the moon’s shadow, where it strikes the earth, is
167 miles. It may, however, cover a larger space on the earth’s surface,
because the latter does not pass perpendicularly through the shadow. To
all persons within the shadow, the eclipse will be total, but to those
on its outer boundary the duration of totality will be for an instant
only. The penumbral shadow has a cross section about 4,500 miles in
diameter, covering sometimes a space on the earth’s surface 6,000 miles
across. To all persons within this area, but not in the central shadow,
the eclipse will be partial. The shadow spot travels over the earth’s
surface, because of the moon’s movement, but its track and speed are
greatly modified by the earth’s rotation. The movement of the shadow, as
affected by the earth’s rotation, would be along a parallel of latitude;
but its ultimate direction of movement, though trending eastwards,
depends upon this, combined with the direction of the moon’s movement at
the time of the eclipse. Thus, a portion of the track of the total
eclipse of April 16, 1893, is as that shown in Fig. 33.

[Illustration:

FIG. 33.—_Track of Eclipse of April 16, 1893._
]

These considerations will suffice to explain the necessity for very
precise calculations as to the position of the central line of an
eclipse, when observers are sent out for the purpose of recording the
phenomena.

Under the most favourable combination of conditions, that is, when the
eclipse occurs at noon at a place on the Equator, an eclipse cannot be
total for more than 7 minutes 58 seconds, nor be annular for a longer
time than 12 minutes 24 seconds. From first to last contact may occupy
as much as 2 hours, when all the circumstances are similarly favourable.
(Loomis.)

THE SOLAR ECLIPTIC LIMIT.—In order that an eclipse of the sun may occur,
the moon must be so near the ecliptic that it can be seen projected on
the sun, either wholly or partially, from some point on the earth. It
must therefore not be very far from the node, and the distance it may be
from the node, while still being seen upon the sun, is called the _solar
ecliptic limit_. As in the case of lunar eclipses, this distance is
determined by the inclination of the moon’s orbit, and the distances of
the moon and sun from the earth. The latter being variable quantities,
the limit is not always the same. It is calculated without much
difficulty that an eclipse _must_ occur if the new moon happens when it
is within 15° 21′ of the node, and may occur within 18° 31′. These are
called the minor and major ecliptic limits respectively. For total or
annular eclipses, the limits are respectively 9° 55′ and 11° 50′.

NUMBER OF ECLIPSES IN A YEAR.—If the moon’s nodes were fixed, the sun
would pass through the line of nodes twice a year. At such times an
eclipse of the sun must necessarily occur if the moon were within 15°
21′ of the node on either side. The sun requires more than a month to
traverse this space of 30° 42′, and the moon must therefore pass through
each node at least once while the sun is traversing these limits. It
follows, then, that there must be at least two eclipses of the sun in a
year. Since the line of nodes of the moon’s orbit revolves backwards in
a period of about nineteen years, the sun returns to the same node after
an interval of 346·6 days, and there must accordingly be two solar
eclipses in this interval. If, then, there be an eclipse early in
January, there will be another about the middle of the year, and another
at the end of the year, so that on this ground alone there is a
possibility of three solar eclipses in a year.

Again, while the sun is passing through the ecliptic limits, it may
happen that an eclipse occurs on its entrance, and then another will
occur before it gets beyond on the other side of the line of nodes. In
this way two eclipses may occur in the region of each node passage, and
if the first of the series occurs early in January, five eclipses of the
sun may occur in a single year.

The sun, however, is not a month in traversing the lunar ecliptic limit.
Consequently, a whole year may elapse without the moon being
sufficiently near the node to pass within the earth’s shadow, and in
many years there are accordingly no eclipses of the moon. Only one full
moon can occur within the lunar ecliptic limits when the sun passes the
node, but if there be an eclipse at one node, there may also be one six
months later at the other node. As in the case of the solar eclipses,
the “eclipse year” is one of 346·6 days, so that if there be an eclipse
of the moon early in January, there may possibly be three altogether in
the course of the year, but there could not be three lunar eclipses if
the extra solar eclipse were possible. Altogether, then, there may be
seven eclipses in the course of a year—five of the sun and two of the
moon. Usually there are four or five, some particulars of which are
furnished by all respectable almanacs. It will be observed that the
number of solar eclipses is much larger than that of lunar ones, but as
the latter are visible at all places having the moon above the horizon,
while the former are restricted to small parts of the earth’s surface,
more lunar than solar eclipses are visible at any specified place.

RECURRENCE OF ECLIPSES.—We have seen that the sun requires only 346·6
days to travel from one of the moon’s nodes back to the same node again,
in consequence of the regression of the nodes, while the moon requires
27·2 days. Suppose, then, that the moon and sun are at a node, and there
is an eclipse at new moon; after 346·6 days the sun will return to the
same node, but the moon will not be at the node, nor will it be exactly
new. It will not be until the sun has returned nineteen times to the
node that the moon is also very nearly new at the same node again.
Nineteen returns of the sun to the moon’s nodes occupy a period of
6,585·78 days; 223 intervals between successive new moons (synodic
months) cover 6,585·32 days, while 242 node passages of the moon require
6,585·357 days. In this period of 18 years 11⅓ days (or 10⅓ days if
there are five, and 12⅓ if there are three leap years in the interval),
the sun and moon thus return to nearly the same conditions as affecting
the possibility of eclipses. This period was called the _Saros_ by the
Chaldeans, by whom it was employed in the prediction of eclipses. The
adjustment of periods, however, is not quite precise, so that
predictions based upon the Saros are only approximations, which serve as
a guide for more accurate computations.

This eclipse period is still more remarkable from the fact that it
almost exactly represents 239 passages of the moon through perigee, so
that after the lapse of 18 years 11⅓ days the moon is almost at the same
distance from the earth, as well as nearly at the same phase and the
same distance from a node.

As the Saros includes a fraction of a day, an eclipse is not necessarily
repeated at the same place after the lapse of 18 years 11⅓ days, for the
reason that the eclipse will not occur at the same time of day, and the
sun may be below the horizon. After three Saroses, however, the eclipse
will be repeated nearly at the same hour, but even then it will not be
seen under the same conditions, because the track of the shadow will be
in different latitudes, for the reason that the moon does not return
_exactly_ to the node in the interval between 223 new or full moons, and
eclipses can only occur when the moon is new or full.

Beginning as a partial eclipse, an eclipse of the moon will gradually
become of greater magnitude at successive intervals of 18 years 11 days,
until it becomes a total eclipse, and will again gradually become of
smaller magnitude, until it ceases to be reproduced at all. Altogether,
it would be repeated once in every 223 months for 865 years.

Since the solar ecliptic limit is greater than the lunar, a solar
eclipse is repeated at similar intervals of 18 years for about 1200
years. Most of these eclipses would be partial, 27 would be annular, and
18 total. During this period, the track of the central eclipse would
shift northwards if the moon were at a descending node, and southwards
if at an ascending node, until finally it passed altogether clear of the
earth.

It must be remarked, however, that, in the period corresponding to a
single Saros, about 28 eclipses of the moon, and 43 of the sun, usually
appear, so that altogether about 71 series of eclipses are in progress.
Of the solar eclipses which occur during a period of 18 years, about 12
are total at some places upon the earth.

OCCULTATIONS OF STARS AND PLANETS BY THE MOON.—In its monthly round, the
moon is constantly passing in front of some of the stars which lie in
its apparent path, and these luminaries will, therefore, at times, be
hidden temporarily by the moons disc. Occasionally a planet may appear
in the same line of vision as the moon, and that also will pass from
view until subsequent motion again removes the intercepting body. These
disappearances are closely allied to the phenomena of eclipses, and
receive the name of _occultations_. On account of the moon’s eastward
movement, it is evident that the disappearance of stars or planets when
occulted will take place on the eastern edge of the moon; but since the
moon trends north or south in some parts of its orbit, the disappearance
near the northern and southern edges may occur slightly on the western
side of the north or south point of the moons limb. Similarly, the
reappearance generally occurs on the western side of the moon, but
occasionally may occur on the eastern side—that is, when the northern or
southern edge of the moon does not much more than appear to graze the
stars.

The calculation of the circumstances of an occultation is very similar
to that involved in the computation of eclipses. (A simple graphical
method for working out the conditions of an occultation is described by
Major Grant, R.E., in the _Geographical Journal_ for June, 1896.)

ECLIPSES AND OCCULTATIONS OF SATELLITES BY PLANETS.—Just as we find the
moon eclipsed by passing through the earth’s shadow, we find the
satellites of other planets to be at times invisible for a similar
reason. We thus observe _eclipses_ of the satellites. The satellites may
also be invisible to us for the reason that they are behind the planet,
and they are then said to be _occulted_. These satellite phenomena are
especially remarked in the case of Jupiter, and their observation is one
of great interest. When a satellite passes between the sun and the
planet it throws a shadow on the surface of the planet similar to that
of the moon upon the earth. This is visible to us as a dark spot, and
from the centre of that dusky patch an inhabitant of Jupiter would
undoubtedly see a total eclipse of the sun. To us on the earth the
passage of such a shadow across the planet’s disc is but a “transit of
the shadow” with its “ingress” and “egress.”

The times of all these appearances are computed from a knowledge of the
movements of the satellites.

CHAPTER IX.
HOW TO FIND OUR SITUATION ON THE EARTH.

DETERMINATION OF LATITUDE.—In order that we may precisely define our
situation upon the terrestrial sphere, we have seen that two
measurements are necessary, namely, latitude and longitude. The first of
these indicates the angular distance from the Equator, and the latter
the angular distance east or west of an arbitrary initial meridian. It
is necessary for us then to learn something of how these important
co-ordinates can be determined.

In considering the apparent movements of the heavenly bodies in
different latitudes, we have already seen that at places on the earth’s
Equator the north celestial pole is on the horizon, while at the North
Pole it is in the zenith, and in other latitudes is elevated at
different angles. If one sails from England to the Cape, for example,
the Pole Star is seen to gradually get lower and lower in the sky,
until, on crossing the Equator, it descends below the northern horizon
and is no longer visible. Sailing northward, as to Norway, the Pole Star
is seen to get higher in the sky.

Now, although the Pole Star is not exactly at the north celestial pole,
it is a convenient guide to the eye as to the location of that very
important mathematical point, and what we learn from its behaviour as
our latitude is changed is that the altitude of the Pole above the
horizon is equal to the latitude of the place of observation.

One of the methods employed for finding the latitude of a place is
accordingly to determine the altitude of the Pole. This can be obtained
by an instrumental measurement of the altitude of the Pole Star, from
which, if the time of observation be known, the altitude of the true
Pole, which occupies the centre of the small diurnal circle traversed by
the star, can be computed. Tables which save an immense amount of labour
in the calculations involved are given in the “Nautical Almanac,” and in
“Whitaker’s Almanac.”

Another method of finding the elevation of the Pole is to take advantage
of the fact, that at intervals of twelve sidereal hours the Pole Star
passes the meridian alternately above and below the Pole. If, then, one
finds the altitudes at the upper and lower transits, and corrects them
for refraction, the average of the readings is a measure of the altitude
of the true Pole, and therefore of the latitude. Other stars which are
circumpolar may be employed for the same purpose, and this method has
the great advantage that a knowledge of the correct time, or of the
exact position of the star observed, is superfluous. The disadvantage is
that the correction for refraction, especially in low latitudes, cannot
be made with the necessary degree of accuracy. It must be remembered
that an error of only 1′ in latitude implies a mistake of a mile
measured on the earth’s surface.

Other methods, however, are available. As we go southwards, not only
does the Pole Star become lower in the sky, other stars in the southern
part of the sky become higher at the same rate that the Pole Star
descends. Other stars can therefore be utilised, and in order that
refraction may affect the observations as little as possible, stars of
known declination near the zenith are observed. Suppose an observer,
situated at O (Fig. 34) on the earth’s surface, observing a star S on
his meridian, O Z will represent his zenith, and O E, parallel to the
Equator, will be the direction in which he will see the celestial
equator where it crosses his meridian. The declination of the star,
represented by the angle S O E, has been previously determined with
great accuracy, and the angle S O Z, the zenith distance of the star, is
the angle which he measures. In the case illustrated by the diagram, the
difference between the declination and the zenith distance will give the
angle Z O E, which is evidently equal to the latitude O C Q. To get rid
of the ever troublesome refraction of our atmosphere, stars which pass
as nearly as possible through the zenith are selected for observation,
and stars both to north and south are observed.

[Illustration:

FIG. 34.—_Determination of Latitude._
]

Another way of determining the latitude, which is very commonly
employed, is known as Talcott’s method. The observations are made with
the aid of a zenith telescope. The latitude being approximately known,
two stars are selected which transit nearly at the same time and nearly
at the same distance from the zenith, one to the north and the other to
the south. That which transits first is brought to the centre of the
field of view, which is marked by a spider thread. The instrument is
then reversed in its bearings so that it points at the same angle on the
opposite side of the zenith. When the second star comes into the field,
the telescope is kept fixed, and a moveable spider thread is made to
coincide with the star passing through the field. The distance between
the spider threads furnishes a measure of the difference in zenith
distances. Half the sum of the declinations added to half the difference
of zenith distances gives the latitude when this method is employed.

Various other methods have been devised for the precise determination of
latitude, but the foregoing will sufficiently serve to illustrate the
processes followed when the observations are made on land.

Before the invention of astronomical instruments, latitude was
approximately measured by the lengths of shadows. At the summer
solstice, at noon, the shadow of a vertical stick is at its shortest,
while at the winter solstice it is longest. By measuring these lengths,
a diagram can be made showing the altitude of the sun at noon on each
occasion. Midway between these will be the altitude of the celestial
equator where it crosses the meridian. Since the altitude of the Pole is
equal to the latitude, the altitude of the Equator, subtracted from 90°,
thus gives the latitude.

[Illustration:

FIG. 35.—_Ancient Mode of measuring Latitude._
]

It will be noted that this _gnomon_ experiment also furnishes a measure
of the obliquity of the ecliptic. The gnomon was in use by the ancient
Chinese, and it is also believed that the Egyptian obelisks which are
now embellishing various cities were originally erected for the same
purpose.

DETERMINATION OF LONGITUDE.—As we have imagined an observer travelling
in a north or south direction in connection with the measurement of
latitude, let us consider what will happen to an observer who travels
only in longitude—that is, east or west. At the starting-point, he will
see the Pole at a certain altitude, and the stars will perform their
diurnal revolutions at a certain inclination to the horizon depending
upon his latitude. If he travels towards the east, the Pole will remain
at the same angle above the horizon, and he will detect no difference in
the apparent movements of the stars. What then is there to indicate that
he has changed his place at all? The answer is simple; he will find that
the sun and stars cross the meridian earlier, and if he be 15° east of
his first station they will transit an hour sooner, because it takes the
earth an hour to turn through that angle. If he travel westward in the
same way, the earth must turn through a greater angle to bring him back
to the same star, so that the stars will appear to cross the meridian
later.

The determination of longitude is accordingly based upon a measurement
of the difference in the times of transit of sun or stars at the place
of observation, and the place from which longitude is reckoned.

Let us take Greenwich as the start-point for our longitudes, and suppose
we are in Dublin. The sun, or a star, will cross the meridian of Dublin
at a certain interval after it has passed that of Greenwich, and if we
measure this interval, the angle turned through by the earth in that
time will determine the longitude. With a transit instrument one can
readily tell the exact moment when the star crosses the meridian of
Dublin, but how is one to know the exact moment at which the star
crossed the meridian of Greenwich without going there?

Looking at the question in another way, let us remember that the clocks
in Dublin register local time, that is time reckoned from the passage of
the sun over the meridian of Dublin, while the Greenwich clock indicates
times based on the transit of the sun over the Greenwich meridian.
Evidently the difference of these times is the difference of longitude,
and our question becomes, how to find the time at Greenwich when
stationed at the observatory in Dublin.

In all modern work, the telegraph is employed whenever it is available,
the two stations being directly connected. An observer at Greenwich is
thus enabled to transmit a signal to the observer in Dublin at the exact
moment a star passes through the centre of his transit instrument, and
the latter observer then notes the interval which elapses before the
same star passes the central line of his own instrument. If the signals
were transmitted instantaneously, the interval elapsed from the
reception of the signal to the observed transit of the same star would
give the longitude as reckoned in time.

Practically, what is done is for each observer to determine his local
sidereal time very accurately, with the aid of his transit instrument,
and in this way to find the error of his clock. It is then only
necessary to compare the two clocks, and this is done in the following
way: the clock at Greenwich has an attachment by which an electrical
contact is made every second, and this is switched in to the telegraphic
circuit, so that the Dublin observer receives a signal every second so
long as the clock is connected. These signals are automatically recorded
by a chronograph, together with similar signals from the Dublin clock,
and the times to which each of them corresponds is easily identified.
Immediately afterwards the Dublin clock is switched into the circuit,
and records its beats on the chronograph sheet at Greenwich, alongside
those sent by the Greenwich clock. In this way the differences between
the clocks can be very accurately measured, and the longitude can then
be reckoned in degrees and minutes by allowing 15° for each hour. Before
the invention of the telegraph, less accurate methods were of necessity
employed. Among others the entrance of the moon into the earth’s shadow
during an eclipse was noted by an observer desiring to know his
longitude. As we have already seen, this occurrence is independent of
the observer’s position on the earth, so that if he records the local
time of the observation and compares with the calculated Greenwich time
of the commencement of the eclipse, he can find his longitude.
Similarly, the eclipses of the satellites of Jupiter may be utilised to
signal Greenwich time to an observer situated elsewhere. Unfortunately,
the shadows are too ill-defined at the edges to permit very accurate
determinations in this way.

METHODS EMPLOYED AT SEA.—One of the most important applications of
astronomy to the needs of everyday life is in enabling the navigator on
the open ocean to determine the situation of his ship. Without the help
supplied by astronomical predictions the sea would be truly trackless,
and commerce by sea would be almost impossible.

A sextant and two or three good chronometers, together with a copy of
the current “Nautical Almanac,” furnish the means of ascertaining the
geographical position of a ship. With the aid of the sextant, the sun’s
greatest angular distance above the sea horizon—that is, its meridian
altitude—is measured, and from the known declination of the sun at the
time, the latitude is deduced in exactly the same way as in the case of
an observation of a star (p. 124).

The sextant also enables the observer, by measuring the sun’s altitude
in the early morning or evening, to determine the local time, as already
explained (p. 83). Greenwich time is kept by the chronometers, and the
difference between this and the local time is a measure of the
longitude. More than one chronometer is carried by a ship, for fear that
a single one might fail, through accident or other causes, to give
correct readings. The rate of each has been previously very accurately
gauged, and by taking the average indications, Greenwich time is known
with considerable accuracy.

Should the chronometers fail, or any doubt be thrown upon their
accuracy, there is another method by which the Greenwich time, and
thence the longitude, can be ascertained. This is the _lunar method_, in
which the heavens become the equivalent of the dial of a clock, while
the moon, with its rapid easterly movement, plays the part of the hands.

In the words of Dr. Lardner, this is “a chronometer of unerring
precision; a chronometer which can never go down, nor fall into
disrepair; a chronometer which is exempt from the accidents of the deep;
which is undisturbed by the agitation of the vessel; which will at all
times be present and available to him wherever he may wander over the
trackless and unexplored regions of the ocean.”

From the known movements of the moon, its position with regard to the
sun, planets, or conspicuous stars, at definite Greenwich times, can be
calculated in advance, and “lunar distances” are accordingly tabulated
in our nautical almanacs. We find, for instance, that the apparent
distances of the moon from the star Regulus, as they would appear from
the earth’s centre, were as follows on Jan. 1, 1896:—

6 P.M. G.M.T. 35° 50′ 22″
9 P.M. „ 34° 3′ 23″
12 P.M. „ 32° 16′ 12″

To utilise these predictions for the purpose in hand, the observer would
measure with the sextant the apparent distance of the moon from Regulus
at a known local time, and he would then compute what the apparent
distance would have been if his observation had been made from the
earth’s centre. From the tabulated distances, he would then be able to
find the Greenwich time at which his observation was made; and, as we
have seen, the difference between this and local time is a measure of
the longitude.

CHAPTER X.
THE EXACT SIZE AND SHAPE OF THE EARTH.

GEODESY.—We have already seen that the earth is a sphere, or of some
form which differs but little from a sphere, and a rough method of
determining its size, on this supposition, has been indicated. Now we
have to inquire more minutely into the size and shape of our planet,
for, as we shall see presently, a knowledge of these facts is essential
to the adequate explanation of the various movements of the heavenly
bodies, besides forming the basis of all our knowledge of the distances
which separate us from the other bodies which people space. As an
illustration of the importance of an exact knowledge of the size of the
earth, it may be remarked that Newton’s grand law of gravitation was
kept from the world for ten years, owing to an error in the generally
accepted value of the earth’s radius, which was afterwards rectified by
the labours of a French astronomer, Picard.

A great amount of labour has been expended in the endeavour to arrive at
the true size and shape of the earth, and the name _geodesy_ is given to
the science which deals with these operations. As a secondary object,
geodesy is concerned with the measurement and description of tracts of
country.

AN ARC OF MERIDIAN.—The measurement of the size of the earth is
accomplished by first measuring relatively small parts of its surface,
and then applying geometrical principles, in order to determine the
whole circumference. If the earth were a true sphere, and we could
measure the exact distance in miles between two places on the same
meridian, a subsequent determination of the difference of latitudes of
the two places would enable us to find the length of a degree, measured
on the earth’s circumference. As there are 360° in a circle, the
circumference would be 360 times the length of a degree, and the
diameter of the earth would be the length of the circumference divided
by 3·14159, this number expressing the constant ratio which exists
between the circumference and diameter of a circle of any size
whatsoever.

The determination of the size and shape of the earth thus involves two
distinct sets of operations; first, measures of distances; and second,
astronomical observations to determine the angular measurements of the
arcs on the earth’s surface comprised between stations separated by
known distances. When two such stations lie on the same meridian, the
arc measured in this way is called an _arc of meridian_. We have already
seen what means are available for finding the latitudes and longitudes
of places on the earth, and it now remains for us to apply a yard
measure, or its equivalent, to the precise measurement of the distance
between places which are many miles apart.

THE BASE LINE.—In the first instance a line of unimpeachable
straightness is measured with scrupulous accuracy. The measuring-rod
which has been most successfully employed is one consisting of a
combination of brass and steel bars, which automatically corrects itself
for changes of temperature in very much the same way that the
balance-wheel of a chronometer, or of a good watch, corrects itself so
as to perform its swing in equal periods at all temperatures. Several of
these compensated rods are used, and they are enclosed in wooden boxes
which are provided with levels and sights. When in use the outer boxes
rest on adjustable trestles, and instead of putting the rods end to end
they are placed a certain definite distance apart by the use of
microscopes, which are themselves mounted on compensating bars. The
first rod is put in position and levelled, and the others are
successively placed in line with it by means of the sights. As the
ground ceases to be perfectly flat it becomes necessary to raise the
level of succeeding bars, but they are kept in the same vertical plane.
Six bars are frequently employed in laying out a base line, and in order
to protect them from extremes of temperature they are usually kept
covered with long tents. In this way a distance of several miles can be
measured with no greater probable error than a couple of inches, and the
ends of such a measured base line are marked on metal plugs built in
columns of masonry. The chief base lines measured in connection with
British map construction were on the sandy shores of Lough Foyle in
Ireland, 41,614 feet in length, and on Salisbury Plain, 36,578 feet
long.

TRIANGULATION.—When a base line has been accurately measured in this
way, a distant object which is clearly visible from both ends is
observed with the aid of an instrument called the _theodolite_, and the
angles between the base line and the lines joining its ends with the
object are very carefully determined. Thus if A B in Fig. 36 represent
the base line, and C a conspicuous object several miles away, the angles
C A B and C B A are measured, and then it becomes easy to determine the
distances A C and B C by trigonometrical calculations. A check on the
accuracy of the observations is obtained by transferring the theodolite
to C and measuring the angle A C B. The sides of the triangle may then
be employed as new base lines for the measurement of other distances.
With the theodolite at C, another object, D, is sighted, and the angle D
C A is measured; similarly, with the theodolite at A, the angle C A D is
determined, and from these observations the distances of D from the
points A and C are easily computed. These distances again become
available for base lines, and so the triangulation can be extended
indefinitely.

[Illustration:

FIG. 36.—_Triangulation._
]

In a mountainous country, the sides of the triangles are often as much
as 100 miles in length. Signals on the Wicklow Mountains in Ireland have
been observed from Ben Lomond in Scotland and from Scafell in
Cumberland. The stations are chosen so that none of the angles to be
measured are very small, and in this way the chances of error are
greatly reduced. Hence the triangles in the immediate neighbourhood of
the base line are comparatively small, but the sides are gradually
extended as the survey proceeds.

The process of triangulation forms the basis of the construction of
accurate _maps_, and for this purpose the great triangles are subdivided
by a secondary triangulation, so that the exact situations of a very
great number of places are determined. These, again, serve for another
set of still smaller triangles, with sides perhaps a mile in length; and
finally the details are filled in by local chain surveys and
draughtsmanship.

There is another point of some importance in connection with these
triangulations when on a large scale. The larger triangles must be
corrected for the curvature of the earth’s surface. The construction of
the theodolite is such that two adjacent sides of any triangle, measured
from their intersection, are referred to the same horizon; but when the
instrument is transferred to another corner of the triangle, the
adjacent sides are referred to a new horizon. The sum of the three
angles of a triangle in these geodetical surveys thus exceed two right
angles, whereas in plane triangles they are always equal to two right
angles; the difference is called the _spherical excess_, and in the
computations the observed angles have to be corrected on this account.

Thus, after an extremely laborious survey, it becomes possible to
determine with great accuracy the distance between any two places
whatever, and so the number of miles between two places at the
extremities of an arc of meridian is ascertained. An arc of meridian
extending nearly 18° has been measured in India, and another over 25°
long extends from Hammerfest in Norway to the mouth of the Danube.

EXACT SHAPE AND SIZE OF THE EARTH.—From the facts which have been
gleaned by the measurements of arcs of meridian in different parts of
the world, it is found that the length of a degree of latitude as
measured on the earth’s circumference increases towards the Poles. In
latitude 66° N. a degree is about 3,000 feet longer than a degree near
the Equator. This means that the curvature of a meridional arc is
greatest at the Equator, whence it is concluded that the earth is
flattened at the Poles. The figure which best accords with the
observations is the ellipse, and thus it becomes possible to calculate
the polar diameter, although no arcs have been measured in the immediate
neighbourhood of the Poles.

Arcs of longitude, extending between two places which have the same
latitude, have also been measured and applied to the determination of
the figure of the earth, and, indeed, any arcs between two places of
known latitude and longitude can be utilised.

When all the facts are brought together it is found that the earth’s
polar diameter is about 26 miles shorter than the average equatorial
diameter, while an equatorial section of the earth is also elliptical,
the diameter passing through longitude 14° E, being two miles longer
than the one at right angles to it. According to the calculations of
Colonel Clarke, R.E., we have the following principal dimensions:

Earth’s mean equatorial semi-diameter = 3,963·296 miles.
„ „ polar „ = 3,950·738 „
Polar compression ¹⁄₂₉₃.₄₆

A solid which has a shape like that of the earth, with three axes of
unequal lengths, is called an _ellipsoid_.

A very important consequence of the ellipsoidal form of the earth is
that lines which are vertical—that is, perpendicular to the surface of
water—do not pass through the centre of the earth, unless they are at
the Poles or at certain points on the Equator.

There is every reason to suppose that at one time the earth was in a
molten condition, and in response to physical laws, such a mass of
matter could not retain a spherical form when set in rotation, although
the sphere would be its natural shape if at rest. This has been
demonstrated by a variety of experiments.

Thus, taking it generally, the shape of the earth is very intimately
associated with its rotation, and it will subsequently appear that the
same holds good for the sun and planets. Those bodies which have the
most rapid rotation show the greatest flattening in the direction of the
polar diameter.

In addition to direct measurements of the earth, there are other ways of
studying the shape of our planet. One of these depends upon observations
of the swing of a pendulum at different parts of the earth’s surface; as
the time of oscillation of a pendulum depends upon the force of gravity,
which itself varies with the distance from the earth’s centre, it is
evident that this method is a practicable one. It is true that the
matter is complicated in various ways, but after everything has been
taken into account, these pendulum observations indicate, not only that
the earth is flattened at the Poles, but they show further that the
amount of polar compression deduced from geodetical work is in all
probably very near the truth.

Again, the movement of the moon around the earth is found to be subject
to certain irregularities which would not exist if the earth were a
perfect sphere. These inequalities being deduced from observations of
the moon’s position, the amount of polar flattening necessary to produce
them can be calculated, and this is found to agree very closely with the
value derived from the measurements of arcs of meridian.

DIFFERENT KINDS OF LATITUDE.—If the earth were a smooth spherical body,
the latitude of a place would be simply equal to the angle made by a
line joining it to the earth’s centre with the plane of the Equator.
Owing to the bulging out of the earth in its equatorial part, however,
it becomes necessary to distinguish between different kinds of latitude.
If we adopt the definition given above, the name of _geocentric
latitude_ is given to the angular measurement. Taking the earth as a
smooth geometrical spheroid, and assuming it to have certain dimensions,
the angle which a line perpendicular to the surface makes with the plane
of the Equator determines the _geographical latitude_. As the line
perpendicular to the surface does not pass quite through the centre of
the earth, the geographical and geocentric latitude differ by as much as
11′ in mid-latitudes, although nearly agreeing at the Poles and on the
Equator.

As there are no direct means of finding the direction of a line passing
through the earth’s centre, or of one perpendicular to the imaginary
standard spheroid, geocentric and geographical latitudes must be
calculated from the _astronomical latitude_, which is determined by
observations of the elevation of the Pole, or its equivalent. The
astronomical latitude is the angle between the direction of gravity and
the Equator, and is therefore to a small extent dependent upon local
irregularities of the earth’s surface.

A knowledge of geocentric latitude is chiefly of use in making
corrections for parallax, in order that the data calculated for the
earth’s centre may be precisely corrected for the place of observation,
or _vice versâ_, as in the case of a lunar distance measured for the
determination of longitude, or in the calculation of a solar eclipse.

VARIATION OF LATITUDE.—For some years past a widespread interest has
been taken in the question of a possible change in the position of the
earth’s axis with regard to its surface. The subject is by no means a
new one, for as far back as two thousand years ago, such variations were
suspected. Changes amounting to several degrees were then believed to
have occurred, but it is now certain that the supposed variation was due
solely to the imperfection of the observations. As astronomical science
became more and more precise, even before the discovery of aberration,
it became evident that if any changes of latitude were taking place at
all, they must be very minute.

In its geological aspect, the possibility of great changes of latitude
having occurred in the past history of our globe is evidently well worth
serious investigation. Granted a sufficient change in the position of
the earth’s axis, the climate of London might become Arctic, or that of
Greenland tropical. From this point of view the subject has been
mathematically investigated by Professor G. H. Darwin, and it appears
that if only the varying distribution of land and sea indicated by the
geological records be taken into account, past changes of more than
about three degrees are very improbable. Admitting that at any time
during the life-history of our globe the earth was sufficiently plastic
to be deformed by earthquakes or other disturbances, it is possible that
changes amounting to 10° or 15° may have occurred.

Opinion is perhaps best reserved as to what has happened in the past. We
are on surer ground when we consider the variations of latitude which
are now going on.

Many competent observers have investigated the present movements of the
Pole, and it has been conclusively demonstrated that changes in the
position of the earth’s axis do really occur. Dr. Küstner, of Berlin,
commenced a series of observations for a different purpose in 1884, and
found that some anomalous results could only be explained by supposing
that the latitude of Berlin was from 0″·2 to 0″·3 greater from August to
November, 1884, than from March to May in 1884 and 1885. Great interest
was excited by this striking result, and steps were at once taken to
test its truth. Old observations were re-discussed and compared, and new
observations were made, with the final result that the movement of the
earth’s axis of rotation was placed beyond dispute. It was not until Dr.
Chandler attacked the problem, however, in 1891, that the nature of the
changes became clear. His masterly analysis indicated that the observed
variations in latitude arise from two periodic fluctuations superposed
upon each other; one of these has a period of 427 days, and a
semi-amplitude of 0″·12, while the other is an annual change which has
ranged between 0″·04 and 0″·20 during the last fifty years. The
resultant of the two movements produces changes which are seemingly very
irregular in amount and of varying period, but a cycle is completed
about every seven years. When the two sources of difference are at their
maximum at the same time, the total range reaches about two-thirds of a
second of arc. In consequence of the inequality of the annual part of
the change, the apparent average period between 1840 and 1855
approximated to 380 or 390 days; widely fluctuated from 1855 to 1865;
from 1865 to about 1885 was very nearly 427 days, afterwards increased
to near 440 days, and very recently fell to somewhat below 400 days.

[Illustration:

FIG. 37.—_Movements of the Earth’s Pole, 1890–95._
]

At the present time the variation of latitude is being very carefully
investigated by the International Geodetic Association, and the latest
results obtained are illustrated diagrammatically in Fig. 37. The mean
position of the Pole is at the centre of the diagram,[3] and the
horizontal line to the right of this point is directed towards
Greenwich. The remarkable spiral curve shows the wanderings of the Pole
about its mean position during five recent years. To simplify matters,
the amount of deviation is represented in feet instead of in angular
measure, and it will be seen that although the variation of latitude may
be of considerable interest and importance in astronomical matters, it
really does not amount to very much in matters terrestrial, the greatest
change in the position of the Pole not amounting to more than 20 yards.
Nevertheless, it is not inconceivable that it may yet have to be
reckoned with in questions relating to boundary lines which depend upon
latitude determinations.

CHAPTER XI.
THE DISTANCES AND DIMENSIONS OF THE HEAVENLY BODIES.

PARALLAX.—The problem of determining the distance of a heavenly body
resolves itself into a measurement of its _parallax_, that is, of the
apparent change of its position brought about by a change in the
situation of an observer. If one be seated in a room, about a yard from
a window, a very simple experiment may be made to illustrate the meaning
of this term. Closing one eye, the observer will see a vertical line,
such as the partition between two panes, projected upon some particular
part of an opposite building; when the other eye is used the line will
apparently be displaced, and the nearer one is to the window the greater
will be the displacement or parallax. As the heavenly bodies are so far
away, each of our eyes sees them in the same directions. Indeed, the
stars are so distant that to _all_ persons situated on our planet their
apparent positions are identical. With the members of the solar system,
however, the case is different; the earth has an appreciable size as
seen from them, so that when viewed from different parts of the earth
they will not appear in exactly the same part of the heavens.

The earth’s rotation changes the relation of an observer’s position with
regard to a heavenly body in pretty much the same way as a change in his
actual position on the globe. When an object in the zenith is observed,
it will appear in precisely the same part of the sky as if it were seen
from the centre of the earth, but as it approaches the horizon it will
be displaced. Hence the term _diurnal parallax_, meaning the
displacement of a heavenly body depending upon the observer’s position
as affected by the earth’s rotation. Taking it in its general
astronomical sense, the parallax of a heavenly body is the angle between
the two lines which join it to the observer and to the centre of the
earth respectively. Thus, in Fig. 38, let O be an observer, Z his
zenith, and C the centre of the earth; then the parallax of a body S is
the angle O S C. As the observer’s position is changed to O′ by the
earth’s rotation, the parallactic angle is increased to O′ S C. If S be
on the horizon, that is, when O′ C is perpendicular to O′ S, the
parallax is a maximum, and is then called the horizontal parallax. The
_horizontal parallax_ of a body is therefore the greatest angle
subtended by the earth’s radius as seen from the body. We have seen,
however, that the earth’s radius is not of the same length in all parts,
and it is therefore necessary to specify more particularly which radius
is in question. The standard adopted is the equatorial radius, and, when
this is employed, our greatest parallactic angle is called the
_equatorial horizontal parallax_.

[Illustration:

FIG. 38.—_Parallax of a Heavenly Body._
]

In the case of all the heavenly bodies the parallaxes are very small;
that of the moon averages about 57′, while that of the nearest planet
does not exceed 40″. The parallax of a body evidently diminishes as the
distance increases.

DISTANCE DEDUCED FROM PARALLAX.—When the parallax of a heavenly body has
been determined, it becomes a simple matter to calculate the
corresponding distance; thus, in Fig. 38, the distance C O′ represents
the earth’s equatorial radius, O′ S C is the equatorial horizontal
parallax, C O′ S is a right angle, and the required distance is C S. By
a simple trigonometrical rule this distance is the earth’s radius
divided by the sine of the parallax. In the case of a small angle, the
sine is very nearly equal to the angle itself divided by the angle
corresponding to an arc of a circle equal in length to the radius. As
there are 206,265 seconds in an arc equal to the radius, the sine of a
small angle may be taken as the angle itself, expressed in seconds,
divided by this number. Thus, if _p_ be the equatorial horizontal
parallax of an object reckoned in seconds of arc,

Distance = (earth’s equatorial radius)/(sine _p_)
= (206,265 × earth’s equatorial radius)/(_p_)

We shall see presently that the average parallax of the sun is 8″·80,
and its average distance, as derived from the application of this
formula, is accordingly about 92,790,000 miles.

DIAMETERS.—It is a familiar fact that the further an object is removed
from us the smaller it appears. The ascent of a balloon at once suggests
itself as an excellent example. It is necessary, therefore, to
distinguish very carefully between the apparent and the true size of an
object. A halfpenny at a distance of nine feet from the eye will just
cover the moon if the line of sight be directed towards that body, but
we should not say the moon is the size of a halfpenny, because we know
perfectly well that a disc twice the size would produce just the same
appearance if removed to double the distance. Apparent size must,
accordingly, be reckoned in angular measure, and we say, for example,
that the moon has an apparent diameter of a little more than half a
degree.

When the angular diameter and distance have both been measured, the real
diameter, in miles, can at once be deduced by a simple inversion of the
process of determining the distance of an object from its known
parallax. Thus, in Fig. 39 let A B represent the moon or other heavenly
body, and E the centre of the earth. The angle M E A is the angular
semi-diameter, and E M the required distance; then, since the angle E A
M is a right angle,

A M = M E × sine M E A

That is,

Semi-diameter in miles = distance in miles × sine of angular
semi-diameter.

Or,

Diameter = twice the distance × sine of angular semi-diameter.

[Illustration:

FIG 39.—_Diameter of a Heavenly Body._
]

Since the apparent diameters are always small, the sine may be taken as
equal to the circular measure; that is, the number of seconds which the
angle contains divided by 206,265.

DISTANCE AND SIZE OF THE MOON.—If the moon were a fixed body outside the
earth, its parallax could be easily determined by a single observer,
who, in that case, would note the apparent displacement produced by his
rotation. It has, however, a very complex movement, and it is therefore
difficult to separate the real change of position from the parallactic
change. The best method is one in which two observers, far removed from
each other, can observe the moon’s position at nearly the same instant,
so that the effect of its movement is very small and can be sufficiently
allowed for. A necessary consequence of this condition is that the two
observers should be placed as nearly as possible on the same meridian.
Observations with the object of determining the lunar parallax have
accordingly been made at Greenwich and the Cape of Good Hope. From the
known positions of these places and the size of the earth, the distance
between them is very accurately known, and this serves as a base line in
a triangulation of the moon.

[Illustration:

FIG. 40.—_Measurement of the Moon’s Distance._
]

If G and C, in Fig. 40, represent Greenwich and the Cape respectively,
the celestial equators at the two places will be in the directions G E
and C E. M being the moon, its declination, as measured at G, will be
the angle M G E, and as measured at C it will be the angle M C E′. Since
G E is parallel to C E′, the difference of these declinations (when both
are north declinations, as in the diagram) will be the value of the
parallactic angle G M C, which is about 1½°. From these data it is easy
to calculate the distance of the moon either from Greenwich, the Cape,
or the earth’s centre. In this way the distance of the moon is found at
some particular moment, and the additional knowledge of the shape of its
orbit enables us to determine the semi-major axis of the orbit, which is
nothing more than the average or mean distance of the moon. The mean
equatorial horizontal parallax of the moon is 3,422″·5, and the
corresponding mean distance from the earth is 238,855 miles.

The average apparent diameter of the moon, as it would appear from the
centre of the earth, is 31′ 7″, from which it results by the method
already stated that the true diameter is 2,162 miles.

The apparent diameter of the moon is affected by the observer’s position
upon the earth, as well as by the situation of the moon in its orbit. An
observer to whom the moon is directly overhead is nearly 4,000 miles
nearer to it than another observer who has it on his horizon. Tables
have accordingly been drawn up to indicate the _augmentation_ of the
moon’s apparent diameter as it rises above the horizon. The greatest
possible apparent diameter is about 36″.

Everyone must have noticed that when the moon is rising or setting, it
looks much larger than when it is high up in the sky, an appearance
which does not seem to accord with the fact that its measured angular
diameter is least when on the horizon. It is evident, however, that the
seeming increase of size is a subjective phenomenon, due to our
incapacity to correctly judge distances.

RELATIVE DISTANCES OF PLANETS.—The relative distances of the planets
from the sun were found long before any of the actual distances were
known with any reasonable degree of accuracy. Kepler discovered the
relation which exists between these distances, and expressed it in his
third or harmonic law, which states that “the squares of the periodic
times of the planets are proportional to the cubes of their mean
distances from the sun.”

In the case of the interior planets, the angles of greatest elongation
furnish the means of finding their distances from the sun as compared
with that of the earth. Thus, if V in Fig. 41 represents Venus, E the
earth, and S the sun, the angle E V S is a right angle when Venus is at
greatest elongation. The observed value of the angle S E V is 46°, and
this definitely determines the shape, though not the size, of the
triangle S E V. The distance of Venus from the sun, S V, is thus found
to be 0·72 times the distance of the earth from the sun, S E. If Venus
be at inferior conjunction, that is, at V′, its distance from the sun
will be represented by 72, if the earth’s distance from the sun be
denoted by 100.

This method can also be applied in the case of Mercury, but as the orbit
is so eccentric, it is necessary to take the average of a large number
of greatest elongation angles.

The process of determining the relative distance of an exterior planet,
such as Jupiter, is a little more complex, but involves no considerable
difficulties.

[Illustration:

FIG. 41.—_Relative Distance of Venus._
]

There is a curious relationship between the relative distances of the
planets, which is commonly known as _Bode’s law_. A series of figures,
0, 3, 6, 12, 24, 48, 96, 192, 384, each, with the exception of the
second, being double the preceding one, is written down, and the number
4 added to each. Then the resulting numbers approximately represent the
relative distances of the planets from the sun. Thus:—

4 7 10 16 28 52 100 196 388
Mercury Venus Earth Mars Asteroids Jupiter Saturn Uranus Neptune

It is interesting to note that this law was announced in 1772, when the
asteroids and the planets Uranus and Neptune were still unknown, so that
there was a break in the series corresponding to the number 28. The
discovery of Uranus in 1781, and the fact that its distance agreed
roughly with Bode’s law, strengthened the conviction that an unknown
planet revolved round the sun in an orbit between those of Mars and
Jupiter. An association of astronomers was then formed to search
systematically for the missing planet; but the actual discovery was made
in 1801 by Piazzi, the Sicilian astronomer, who had not joined the
association. The new planet was a very small one, and its discovery was
rapidly followed by the detection of several others. At the present
time, more than 400 of these asteroids, or minor planets, are known, and
their average distance fits in very well with Bode’s law.

THE SUN’S DISTANCE.—One of the grandest problems which astronomical
science requires us to solve is the determination of the sun’s distance.
Starting with a knowledge of the earth’s dimensions, the subsequent
measurement of the sun’s distance enables us to get a clear idea of the
scale, not only of the solar family to which we ourselves belong, but of
the whole sidereal universe. No wonder then that a vast amount of
astronomical energy has been expended on this investigation.

The problem, however, is beset with many practical difficulties, and the
greatest possible skill is required to cope with it. In the first place,
the parallax of the sun is so small that the method employed for the
moon fails, and it can only be determined by indirect means.

We have already seen that the constant of aberration gives us a means of
determining the size of the earth’s orbit, and consequently the distance
of the sun. When proper allowance is made for the eccentricity of the
orbit, this method is a very valuable one.

Other methods which have been employed depend upon the measurement of
the parallax of one of the nearer planets, from which the distances of
all the planets, including the earth, from the sun, can be found from
our previous knowledge of the relative distances. Mars and some of the
asteroids have been thus utilised at their oppositions, and Venus when
at inferior conjunction.

[Illustration:

FIG. 42.—_The Parallax of Mars._
]

The parallax of Mars can be determined in the same way as that of the
moon, either by concerted observations at two distant places, or by a
single observer who utilises the earth’s rotation to provide him with a
base line. The actual measurements do not consist of direct estimations
of the right ascension and declination of the planet, but of its angular
distances from stars among which it appears, the measurements being made
with micrometers or heliometers. In this way certain errors due to
refraction, etc., are minimised. To take an extreme case, let the planet
M (Fig. 42) be rising to an observer at O; it will then be seen in the
direction O M, while a neighbouring star will be seen along the line O
S. After twelve hours the rotation of the earth will have carried our
observer to O′, and he will now see the planet in the direction O′ M,
while the star will remain in the same direction, O′ S′. In each case he
would measure the angle separating the planet from the star, and would
thus obtain the values of the angles S O M and S′ O′ M, which, in the
case shown in the diagram, would be together equal to the angle O M O′.
When corrected for the observer’s latitude, and for the planet’s change
of place in the interval, the equatorial horizontal parallax of Mars
would be determined. Then the distance of Mars from the earth would be
known, and at opposition this is the difference between the distances of
the earth and of Mars from the sun; the ratio between the latter is
already known, and their actual distances at once follow.

[Illustration:

FIG. 43.—_The Transit of Venus._
]

TRANSIT OF VENUS.—The planet Venus at inferior conjunction is near
enough to the earth to have a considerable parallax, but the method
employed in the case of Mars cannot be used, as the planet is not
visible when between us and the sun, except on the very rare occasions
when it transits across the sun’s disc. When a transit occurs, the
distance of the planet from the earth can be measured in essentially the
same way as that of Mars at opposition, when two observers work
together. The difference is that the apparent place of the planet is
referred to the sun’s disc instead of to neighbouring stars. Suppose the
conditions to be as represented in Fig. 43, E being the earth, V the
planet, and S the sun. Two observers on the earth, at _a_ and _b_, will
see the planet projected on different parts of the sun’s disc. If we at
first regard them as being at rest, the observer at _b_ would see the
planet cross the sun along the line C D, while to the one at _a_ it
would appear to cross the line F G. The times of crossing would, under
the assumed conditions, depend upon the orbital velocity of Venus, and a
measure of these times at the two stations would determine the relative
lengths of the chords C D and F G. We already know that the distance of
Venus from the sun is to its distance from the earth at inferior
conjunction in the proportion 72 to 28. (See p. 145.) The rectilinear
distance between the two places is also known, and the distance _x y_
between the chords is ⁷²⁄₂₈ of that from _a_ to _b_, whatever the actual
distance of the sun may be. We thus know the ratio of the lengths of two
parallel chords, and the distance between them in miles, from which it
is a simple matter to find the diameter of the sun’s disc in miles. The
angular diameter of the sun is measured with a transit instrument, and
to find the sun’s distance we have simply to calculate the distance at
which a body of known size subtends a known angle.

We have supposed the observers at rest, but they are in reality carried
forward by the earth’s orbital motion, and are turned about the earth’s
axis. The first of these movements will affect both observers in the
same degree, and will simply lengthen the duration of the transit. The
effect of rotation, however, depends upon the position of the sun and
planet, with regard to the observer’s meridian. At sunrise, an observer
is carried by the rotation of the earth almost directly towards the sun,
while at sunset he is carried away from it. The rate at which the planet
traverses the sun’s disc would, therefore, be little affected by the
earth’s rotation at sunrise or sunset. About mid-day, however, the
effect of the earth’s rotation is to accelerate the apparent motion of
the planet, and to shorten the time of transit. If the beginning of the
transit be observed at sunset, and the end soon after sunrise, as it may
well be in high latitudes, the duration of the transit is retarded by
the earth’s rotation. Corrections for rotation, however, are not
difficult to apply.

In this method of observing a transit of Venus, which was suggested by
Halley, when it was impossible that he would live to see it carried out,
the places of observation must be widely separated in latitude, and the
beginning and end of the transit must both be observed.

Another method of utilising a transit of Venus is known as Delisle’s
method. In this case the two stations are near the Equator, and each
observer notes the Greenwich time of internal contact, when the planet
fully enters upon the sun’s disc.

Owing to various causes, chief among which is the so-called “black
drop,” the time of ingress and egress cannot be actually recorded with
the desired degree of accuracy, and the transit Venus is no longer
looked upon as the best method of determining the distance which
separates us from the sun.

Some of the results which have been obtained for the solar parallax are
as follows:—

Transit of Venus, 1874, contact observations, 8″·859
„ „ „ photographs, 8·859
„ „ 1882, contact observations, 8·824
„ „ „ photographs, 8·842
Gill’s observation of Mars, 1877, 8·780
Galle’s „ Flora, 1873, 8·873
Gill’s „ Juno, 1874, 8·765
„ „ minor planets, 1896, 8·80

From a discussion of all the available data, Professor Harkness
considers the most probable value of the solar parallax to be 8″·80905,
with a probable error of 0·00567″. Turning this into miles, we find the
distance of the sun to be 92,796,950 miles, and this is in all
probability not more than 60,000 miles in error. This agrees very
closely with Dr. Gill’s latest value, which has been accepted by the
superintendents of the British and American nautical almanacs.

THE SUN’S DIAMETER.—The real diameter of the sun is found from the
parallax, and its mean angular diameter in the manner already explained
(p. 142). Taking the distance as 92,780,000 miles, and the mean apparent
semi-diameter as 962″, we have

Sun’s diameter = (2 × 92,780,000 × 962)/(206,265)
= 865,400 miles.

The sun’s diameter is the same in all directions, so far as our
measurements give any information on the point, so that there is no
appreciable polar flattening corresponding to that of the earth and some
of the other planets. This result is what we should expect from the
relatively slow rate at which the sun turns upon its axis.

DISTANCES AND DIAMETERS OF PLANETS.—It has already been pointed out that
our knowledge of the relative distances of the planets from the sun
enables us to determine their absolute distances when the distance of
one of them has been ascertained. In this way the determination of the
earth’s distance leads us to those of the other planets.

Our additional knowledge of the planetary orbits further permits the
calculation of the distance of any planet from the earth at a stated
time. If, then, the angular diameter of a planet be measured with a
micrometer attached to a telescope, the absolute diameter in miles can
be determined in the same way as that of the sun or moon.

To take an actual example, the equatorial angular diameter of the globe
of Saturn, as measured by Prof. Barnard with the great telescope of the
Lick Observatory on April 14, 1895, was 19″·4. It was then computed that
if the observation had been made from the sun this would have been
reduced to 17″·9. The distance of Saturn from the sun being 9·5388 times
the earth’s distance, it results from this measurement that the true
equatorial diameter of the ball of Saturn is 76,500 miles. A number of
independent measures made at intervals from March to July gave an
average value of 76,470 miles for the diameter.

CHAPTER XII.
THE MASSES OF CELESTIAL BODIES.

MASS AND WEIGHT.—As a matter of daily experience, we know that a certain
effort is required to prevent a body from falling to the ground, and the
larger the bulk of any particular kind of matter, the greater is the
effort demanded. Again, equal bulks of different kinds of matter require
unequal efforts to sustain them in the hand. From facts such as these we
get the idea of _weight_, and we say that one body is heavier than
another when it has the greater tendency to fall to the ground. For the
purposes of everyday life, the weight of a body is used as a measure of
the quantity of matter which it contains, and the standard of weight in
our own country is that of a certain piece of platinum kept at the
Exchequer Office, in London, which is called a _pound_. The weight of
the same piece of matter varies at different parts of the earth’s
surface, and also at different distances from the ground, and it is
evident, therefore, that weight is not a very scientific measure of the
quantity of matter which a body contains. The standard of comparison
must be one which is invariable not only in all parts of the earth, but,
if we wish to investigate the quantity of matter in the celestial
bodies, it must be unalterable through all parts of the universe.

One’s first idea is that the bulk, or space which a body occupies, will
furnish a means of measuring the quantity of matter which it contains,
but here again we find that the volume of a body can be varied without
either adding to or subtracting from it, its weight remaining constant.
A piece of ice, for example, occupies a greater space than an equal
weight of water.

It is evident then that some other property of matter must be used as a
measure of quantities. Now, there is every reason to believe that the
same piece of matter, in whatever part of space it may be situated,
requires the same force to set it moving with the same speed in a given
time. By the continued application of a force, a body will first be set
in motion, and at the end of a second it will have a certain speed; in
the next second the velocity will have increased by an amount equal to
that acquired at the end of the first second, and so on for subsequent
intervals. For example, if at the end of a second the velocity were 3
feet per second, at the end of the next second it would be 6 feet per
second, and after other equal intervals it would be successively 9, 12,
15, and so on. In this way the velocity is increased uniformly, and is
said to be uniformly accelerated, while the gain per second is called
the _acceleration_. The greater the force applied, the greater will be
the acceleration it produces, and the acceleration can be used as a
measure of the force at work.

If the same force be applied to different quantities of the same
substance, the acceleration produced will be in inverse proportion to
the quantities. We thus arrive at the important result that two bodies,
whatever their nature, contain equal quantities of matter, or have equal
_masses_, when equal forces give them the same acceleration. The mass of
a body can thus be ascertained by observing the acceleration due to the
action of a known force.

As a matter of observation, it is found that all bodies, whatever their
composition or size, fall to the ground from the same height in the same
time if the observations be made at one place. This means that the
forces corresponding to weights produce equal accelerations in all
bodies at the same place, and it follows, therefore, that the weights of
bodies at the earth’s surface, are proportional to their masses. Hence,
it is that weight can be practically employed in comparing masses, or
quantities of matter, for the purposes of everyday life. It must be
clearly understood, however, that a _mass_ of a pound is in reality
quite distinct from a _weight_ of a pound, the former specifying a
certain quantity of matter, and the latter its tendency to fall towards
the earth.

THE LAW OF GRAVITATION.—The idea that weight is due to the attraction of
the earth for all bodies in its neighbourhood was first suggested by
Newton, and an extension of this idea led him to formulate the great law
which underlies the whole science of astronomy. All bodies near the
earth’s surface are acted upon by forces proportional to their masses,
and the same acceleration is produced in all of them if they are allowed
to fall to the ground. Falling freely for a second, all bodies
whatsoever, when the resistance of the air is eliminated, pass through a
little over 16 feet, and acquire a velocity of just over 32 feet per
second. The acceleration due to gravity is thus 32⅙ feet per second for
bodies near the earth’s surface. If the experiment be made at the top of
a high mountain, the distance fallen through and the acceleration
acquired in a second is found to be less.

If we could ascend still higher, the acceleration produced in falling
bodies would be again reduced, and, in the light of what has gone
before, it is evident that the force with which bodies tend to fall to
the earth is diminished as the distance from the earth’s surface is
increased. It was such considerations as these which led Sir Isaac
Newton to formulate the law that _the force with which a body is
attracted towards the earth diminishes in inverse proportion to the
square of the distance from the earth’s centre_. Terrestrial means of
testing the truth of this statement are obviously very limited, and
hence it was that Newton looked to the moon for its verification. If the
law holds good at the distance of the moon, an object so far removed and
not acted upon by other forces, should fall towards the earth, and as
its distance is about sixty times that of a body at the surface from the
centre of the earth, the acceleration produced should be only ¹⁄₃₆₀₀th
part of that imparted to bodies near the surface. In other words, since
a body near the surface falls through 16 feet in the first second, one
at the moon’s distance should only fall through about ¹⁄₂₀th of an inch.
If, then, the moon be subject to the earth’s attraction, this fall
towards the earth must be exhibited in some form or other, although the
fact that the moon does not fall down upon the earth shows that there is
some counteracting tendency.

Observations have shown us that the moon moves in a curved path. It has
been put in motion somehow, and since there is no reason why it should
turn to one side or the other, or come to rest, unless some forces are
acting upon it, it would tend to go on uniformly in a straight line for
ever. That its movement is curvilinear is at once an indication of the
action of a force besides that which originally set it in motion. This
force is directed towards the earth, and the moon is drawn out of its
rectilinear path just as far in any specified time as it would fall
towards the earth if at rest.

Let E and M in Fig. 44 represent the earth and moon respectively. Then,
if the moon were not hindered in any way, it would move in the direction
M _b_, and would reach the point _b_, let us say, at the end of a
second. It is, however, found to be at the point _a_, and it has
therefore fallen towards the earth through the distance _b a_. The size
of the moon’s orbit and the angle through which it moves in a second
being known, it is easy to calculate the distance _a b_, which is found
to be about ¹⁄₂₀th of an inch, as demanded by Newton’s law.

[Illustration:

FIG. 44.—_The Moon’s Curvilinear Path._
]

In his first attempt to thus verify the law of gravitation, Newton
failed for the want of a sufficiently accurate knowledge of the earth’s
diameter, but a few years later a new arc of meridian was measured, and
he had the untold satisfaction of demonstrating its truth.

The curved path of the moon is, indeed, similar to that of a projectile.
A cannon ball thrown out horizontally will reach the ground after
describing a curved path; but if it could be projected from a great
elevation, with sufficient velocity, its forward movement would prevent
its ever reaching the earth’s surface at all, and a new satellite of the
earth would have been manufactured.

The same kind of reasoning can be applied to the paths of the earth and
planets around the sun, and Newton demonstrated that the laws of Kepler
were a necessary consequence of the law of gravitation extended beyond
the system of the earth and moon. By mathematical reasoning it was
proved that if one body describes an elliptic orbit around another, and
the line joining them describes equal areas in equal times, the
attractive force must be directed to the central body, and, moreover,
must vary inversely as the square of the distance between the two
bodies. In this way the movements of the planets round the sun are
perfectly explained by supposing that an attractive force, similar to
that which causes bodies to fall to the earth’s surface, is exerted
between all masses of matter, and hence the origin of the term
_Universal Gravitation_. In its complete form, the law of gravitation
states that “any particle of matter attracts any other particle with a
force which varies directly as the product of the masses, and inversely
as the square of the distance between them.”

Confirmation of this grand law, which controls the movements of all the
vast array of heavenly bodies, is furnished by many other phenomena. We
see one of its effects in the tides, and another in the disturbances of
the movements of planets brought about by their mutual attractions. Even
in the depths of stellar space the same law holds good for those systems
of stars which are sufficiently close together for their attractions to
produce effects which we can study at our immense distance from them.

The cause of gravity is still one of the greatest mysteries of physical
science, although many ingenious attempts have been made to furnish an
explanation of its mode of action.

MASS OF THE SUN.—When we know the distance of the sun, and the time in
which the earth travels completely round it, it is easy to calculate the
fall of the earth towards the sun in the same way that the moon’s fall
towards the earth is determined.

The distance which a body 93,000,000 miles distant falls towards the sun
in a second is thus found to be 0·116 of an inch. A body at the earth’s
surface is about 4,000 miles from the centre, and it falls 16¹⁄₁₂ feet
in a second; if removed to a distance of 93,000,000 miles, its fall
towards the earth would be reduced inversely as the squares of 4,000 and
93,000,000, and would amount to ·000,000,349 of an inch. This is only
1/332,000th part the fall due to the sun’s attraction, and hence it is
concluded that the mass of the sun is 332,000 times that of the earth.

Strictly speaking, the accelerations produced by the sun and earth
should be compared, but the fall during the first second is proportional
to the acceleration due to gravity, and the same result is therefore
obtained. It may be observed also that the fall of the earth towards the
sun would not be appreciably effected if it were twice the size. All
bodies fall towards the earth at the same rate, whatever their weights,
and so in the case of a planet, the distance fallen towards the central
sun is independent of the planet’s mass; the greater the mass the
greater the attractive force.

The sun occupies about 1,300,000 times the space occupied by the earth,
and as its mass is only 332,000 times that of the earth, it follows that
the sun’s density is only about a quarter that of the earth.

MASSES OF PLANETS.—The process employed for the determination of the
sun’s mass can be utilised for finding the masses of those planets which
are accompanied by satellites. From the known distance of the planet,
the size of the orbit of a satellite can be calculated in miles, and
knowing the period of revolution of the satellite, its fall towards the
planet can be determined. This fall is then compared with that of the
planet’s fall towards the sun, and the mass of the planet in terms of
the sun’s mass is thus arrived at.

A convenient way of employing this method is to make use of a
modification of Kepler’s third law. If _m_ be the mass of a planet in
terms of the sun’s mass, M, _a_ and T respectively denote the semi-axis
major of the orbit of the planet and its time of revolution round the
sun; _a′_ and T similar quantities pertaining to the satellites’
revolution round the planet: The following formula gives the relation of
the masses:—

_m_/M = (_a′_/_a_)^3 (T/T′)^2

This formula can be applied in the case of Mars, Jupiter, Saturn,
Uranus, and Neptune, but fails in the case of Mercury, Venus, and the
asteroids, which, so far as we know, have no satellites.

The mass of Jupiter obtained in this way can be further checked by the
influence of this giant planet upon other bodies in its neighbourhood.
This planet has such an enormous mass that it produces very notable
effects on the motions of Saturn, the asteroids, and of comets which
travel in its neighbourhood, and, by measuring the amounts of these
_perturbations_, the mass of the planet can be deduced.

This method of perturbations is at present the only one by which we can
obtain a knowledge of the masses of those planets which have no
satellites. The motion of Mercury is disturbed by its nearest
neighbours, Venus and the earth; that of Venus by the earth and Mercury.
The differences between the observed positions of the planets and those
calculated on the supposition that the others did not affect them, give
the necessary data for the computation of the masses. The process,
however, is one requiring profound mathematical knowledge, and even yet
the mass of Mercury is not very certainly known.

The asteroids, again, present no little difficulty. Their feeble light
and small size point to small masses, and their mutual perturbations are
almost insensible, except when two of them come into line with the sun.
They produce no appreciable effects upon the movements of comets, so
that it is almost impossible to determine their individual masses. Each
asteroid, however, tends to produce a revolution of the major axis of
the orbit of the nearest planet, Mars, and all tend to give it a motion
in the same direction. If the total mass of all the asteroids put
together were a quarter of the earth’s mass, a measurable displacement
of the position of Mars would be produced. Professor Newcomb has
recently shown that such a displacement actually occurs, but cannot
amount to more than 5″·5 per century. From this it has been recently
calculated that the total mass of the asteroids is probably about
¹⁄₁₁₅th that of the earth’s mass.

MASS OF THE MOON.—As the moon has no satellite, we must again have
recourse to indirect methods if we wish to know anything as to its mass.
Various processes are open to us; but although the moon is so near to
us, it is more difficult to determine its mass than that of the most
remote planet in our system.

It has already been explained (p. 77) that as the earth is accompanied
by the moon, it is really the centre of gravity of the two bodies which
obeys the laws of planetary movement. As this point lies between the
centres of the two bodies, at distances which are in inverse proportion
to the masses, the centre of the earth describes a small monthly orbit,
which, as we have already seen, produces a small monthly inequality in
the sun’s apparent movement.

By a careful investigation of this monthly oscillation of the sun, it
has been found that the centre of gravity of the earth and moon must lie
within the earth at a distance of about 2,900 miles from the centre.
This is about ¹⁄₈₁th of the moon’s distance, whence it follows that the
mass of the moon is about ¹⁄₈₁th that of the earth.

Other methods of ascertaining the moon’s mass are also available. Among
these are the investigation of the parts played by the moon in the
production of the tides which swell our shores, and in the displacement
of the earth’s axis which causes “nutation.”

MASSES OF SATELLITES.—The earth’s satellite is of exceptional magnitude
in comparison with its primary, and the method of finding its mass from
the situation of the centre of gravity cannot be applied to the
satellites attending other planets. In the case of the satellites of
Jupiter and Saturn, the masses have been approximately determined by
their mutual perturbations, these generally resulting in a revolution of
the major axes of the orbits. Even this method fails for the satellites
of Mars, Uranus, and Neptune, so that practically nothing is known with
regard to their masses.

MASS AND DENSITY OF THE EARTH.—So far we have been concerned entirely
with relative masses, referring the masses of the various orders of the
heavenly bodies either to the earth or sun. Although this is usually all
that is required for astronomical purposes, it is of great interest to
determine the absolute mass of the earth, and from this the absolute
masses of the heavenly bodies can at once be deduced.

We already know the dimensions of the earth, and therefore the number of
cubic miles or feet which it occupies. We know also the weight or mass
of a cubic foot of water or lead, and if the earth were of uniform
specific gravity throughout its bulk, and composed of water or lead, we
could at once calculate its total mass. It is, however, neither water
nor lead; but if we can compare the mass of the earth with what it would
be if composed of either of these substances, we can deduce either its
mass or its specific gravity.

A very simple method of “weighing” the earth has been employed with much
success by Professor Poynting. The experiment was carried out at the
Mason Science College, Birmingham, with a large bullion balance in which
the beam was 123 centimetres long. Two spheres of lead and antimony,
each weighing about 21 kilograms, were suspended from the arms of the
balance. Another sphere of lead and antimony, weighing 153 kilograms,
was successively brought by means of a turn-table under each of the two
smaller weights. The alteration in the weights of the attracted balls
were measured by observing the deflection of the beam, this being
immensely magnified by a simple optical arrangement in which a mirror
reflecting a pencil of light was made to turn through 150 times the
angle moved through by the beam itself. The weight corresponding to a
given deflection of the beam was determined by observing the disturbance
produced by the addition of “riders” of known weights. In order to
reduce the chances of error, the large weight was balanced on the
turn-table by another mass of half the weight and at twice the distance
from the centre, this being necessary in order that the attracting
weight should rotate horizontally. The effect of this additional mass
was calculated and allowed for, and the weighings were also repeated
with the weights in various positions. The principle of the subsequent
calculation is briefly as follows:—A mass A of lead and antimony of
known bulk attracts another mass B with the force measured; if A were of
the same size as the earth, the attraction would be increased by as many
times as the earth is larger than A. If the average specific gravity of
the earth were the same as that of the mass A, this calculated
attraction would be equal to the weight of B. The ratio of this
calculated weight of B to the actual weight accordingly gives the
proportion between the specific gravity of the experimental ball and the
average specific gravity of the whole earth. From this experiment it was
estimated that the mean density of the earth is 5·4934 times that of
water.

The same principle is applied in the case of the famous Cavendish
experiment, and its subsequent modifications by Baily, Cornu, and Boys.

Another method of finding the earth’s density, and therefore its mass,
is chiefly of historical interest. This is known as the “mountain
method,” and was carried out in 1774 by Maskelyne, Hutton and Playfair
on the Schiehallion Mountain, in Perthshire. A plumb-line suspended at
the north side of the mountain is drawn towards the mountain, and so
will not hang quite vertically. If removed to the opposite side of the
mountain it will be deflected in the reverse direction. The amount of
this deflection can be measured by reference to the stars, the positions
of which are in no wise influenced by the attraction of the mountain. A
survey of the mountain was next made in order to determine its bulk, and
then the average specific gravity of the rocks composing it was
determined with the greatest possible accuracy.

The volume of the earth is 9,933 times that of the mountain, and its
attraction would be this number of times greater if it were composed of
the same materials as the mountain throughout. It was found to be in
reality 17,781 times as great as the attraction of the mountain, and as
this is 1·79 times 9,933, it follows that the average specific gravity
of the matter composing the earth would be 1·79 times that of the rocks
which build up Schiehallion. The mean specific gravity of the rocks
being 2·8, the mean density of the earth was thus found to be 5·012
times that of water.

As a general result of all the observations which have been made, the
value of the earth’s density may with much probability be considered to
be not far from 5·576, or a little over 5½ times that of water.

Whatever may be the composition of the earth’s interior, it is clear
that the density must increase as the centre is approached.

This knowledge of the earth’s density, in conjunction with the
known number of cubic miles occupied by the earth, readily enables
us to determine that the total mass of the earth is about
6,000,000,000,000,000,000,000 tons.

CHAPTER XIII.
GRAVITATIONAL EFFECTS OF SUN AND MOON UPON THE EARTH.

THE TIDES.—The familiar phenomena of the tides are of such importance to
commerce in so many parts of the world that they have been carefully
investigated from very early times. The necessities of coast navigation
would soon lead to the recognition of a periodic character in the tides,
as well as to their association with the age and position of the moon.
With the march of science, an explanation of tidal phenomena was
therefore sought in the motion of the moon. A great impetus was given to
this inquiry by Newton’s generalisation, and the tides were shown to be
a necessary consequence of the gravitational attraction of the sun and
moon. Regarding the earth merely as a cosmical particle, we have seen
that its orbital motion is perfectly explained by the gravitational
attraction of the sun, and some of its minor movements by the
attractions of other members of the solar system. The law of
gravitation, however, compels us, in a closer investigation of these
mutual attractions, to regard each globe as an assemblage of particles,
each of which individually influences and is influenced by other
particles. If such a collection of particles be spherical and perfectly
rigid, it will behave precisely as a simple particle in which the whole
mass is concentrated.

When we cease to consider the earth as a mere particle, we must regard
the waters of the oceans as being free to move over the more rigid crust
of the globe. Imagine our globe to be a spherical mass completely
surrounded by a liquid envelope. At any moment one half of this is
presented towards the moon. The solid earth we may conceive to be
attracted by the moon as a simple particle; but the water on the side
nearest to the moon is attracted with a greater force than the solid
globe, because of its greater proximity to the attracting body, and it
has therefore a tendency to heap itself up directly under the moon.
Being free to move, the water thus remains heaped up under the moon,
notwithstanding the earth’s rotation, and if there were only one such
elevation, there would only be one tide a day. Observation shows us that
there are two high tides a day, and the water must therefore be heaped
up on the side of the earth which is turned away from the moon. This is
perfectly true, though seemingly at first sight inconsistent with the
moon’s attraction. The fact is that the solid earth is attracted by the
moon with greater energy than the water on the side most remote from it,
so that the heaping up of the water on the side away from the moon is to
be regarded as due to the earth having left it behind.

[Illustration:

FIG. 45.—_The Tides._
]

There is thus a double tidal wave produced by a spheroid of water which,
in the simple case we have considered, has its axis directed towards the
moon, as in Fig. 45. The earth, rotating within this liquid shell,
successively brings different parts of the solid earth to the points of
high and low water. If the moon were fixed, we should then experience
two high and two low waters every day, but as it revolves in the same
direction that the earth rotates, the average interval between two
successive meridian passages is 24 hours 51 minutes. This, then, is the
period in which alternate high waters or alternate low waters are
experienced.

A similar train of reasoning applies to the attraction of the sun upon
different parts of our planet, so that there are solar as well as lunar
tides. Nevertheless, the moon is the dominating cause, for although the
total attraction of the sun upon the earth is about 200 times that of
the moon, its differential attraction upon the opposite sides of the
earth, which is alone effective in producing tides, is only about ⅖ths
that of the moon.

A simple mathematical investigation shows that the tide-raising force of
a body is proportional to its mass, and approximately in inverse
proportion to the cube of its distance from the affected body. Thus, it
appears that if the moon were removed to 1·36 times its present
distance, solar and lunar tides would be equal.

At the times of new and full moon, the sun and moon will produce two
tidal spheroids of water upon our imaginary earth, having their axes
coincident, and an exceptionally high tide will occur. This is a _spring
tide_. When the moon is at its quarters the two ellipsoids tend to
neutralise each other, and an exceptionally low or _neap tide_ results.
Two spring tides and two neap tides thus occur in each synodic month of
29½ days.

The height of the tide will also be affected by the variations in the
distance of the moon. If the moon be at perigee the tide will be greater
because of the smaller distance, and if this occur at new or full moon
there will be a very high spring tide, while a less notable spring tide
will occur when the new or full moon is at apogee.

The combination of the solar and lunar tides gives rise to what is
called the _priming_ and _lagging_ of the tides. At new and full moons
the combined tides will produce a spheroid of water with its axis
directed towards the moon. When the moon is a few days old however, the
crest will take up a position intermediate between the direction of the
moon and that of the sun, and high water will therefore be accelerated.
The same thing will happen during three or four days after full moon.
Three days before full or new moon the combination of the two tides will
displace the crest towards the sun, and therefore in advance of the
moon, so that high water will be retarded. The retardation and
acceleration correspond to lagging and priming respectively.

At the quadratures the combined tides simply reduce the height of the
crest, since there is no reason why the deviation should be to one side
any more than to the other. On account of priming and lagging, the tides
on successive days are accelerated or retarded by as much as 13 minutes
when the effects are greatest.

Sufficient has been said to indicate that tidal phenomena are very
complex even when we suppose the earth to be very simply constituted.
When we take into account the actual configuration of the land and the
consequent restrictions in the movements of the water, these
complications are increased tenfold. Yet, by continued observations, the
recurrence of tides at any port can be predicted with tolerable
accuracy. It is observed that there is a certain pretty regular interval
of time between the moon’s meridian passage and the time of next high
water; this is different at different ports, but is so nearly constant
at a given place as to be called _the establishment of the port_.
Observations being made at a great many places, the peculiar movements
of the tidal wave can be investigated. For this purpose, it is
convenient to draw on a map what are called _co-tidal lines_ that is,
lines passing through places at which high water occurs at the same
moment. It then appears that it is only in the Southern Pacific where
the water is of sufficient extent to permit the formation of the tide
crest. The effect of this wave, which commences twice a day, is
gradually spread over different parts of the world, but before it
reaches most places other waves have commenced a similar journey. The
tide at London, for example, coming round the north of Scotland and down
the North Sea, really started in the Southern Pacific 66 hours before,
and in the same way the tide at New York is a little over 40 hours old.

The height of a tide is thus regulated by the conditions of the sun and
moon with regard to the earth when the primary tide was formed, and not
by their relation when a tide is actually observed.

In the Pacific Ocean the tides are very feeble, but near the coast they
vary enormously, and sometimes reach great heights. At Bristol the
difference between high and low water sometimes amounts to fifty feet,
and in the Bay of Fundy, Nova Scotia, it has been as much as a hundred
feet.

The peculiarities of the tides at many places are due to interference.
The primary tidal wave striking the British Islands travels partly up
the English Channel, and partly round to the North Sea by the north of
Scotland. At some places on the east coast the two waves almost
neutralise each other, while at others there are even four high tides in
a day.

The circumstances under which tides occur at a given place can only be
determined by actual observations, as theory is at present utterly
inadequate to deal with the manifold complications brought about by the
configuration of the land, and the varying depth of the water.

TIDAL FRICTION.—The regular influx of the tide supplies us with a source
of mechanical energy, which in the future will no doubt become of
immense importance to mankind. A great mass of water is raised to a
higher level, and by suitable contrivances it can be made to do useful
work during its subsequent flow to the ocean from which it came.
Ordinarily, however, the water simply rushes back without its energy
being utilised, and the potential power is merely transferred to another
locality. It is manifest, however, that a certain amount of tidal energy
is lost by friction as the water rolls to and from the rocky shores.
This energy is converted into heat, and finally radiated into space, or
dissipated. Now, the principle of the conservation of energy tells us
that energy can neither be created nor destroyed, although its form may
change from a useful to a useless one. It follows, therefore, that the
energy lost through the tides must be abstracted from one source or
another, and it has been shown that this energy is really derived from
the earth’s rotation. As the earth steadily ploughs its way through its
liquid envelope, the tides act as a break, and its rotational velocity
is reduced; it is part of this lost energy of rotation which is
dissipated by the tides.

One tendency of tidal friction is accordingly to lengthen the period of
the earths rotation, and, therefore, to increase the length of the day.
There are, however, counteracting causes, so that there is no certain
direct evidence that the day has actually lengthened in historical
times.

All the energy of rotation which is lost by the earth is not, however,
dissipated by the tides. Some of it is transferred to the moon, with the
result that the velocity of our satellite, and consequently the size of
its orbit, must be increasing. From this it is inferred that the moon
was formerly very much closer than at present, and an elaborate
investigation of the conditions of its retreat has led Professor G. H.
Darwin to his interesting theory of “tidal evolution.” (See p. 236.)

Professor Darwin has shown that if the term “tide” be extended to
include distortions of the earth and moon at an earlier stage of their
history, when both were fluid or viscous, a similar grinding down of the
energies of rotation of both bodies must have taken place. The axial
rotation of the moon, under these circumstances, would be retarded by
the attraction of the earth on the tides raised in the moon, while that
of the earth would also be slowed down, but in a less degree because of
the moon’s smaller mass.

CAUSE OF PRECESSION.—On account of the spheroidal form of the earth, we
may regard it as a sphere which is surrounded by a ring of protuberant
matter at the Equator. Now the attraction of the sun upon the spherical
part will be quite independent of the position of its axis of rotation,
and will, therefore, not affect the position of the Equator. It is
different, however, with the ring; at the solstices the ring is inclined
to the line joining its centre with the sun, and the near side is
subject to a greater attraction than the side more remote from the sun.
On account of this difference of pull, there is a tendency for the ring
to move into the plane of the ecliptic, and this is what would happen if
the ring were not in rotation. The practical outcome of this tendency,
combined with the rotation, is to produce the twisting of the plane of
the ring, and, therefore, of the plane of the Equator. At the equinoxes
the plane of the ring passes through the sun, and although there is
still a difference of attraction on opposite sides of the ring, the
differential force is entirely directed to the sun, and therefore cannot
produce any precessional effect.

The ultimate tendency to turn into the plane of the ecliptic thus
depends upon the _difference_ of the attractions on opposite sides of
the ring, or rather that part of the difference which acts in a
direction perpendicular to the Equator.

The terrestrial ring cannot change the position of its plane without
taking the whole earth with it, and the rate of precession is thus very
slow. The effect of solar precession alone would cause the equatorial
plane to twist round with but little change of inclination; or the
earth’s axis would travel with a conical movement round a perpendicular
to the ecliptic passing through the earth’s centre.

It will be remarked that as the force-producing precession is identical
with that which is effective in producing the tides, the moon must have
a greater precessional effect than the sun. This is quite true, and on
the average the precession-producing force of the moon is 2½ times that
of the sun. When the moon is on the celestial equator, as it is twice a
month, the differential force acts in the plane of the ring, and no
precessional effect results. On the other hand, the greatest effect is
produced by the moon when the earth’s Equator is most inclined to the
line joining the earth and moon. The amount of this greatest inclination
is different in different months according to the position of the moon’s
nodes. In consequence of the revolution of the moon’s nodes, the moon’s
orbit is inclined to the Equator at all angles from 18° to 28°, and back
again to 18° in a period of 19 years. The precessional effect of the
moon thus has a principal period of 19 years, while that of the sun has
a period of a year during which it has two maxima and two minima. The
summation of the effects of the sun and moon gives us the _luni-solar
precession_, which is very variable in its actual rate, but averages
about 50″·2 per annum.

[Illustration:

FIG. 46.—_Nutation._
]

NUTATION.—If the precession-producing force were of constant amount,
there would be no change in the inclination of the earth’s axis to the
ecliptic. When the force is increasing, the equatorial ring is slightly
tilted towards the ecliptic, and when it is decreasing the converse
takes place. As the moon has the preponderating effect, these changes in
the inclination will evidently depend mainly upon the changing value of
the moon’s precessional force; that is, they will have a period of 19
years. Thus, if _P_, Fig. 46, represents the pole of the ecliptic, the
north celestial pole would travel in a circle of 23½° radius about _P_
if precession were uniform. Suppose, then, the celestial pole to be at
_a_ when the moon’s node is on the Equator—that is, when the inclination
of the moons orbit to the Equator is greatest—from this time the
integrated effects of the moon’s precessional force will be decreasing,
and the inclination of the Equator to the ecliptic will be increased;
the celestial pole will consequently recede a little more than the
average from the pole of the ecliptic, so that after 9½ years it will be
at _b_ instead of _c_. During the next 9½ years the inclination of the
moon’s orbit to the ecliptic will be gradually getting smaller, the
precessional force will be proportionately reduced, and the obliquity of
the ecliptic will be increased, so that the north celestial pole will
have arrived at _d_ after the lapse of 19 years. The prolongation of the
earth’s axis thus describes a wavy curve, each wave extending over 19
years, so that there are about 1,400 waves during the great precessional
cycle. This approach and recession of the two poles is called
_nutation_, or nodding of the earth’s axis. The most recent
investigation of its maximum amount, by Dr. Chandler, gives it as
9″·202. Besides the principal nutation there are others of very much
smaller amount, due to the monthly changes of the moon’s declination and
to the annual change of the sun’s declination.

The most obvious effect of nutation is that upon the inclination of the
earth’s axis to the ecliptic—the “nutation in obliquity.” There is,
however, a displacement of the equinoctial point, and corresponding
nutations in longitude and right ascension.

As pointed out by Sir John Herschel, we have in nutation a splendid
example of a periodical movement in one part of a system giving rise to
a motion having the same precise period in another.

EFFECTS OF PRECESSION.—The effects of precession may be conveniently
summarised here, although some of them have necessarily been mentioned
elsewhere:

(1) The first point of Aries revolves completely round the ecliptic, so
that it passes through all the constellations of the zodiac in a period
of 25,800 years. The “signs” of the zodiac, accordingly, no longer
correspond with the constellations after which they are named.

(2) The Pole Star is constantly changing, since the north celestial pole
travels round the pole of the ecliptic at a distance of about 23½° in a
period of 25,800 years. About 14,000 years ago the bright star Alpha
Lyræ was the Pole Star.

(3) The position of the north celestial pole is in time changed by 47°,
and there may accordingly be this change in the north polar distances or
declinations of all stars whatsoever. As the position of the ecliptic is
almost constant, the celestial latitudes of stars will be but little
affected by precession.

(4) The right ascensions and longitudes of stars, being reckoned from
the shifting first point of Aries, are themselves changeable, passing
through all possible values in the precessional period.

(5) The tropical year is shorter than the sidereal year by the time
taken for the earth to travel through 50″·2—that is, 20 minutes 23
seconds.

(6) Celestial globes and maps, as well as star catalogues, can only
represent the right ascensions and declinations of stars at a specified
epoch.

CHAPTER XIV.
INSTRUMENTAL MEASUREMENT OF ANGLES AND TIME.

GRADUATED CIRCLES.—Astronomy is essentially a science of precision, and
the progress of our knowledge has to a large extent been dependent upon
the increasing power of accurately measuring angles and time.

Let us see, first of all, how to measure angles.

A circle is divided into 360 degrees, each degree again into 60 minutes,
and each minute into 60 seconds of arc; and yet, a second of arc is not
a small enough quantity for many astronomical purposes. Now, unless a
very large circle be employed, it is mechanically impossible to even
mark the minutes of arc directly upon it, and if a very large circle
were constructed, the distortion of its shape produced by its own weight
would be sufficient to mar its accuracy.

What is actually done then is to get a circle of convenient size, and to
graduate it, as well as the highest mechanical skill is capable of, into
such parts as may leave distinct and equal spaces between the separate
divisions. A competent instrument maker would, for instance, put 4,320
divisions on the _limb_ of a circle 16 inches in diameter, two
consecutive divisions thus being 5′ apart. For work of the highest
precision it is necessary to strictly investigate the errors of the
divisions and to correct for them in all observations.

For the further subdivision of these graduations, verniers or reading
microscopes are introduced.

THE VERNIER.—A graduated circle being attached to an instrument, what
one has to do is to take a _reading_ with reference to some fixed mark.
If the fixed mark is seen to fall precisely on one of the divisions of
the circle when observed with a magnifying-glass, the reading can be
written down exactly. If there be no such coincidence, some means are
required for accurately reckoning the fraction of a division. One method
in general use on small instruments, and where extreme precision is
unnecessary, is to employ a subsidiary scale which is called a
_Vernier_, in honour of the Frenchman who invented it. This can be
applied indifferently to a scale of degrees and parts of degrees on a
graduated circle, or to a straight scale. With the aid of this device it
becomes possible to measure angles with no greater probable error than a
few seconds of arc.

[Illustration:

FIG. 47.
]

THE READING MICROSCOPE.—If a greater degree of accuracy than 10″ be
required, the vernier is superseded by a _reading microscope_. This is a
compound microscope (Fig. 48) by which the scale can be observed, and at
the focus of its eye-piece is a pair of spider threads which can be
moved by a fine screw S. Looking into such a microscope, one sees a
magnified picture of a very small part of the scale running through the
field of view, as in Fig. 47. Running across the field, in the same
direction as the marks on the scale, are the spider threads _a b_, which
can be given a right and left movement by means of the screw. At the top
of the field is the part called the “comb,” having its edge cut with
saw-like teeth; like the threads, this is at the focus of the eye-piece.
The scale is divided so that the smallest part is 5′, and in that case
the teeth of the comb are arranged so that five of them equal a scale
division. The reading microscope is a fixture, and the circle is brought
into the position in which its reading is required by moving the
instrument with which it is connected. The zero of the microscope is a
point at the middle of the comb, and one has to determine what part of
the scale corresponds with it. In order to do this, the threads or
“wires” are moved until the next division lies between them, and the
amount which the screw has been turned from the position of zero is read
off on the graduated head of the screw. The dimensions of the parts, and
the magnifying power of the microscope, are adjusted so that the screw
must be turned five times to carry the wires through a space equal to a
division on the scale. One division, therefore, will move the wires
through 1′, and as the screw head is divided into 60 parts, a movement
of ¹⁄₆₀th of a revolution will shift the wires through a second of arc.
Even fractions of a second can be thus measured.

[Illustration:

FIG. 48.—_The Reading Microscope._
]

The introduction of this method of measuring minute angles is due to
Ramsden, who first applied it at the end of the last century. The
microscopes themselves are used for measuring fractional parts of the
graduations of the circles, and usually four to six of them are applied
to different parts of the same circle. In this way, errors arising from
flexure of the circle, fluctuations of temperature, want of exact
circularity, etc., are eliminated, so that finally, after taking every
conceivable precaution, the astronomer can measure angles with the
accuracy which is absolutely necessary in many branches of research.

ASTRONOMICAL CLOCKS.—Means for the exact estimation of time are of no
less importance in an observatory than arrangements for the accurate
measurement of angles. Astronomical clocks are constructed with extreme
care, but in principle they do not differ from ordinary time-keepers. As
sidereal time is of the greatest use in an observatory, the hour hand
only makes one revolution a day, and the face is provided with a seconds
hand, which is plainly visible. The pendulum is of such a length that it
performs its swing in a second. One of the most important improvements
in clocks was the introduction of the “compensation” principle, whereby
the equivalent length of a pendulum remains constant in spite of
fluctuations of temperature. The mercurial pendulum which one very
frequently sees in a watchmaker’s establishment has a glass or steel
cylinder near the bottom partly filled with mercury; as the rod
lengthens by increased temperature, the centre of gravity is raised by a
corresponding amount, on account of the upward expansion of the mercury,
and the rate of swing remains constant when the quantity of mercury is
properly adjusted. The chief defect of this plan is that the mercury and
the steel rod do not respond equally well to a change of temperature.

In the most approved clocks the pendulum rod is a compound one,
consisting of rods, or concentric tubes, of zinc and steel. The pendulum
bob is hung on a steel rod suspended from the top of a zinc tube, which
in turn is fixed at the bottom end to a larger tube of steel; a rod
attached directly to the latter is suspended by a flat spring in the
usual manner. By this arrangement the unequal expansions or contractions
of the different parts due to changes of temperature neutralise each
other, so that a constant rate is the result. The tubes are pierced with
numerous holes so that the inner and outer ones acquire the same
temperature almost at the same time.

The rate of a clock is disturbed slightly by changes in the pressure of
the atmosphere. When the air is densest there is a greater resistance to
the swinging of the pendulum, and the clock will go more slowly.
Although this only amounts to a small fraction of a second a day, it
must necessarily be taken into account in such an establishment as that
at Greenwich, to which all the country looks for the precise control of
time-keepers. In the standard clock at Greenwich a magnet is raised or
lowered by the changing height of a barometer, and its varying
attraction upon a certain piece of iron attached to the pendulum
compensates for the differences produced by change of pressure.

Pendulum clocks are obviously unsuitable for use at sea, so that
_chronometers_ are usually employed on ships. These are like large
watches, very carefully constructed, with “compensation” balance wheels,
and can generally be relied upon as good time-keepers.

After all precautions, however, no astronomer would put his faith in any
clock for any length of time, as the best of them is liable to change
its rate rather irregularly. The “error” of the clock is therefore very
frequently determined by the observation of certain standard stars with
the transit instrument. The stars can be relied upon to come to the
meridian at the proper time, and any apparent departure from this time
must be set down to the account of the clock.

THE CHRONOGRAPH.—A good clock, however, is not the only requirement of
an observatory. It is necessary further to be able to record very
precisely the moment at which an observation is made. If the clock be in
the immediate vicinity of the observer, the time can be noted by
counting the beats of the pendulum, and a practised observer will, by
this “eye and ear” method, record times to the nearest tenth of a
second. Mere estimation, however, is not very reliable, so that a
mechanical method, which also permits greater subdivision of the second,
is very generally adopted. The instrument is called a _chronograph_,
and, although constructed in various forms, its function is to record on
a sheet or strip of paper the regular beats of the clock, as well as the
signals made by the observer. In one form of the instrument the
recording sheet is fixed on a cylindrical drum which is made to revolve
once a minute by a small clock. Beneath the drum is a pair of prickers
worked by the armatures of electromagnets. One of these magnets is in
connection with the clock, and a simple arrangement sends an electric
current through it every second, with the result that the seconds are
marked by small punctures on the paper. As the cylinder revolves, the
marker travels slowly lengthwise, so that the clock record runs spirally
from one end to the other. To facilitate the identification of the
punctures, one is omitted at the end of every minute. When an
observation is made, the observer presses a button, and a current is
sent through the second magnet, with the result that a puncture is made
alongside those made by the clock. In this way the exact moment at which
an observation is made can be easily registered, and read off at any
convenient time.

At Greenwich a room is set apart for a number of chronographs, each in
communication with an instrument in the various observatories.

CHAPTER XV.
TELESCOPES.

THE REFRACTING TELESCOPE.—The function of a telescope is two-fold.
First, to magnify the heavenly bodies, or, what comes to the same thing,
to make them look as if they were nearer to us, so that we can see them
better. Second, to collect a much greater number of rays of light than
the unassisted eye alone can grasp, so that objects too dim to be
otherwise perceptible are brought within our range of vision.

There are two forms of telescope, distinguished as _Refractors_ and
_Reflectors_. The simplest form of refracting telescope is exemplified
by the common opera-glass, and large refractors are not essentially
different. Such instruments depend for their action upon the formation
of an image by a lens. One can easily illustrate this by producing upon
the wall of a room an inverted image of a candle or gas flame with a
spectacle lens (one adapted for a long-sighted person), or with one of
the larger lenses from an opera-glass. Having such an image, it may be
magnified by means of another lens, just as one may magnify a photograph
with an ordinary reading glass. Technically, the lens which forms the
primary image is called the _object-glass_ of the telescope, and that
which is used to magnify this image is called the _eye-piece_. The
object-glass is usually a large lens, which is placed at one end of a
tube, while the eye-piece is a much smaller lens, placed at the other
end. Means are provided for adjusting the distance between the two
lenses so as to admit of distinct vision.

[Illustration:

FIG. 49.—_The Achromatic Object-Glass._
]

Matters are, however, not quite so simple as has been stated. There is a
very great difficulty introduced by the fact that a lens made out of a
single piece of glass gives an image which is surrounded by fringes of
colour, so that some device has to be adopted in order to destroy, as
far as possible, this enemy of good definition. In the early history of
the telescope, this so-called _chromatic aberration_ was considerably
reduced by making small object-glasses of very great focal length.[4]

Lenses of 100-feet focus, however, are not easy to employ as
object-glasses, and astronomy was, therefore, greatly benefited by
Dollond’s invention of the _achromatic lens_ in 1760. This is a compound
lens, usually consisting of a double convex crown-glass lens and a
concavo-convex, or double concave, lens of flint glass. The curvatures
of the lenses, and the optical properties of the two kinds of glass
composing them, are such that the colour due to one of them is
practically neutralised by that due to the other acting in opposition. A
section of such an object-glass, with the “cell” in which it rests, is
shown in Fig. 49.

In this way the focal length of the lens, and, therefore, the length of
the telescope tube, can be kept within reasonable dimensions, while the
definition is improved. There is, however, usually a little outstanding
colour, due to the imperfect matching of the two lenses, and if one
looks through a large refractor, even of a good quality, a purple fringe
will be noticed round all very bright objects. This only affects a few
of the brighter objects, while millions of others which are dimmer may
be seen free from spurious colour.

It may be remarked that the curved surfaces of the lenses forming
telescopic object-glasses must not be parts of spheres. If they are, the
images will be rendered indistinct by _spherical aberration_, and the
optician has to design his curves to get rid of this defect at the same
time as chromatic aberration.

A new form of telescopic objective, consisting of three lenses, which
has many important advantages, has recently been invented by Mr. Dennis
Taylor, of the well-known firm of T. Cooke & Sons, York.

Such a lens as this illustrates the perfection which the optician’s art
has now attained. Six surfaces of glass have to be so accurately figured
that every ray of light falling upon the surface of the lens shall pass
through the finest pinhole at a distance of eighteen times the diameter
of the lens.

THE REFLECTOR.—In a reflecting telescope, the object-glass of the
refractor is replaced by a concave mirror. In order that such a mirror
may reflect all the rays from a star to a single point, its concave
surface must be part of a paraboloid of revolution, that is, a surface
produced by the revolution of a parabola on its axis. If a spherical
surface be employed, all the rays will not be reflected to a single
point, and the images which it gives will be ill-defined. Yet it is
astonishing to find that the difference between a parabolic and
spherical surface, even in the case of a large mirror, is exceedingly
small. Sir John Herschel states that in the case of a mirror four feet
in diameter, and forming an image at a distance of forty feet, the
parabolic only departs from the spherical form at the edges by less than
a twenty-one thousandth part of an inch.

[Illustration:

FIG. 50.—_The Newtonian Reflector._
]

An image being formed by a mirror, it is next to be viewed with an
eye-piece just as in the case of a refracting telescope. Here there is a
little difficulty, for if the eye-piece be applied in the direct line of
the mirror, the interposition of the observer’s head will block out the
light. Several ways of overcoming this have been devised, but the plan
most generally followed is that which Newton adopted in the first
reflecting telescope which was ever constructed. With his own hands
Newton made a small reflector, 6¼ inches long and having an aperture of
1⅓ inches, with which he was able to study the phases of Venus, and the
phenomena of Jupiter’s satellites. This precious little instrument is
now one of the greatest treasures in the collection of the Royal Society
of London. The general design of this telescope is shown in Fig. 50. The
concave mirror is at the bottom of the telescope tube, and normally it
would form an image of a star near the end of the tube. A plane mirror,
however, of small size intercepts the rays and reflects them to the
side, where they converge to a focus. This image is observed and
magnified by an eye-piece, as in the refractor. It is true that in this
arrangement the plane mirror, or _flat_, renders the central part of the
principal mirror ineffective, but the loss of light is very much less
than would be the case if the eye-piece were placed in position to view
the image centrally.

In the hands of Sir William Herschel the reflecting telescope was
greatly developed. The great telescope with which he enriched
astronomical science had a mirror four feet in diameter, and its tube
was 40 feet in length. With the view of utilising the whole surface of
the mirror and dispensing with a second reflecting surface, the four
foot mirror was placed at a small angle to the bottom of the tube, so
that its principal focal point was no longer at the centre, but at the
side of the tube.

In practice, however, it is found that the Herschellian form of
reflector does not give the best definition, and it is now very seldom
seen.

Among other forms, the “Cassegrain” is perhaps the most important.
During the last year or two this form has received a great deal of
attention, more especially in regard to its special adaptability for
photographic purposes.

In the Cassegrain telescope, the plane mirror of the Newtonian form is
replaced by a small convex mirror which is part of a hyperboloid of
revolution, its axis and focal point being coincident with those of the
primary mirror. The rays are in this way reflected back to the mirror at
the bottom of the tube, and in order that the image may be seen, it is
necessary to cut out the middle part of the mirror to admit the
eye-piece.

Although the small mirror must theoretically be hyperbolic, tolerable
definition is obtained even if it be spherical or ellipsoidal, and its
actual departure from these forms is so slight as to be beyond detection
by measurement, so that the figuring of such mirrors can only be tested
in the telescope. For photographic purposes this telescope has the very
important advantage that a short telescope is equivalent to a very long
one of the Newtonian form, or refracting telescope, so that the image of
sun, moon, or planets formed at the focus is very large in comparison
with the size of the telescope. A modification of this form of
telescope, in which the small mirror is out of the path of the rays
falling upon the larger one, and no longer obstructing the central part,
has been recently revived by Dr. Common, and has become generally known
as the “Skew Cassegrain.”

In reflecting telescopes the mirrors were formerly made of _speculum_
metal (an alloy of copper and tin), and the word speculum is even now
commonly employed to signify a telescopic mirror, although it is usual
to make the mirror of glass, with the concave surface silvered and
highly polished.

[Illustration:

FIG. 51.—_The Cassegrain Reflector._
]

One is frequently asked for an opinion as to which is the better form of
telescope, the reflector or refractor, and it is a question that one
finds some little difficulty in answering. On one point, however, all
are agreed, namely, that the reflector has the advantage in regard to
its achromatism; it is indeed perfectly achromatic, while the so-called
“achromatic” refractor is at best only a compromise. For the rest, one
cannot do better than quote the evidence of Dr. Isaac Roberts before the
International Astro-photographic Congress:—“The reflector requires the
exercise of great care and patience, and a thorough personal interest on
the part of the observer using it. In the hands of such a person it
yields excellent results, but in other hands it might be a bad
instrument. The reflector gives results at least equal, if not superior,
to those obtained with the refractor, if the observer be careful of the
centering, and of the polish of the mirror, and keeps the instrument in
the highest state of efficiency; but when entrusted to an ordinary
assistant the conditions necessary for its best performance cannot be so
well fulfilled as the same could be in the case of the refractor.” One
great practical advantage of the reflector is that there are fewer
optical surfaces, so that a large reflector may be obtained for the
price of a much smaller refractor.

EYE-PIECES.—So far we have regarded the eye-piece of a telescope as a
simple lens, but it is evident that the spherical and chromatic
aberration of such a lens will interfere with its performance. For
occasional use, however, even a simple lens is very serviceable if the
object observed is brought to the centre of the field of view.

Compound eye-pieces are of various forms, each having certain
advantages, the desiderata being freedom from colour and “flatness of
field”—that is, stars in different parts of the field are to be equally
well in focus. Those most commonly employed are the Ramsden and
Huyghenian eye-pieces. The former consists of two plano-convex lenses of
equal focal lengths, having their curved faces towards each other, and
being placed at a distance apart equal to two-thirds of the focal length
of either lens. Such an eye-piece can be used as a magnifying-glass, and
it is therefore placed outside the focal image formed by the telescope
with which it is used; on this account it is called a _positive
eye-piece_. This kind of eye-piece is not quite achromatic, but its flat
field of view gives it a special value for many purposes.

In the Huyghenian eye-piece there are again two lenses, made of the same
kind of glass. That which comes nearest to the eye has a focal length of
only one-third that of the _field_ lens, and the distance between the
two lenses is half the sum of the focal lengths. This form of eye-piece
cannot be used as a magnifying-glass in the ordinary sense, and as the
field lens must be placed on the object-glass or mirror side of the
focus, it is called a _negative eye-piece_. The Huyghenian eye-piece is
more achromatic than the Ramsden, and is more widely used when it is
only required to view the heavenly bodies. In instruments employed for
purposes of measurement, a positive eye-piece is essential in order that
the spider threads may be placed at the focus of the telescope. The
images formed by an astronomical telescope are upside down, and neither
of the eye-pieces described reinverts them.

A special form of eye-piece is therefore used when a telescope is
employed for terrestrial sight-seeing. The desired result is obtained by
the introduction of additional lenses, but there is a corresponding
reduction of brightness.

For viewing the sun some device is necessary to reduce the quantity of
light entering the eye. To look at the sun directly, even with a small
instrument, is very dangerous. The arrangement usually adopted is a
_solar diagonal_, in which the light is reflected from a piece of plane
glass before entering the eye-piece; the piece of glass is wedge-shaped,
so that the reflection from one surface only is effective; if the glass
had parallel sides, the solar image would be double.

MAGNIFYING POWER.—The magnifying power of a telescope depends upon the
focal length of the object-glass, or speculum, and that of the
eye-piece. Optically, it is equal to the former divided by the latter,
so that the greater the focal length of an object-glass, or the smaller
the focal length of the eye-piece, the greater will be the magnifying
power. In a given telescope, the object-glass, or speculum, is a
constant factor, and the magnifying power can only be varied by changing
the eye-piece. The focal length of the Lick telescope, for example, is
about 600 inches; with an eye-piece which is equivalent to a lens of
one-inch focus, the magnifying power would be 600; with a lens of half
an inch focus, it would be 1,200, and so on.

The magnifying power which can be effectively employed, however, depends
upon a great variety of circumstances. First, the clearness and
steadiness of the air; then there is the quality of the object-glass, or
speculum, to be considered; and also the brightness of the object to be
observed, for when the object is very dim, its light will be spread out
into invisibility if too high a power be used.

In practice, good refractors perform well with powers ranging up to 80
or 100 for each inch in the diameter of the object-glass. Thus, on
sufficiently bright objects, a six-inch telescope will work well with a
power of about 500, while a 30-inch may be effectively employed with
powers between 2,000 and 3,000.

ILLUMINATING POWER.—It has already been pointed out that magnification
is not the only function of a telescope. As a matter of fact, the most
powerful telescopes in the world fail to produce the slightest increase
in the apparent size of a star, for even if these objects be brought to
apparently a 3,000th part of their real distances, they are still too
far away to have any visible size. But although a star cannot be
magnified, it can be rendered more visible by the telescope, for the
reason that the object-glass collects a greater number of rays than the
naked eye. The pupil of the eye may be taken to have a diameter of
one-fifth of an inch; a lens one inch in diameter will have 25 times the
_area_ of the pupil, and will therefore collect 25 times the amount of
light from a star; a two-inch lens will grasp 100 times, and a 36-inch
32,400 times as much light as the pupil alone. Practically all these
rays collected by the object-glass, or speculum, of a telescope cannot
be brought into the eye; some are lost through the imperfect
transparency of the glass, or the imperfect reflecting power of the
speculum. Still, allowing a considerable percentage for loss, there is
an enormous concentration of light when a large telescope is employed.

THE ALTAZIMUTH MOUNTING.—Having got a telescope, we have next to see how
it can be best supported, for unless it be a very small instrument
indeed, it will be impossible to hold it in the hand like a spy-glass.
However a telescope be mounted, provision must be made for turning it to
any part of the sky whatsoever. Very frequently one of the axes on which
the instrument turns is vertical, while the other is horizontal. Such a
stand for a telescope is called an _altazimuth mounting_, for the reason
that it permits the instrument to be moved in altitude and in azimuth.

As a rule, one finds only small telescopes mounted in this manner. The
objection to it is that, as one continues to observe a heavenly body,
two independent movements must be given to the telescope in order to
follow the body in its diurnal movement across the heavens. If we
commence observing a star newly risen, for example, the telescope must
trace a stair-like path in order to follow it, as it ascends into the
heavens.

THE EQUATORIAL TELESCOPE.—A much more convenient method of setting up a
telescope is to mount it as an _equatorial_. The essential feature of
this instrument is that one of the axes of movement, instead of being
vertical, is placed parallel to the axis of the earth. This is called
the _polar axis_, and, when the telescope is turned around such an axis,
it traces out curves in the sky which are identical with those described
by the stars in their diurnal motions. If, then, the telescope be
directed to a star or other heavenly body, it can be made to follow the
object and keep it in view by a single movement. The axis at right
angles to the polar axis is called the declination axis, and is
necessary in order that the telescope may be moved towards and from the
Poles so that all the heavenly bodies above the horizon may be included
in its sweep.

One very important advantage of the equatorial is that as only one
motion is required to keep a star in view, so long as it is above the
horizon, the necessary movement may be furnished by clock-work. A good
equatorial is accordingly provided with a driving clock, which is
regulated so that it would drive the telescope through a whole
revolution once a day. Unlike an ordinary clock, the driving clock of a
telescope is regulated by a governor, in order that the instrument may
have a continuous and not a jerky movement.

The telescope is also provided with clamps and fine adjustments, one
each in R. A. and declination, in order that it may be under the control
of the observer. It is evident that the telescope must be capable of
moving independently of the driving gear, so that it may first be placed
in the desired direction; when this is accomplished, the R. A. clamp is
used to put the telescope in gear with the clock. The declination clamp
is them made to fix the telescope firmly to the declination axis. Fine
adjustments in both directions are necessary, because it is impossible
to sight a large instrument with such precision as to bring an object
exactly to the centre of the field of view.

Some of the driving clocks fitted to equatorials are very elaborate. As
clocks regulated by governors are not such reliable time-keepers as
those regulated by pendulums, arrangements are made by which the
accuracy of a pendulum can be electrically communicated to a governor
clock. One of the best forms of electrically-controlled clocks is that
devised by Sir Howard Grubb.

Another important feature of an equatorial is that it can be provided
with circles which enable the telescope to be pointed to any desired
object of known right ascension and declination. One of these is the
declination circle, attached to the declination axis and read by a
vernier fixed to the sleeve in which the axis turns; this is adjusted so
as to read 0° when the telescope points to any part of the celestial
equator, and 90° when it is directed to the Pole. The other circle is
attached to the polar axis, and determines the position of the telescope
with regard to the meridian; this is called the _hour circle_, and is
divided into 24 hours. When the telescope is on the meridian, the hour
circle reads zero, so that its reading in any other position gives the
hour angle of the telescope. Having given the right ascension and
declination of a heavenly body which it is desired to observe, the
telescope is turned until the declination circle reads the proper angle,
and the hour circle indicates the hour angle which is calculated for the
particular moment of pointing the telescope. [The hour angle is the
difference between the right ascension of the object and the sidereal
time of observation.] In this way it is easy to find objects of known
position which are invisible to the naked eye, and one can even pick up
the planets and brighter stars in full sunshine. Conversely one can
determine from the circles the right ascension and declination of any
object under observation, but for various reasons only approximate
results can be obtained in this way. The chief use of the circles on an
equatorial is therefore to provide a means of pointing the telescope.

Telescopes of 4 inches aperture and upwards are usually provided with a
smaller companion called a _finder_. This has a larger field of view
than the main telescope, so that objects which are of sufficient
brightness can readily be picked up and brought to the centre of the
finder, the adjustments being such that the object is then also at the
centre of the field of the large telescope.

There are, of course, many practical details connected with the working
of an equatorial with which space does not permit us to deal. It may be
remarked, however, that the adjustment of the polar axis is very simply
performed by first inclining it at an angle approximately equal to the
latitude of the place where it is set up, and setting it as nearly as
possible in the meridian by means of a compass or by observations of the
sun at noon. The final adjustment is then made by a series of
observations of stars of known position.

SOME OF THE WORLD’S GREAT TELESCOPES.—Thanks to the wide public interest
taken in astronomical matters, a large number of powerful telescopes has
been set up in various parts of the world. To the British Islands
belongs the honour of possessing the largest telescope in the world.
This is the giant reflector erected by Lord Rosse, in 1842, at
Parsonstown, the mirror being 6 feet in diameter, and the focal length
60 feet. Many very valuable observations were made with this instrument
in its early days, but of late years it seems to have fallen into
disuse. One reason may be that the mounting is not of the most
convenient form, and makes the telescope unsuitable for photographic
work.

Coming next in point of size to the Rosse telescope is the reflector
erected at Ealing, by Dr. A. A. Common. The glass mirror of this
telescope is 5 feet in diameter, 5 inches thick, and weighs more than
half a ton. Dr. Common aimed specially at constructing the largest
possible telescope which could be equatorially mounted and provided with
a driving clock, and he was only limited to an aperture of 5 feet by the
impossibility of obtaining a glass disc of larger size. He has attained
such great skill in this work that he was able to produce a perfect
mirror 5 feet in diameter in three months time, although no less than
410,000 strokes of the polishing machine were required.

The telescope is of the Newtonian form, and the mounting is quite
unique. The polar axis consists of an iron cylinder, made up of boiler
plates, 7 feet 8 inches in diameter, and about 15 feet long. From the
top of the cylinder, near its outer edge, two horns, each 6 feet long,
project outwards, and the tube of the telescope swings on trunnions
attached to the ends of the horns. The main part of the telescope tube
is square, built up of steel angle iron, and carries the mirror at its
lower end; the upper part of the tube, which carries the “flat” and
eye-piece, is round, and of tinned steel strengthened by a skeleton
framework.

It is evident that such an enormous instrument as this cannot be made to
travel by clock-work with the necessary uniformity without some very
efficient arrangement for reducing friction. Dr. Common’s plan—and it is
here that his instrument is unlike others—is to make the hollow polar
axis water-tight, and to fix it in a tank of water. At the bottom of the
polar axis is a ball and socket joint to keep it in position, and at the
top is another bearing, which can be adjusted so that the polar axis
lies truly in the meridian. It was found necessary to introduce 9 tons
of iron into the bottom of the hollow polar axis in order to sink it to
the proper angle, and to put sufficient weight on the bearings to give
stability to the instrument. In this way the great mass is brought into
the region of manageability, and the driving clock, which is driven by a
weight of 1½ tons, is able to do its work efficiently. Such, in general
outline, is this wonderful telescope, which, although not so large as
Lord Rosse’s famous instrument, is undoubtedly its superior in
light-grasping power and general utility, and more especially in its
adaptability for photographing the heavens.

Among other large reflecting telescopes now in use are the four-foot
reflectors at Melbourne and Paris, and the three-foot reflectors at
South Kensington and the Lick Observatory, California.

The largest refracting telescope yet constructed is one of 40 inches
aperture for the new Yerkes Observatory of the University of Chicago. It
is interesting to note here that Professor Keeler, in his report as an
expert upon the performance of the object-glass, considers that there is
“evidence for the first time that we are approaching the limit of size
in the construction of great objectives.” Unlike a mirror, a lens can be
supported only upon its circumference, and it is the bending by its own
weight that proves detrimental to its defining power. If the lens be
made thicker with a view of overcoming this defect, the absorption of
light by the glass increases, so that there is in the end no special
gain by increasing the size.

The length of the Yerkes telescope is 62 feet, and it will be provided
with all accessories pertaining to astrophysical research. The Yerkes
telescope, however, is not yet in actual use, and meanwhile the
world-renowned Lick telescope, of 36 inches aperture, keeps the lead
among active big refractors. The story of the foundation of this monster
instrument is not much less wonderful than the telescope itself. Brought
up in poor circumstances, with few opportunities for intellectual
development, James Lick, nevertheless, amassed a fortune in business,
and having few relations, he was anxious to dispose of his wealth in
such a way as to bring him that fame which he had failed to achieve in
other directions. Although it is very probable that he had never looked
through a telescope in his life, the idea of a large telescope had taken
a very firm hold upon his mind, and, thanks to the influence of his
advisers, it was definitely announced in 1873 that Mr. Lick’s bid for
immortality was to take this form. Several sites were examined by
experts, and finally Mount Hamilton, California, 4,200 feet above
sea-level, was selected. An excellent road, 26 miles in length, made at
the cost of the county authorities, connects the observatory with the
nearest town, San José, 13 miles distant.

Owing to various delays, operations were not commenced until 1880, and
five years were consumed in clearing away 72,000 tons of rocks and in
erecting the buildings.

Mr. Lick had stipulated for the erection of “a telescope superior to and
more powerful than any telescope yet made,” and Messrs. Alvan, Clark &
Co. contracted to supply a lens of 36 inches aperture for the sum of
50,000 dollars. It turned out, however, that it was much easier to make
such a contract than to fulfil it. To produce large discs of optically
perfect glass, even in the rough, requires the greatest possible skill
and patience, and this part of the work was undertaken by Feil & Co. of
Paris. The flint glass disc was safely delivered in America in 1882, but
the crown disc was cracked in packing. The elder Feil having retired
from business, the duty of providing a new block of crown glass devolved
upon his sons, who, after two years spent in vain attempts, ended in
bankruptcy, and it was only through the elder Feil again resuming
business that the much-required disc was finally completed in 1885.
After the lapse of another year, the rough discs were fashioned, in the
workshops of the Clarks, into the most marvellous of telescopic lenses.

The mounting of the object-glass is worthy of the occasion, as will be
seen from our illustration (see page 40). The tube is no less than 57
feet long, and 4 feet in diameter in the middle part. An iron pier, 38
feet high, beneath which lie the remains of Mr. Lick, supports the
equatorial head, and a winding staircase enables the observer to reach
the setting circles. Inside the hollow pier is the powerful driving
clock which turns the telescope to follow the heavenly bodies in their
apparent movements. Finders of 6, 4, and 3 inches diameter, rods for the
manipulation of the instrument, and all necessary accessories, complete
what must long remain one of the most perfect instruments at the service
of astronomical science. The 200,000 dollars expended upon it have
already been amply justified by the work accomplished, while Mr. Lick’s
dream of immortality has become a reality.

The following list indicates some of the large refractors now (Feb.,
1897) doing active service:—

_Aperture._ _Observatory._
36 inch [Lick] California.
30 „ Pulkowa, Russia.
30 „ [Bischoffeim] Nice.
28 „ Greenwich.
27 „ Vienna.
26 „ Washington.
25 „ [Newall] Cambridge.
24 „ [Lowell] Mexico.
23 „ Princeton, New Jersey.

It is right to add, however, that opinion is still greatly divided as to
whether these telescopes of large aperture really repay the expense and
labour involved in their erection and use. On the very rare occasion
when the “seeing” is practically perfect—which occurs perhaps only a few
hours in a year—it is probable that the superiority of a large telescope
is very marked, but under average conditions there seems to be little
advantage over instruments of moderate size for many classes of
observations.

Certain it is that a great deal of valuable work is done with
comparatively small telescopes, ranging from six to fifteen inches
aperture, and this in all departments of astronomical research. Hence,
some of the most active observatories do not figure in the above list;
among them may be mentioned the observatories of Harvard College
(U.S.A.), Potsdam, Paris, Heidelberg, Cape of Good Hope, Edinburgh,
South Kensington, Stonyhurst College, and the observatory of Dr. Isaac
Roberts at Crowborough, Sussex.

HOUSING OF EQUATORIALS.—The building which accommodates an equatorial
telescope must evidently be designed to admit of giving a clear opening
to any part of the sky. Usually this is accomplished by making the roof,
or _dome_, with a circular base, provided with wheels, which run on
rails. It is then only necessary to open a narrow portion of the dome,
extending from top to base, and to turn the dome until this aperture is
in the required direction. One of the most elaborate domes now in
existence is that built by M. Eiffel for the great refractor of the Nice
Observatory. The lower part of the building is in the form of a square
(see Frontispiece), having a side of about 87 feet, and a height of
about 30 feet. The dome itself is 74 feet in diameter, and the moving
parts alone weigh 95 tons.

As will be seen from the illustration, there are two shutters, each a
little wider than half the possible opening: these run on short rails,
and are moved simultaneously by means of an endless rope. The whole of
the dome is built up of steel angle iron, covered with very thin sheet
steel. In order to facilitate the manipulation of the dome, its great
weight is buoyed up by means of a float attached to its base and
immersed in a circular tank of water of a little greater size than the
base of the dome. If any mishap occurs with this gigantic tank, the dome
rests on wheels which run on a circular rail, so that the work need not
be interrupted. The whole arrangement is very easily turned with the aid
of a winch by one man when the dome is floating, but when resting on the
wheels several men are required at the winch.

This brief description will serve to illustrate some of the problems
which confront the possessor of a very large telescope. For smaller
instruments, the observatories follow pretty nearly the same plan,
except that it is unnecessary to provide an arrangement for floating the
dome.

The observatory which shelters a reflecting telescope need not differ
very greatly from one which contains a refractor. If the instrument be a
Newtonian, it is generally convenient to sink the polar axis below the
level of the floor in order that the observer may not be at too great a
height from the ground, and in that case, the dome, or its equivalent,
is all that is necessary. For his five-foot reflector, Dr. Common
designed an observatory which is not of the ordinary form, but gives the
necessary opening partly by means of large shutters, and partly by a
revolution of the whole house. It is not everyone who is able to lay out
£8,000 on such a dome as that erected at Nice by M. Bischoffeim.

The varying position of the eye end of a telescope, when it is turned to
different parts of the sky, makes it necessary to provide comfortable
and safe seating accommodation for the observer, more especially when
the telescope is a very large one. In the case of the Yerkes telescope,
the eye-piece will be 30 feet higher when observing near the horizon
than when observing near the zenith, and the observer must necessarily
follow the telescope. The most convenient arrangement in such a case is
to raise or lower the floor of the observatory as occasion demands. The
floor of the Yerkes Observatory is 75 feet in diameter, and by means of
electric motors it can be given a vertical motion of 22 feet. A similar
arrangement was provided for the Lick telescope from the designs of Sir
Howard Grubb. With smaller instruments, observing ladders and adjustable
chairs of various forms are employed.

THE EQUATORIAL COUDÉ.—A form of equatorial telescope which has possibly
a great future before it is one introduced at Paris under the name of
the _equatorial coudé_, or elbowed telescope. Its practical advantage is
that the observer remains in a constant and comfortable position, so
that revolving domes and elevating floors, or other arrangements serving
similar purposes, are no longer necessary. The telescope tube is of two
parts of nearly equal length, and what is ordinarily the lower half of
the tube forms part of the polar axis, while the other half is attached
to it at right angles. At the point of intersection of the two halves of
the tube is a plane mirror, and there is another mirror in front of the
object-glass. If the latter mirror were removed, such a telescope would
only enable the observer to see objects lying along the celestial
equator, but by its means objects in all parts of the heavens can be
brought within range to an observer gazing down the hollow polar axis.
The largest instrument is that at the Paris Observatory, which has an
object-glass 23½ inches in diameter for visual observations, and another
of the same size for photographic purposes.

FIXED TELESCOPES.—There is still another method of using a telescope.
The telescope itself may be fixed, and the light of the heavenly bodies
may be reflected into it by means of a mirror which is made to revolve
so as to keep pace with their movements. Foucault devised an instrument
called the _siderostat_ for this purpose, and although it is not largely
employed for telescopic observations, it is very widely utilised for
spectroscopic work, where the spectroscope is of a kind not readily
attached to a telescope.

Another instrument used for the same purpose has recently been brought
forward under the name of the _coelostat_. This is simply a mirror which
is made to turn on a polar axis in its own plane, and since a reflected
ray of light moves through twice the angle that the reflecting surface
turns through, the mirror is made to revolve at the rate of one
revolution in two days. As the name indicates, the whole heavens appear
stationary in such an instrument, whereas in a siderostat, only one star
at a time appears at rest, while its neighbours slowly revolve round it.

PHOTOGRAPHIC TELESCOPES.—The application of photography to the study of
the heavenly bodies marks one of the greatest advances of the present
century. The instruments which are employed for this purpose range from
the ordinary tourist camera to the largest telescope. Unlike a person
sitting for a portrait, the heavenly bodies cannot be made to stand
still for the purpose, and as instantaneous photographs can only be
obtained in the case of the sun and moon, it is usually necessary to
make the camera follow the stars very exactly during the time of
exposure, in order that the images may fall on precisely the same parts
of the photographic plate.

Some guiding arrangement is, therefore, essential, and generally the
photographic camera or telescope is attached to an ordinary equatorial
which is driven by clock-work, or very carefully by hand if the camera
be a small one. In the guiding telescope are two spider threads at right
angles to each other, and it is by constantly keeping the image of a
star at the intersection of these “wires” that the operator ensures the
images remaining in a constant position upon the sensitive plate.

An ordinary portrait camera, in the hands of a skilled observer, yields
very beautiful pictures, but they are naturally on a small scale. The
field of view of such an instrument is so large that a whole
constellation may be photographed with a single exposure.

Portrait lenses of 6 inches aperture in the hands of Dr. Max Wolf and
Professor Barnard have given magnificent delineations of the Milky Way,
and of the extremely faint nebulosities which are to be found in many
parts of the heavens.

For many purposes, however, telescopes of greater power are required,
and here it may be remarked that the distance between the images of any
two adjacent stars will vary in direct proportion to the focal length of
the telescope. In the same way the size of the image of a planet, the
moon, or a comet, increases as the focal length of the objective is
increased.

Refracting telescopes which are employed for photography require
object-glasses which are specially “corrected” for the photographic
rays. White light is compounded of light of all colours, but it is the
blue and violet constituents which are effective in producing
photographic action on an ordinary sensitive plate. Now, an object-glass
which is intended for visual purposes is made to focus at the same point
as many as possible of the rays which are most effective to the human
eye, that is the green, yellow, and red, and usually there is a blue or
purple halo round the images of the brighter objects, which is, however,
too feeble as a rule to interfere with visual observations. This blue
halo, will evidently result in defective definition if the lens be
employed for photography. By putting the plate at the point where the
blue rays are most nearly focused, a better image is obtained; but for
really good work a photographic object-glass must be so designed that
all the blue and violet rays are brought to one and the same focus. Such
a lens will consequently be a very poor one for visual observations. At
the present time, 18 photographic telescopes, each of 13 inches
aperture, and corrected in this way, are at work in various parts of the
world for the international star chart.

[Illustration:

FIG. 52.—_The Photographic Telescope employed by Dr. Isaac Roberts._
]

The new “photo telescopic” object-glass now manufactured by Messrs.
Cooke appears to be full of promise. In this lens all the colours of the
spectrum are brought to almost exactly the same focal point, so that it
serves equally well for photographic or visual purposes.

This difficulty in regard to achromatism does not exist in the case of
the reflecting telescope, since rays of light of every colour are
reflected at precisely the same angles. For this reason reflectors, when
properly managed, give the best photographic results. Dr. Isaac Roberts
and Dr. Common are especially identified with the application of the
reflecting telescope for celestial photography. The instrument employed
by the former consists of a 20-inch reflector, and a 7-inch guiding
telescope of the refracting form. The two telescopes are mounted on the
extreme ends of the declination axis of an equatorial, a photograph of
which we owe to the kindness of Dr. Roberts.

Dr. Common does not employ a guiding telescope at all. The photographic
plate which he places at the focus of the reflector is smaller than the
field of view, so that by means of an eye-piece fitted with a cross wire
at the side of the dark slide, he is able to watch a star near the edge
of the field. Both eye-piece and dark slide are attached to a frame
which can be controlled by two screws at right angles to each other. If
the guiding star leaves the cross wire through errors in driving, or
other causes, the eye-piece and dark slide are bodily moved after it by
means of the adjusting screws. This method not only has the advantage of
saving the cost of a guiding telescope, but reduces the effects of
vibration consequent upon the correction of errors by moving the whole
telescope.

For photographing the sun a special instrument called a
_photoheliograph_ is usually employed. This differs only from an
ordinary photographic telescope in being provided with a secondary
magnifier, by which means the focal image formed by the object-glass is
amplified before falling upon the photographic plate. On a bright clear
day, pictures of the sun 8 inches in diameter can be taken with an
exposure of about ¹⁄₅₀₀th of a second, and such a photograph will
frequently record more facts as to the state of the solar surface than a
whole day’s observation. Lenses or mirrors of very long focus are also
occasionally employed in solar photography, and in this way a large
image is obtained without the use of a secondary magnifier.

Photographs of the moon and planets may be taken either with or without
a secondary magnifier, but in either case the exposures are longer than
for the sun.

Finally, it may be added that the sensitive plates and processes used in
astronomical photography do not differ from those employed by ordinary
photographers.

CHAPTER XVI.
INSTRUMENTS OF PRECISION.

THE MERIDIAN CIRCLE.—The accurate registration of the positions of the
heavenly bodies is one of the most important functions of an
astronomical observatory. When the apparent places of an object at a
sufficient number of different times have been duly recorded, it becomes
possible to investigate the laws upon which its changes of position
depend, and to predict its positions at subsequent times for the benefit
of navigators and others to whom such predictions are of practical
utility. For this purpose various instruments have been devised, but in
all cases where it can be employed, the _transit circle_, or _meridian
circle_, as it is indifferently called, is generally conceded to give
the most trustworthy results.

With this instrument the observations are made when the celestial body
under observation is crossing the meridian of the place where the
instrument is set up, that is, when it “transits,” or “souths.” At this
time the accuracy of the observations is least impaired by the
ever-varying effects of atmospheric refraction.

The meridian circle consists of a refracting telescope—seldom exceeding
6 inches in aperture—which is fixed to a hollow axis at right angles to
itself, and this axis is supported horizontally in an east and west
direction, so that the telescope is only free to move in the plane of
the meridian. A large graduated circle—or frequently two such
circles—attached perpendicularly to the hollow axis, and read by
microscopes fixed to the walls or iron pillars which support the axis,
completes the essential parts of the instrument.

As the field of view of the telescope covers a considerable area, it
becomes necessary to provide some means of marking the exact point
within it which represents the meridional axis of the instrument. This
is accomplished by placing at the common focus of the object-glass and
the positive eye-piece a system of “cross wires,” consisting of
tightly-stretched spider threads, two of which are fixed horizontally
and nearly in contact, and five or seven vertically at equal distances
apart. What the observer has actually to do is to incline the telescope
at such an angle that the star is seen to traverse the space between the
two horizontal threads, and then to record the exact times, by means of
a chronograph and sidereal clock, at which the star appears to cross
each of the equidistant vertical threads. By thus making five or seven
observations and taking the average, greater accuracy is attained.

The time observations, as we have already seen, determine the right
ascension of the star under observation, while the declination is
indicated by the readings of the graduated circle, if the latter is so
placed as to read 90° when the telescope is directed to the Pole.

The ideal meridian circle is thus simplicity itself, but the mechanical
difficulties encountered in making such an instrument are insuperable.
Perfect right angles and perfect circles exist only in our minds, so
that after all the undoubted skill and care bestowed on its
construction, the actual meridian circle is only an approximation to the
ideal. Still, when the instrument is provided with levels and other
means for estimating its deviation from the meridian plane in which it
ought to move, the actual observations are capable of correction by
mathematical processes, so that the final statements of positions
sensibly represent those which would follow from the use of a perfect
instrument.

The greatest possible care is taken to secure rigidity in all parts of
the meridian circle. The hollow horizontal axis is supported on bearings
which rest either on heavy piers of iron or walls of masonry, and the
axis and telescope tube are firmly joined together at their
intersection. The bearings for the axis are turned with extreme
precision, and, to reduce the friction upon them, the pressure of the
instrument is counterpoised by an arrangement of balancing weights.

Adjustments are provided for every needful purpose. The cross wires are
fitted in a small frame which can by suitable fittings be given a small
movement in the field of view until the right place for them is found,
while the horizontality of the axis and its correct direction can be
secured by other adjusting screws.

Since most of the observations have to be made at night, the field of
view will generally be dark, and the exceedingly delicate spider lines
will be invisible unless some means of illuminating them be provided.
Usually a very tiny mirror is fixed diagonally at the intersection of
the axis and the telescope, where it is held in position by a stiff
wire. A light shining through the hollow axis is thus reflected into the
field of view, and the threads are rendered visible. The intensity of
this illumination of the field can be regulated in accordance with the
brightness of the star under observation.

The instrument having been erected, one of the first tests applied to it
is to see that it is correctly _collimated_, or, in other words, that
the optical axis of the telescope is perpendicular to the axis of
movement. For this purpose the telescope is directed to some distant
object, such as a building, and some mark which falls on the
intersection of the central spider threads is noted. The axis is then
reversed end for end by a mechanical arrangement, and the telescope
again pointed at the same object. If the mark again falls on the
intersection of the cross wires, the collimation is correct; if not, the
wires are moved with the frame containing them until the error is
corrected.

To test the horizontality of the axis, a spirit-level long enough to
stretch across the bearings, and called the “striding level,” is
provided.

Various methods are employed for adjusting the instrument so that the
telescope moves as truly as possible in the plane of the meridian.
Collimation and level being correct, the telescope will move in a
vertical plane, whatever may be the error in the direction of the
horizontal axis, and therefore any star passing through the zenith will
cross the centre of the instrument at the same moment that it crosses
the meridian. A star away from the zenith, however, will not be seen on
the cross wires when it crosses the meridian, unless the axis be truly
east and west. Hence, by taking the difference of time between the
observed transits of a star near the zenith and one a long way from the
zenith, and turning the whole instrument in azimuth until this
difference is equal to the difference of right ascensions of the two
stars, the instrument is readily placed in the meridian.

Another useful method of adjustment is to observe the upper and lower
transits of a circumpolar star. If the instrument moves truly in the
meridian, the interval between the two transits will evidently be twelve
sidereal hours.

Next, the declination circle has to be adjusted so that it reads 90°
when the telescope is directed to the celestial pole, or zero when an
equatorial star is under observation. An obvious way of doing this is to
take the readings when Polaris, or other circumpolar star, is at upper
and lower transits; the celestial pole lying midway between these
positions, the average of the two readings, when corrected for
refraction, should be 90°, and the circle would be shifted round in its
fittings until this was the case.

Such, in mere outline, are the processes by which the meridian circle is
set up. In actual practice, the greatest possible refinement is brought
to bear on the adjustments, and every precaution taken to estimate the
various errors so that due allowance may be made for them in the
reduction of the observations. It has even been shown that the heat of
the observer’s body, by affecting the lower side of the telescope tube
more than the upper, introduces sensible errors in the measures of
declination. Hence it is important to use metals of high conductivity in
the construction of meridian instruments, so that errors due to the
varying temperatures of different parts may be reduced to a minimum.

As an illustration of a modern meridian circle, we select that of the
Lick Observatory. (Fig. 53.) This instrument has an aperture of six
inches, and embodies all the improvements which have been introduced by
the Berlin firm of Repsöld & Co.

The observatory containing a meridian circle is usually a very simple
structure, as it is only necessary to provide an opening to the sky
along a north and south line. This is sufficiently provided for by a
series of narrow shutters in a building of ordinary construction.

To prevent confusion it may be pointed out that the term “transit
instrument” is frequently restricted to a meridian instrument which is
not supplied with large circles for the accurate measurement of
declinations, although it may have a small circle to assist in directing
the telescope. The use of such an instrument is evidently limited to the
determination of time and right ascension.

[Illustration:

FIG. 53.—_The Meridian Circle of the Paris Observatory._
]

THE ALTAZIMUTH.—Although the meridian circle furnishes us with the most
accurate method of determining celestial positions, its use is somewhat
restricted by the fact that it can only be employed for the observation
of objects on the meridian. It sometimes happens, however, that bodies
cannot conveniently be so observed, and other methods become necessary.
This is especially the case with the moon during the first and fourth
quarters, when it crosses the meridian in daylight, and it is then that
an instrument called the _altazimuth_ is of special value. This is
something like a transit circle in which the base supporting the piers
is made to turn on a vertical axis, so that the telescope can be
directed to any part of the heavens whatsoever. A fixed horizontal
graduated circle, read by verniers or microscopes attached to the
revolving part, gives the azimuth of the telescope when an observation
is made, and the altitude is furnished by the vertical circles. The
azimuth circle is adjusted to read zero when the telescope is pointed
due north, and the altitude circle to zero when the telescope is
horizontal. To secure the first adjustment, after correcting level and
collimation, a star may be observed before it crosses the meridian, and
again when it has exactly the same altitude after passing to the west;
midway between the two positions would be due south, and the circle
should read 180°. In adjusting the vertical circle, the telescope is
made to point downwards to a trough of mercury, and it is known that the
telescope is truly vertical when the reflected image of the cross wires
is coincident with the wires themselves; the circle should then read
90°.

From a knowledge of the sidereal time at which a celestial body has an
observed altitude and azimuth, the more useful co-ordinates of right
ascension and declination can be calculated by spherical trigonometry.

One of the largest instruments of this class has recently been erected
at Greenwich Observatory. The aperture of the telescope is 6 inches, and
the rigidity of the various parts may be gathered from the fact that the
instrument weighs something like six tons.

A _theodolite_ is a small portable form of altazimuth specially adapted
for the needs of surveyors, but occasionally employed in astronomical
work.

THE WIRE MICROMETER.—Notwithstanding that an equatorial telescope is
usually furnished with circles for estimating the positions of objects
observed, or to serve as a guide in directing the telescope to objects
of known position, it is not entitled to be called an instrument of
precision in the sense we are now considering. The provision for driving
by clock-work and other causes are antagonistic to constancy of
adjustment, and hence determinations of positions by the circles alone
might be many seconds in error. Most large telescopes, however, are
provided with some form of micrometer which not only serves for the
measurement of planets, lunar craters, and the like, but may also be
used to measure the angular separation of adjacent stars. In this way,
by making a “triangulation” of stars visible in the field of view, and
including at least two which have had their precise positions determined
by the meridian circle, the positions of objects can be measured with
great accuracy.

This method is especially valuable in the case of comets, which may
cross the meridian in daylight, and are often too dim to be seen with
the altazimuth.

Several forms of micrometers are in use, but the so-called _wire_ or
_filar micrometer_ is most commonly seen in our observatories. The
essential parts are very similar to those of the reading microscope (p.
172). Two parallel spider threads are so arranged on sliding frames that
they may be brought into coincidence, or separated, by means of very
finely-cut screws. Perpendicular to these are two fixed threads almost
close together. The system of “wires” is viewed by a positive eye-piece,
and the whole is attached to a draw tube so that it may be placed in
position at the eye end of the telescope. In order that the wires and
telescopic images may be sharply defined at the same time, the plane of
the wires must be at the principal focus of the object-glass. The screws
are provided with large heads which are graduated so as to show the
hundredth of a revolution, and counting wheels register the numbers of
complete turns.

Matters are so arranged that when both counting wheels indicate zero,
the spider threads are coincident. Then, supposing one of the screws be
turned through a revolution, the threads will be separated by a definite
amount; an equal and opposite movement of the other screw will double
the separation, and in all cases the distance between the threads will
be registered in turns, and fractions of turns of the screws.

The next proceeding is to ascertain what is called the “value,” in
angular measure, of the micrometer screw. This value will evidently
depend upon the pitch of the screw and the focal length of the telescope
to which the micrometer is applied, so that measurements merely stated
in terms of revolutions of the screw would serve no useful purpose. It
can easily be calculated that the images of two stars which are 28′ 39″
apart will be separated by an inch at the focus of a telescope of 10
feet focal length; then, if the screws have 100 threads to the inch, the
angular separation of the wires corresponding to a single revolution
will be one-hundredth part of 28′ 39″, that is, 17″·15, and the latter
would be the value of that particular micrometer when used with the
telescope in question. If the focal length of the telescopic
object-glass were 20 feet, the linear separation of the images of two
such stars as we have considered would be 2 inches, and the value would
therefore be halved, so that measures of twice the accuracy would be
possible. Since the stellar images and the cross wires are equally
magnified by the eye-piece, the value of the screw is in no way affected
by using eye-pieces of different powers.

In practice it is necessary to determine the value of the micrometer
screw by actual measurement. For this purpose, the wires are separated
by a known number of revolutions, say twenty, and the micrometer is
adjusted so that a star of known declination travels exactly between the
two fixed wires when the telescope remains at rest. With the telescope
still fixed, the number of seconds required by the image of the star to
traverse the distance between the separated wires is noted, and knowing
the angle through which the star must have moved in that interval, the
angular value of one turn of the screw is at once deduced. For work of
extreme precision each individual turn of the screw must be separately
evaluated, and allowances must also be made for changes of temperature.

When measuring the apparent diameter of a planet, the two threads are
separated until the image just lies between them, and the sum of the
readings of the two screws multiplied by the angular value of one turn
gives the diameter in seconds of arc. The distance having been formed by
other observations, the diameter of the planet in miles can be
determined in the manner to which reference has already been made (p.
142).

[Illustration:

FIG. 54.—_The Micrometer applied to a Binary Star: a b, Fixed Threads;
c d, e f, Movable Threads; s s, Components of Binary Star._
]

One of the most important applications of the micrometer is in the
measurement of double and binary stars. In this case the fixed threads
are made to enclose the two stars, and the movable threads are made to
bisect the star-images. (Fig. 54.)

THE POSITION CIRCLE.—It is frequently necessary to be able to specify a
direction, as in the case of a planet’s equator, or the line joining the
components of a double star. Such directions are expressed by “position
angle,” which may be defined as the angle from the north point, reckoned
from 0° to 360° through east, south, and west. For these observations, a
_position circle_ is usually attached to the micrometer. This is a
circle graduated from 0° to 360°, which can remain fixed in position as
regards the telescope, while the part containing the wires and
micrometer screws can be rotated by means of a rack and pinion. A
vernier attached to the movable frame indicates the required angles.

To adjust the position circle the vernier is set to zero, and the
telescope directed to a star; the circle and micrometer are then
together turned round until the diurnal movement of the star, which is
east and west, makes its image to traverse the space between the fixed
wires. The movable threads will then lie in a north and south direction.
The circle remains in this position during subsequent observations,
while the micrometer is rotated until the movable threads are in the
required direction, the position angle then being read off on the
circle.

THE HELIOMETER.—Another means of measuring small angles for astronomical
purposes is afforded by the instrument called the _heliometer_, which,
as the name will at once suggest, was invented for measurements of the
sun. This instrument is a telescope mounted equatorially, but differs
from the ordinary telescope, inasmuch as the object-glass is cut across
the centre, and means are provided for separating the two halves by
moving one or both parts in the direction of the line of bisection, and
also for measuring the amount of displacement. The cell containing this
somewhat peculiar object-glass can be rotated so that the line of
division of the lens may be placed in the same direction as the line
representing the distance to be measured.

The action of the instrument depends upon the fact that any small part
of a lens is competent to form a complete image of a celestial body, so
that when an object-glass is bisected, and the two halves separated
laterally, two distinct images will be produced, each differing only
from the image formed by the complete lens in being less bright.

To measure the distance from a star to a planet, let us say, as in
observations of the parallax of Mars, the lenses are separated to such
an extent that the image of the star formed by one half, coincides with
that of the planet formed by the other half, and the amount of
separation noted. As a check, the measurement is repeated with the
lenses separated in the opposite direction. The angular value
corresponding to a known separation of the semi-lenses being determined,
just as in the case of the micrometer screw, the angle between star and
planet at once follows. Angles ranging from a few minutes to about two
degrees can be measured in this way with great accuracy.

In the hands of Dr. Gill, of the Cape Observatory, the heliometer has
yielded very valuable results in connection with the distances of the
sun and stars.

OTHER INSTRUMENTS.—There are other instruments which may fairly be
classed as instruments of precision, but space permits little more than
a mention of their names.

The _zenith telescope_ is a telescope specially designed for the
measurement of the angular distances of stars from the zenith, for
precise determinations of latitude by Talcott’s method.

The _prime vertical instrument_ is nothing more than a transit
instrument, so arranged that the observing telescope swings in a
vertical plane which is perpendicular to the plane of the meridian. From
the observed times at which a star passes the prime vertical on the
eastern and western sides, the latitude of the place of observation can
be ascertained with great accuracy.

It is perhaps at sea that the labours of astronomers are of most direct
value in everyday affairs, and it is precisely here that the instruments
of high precision cannot be employed, in consequence of the absence of
firm supports. Nevertheless, there is one instrument—_the sextant_—which
yields results that satisfy all requirements when carefully constructed
and placed in good hands. A graduated arc extending over about 60° (from
which the name is derived) is supported by a light framework, and
pivoted truly on the centre of the arc is the radius bar, or index arm,
which carries a vernier for reading off the angles to be measured. A
plane mirror is fixed to the index arm, over the centre of movement, and
another, of which only half is silvered, is fixed to the frame near its
outer edge. A small telescope parallel to the surface of the frame is
directed towards the fixed mirror, so that the continuation of its axis
is in line with the boundary between the silvered and clear part of the
glass. Thus, while one object may be seen by direct observation through
the clear glass, another, in quite a different direction, may be seen
after reflection from the surfaces of the two mirrors.

The sextant is chiefly used for measuring the altitude of the sun, about
noon for the determination of latitude, and in the morning or evening
for the correction of chronometers. In such observations, the sextant is
held in the right hand, with its plane vertical, and the sea horizon is
sighted directly with the telescope; the index arm is then moved until
the reflected image of the sun is brought into coincidence with the
horizon. The reading is then taken, and if the adjustment is such that
zero is indicated when the reflected and direct images of the same
object are observed, it will give the altitude. The actual angle
recorded by the sextant is only half that between the objects observed,
but by numbering half degrees as whole ones, the true angles are read
off directly. For observations of the sun the instrument is provided
with coloured glasses of different shades, attached so that they can
readily be interposed to reduce the intensity of the light.

CHAPTER XVII.
ASTROPHYSICAL INSTRUMENTS.

So far we have been concerned with instruments which enable us to
ascertain the positions, dimensions, and appearances of the various
orders of heavenly bodies; but we can go further than this, and learn
something of the physical and chemical constitutions of the glittering
orbs by which we are surrounded. We can, for instance, bring
instrumental aid to bear upon the determination of the brightnesses of
the heavenly bodies, and by means of that powerful appliance of modern
astronomy—the spectroscope—we can study the chemistry of all those
bodies which shine by light of their own, and which are not so feebly
luminous as to be out of our range.

PHOTOMETRY.—The naked eye was alone employed in observations of stellar
brightness until quite recently. Each step in the advance of
astronomical research, as in most other branches of science, however,
depends upon the greater precision of observation which can be
introduced, and so we now find the eye to be assisted in these inquiries
by a _photometer_ of some kind or other. The general purpose of
photometry will be familiar to all in connection with such practical
matters as the determination of the illuminating power of coal gas. The
methods here employed, however, are not directly applicable to the
comparatively feeble light-sources which have usually to be dealt with
in astronomical photometry.

As will be more fully explained in another part of this work, the stars
visible to the naked eye are divided into six grades of magnitude. The
brightest of them are classed as first magnitude, while those only just
visible to the naked eye are of the sixth magnitude. Now that telescopes
are used, this division of stars into magnitudes must be continued in
some form or other, so as to include telescopic stars. From photometric
comparisons it has been ascertained that the average star of the first
magnitude may conveniently be reckoned 100 times as bright as a sixth
magnitude star. Hence, the light-ratio corresponding to a difference of
a single magnitude is 2·5. Thus, a star which is 2½ times less bright
than one of the sixth magnitude ranks as seventh magnitude, and so on.
Fractions of magnitudes are also necessary to express the results which
can now be obtained.

LIMITING APERTURES.—For the reason that a large telescope enables us to
see stars which are too dim to be visible in a smaller one, the
brightnesses of stars may be compared with more or less satisfactory
results by reducing the aperture of a telescope until the star in
question ceases to be visible. This is called the method of _limiting
apertures_, and in practice a telescope intended for this work would be
provided with a series of diaphragms, or other arrangement for
conveniently reducing the effective area of its object-glass. A
telescope which has an object-glass 10 inches in diameter should just
show stars of the fourteenth magnitude under favourable conditions; a
star which could just be seen when this aperture was reduced to an inch
would be of the ninth magnitude, and so on.

There are numerous reasons why this method fails to give satisfactory
results, but one of the most important is that the image of a star
becomes more diffuse with each reduction in the aperture of the
telescope. At best it must evidently fail for a comparison of stars
which are visible to the naked eye.

WEDGE PHOTOMETER.—One of the simplest and best methods of estimating
star magnitudes is afforded by the _wedge photometer_. This is a strip
of neutral-tinted glass about six inches in length, and a quarter to
half an inch deep, tapering from one end to the other, so as to present
a gradual reduction in depth of tint from the thick to the thin end. A
similar wedge of clear glass, tapering the opposite way, is cemented to
this, in order to get rid of prismatic action. Compensated in this way,
and mounted in a suitable frame, the wedge is placed in front of the
eye-piece of a telescope, and is pushed along until the star under
examination is just extinguished. A scale is then read off, and from the
results of a previous evaluation of the wedge in the laboratory, the
corresponding star magnitude is easily deduced.

In order to eliminate the effects of differences in the state of the
sky, the position of the wedge at which a standard star, such as
Polaris, ceases to be visible, is determined, and then it is the
difference of wedge readings upon which the final calculation is based.

The great value of the wedge in stellar photometry was demonstrated by
the labours of the late Prof. Pritchard, to whom we owe the catalogue of
the magnitudes of naked eye stars in the northern hemisphere known to
the astronomical world as the “Uranometria Nova Oxoniensis.”

OTHER PHOTOMETERS.—Some photometers depend for their action upon
comparisons with terrestrial sources of light. In some cases, an
artificial star, consisting of a pinhole illuminated by a standard lamp,
is brought into the same field of view as the star to be compared, and
then, by polarising apparatus, the brightnesses of the two images are
equalised. The amount of reduction of either of the stars is determined
by a scale which measures the rotation of the polariscope, and in this
way all the stars are compared with an artificial star of known
brightness.

One of the most notable achievements in this field of astronomical work
is that of Professor Pickering of the Harvard College Observatory, who
invented and made splendid use of the so-called _meridian photometer_.
Here the telescope has two object-glasses of equal aperture side by
side, and in front of each is a silvered flat mirror inclined at an
angle of 45° to the optic axes. The telescope is supported in an east
and west direction, so that one mirror reflects the Pole Star into its
object-glass, while the other can be rotated so as to reflect any other
star which is on the meridian into the second object-glass. Again, by a
polariscope at the eye end of the telescope the images of the two stars
are made of equal brightness, and the readings give the data for
calculating the required magnitude.

Photographs of the stars are also largely employed for the estimation of
magnitudes, stars of different magnitudes being represented on the
photographs by spurious discs of different sizes. If all stars gave out
light of the same quality, the photographic method would be very
trustworthy, but as the colours of the stars vary, the photographic and
visual magnitudes are not invariably in agreement A bright, reddish
star, such as Betelgeuse, would photographically be only equivalent to a
white star which was much less bright to the naked eye.

THE PRISMATIC SPECTROSCOPE.—Reference has already been made in these
pages to the wonderful field of astronomical research which has been
opened up by the discovery of the action of a triangular glass prism
upon rays of light, and the subsequent improvements in the method of
utilising this effect.

A prismatic spectroscope may be regarded as an arrangement which will
enable us to get a pure spectrum, and to observe it to the best
advantage. The light to be analysed is admitted through a narrow
aperture called the _slit_, which is placed at the focus of a double
convex lens. Emerging from this _collimator_, as a parallel beam, the
rays pass through the prism, and after deviation and dispersion they
fall upon another double convex lens, which brings them to a focus in
the form of a spectrum. An eye-piece may then be employed to view the
spectrum, or a sensitive plate may be placed at the focus to photograph
it.

In a simple form of spectroscope the prism is supported at the centre of
a graduated circular plate, to which the collimator is firmly fixed,
while the observing telescope is attached to an arm pivoted at the
centre of the plate. A vernier moving with the telescope indicates the
position, on a scale of degrees, of any colour brought to the centre of
the field of view.

The best results are obtained when the rays of light emerge from the
prism at the same angle at which they enter it, in which case the prism
is said to be at _minimum deviation_, for the reason that the deflection
of the rays from their original path is then the least possible. As
lights of different colours are refracted unequally, it is clear that
the prism can only be at minimum deviation for rays of one particular
colour at any instant. Frequently, however, there is an automatic
arrangement by which, as the observing telescope is moved so as to bring
different colours into the field of view, the prism is turned so as to
be at minimum deviation for the colour actually under observation.

The appearances observed in the spectroscope are a series of images of
the aperture through which the light is admitted. If the source of light
be yellow, such as that of a spirit lamp flame when common salt is
introduced, a yellow image of the aperture will be seen, and so on for
other monochromatic radiations. When a white light is observed, images
of every gradation of colour are formed, and in such a “continuous
spectrum” the separate images cannot be recognised. The form of aperture
most widely adopted is a narrow straight slit with parallel sides. In
this case there is the least possible confusion, because the several
images of the slit appear as so many spectrum “lines.”

For observations of the sun, where the light is so intense, a great
number of prisms, each drawing out the spectrum into a longer band, may
be employed, so that the lines of the spectrum may be widely separated,
and the peculiarities of each more closely investigated. For the fainter
bodies, however, the instrument must generally be one of comparatively
small dispersion, so that the light may not be spread out into
invisibility. It will be evident that the longer the spectrum the
greater will be the chances of accurate measurements.

Another way of obtaining great dispersion is to use prisms of the new
dense Jena glass, one of which is equal to three or four of the flint
glass prisms in general use.

There are various forms of the prismatic spectroscope. In some of them
reflecting prisms are introduced to turn the rays back through the
dispersive train, so as to get increased dispersion without increasing
the number of prisms. In the so-called _direct vision spectroscope_,
prisms of different kinds of glass are combined so that the rays of
light leave them in nearly the same direction that they enter. Here the
collimator and observing telescope are in the same straight line, and
this is a great convenience in certain classes of observation.

THE GRATING SPECTROSCOPE.—Sometimes, especially in instruments designed
for solar observations, the prisms are replaced by what is called a
diffraction grating. Usually this consists of a piece of highly polished
speculum metal, upon which is ruled a great number of equidistant
parallel scratches or lines. A portion of the light falling upon the
grating is simply reflected, while the remainder is spread out into two
series of beautiful spectra, one on each side of the directly reflected
beam. The two nearest to the directly reflected beam are called spectra
of the first order, while following these are spectra of the second,
third, and fourth orders; the length of spectrum increasing in each
case, and all being available for observation if the light dealt with be
sufficiently bright. The production of these spectra is due to the
interference of light waves.

All gratings produce exactly similar spectra, so that the distances
between identical lines as seen with one grating are always strictly
proportional to their distances as seen with any other. With prisms, the
relative separation of colours is by no means constant; a prism made of
one kind of glass may, for example, separate the green and yellow more
than another prism made from different material, while the separation of
yellow and red might be the same in both cases. The grating spectrum
accordingly affords a constant standard of reference, and what is called
the “normal solar spectrum” is the spectrum of the sun mapped with the
various dark lines in the relative positions shown by a grating
spectroscope.

Prof. Rowland, of John Hopkins University, has introduced a form of
grating spectroscope, in which the grating is ruled on a concave
spherical surface of speculum metal. After passing through the slit the
rays of light fall directly upon this concave surface, and are brought
to a focus after reflection, so that no lens except the eye-piece used
for visual observations is required. Several of these gratings, having
mostly a radius of curvature of about 21 feet, and a ruled surface of
about 5½ inches x 2 inches, with 20,000 lines to the inch, are in use at
the present time. Some idea of the difficulties to be faced in making
these magnificent aids to research maybe gathered from the following
remarks of Mr. J. S. Ames:—“It takes months to make a perfect screw for
the ruling engine, but a year may easily be spent in search of a
suitable diamond point.... When all goes well it takes five days and
nights to rule a 6 inch grating having 20,000 lines to the inch.
Comparatively no difficulty is found in ruling 14,000 lines to the
inch.”

With the aid of these wonderful gratings, the solar spectrum can be
photographed with perfect definition, and extending over a total length
of several yards. Thousands of the tell-tale Fraunhofer lines are
rendered visible in this way.

MEASUREMENT OF SPECTRA.—The spectra of many substances, including
hydrogen and iron, are so characteristic as to be recognisable at a
glance by an experienced observer, but one must as a rule resort to
measurement for the identification of lines, or for the purpose of
locating unknown lines for future reference. One of the simplest methods
of measurement is that of reading the position of the observing
telescope upon a graduated circle, when the line is seen at the centre
of the field. If supplemented by a micrometer eye-piece, for
differential measures with regard to known spectra, this method is
extremely convenient. As recorded on arbitrary scales of this character,
the position of the same line would be represented by a number which
would be different for every instrument, and it is therefore necessary
to reduce all measurements to a common scale; that now universally
adopted is the natural one of wave-lengths. The position of a line in
the spectrum depends upon the length of the waves constituting the rays
of light which produce it, so that a measure of wave-length completely
specifies the situation of a line whatever spectroscope maybe employed.
Light waves are excessively minute, but by the use of the diffraction
grating they can be measured with great accuracy. So small are they,
that the most convenient unit of wave-length is the ten-millionth part
of a millimetre[5]—or tenth metre, as it is technically named. Expressed
in this way, the wave-length of the glorious red line seen in the
spectrum of hydrogen is 6563·07, while that of the blue line
characteristic of the same gas is 4861·51.

When the positions of a certain number of lines of known wave-length
have been read off on the scale of any spectroscope, the required
wave-lengths of other lines are ascertained by a graphical
interpolation, or by calculation. Elaborate tables of the wave-lengths
of the lines in the spectra of the sun and chemical elements have been
prepared by various investigators, and these are in constant demand by
all workers in the field of astrophysics.

THE TELESPECTROSCOPE.—For the examination of the spectra of the heavenly
bodies, a spectroscope is attached to the eye end of a telescope from
which the eye-piece has been removed, such a combination forming a
_telespectroscope_. The slit is placed at the principal focus of the
object-glass of the main telescope, and an image of the object to be
observed is thus produced upon it. If the sun be under observation, any
special part of it, such as a sun-spot or the chromosphere, may be
separately investigated by bringing the corresponding part of the image
upon the slit.

In the case of the sun, moon, comets, planets, or nebulæ, the image is
one of sensible size and the spectrum lines have a perceptible length.
With a star, however, the image is only an illuminated dot upon the
slit, and the spectrum would have no appreciable breadth, so that all
but the strongest lines would in general fail to show themselves.
Accordingly, when observing star spectra, a cylindrical lens is placed
in front of the slit, so that the stellar image is drawn out into a
bright line, and the necessary breadth of spectrum and length of the
spectrum lines are secured.

For photographing the spectra of the heavenly bodies it is simply
necessary to replace the eye-piece by a small camera, and to expose a
sensitive plate for a length of time dependent on the brightness of the
spectrum. The spectrum of a terrestrial substance, such as hydrogen or
iron, photographed in juxtaposition, is always a great convenience, and
is essential for the investigation of stellar movements by the
displacement of spectrum lines.

THE LICK STAR SPECTROSCOPE.—Among the most complete and perfect
spectroscopes adapted for use with the telescope is that designed by
Prof. Keeler for the great refractor of the Lick Observatory. It is
illustrated in Fig. 55, and it will be at once evident that there are
ample means for keeping the instrument under control. Towards the upper
part of the diagram, on the left, is the eye end of the telescope,
without the eye-piece. Two stout brass rods 3 inches in diameter and 6
feet long are attached by clamps to a revolving jacket which surrounds
the end of the telescope tube, and on these the spectroscope is
supported by clamps which allow of it being moved inwards or outwards
from the focus of the telescope. The collimator of the spectroscope lies
midway between the rods, and in order to facilitate the focussing of the
image upon the slit, it has a small longitudinal movement independently
of that of the whole spectroscope. The observing telescope is seen on
the left of the diagram, while the grating rests on the circular
graduated plate over which the observing telescope can be moved. The
grating has 14,438 lines to the inch.

Three prisms can also be used with the spectroscope, two of them being
single prisms of 30° and 60° refracting angles respectively, and the
third a compound prism giving a very high dispersion. Two observing
telescopes are provided, one being of extra power for use with the
grating in solar spectroscopy

The instrument is generously supplied with the small refinements which
contribute so largely to easy and successful manipulation. Among these
are a diagonal eye-piece for viewing the image of the object on the slit
plate, electrical illumination of the graduated scale and wires of the
micrometer eye-piece, and an automatic arrangement for keeping the
prisms at minimum deviation.

There is a small totally-reflecting prism covering half of the slit, by
which the light from an electric spark, or other source of luminosity,
can be made to pass through the spectroscope so as to produce a series
of known reference lines which serve as so many mile-posts for the
measurement of the spectrum of the celestial body under observation. The
induction coil, seen to the right of the diagram, is for the purpose of
producing these electrical sparks.

In mounting the spectroscope, which weighs no less than 200 pounds, the
eye end of the great telescope tube is first supported by a prop, and
the long rods are inserted. The spectroscope is then placed on the rods,
and balancing weights equivalent to the weight of the spectroscope are
removed from the lower part of the telescope tube.

[Illustration:

FIG. 55.—_The Spectroscope adapted to the Eye End of the Lick
Telescope._
]

THE OBJECTIVE PRISM.—It is a very remarkable fact that many of the
recent advances in our knowledge of the spectra of stars have followed
from the revival of a method first employed by Fraunhofer in 1814, in
which the slit and collimating lens, forming part of an ordinary
spectroscope, are dispensed with. The rays coming from a star being
already parallel, and the star itself being a virtual slit without
length, a large prism placed in front of the object-glass of a telescope
makes a complete stellar spectroscope. A prism employed in this way is
known as an _objective prism_.

In place of the image of a star, which would be seen in the absence of
the prism, a spectrum without appreciable width appears at the focus of
the telescope, and the spectrum lines will be represented by mere dots.
To turn these dots into lines so that they may be better visible, a
cylindrical lens must be employed in conjunction with the eye-piece.

It is to the application of photography, however, that we owe so much,
and in this case the cylindrical lens is removed, while a small camera
replaces the eye-piece of the telescope. In this form the instrument is
often called a _prismatic camera_.

The prism is so arranged that the spectrum lies along the meridian
passing through the star, and it is then only necessary to allow the
driving clock to be slightly in error in order that the spectrum may
trail a short distance perpendicular to its own length, and in this way
broaden the photographed spectrum. On the proper regulation of the clock
rate, and consequent “trail” of the spectrum across the plate parallel
to itself, depends very largely the success of the photograph obtained.
The spectrum of a bright star must obviously be made to travel more
quickly than that of a fainter one, and a short exposure suffices. For
the same clock rate, and in the same time, a star near the Pole will
give a shorter trail than one nearer the Equator, and declination must
therefore be taken into account in adjusting the clock error for this
method of photography.

One great advantage of the objective prism in the photography of stellar
spectra depends upon the fact that all the light passing through the
object-glass is utilised in the production of the spectrum, whereas in
an ordinary telespectroscope a large percentage of the light is lost in
the jaws of the slit. The large focal length of the telescope also
enables a long spectrum to be obtained even with a single prism of small
angle.

When the dispersion is only small, the spectra of stars as faint as the
tenth or eleventh magnitude can be photographed by this method, so that
sometimes as many as 200 spectra are registered with a single exposure.
Here, again, the objective prism has an immense advantage over the
telespectroscope.

Professor Pickering, of Harvard College, was among the first to
recognise the value of the objective prism for the photography of
stellar spectra, and the munificent endowment of this research, by Mrs.
Draper, as a memorial to Dr. Henry Draper, has enabled him to produce
the Draper catalogue of stellar spectra, giving the chief
characteristics of the spectra of over 10,000 stars.

Professor Norman Lockyer, at South Kensington, has also been
conspicuously successful in this department of astrophysical research.
The chief instrument he employs is a photographic telescope of only six
inches aperture, with an objective prism of 45° refracting angle. The
spectra thus obtained show hundreds of lines in such stars as Arcturus,
with very fine definition, so that they bear almost unlimited
enlargement.

An objective prism of twenty-four inches aperture will form one of the
accessories of the fine telescope which is now being erected at the
expense of Dr. Frank McClean, for the Cape Observatory, and there can be
no doubt that the use of this gigantic prism will add greatly to our
knowledge of the chemistry of the fainter stars.

As yet there is no very practicable method of employing the objective
prism for determining the velocities of stars in the line of sight from
the displacement of spectrum lines, and herein lies its one great
disadvantage as compared with the telespectroscope. The difficulty is to
ensure that the spectrum always falls absolutely in the same position
with respect to the terrestrial spectrum, which must be photographed
alongside for purposes of measurements. It is true that the spectrum of
an approaching star is somewhat shorter, and of a receding star slightly
longer than that of one at rest relatively to the observer, but these
changes are so small as to little more than indicate the direction of
movement even when a large instrument is employed.

Under the direction of Professor Norman Lockyer, the objective prism was
very successfully used for photographing the spectra of the solar
surroundings during the total eclipses of 1893 and 1896. In place of the
picture of the solar corona, which would appear in the absence of the
prism, the prismatic camera shows a spectrum consisting of bright rings.
If, for instance, the corona were wholly composed of hydrogen, there
would be a picture of it in red, blue-green, blue, and violet,
corresponding to the lines ordinarily seen in the spectrum of that gas.
These rings thus indicate the chemical nature of the corona, and at the
same time show, by their differing forms, the distribution of different
gases throughout its extent. The spectra of the solar prominences and
chromosphere are also depicted during the brief time of their
visibility, during an eclipse, with such distinctness that a series of
“snap shots” is all that is required to give a lasting record.

THE SPECTROHELIOGRAPH.—A special form of spectroscope—called the
_spectroheliograph_—has been devised by Prof. Hale, of Chicago, for
photographing the sun in monochromatic light. It consists of a
spectroscope, arranged for photography, in which the slit can be made to
travel by clock-work across the sun’s image, which is projected upon it
by the telescope to which the instrument is attached. In front of the
photographic plate there is a secondary slit, so that only a very
restricted part of the spectrum reaches the sensitive film. The
secondary slit is connected by mechanism with the primary one, so that
as the latter traverses the sun’s image, the former exposes different
parts of the photographic plate to the light which passes through it,
and in this way builds up an image of the sun in monochromatic light,
matters being so arranged that light of the same wave-length always
falls upon the secondary slit. By utilising the brightest lines which
appear in the spectrum of the solar prominences, monochromatic images of
those interesting appendages to our luminary have been successfully
photographed without waiting for a total solar eclipse.

THE BOLOMETER.—Besides the luminous effects of the spectrum, there are
heating effects which can be measured by the _bolometer_, an instrument
invented by Prof. Langley. A very thin strip of metal is connected with
a delicate galvanometer, and is arranged so that it can be passed a long
the whole spectrum. The electrical resistance of the strip varies
according to its temperature, and the galvanometer at once signals any
fluctuations which may occur. If, for instance, the strip comes to the
place occupied by a dark line, there will be a notable fall of
temperature. In this way, the bolometer is used to map the solar
spectrum in the “infra-red” region—a part of the spectrum invisible to
the eye, and of which we should otherwise have remained in ignorance.

ASTRONOMY

[Illustration:

DONATI’S COMET, OCTOBER 9, 1858. (FROM LANGLEY’S “NEW ASTRONOMY”.)
]

SECTION III.—THE SOLAR SYSTEM.

BY AGNES M. CLERKE.

CHAPTER I.
THE SOLAR SYSTEM AS A WHOLE.

The solar system consists of one supereminent body, with a train of
miscellaneous attendants. By its immense gravitative power, their
movements are so governed that they not only revolve round it as a
common centre, but accompany its march through space; they are, in
various degrees, warmed and enlightened by its copious emissions of heat
and light; they are linked with it by origin and destiny. Some, indeed,
much more closely than others. Planets, satellites, and asteroids belong
to the immediate family of the sun; periodical comets and revolving
meteoric rings have been adopted into it. The planets are eight in
number; the six nearest the sun—Mercury, Venus, the Earth, Mars,
Jupiter, and Saturn—have been known immemorially; Uranus and Neptune
were discovered respectively in 1781 and 1846. Mercury, Venus, and Mars
form, with the Earth, a group of “terrestrial planets,” so-called
because they differ not very greatly in scale from our globe, and are
constructed on nearly the same lines. The outer quartette of planets are
giants by comparison, and show obvious symptoms of being in a very
different physical condition. And it is noteworthy that the zone of
asteroids, lying between Mars and Jupiter, divides the planetary
classes.

The asteroids are sometimes designated minor planets; but the former
term is preferable, as accentuating their distinctive character. For
they are not simply diminutive planets. A planet revolves in solitary
state within its own broad domain. The asteroids traverse intercrossing
and entangled paths, indefinitely numerous, ranging widely in celestial
latitude, and covering with their network nearly the entire chasm of
space between Mars and Jupiter. The small bodies moving in them have
doubtless been formed in a manner totally different from that by which
the single body they seem to replace would have taken shape.

Satellites bear in many respects the same relation to planets that
planets bear to the sun. They are united with them into secondary
systems, one of which is particularly well known to us, since it is
constituted by the earth and the moon. The existence of twenty-one
satellites has been ascertained, and many more possibly remain to be
detected. Their apportionment is singularly unequal. Only three of the
twenty one belong to the four small interior planets, while eighteen are
attached to the four exterior giants. Moreover, both Mercury and Venus
are solitary; so that the solar neighbourhood appears to be a region
unpropitious to the development of subordinate systems.

Seventeen comets certainly, and many more probably, are domiciled in the
solar kingdom. And even these preserve traces of an alien origin. They
revolve round the sun in closed orbits, and are hence periodical in
their apparitions; but their periodicity has to be qualified by a saving
clause. They come up to time _barring accidents_. For their orbits, not
being adjusted to stability, are liable to violent changes through the
influence of the powerful masses, the tracks of which they intersect. In
running up to, or back from perihelion, comets have to cross many
railroads, so to speak, and do not always escape disturbing or
destructive encounters with passing trains. Thus, many are entered in
our astronomical visitor’s book as lost or strayed. Halley’s is the only
well-secured cometary prisoner of the sun of imposing magnitude; the
rest are of little spectacular, although of very high theoretic,
interest. Comets are the only self-luminous members of the solar system.

Meteorites, besides being intrinsically obscure, reflect, owing to their
minuteness, so little sunlight that they remain invisible until ignited
in our atmosphere. They travel round the sun in annular systems, each
mote-like component of which pursues its way, independently of the
others, under the strict regimen of gravitational law. The number of
these meteoric rings must be prodigious. Some hundreds have been brought
to our acquaintance, which can only include such as cut the earth’s
orbit; and these must be an insignificant fraction of the whole. The
innumerable closely-related orbits grouped into each ring are
ill-regulated for the safety of the bodies moving in them, since they
conform in no way to the rules of planetary circulation. Hence the
numerous encounters with the earth announced by the luminous trails of
shooting stars.

Our system, as at present known, is 5,585 millions of miles in diameter.
It is limited by the orbit of Neptune. But no less than three
trans-Neptunian planets have been, on some show of evidence, alleged to
exist. One of them, held by Professor Todd of Amherst College, U.S., to
be responsible for some outstanding perturbations of Uranus, was placed
by him in 1877 at a distance from the sun fifty-two times that of the
earth (the radius of Neptune’s orbit being measured by thirty of the
same units); the two others, called into existence by Professor Forbes
of Edinburgh in 1880, to account for the formation of two groups of
comets with aphelia respectively at one hundred, and three hundred
astronomical units, were believed to occupy those enormously remote
positions. Although none of the three, in spite of telescopic and
photographic search, has yet been found, the possibility is not excluded
that the appearance on a long-exposed sensitive plate of a line in lieu
of a dot as the representative of a seeming star, may in the future
announce the annexation by the sun of a further immense slice of
territory out in the depths of space. The boundaries of our system are
thus only provisionally fixed.

Intra-Mercurian planets have proved equally recalcitrant to
prediction; and it may safely be said that no globe of the superficial
dimensions of an English county lies concealed in the comparatively
narrow space available for its circulation. The necessity for the
presence of “Vulcan” was deduced by Leverrier from an unexplained
displacement of Mercury’s perihelion, and a transit of the required
body, supposed to have been observed March 26, 1859, was thereupon, in
all good faith, brought forward by Dr. Lescarbault of Orgères. Another
pseudo-discovery—this time of a pair of Vulcans—was made during the
total eclipse of July 29, 1878; but neither on nor off the sun has the
body needed to satisfy the French mathematician’s theory been
genuinely seen, and few believe that it will ever be forthcoming.

Professor Titius of Wittenberg pointed out in 1772 that the relative
distances of the planets from the sun could be expressed by adding 4 to
the series 0, 3, 6, 12, 24, 48, etc. Thus, if the distance of Mercury
were called 4, those of Venus, the Earth, Mars, and so on, would
severally be 7, 10, 16. The validity of this relation—known as “Bode’s
Law”—was strengthened by the conformity to it of Uranus and Ceres,
neither of which had been discovered when it was enunciated; Neptune,
however, proved to be much nearer to the sun than he should have been,
and the formula hence ranks as an empirical one, not grounded in the
nature of things.

Yet the grand outlines of the solar system are traced on a visibly
symmetrical plan. The larger bodies composing it move nearly in the same
plane, in orbits nearly circular, and at regulated intervals, augmenting
rapidly outward. All revolve from west to east, or “counter clockwise,”
and this fundamental current of motion carries with it, besides the
asteroids, all the periodical comets, save Halley’s. Among secondary
systems only the Uranian and Neptunian escape from its sway; there being
a visible tendency towards deviations from rule towards the confines of
the solar domain. These deviations, however, are not of a subversive
character.

The planetary machine may continue working forever without a hitch. Such
irregularities as would be likely to throw it out of gear are found only
in parts of almost evanescent mass and negligeable influence. Two modes
of action which should, in the long run, bring about a collapse, are
non-existent or insensible. These destructive agencies are a resisting
medium, and the progressive transmission of gravity. The presence of
either should prove fatal in the same ultimate fashion. Along slowly
narrowing tracks, the planets would descend, one after the other, into
the ample lap of the sun. Their circulation is, however, to the best of
our present knowledge, unimpeded and undeflected; the disturbances
affecting it are self-compensatory.

But while the mechanical stability of the system is assured, its
physical state is continually changing. And the change is always in the
same direction. A degradation of energy steadily progresses. The sun is,
in fact, spending his capital, and even with a millionaire of his stamp
this cannot last. The time must come, if science is to be believed, when
his radiative powers will have become exhausted. Five millions of years
hence they will, in all probability, be much less efficacious than they
are now. Within twice or thrice that interval they may have become
almost extinct.

Planetary globes, too, grow old through the wasting of their internal
heat. The moon seems in a measure to prefigure the future condition of
all, should their decay not be arrested. Possibly the lunar stage is not
the last. Death may, in the long ages to come, be succeeded by
disintegration, when a ring of rubbish will be substituted for our
“wan-faced” companion. To what purpose, then, our readers will ask, the
mechanical perfections of a system destined eventually to be involved in
darkness and destruction? To what purpose its exquisite balance, the
nicely-adjusted relations of its members, its self-righting faculty, its
compensatory springs? We can reply only by recalling that the extreme
conclusions of science are invariably pessimistic, because they are
reached without taking any account of the intelligent control
perpetually, though insensibly, overruling the workings of blind forces.
If, in one sense, heaven and earth pass away, we still know that, in
good time, “a new heaven and a new earth” shall inscrutably arise. Not
“faintly,” then, but boldly and ardently, we “trust the larger hope”
that renovation will succeed, or anticipate subversion.

Whatever _can_ have an end _must_ have had a beginning, and the origins
of things have an especial fascination for our minds. As regards the
history of the planetary world, we are not altogether in the dark. The
problem of the maintenance of the sun’s heat was satisfactorily solved
by Helmholtz in 1854. Its radiative supplies, as he showed all but
conclusively, are derived from gravitative power. As they are diffused
into space, the cooled particles from which they proceed, clash
together, and their arrested motion is converted into a fresh thermal
stock. This implies a steady diminution, although to a surprisingly
slight extent, in the bulk of the solar globe. It has been computed that
a shortening of the sun’s diameter by 380 feet yearly would suffice to
keep this grand heat-producing machine in full working order; and at
least ten thousand years should elapse before the contraction became
measurable by any instrumental means at our command. Its progress
should, nevertheless, eventually reduce our glowing luminary to an
obscure, inert mass.

Now, evidently, its shining in the past was sustained in the same way as
at present. The globe that blazes in our summer skies is, accordingly,
but the shrunken remnant of what it once was. It is shrunken in
proportion to the vast quantity of its former emissions. Hence, the
farther we look back into the ages, the more voluminous its dimensions.
And, sounding the utmost profundities of time, we arrive at an epoch
when all the planets were swallowed up in a sphere girdled by the
present orbit of Neptune.

The tenuity of this distended body was unimaginable. At ninety miles of
altitude, our air is one hundred million times rarer than it is at
sea-level; yet the primitive solar “nebula” was considerably more
attenuated still. This aerial mass had, doubtless, been in some way
impressed with a slow movement of rotation, which, by mechanical
necessity, quickened as condensation progressed. The planets represent a
few fragments detached during the process; nearly the whole of its
substance being compacted into the sun. How the fragments came to be
detached is the crux of cosmogonists. According to Laplace’s famous
hypothesis, equatorial rings of matter separated successively from the
parent nebula at certain critical epochs when gravity was overcome by
the gaining centrifugal tendency due to accelerating rotation. These
rings drew together into planets, from which satellites were generated
by a repetition of their own birth-process. Many incongruities are,
however, involved in this _modus operandi_. Only two need here be
mentioned. Reason and experience teach us that globes of small interior
consistence easily break up into rings, while cosmic rings show not the
slightest tendency to collect into globes. Again, Laplace supposed that
the production of each planet relieved a long antecedent strain. But
nebulous stuff is almost absolutely incoherent. Hence it _cannot be
stretched or strained_. As the nebula condensed and whirled, it would,
accordingly, have left behind innumerable disaggregated particles, but
no massive rings.

M. Faye of the French Academy has attempted to remedy these defects. The
planets, he considers, were not abandoned, but formed at centres of
condensation within the nebular matrix. The order of their formation
would thus have been quite different from that assigned by Laplace, in
whose theory the exterior globes were necessarily the earliest to take
shape. M. Faye, on the contrary, argues Uranus and Neptune, from their
retrograde rotation, to be the _youngest_ instead of the _oldest_
members of the solar system, while the terrestrial group belong to the
first era of planetary development.

Astronomers are now virtually agreed that “The world was once a fluid
haze of light,” but by what precise means, in what succession, under
what compulsion, its constituent bodies were set wheeling in the void,
they are less ready to pronounce than were their predecessors, who,
dazzled with the analytical triumphs of the eighteenth century, accepted
unquestioningly the plan of creation it complacently transmitted to
them. The complexities of world-making have, besides, been instructively
illustrated by Professor G. H. Darwin’s discovery that tidal friction
was essentially concerned in the process. By an able mathematical
investigation, he showed, in 1879, that it was particularly effective in
modelling the earth-moon system, owing to the fact that our satellite,
comparatively to its primary, is by far the largest in the solar system.

Tidal friction may be regarded under a two-fold aspect. Its effect in
grinding down the speed of rotation has been explained in Section II.
(page 166). The energy, however, thus apparently destroyed is only
transformed. The rotational momentum subtracted from the earth is added
to the orbital momentum of the moon, which thus travels (setting aside
other causes of change) along continually widening spires. This retreat
from the earth is even now going on, although with elusive slowness,
amid the rise and fall of secular change. Its effects in past ages,
nevertheless, coupled with those due to the slackening of rotation by
the friction of the tidal wave—the two forming, as it were, the obverse
and reverse of one medal—must have been of overruling importance. Laying
hold of the clue they offer, Professor Darwin succeeded in tracing back
the history of the moon through a “corridor of time” nearly a hundred
million years long. It was then spinning at a vertiginous rate, round,
and nearly in contact with the earth, which must have been fluid or
plastic, while of about its present size. The _month_ of that epoch was
three or four hours in duration; the _day_ was shorter still. The actual
existence of the moon convinces us of this latter fact. Otherwise, the
huge tidal wave raised by the moon upon the earth should have lagged,
however slightly. Its attraction would have pulled the moon backwards at
the decisive moment of its emergence into separate being, and led
infallibly to its re-engulfment.

The origin of the moon has been, by Professor Darwin’s analysis, made
clearer than that of any other heavenly body. Certainty regarding such
remote events is unattainable; but it is highly probable that our globe,
at a late stage of its development, gave birth, amid the throes of
disruption, to its solitary offspring. But the case is unique. The
terrestrial system presents conditions not repeated elsewhere.
Generalisations founded upon them are sure to be misleading. We have
indeed gained, from all recent inquiries into cosmogony, the profound
conviction that no single scheme will account for everything; that the
utmost variety prevailed in the circumstances under which the heavenly
bodies attained their present status; and that a rigidly constructed
hypothesis can only misrepresent the boundless diversity of nature.

CHAPTER II.
THE SUN.

The sun is an immense reservoir of radiant energy. For our daily uses we
have no other store worth mentioning to draw upon, our fuel being the
embalmed sun-heat of former ages; and all the physical and vital
operations carried on over the whole globe derive their motive power
from the same copious source. Yet only 1/2,128,000,000th part of the sum
total of solar radiations strike its comparatively diminutive surface;
while all the planets combined intercept no more than 1/234,000,000th of
that inconceivable effluence.

The sun gives as much light as 600,000 full moons, or two and a half
billions of the most powerful electric lights, or as 1,575 billions of
billions of standard candles. And since his disc is the projection of a
hemisphere, and is thus equivalent only to one-fourth the globular
surface, these vast numbers must be quadrupled to represent the whole
luminous emissions of this surpassing body. Their amazing profusion is
the combined result of immensity of shining area, and vivid intrinsic
brilliancy. Each square inch of the sun’s surface has been estimated to
integrate the lustre of twenty-five electric arcs,[6] and Professor
Langley, by direct experiment, proved it to be 5,300 times brighter, and
87 times hotter, area for area, than the white-hot “pour” from a
Bessemer converter; notwithstanding that the circumstances of the
comparison were exceedingly “unfair to the sun.”[7]

Radiant heat and light do not indeed differ in themselves, but only in
their effects. The sun sends out into space ethereal waves of various
lengths, but all of the same kind, subject to the same laws, and
travelling with the same velocity of 186,000 miles a second. They
appear, however, under diverse forms of energy according to the
qualities of the substances upon which they impinge. Thus a small
section of this long range of undulations affects our eyes as light, the
human retina being so fashioned as to be able to _see_ with their help.
There is nothing in the nature of the rays themselves to make them
visible, and it is in fact more than probable that other living
creatures perceive vibrations to which we are blind. Our eyes are
sensitive over nearly two octaves; from waves measuring about 760
millionths of a millimetre, to those of less than 400 millionths. In the
solar spectrum the limits are roughly marked at one end by a great dark
band in the deep red—Fraunhofer’s “A,”—and at the other by “H,” in the
extreme violet. Beyond H extend undulations so short as to be visually
imperceptible, while photographically active. This means that certain
salts of silver are capable of taking up the energy they bring from the
sun, and of using it to break their chemical bonds; while on differently
prepared plates similar effects can be produced by rays in all parts of
the spectrum, even in the ultra-red, where the undulations, too long to
be sensible as light, are mainly felt as heat. Here, as Professor
Langley has shown by “bolometric”[8] explorations, reside three-fourths
of the energy distributed throughout the solar spectrum; nor is it
impossible that this great stretch of heat waves may merge, without
interruption, into electrical _rollers_, measured, not by millionths of
a millimetre, but by metres, or even by kilometres. The important point
to be borne in mind, however, is that the solar energy is diffused
abroad by means of ethereal vibrations of a single type, but immensely
varied size and frequency, and hence susceptible of dispersion into a
spectrum.

The “solar constant” expresses the quantity of heat received by the
earth from the sun. Its value, according to the most trustworthy
determinations, is three calories per square centimetre per minute. This
means that a vertical sun pours down upon each square centimetre of the
globe heat enough (supposing the atmosphere out of the way) to raise the
temperature of three grams of water by one degree centigrade in a
minute. Putting it otherwise, the energy imparted would suffice to keep
an engine of three-horse power continually at work on every square yard
of the terrestrial surface. Or, if the heat were distributed uniformly
in all latitudes, it would annually melt a complete ice-jacket one
hundred and seventy feet thick.

The temperature of the body lavishing heat at this tremendous rate must
obviously be very high; but enquiries on the point are necessarily
limited to the actual emitting shell, or “photosphere.” Their success is
testified to by a noteworthy reduction of late in the range of
uncertainty. The difficulty attending them consists mainly in our
ignorance of any systematic relation between temperature and radiation.
Excessively hot bodies lose heat much more rapidly, under the same
conditions, than moderately hot ones; and empirical “laws of radiation”
have been, over and over again, arrived at as the upshot of long series
of laboratory experiments. But such laws are only too apt to turn
traitors if trusted without control; and since the thermal power of the
sun vastly exceeds that of any terrestrial source, they are precarious
guides in this particular research. Nevertheless, as the outcome of
various improvements and refinements, it has, within the last few years,
been prosecuted with excellent results. That obtained in 1894 by Messrs.
Wilson and Gray deserves particular confidence. The _effective_
temperature of the sun was by them fixed at 8,000°, or allowing for
absorption in the solar atmosphere (measured by Wilson and Rambaud), at
8,800° centigrade. This estimate, which makes the sun’s surface more
than twice as hot as the carbons of the electric arc, is unlikely to be
widely erroneous. The word “effective” signifies the condition that the
photosphere is equivalent in radiative power to a stratum of lampblack;
if it fall short of this standard, as appears probable, then the
temperature must be raised by a corresponding amount.

The solar atmosphere, of which the absorptive effects have just been
alluded to, is a shallow envelope, stopping predominantly the shorter
wave-lengths of the light transmitted through it. Hence, if it were
removed, the sun would appear, not only much brighter, but also much
_bluer_ than it does at present. The general darkening of the limb due
to its action is apparent to visual, and conspicuous in photographic,
observations. By its aid, “faculæ”—brilliant and elevated portions of
the photosphere—were early detected. Invisible on or near the middle of
the disc, they stand out in relief against its dusky edges as they are
brought round, and carried off again by the sun’s rotation.

The magnitude of this astonishing luminary fairly baffles our
conceptions. Its mass is 745 times that of all the planets taken
together. Its volume is such, that if Jupiter were located centrally
within it, two of his Galilean moons, besides the lately discovered
inner satellite, would have “ample room and verge enough” to revolve
round him, keeping well inside the photosphere. The entire Uranian
system could be easily accommodated in the same way; while Neptune and
his satellite, and the earth and moon, could very nearly perform their
evolutions side by side in the sun’s excavated interior.

The sun is 865,000 miles in diameter, and in figure is sensibly
spherical. Its surface is 12,000 times, its volume 1,300,000 times that
of the earth. In mass it is equal to 332,000 earths. Its mean density,
then, is only one-quarter that of the earth, or 1·4 times that of water.
In other words, the terrestrial globe, if equally bulky, would contain
four times the quantity of matter contained in the solar globe. Yet we
know that it is largely made up of iron and still heavier metals; while
gravity at its surface is 27·6 more powerful than it is here. Thus, the
sun’s materials are weighed down by an inconceivable pressure, and would
be of a density utterly transcending our experience but for the
counteracting agency of heat. The comparative insubstantiality of such a
globe gives us some faint notion of the violent molecular agitation
affecting every particle of its mass. Contrasted with the fires raging
within, the surface temperature of 8,000° or 9,000° might perhaps be
deemed moderate or cool. There is much evidence that it is throughout
gaseous, although of a consistence approaching more nearly that of pitch
or treacle than can easily be reconciled with established ideas as to
the qualities proper to an aerial substance. Yet the laws governing the
gaseous state are plainly those obeyed in the sun.

Its function, as a great thermal engine, is to produce and diffuse heat
For these purposes it is essential that the interior stores should be
brought rapidly to the surface; and this is accomplished, not, as in
solids, by conduction, but by actual transport, or “convection.” Only
the enormous elasticity of highly compressed gases could render this
process swift enough to sustain the incessant outpourings of heat from
the photosphere. It may be accompanied by an actual rise in temperature.
If the sun be truly gaseous throughout, it _must_ be so accompanied. The
reason of this seeming anomaly is that a sphere of radiating and
contracting gas develops by shrinkage more heat than it can dispose of
by radiation. Whether or no the sun comes within the scope of this
principle, known as “Lane’s Law,” cannot at present be decided. It is,
in other words, an open question whether the sun is growing hotter or
colder. Help towards answering it might have been expected from the
study of geological climates; but their variations have evidently been
due to a complexity of causes. At any rate, the sun’s decline, if the
inevitable turning-point has already been reached, is going on with
extreme slowness.

The visible structure of the photosphere, or lustrous envelope of the
solar globe, is, in itself, suggestive of the vertical circulation by
which the indispensable communications between its interior and exterior
are kept up. It is composed of brilliant granules and dusky interstices,
the former representing, it is supposed, the vividly incandescent
summits of uprushing currents, the latter the cooled, descending
return-flows. It may be safely described as the limiting surface of
thermal interchange, and is often spoken of as a cloud-sphere, or level
of condensation, where the ascending vapours, like mounting volumes of
water-gas in our atmosphere, are chilled into liquid droplets. To the
brilliant luminosity of these incandescent droplets, the blaze of the
solar emissions is ascribed. Or the droplets might equally well be solid
particles on the model of the ice-spicules collected to form the
delicate fields of cirrus in our upper air. The cloud theory of the
photosphere is, however, hampered by the difficulty of finding a
substance capable of liquefying or solidifying at a temperature of
8,000° C. Carbon has generally been selected as the material of the
solar “granules,” but carbon evaporates at about 4,000°, and although
its boiling point might be raised by enormous pressure, there are no
signs that the requisite conditions exist in the sun. Hence, some
speculators turn towards electricity as the exciting agent of the
photospheric radiance; but it would be waste of time to attempt, at
present, to discuss the vague possibilities connected with an hypothesis
which offers no holding ground for distinct reasoning.

[Illustration:

FIG. 1.—_Photograph of a Sun-spot._ (From _Knowledge_, February,
1890.)
]

The photospheric texture is often rent and perforated. This ragged
condition (well exemplified in Fig. 1 from a photograph taken by Dr.
Janssen at Meudon) is accompanied or caused by a violent disturbance of
the sun’s bodily circulation. A typical sun-spot consists of a dark
opening, or “umbra,” within which a still darker “nucleus” can often be
discerned. The umbra is garnished all round with a semi-luminous
“penumbra,” composed of elongated shining bodies placed side by side,
and all, when undisturbed, pointing radially inwards towards the centre
of the spot. The effect has been compared to that of “straw-thatching,”
although the solar “straws” are, at times, thrown somewhat wildly about.
Where they hang over the _eaves_ of the spot they are always brightest,
because set most closely together. The penumbra may be called a modified
extension of the ordinary mottled surface of the photosphere, the
lustrous grains being drawn out into filaments, the “pores” into obscure
interspaces.

Spots commonly occur in groups (as in our Figure) belonging to a single
area of disturbance marked by the brightening, and probably by an
elevation of the photosphere. The members of such families show curious
and unexplained mutual relations. The size of these extraordinary
formations is on the gigantic scale of all solar phenomena. They are
often visible, individually or collectively, to the naked eye, and
attracted notice accordingly in pre-telescopic times. In 1858, a spot
opened to the extent of 144,000 miles, so that sixteen earths, side by
side, might have been engulfed in it. A still more remarkable outbreak
took place in February, 1892. Three thousand three hundred and sixty
million square miles of the photosphere were riddled as if by some
tremendous bombardment, the extreme dimensions of the affected district
being 150,000 by 75,000 miles. This spot, the largest ever photographed
at Greenwich, attained its acme on February 13th, when a magnetic storm
and widely diffused auroral display attested the sympathy of the earth
with commotions in the sun. Five times brought back to view by the sun’s
rotation, its history was followed from November until March; but this
duration is not an extreme case, a spot having been known to survive
throughout eighteen rotations. Although the group of February, 1892,
covered ¹⁄₇₀₀th of the sun’s entire surface, its proportions were
outdone by those of a spot and its immediate attendants, without
counting outliers, measured by Sir John Herschel at the Cape, March
29th, 1837.

Spots are always associated with faculæ. The two are correlated
phenomena. There is no certainty as to their order of precedence, if any
fixed order there be, but faculæ both survive spots and develop apart
from them. Not infrequently the faculæ garlanding a spot throw a
“bridge” right across it (see Fig. 1). In stereoscopic views these
brilliant projections show as veritable _suspension bridges_. They float
almost palpably at a high altitude above the black gulf they span.

The distribution of spots is easily perceived to depend immediately upon
the sun’s rotation. Two zones of its surface, parallel to the solar
equator, are alone infested by them. These may be defined as lying
between 6° and 35° of north and south latitude; but the prohibition of
spot-development is much more absolute in the polar than in the
equatorial direction. One solitary macula has been observed in 50° north
latitude.

The periodicity of sun-spots was first recognised by Schwabe at Dessau
in 1851. Since abundantly confirmed, it constitutes one of the
fundamental data of solar physics. Once in about eleven years a
“maximum” is attained; for months together the photosphere is never calm
and unbroken; its agitated condition betrays the turmoil of the
interior. The superabundance of spots is succeeded, after some years, by
a scarcity, or “minimum,” when the perturbing agencies appear to have
sunk into repose, preparatory to another outburst of activity. In this
highly irregular, although well-marked, cycle, the ascent is almost
always much more rapid than the descent; the upspringing of the
disturbance occupies, as a rule, not much more than half the time
allotted to its quieting down. Nor is its intensity by any means
uniform. High and low maxima alternate with, or succeed each other, with
no obvious regularity. Sometimes we have a divided or double maximum, as
in 1882–4, followed by an unusually swift ebb of agitation. The minimum
of 1889 was premature and brief; for spots were again numerous in 1891,
and developed prodigiously throughout the years 1892 and 1893. Only in
January, 1894, a slight falling off became apparent, and the
tranquillity which set in with 1895 may very probably reign with only
temporary interruption for some time. The cause of these vicissitudes is
completely unknown; but they so closely resemble, in character, the
changes of variable stars, that it seems impossible to exclude the sun
from that category, spot-maxima corresponding with stellar light-maxima
and _vice versâ_.

[Illustration:

FIG. 2.—_Sun-spots and Magnetic Variations._ (From Langley’s “New
Astronomy.”)
]

Solar disturbances, however originating, are a sort of universal
pulse-beat, with which the earth, and doubtless every other member of
the solar cortège, throb in unison. The accompanying diagram (Fig. 2)
shows how closely the magnetic needle sympathises with the variations in
the state of the sun. The amplitude of its daily oscillations is
represented by the dotted curve, while the smooth curve is constructed
from the relative numbers of spots. The striking conformity in point of
time-development, between two effects so disparate in their nature,
extends to minute details. Violent commotions on the sun seldom fail to
be reflected in magnetic storms and auroral manifestations on the earth;
and exact correspondences have sometimes been observed; yet it does not
seem possible to trace these simultaneous effects to the immediate
magnetic action of the sun.

No meteorological cycle corresponding with the spot-cycle has yet been
satisfactorily made out. The direct diminution of heat and light through
the obscuration of a small part of the sun’s photosphere amounts, at the
utmost, to ¹⁄₁₀₀₀th of the whole. The spots are far from being totally
dark or cool. Their blackest nuclei are really no less brilliant than
limelight; while about half as much heat is derived from them as from
the surrounding disc when they are centrally situated, and 80 per cent.
when they are near the limb.[9] Their dimming and cooling effects then
are insignificant; they are probably more than compensated by the
quickening of the sun’s circulatory processes, and consequent increase
of emission, through the disturbance of internal equilibrium of which
outbreaks of spots are among the consequences.

The spot-zones do not always occupy the same positions. They shift with
the progress of the eleven-year cycle. This curious circumstance,
discovered by R. C. Carrington in 1856, illustrates, in his words, “the
regular irregularity, and irregular regularity,” distinguishing solar
periodicity. At maxima, the mean latitude of the zones in question is
about 16°; but they close down towards the equator as each wave of
agitation dies out, its few latest products appearing in quite low
latitudes. Then, when minimum is passed, a fresh start is made with the
opening of a few small spots in 30° or 35° north or south latitude; and
this newly-organised disturbance begins to descend as before, gaining
strength as it proceeds. Thus, each impulse acts independently of the
succeeding one.

The most cursory observation of sun-spots suffices to show that the
shining body marked by them rotates on an axis from west to east, in the
same direction as the planetary revolutions. True, they emerge to sight
on its eastern, and vanish at its western limb; but this is because we
are located at its _backside_, and see their courses inverted. Attempts,
however, to fix the sun’s period of rotation were long baffled; for the
spots, instead of being carried round as if attached to a rigid surface,
gave signs of possessing “proper motions” of uncertain and inconstant
amount. The subject was first thoroughly investigated by Carrington; and
he reached the unexpected conclusion that the sun has no uniform period,
but gyrates in a composite fashion, quickest at the equator, and
gradually slower towards the poles. From less than twenty-five days, he
found the time of circuit to lengthen steadily to twenty-seven and a
half in 50° of latitude. The axis round which this remarkably
conditioned movement is performed makes an angle of 7° 15′ with the pole
of the ecliptic; it inclines towards the earth’s northern hemisphere
from June to December, when the spots describe, in crossing the disc,
paths curved downwards (to the eye of a northern observer); but the
conditions being reversed between December and June, their paths are
then curved upwards; while on June 3rd and December 5th, they pursue
straight tracks, the earth being on those two days in the line of
intersection between the sun’s equatorial plane and that of the
ecliptic.

Only a rough approximation, however, to the laws of solar rotation can
be derived from spots. For they do not simply drift with the
photospheric currents, but are subject to accelerations and retardations
connected with their internal economy, as well as to mutual attractions
and repulsions depending, it is supposed, upon their electrical
condition. Fortunately, however, a method has been perfected by which
these complications are abolished. Something has already been said as to
spectroscopic determinations of motion in the line of sight. They are
evidently applicable to the sun’s axial movement. For, through its
effect, his eastern limb is always advancing uniformly towards us, while
the western limb is retreating at the same rate. Thus, the whole
Fraunhofer spectrum is shifted slightly upward, or towards the blue, at
the left-hand edge of the solar disc, and as much towards the red at the
right-hand edge. The same lines of solar absorption, in fact, taken from
opposite sides of the solar equator, and placed end to end, appear
evidently notched, and can be distinguished at a glance from terrestrial
absorption lines, which, having nothing to do with the sun’s rotation,
show no break at the junction of their sections. They in this way
“virtually map” themselves, as Professor Langley proved experimentally
in 1877.

In 1887–9, M. Dunér, of Upsala, succeeded in extending these delicate
measurements to within fifteen degrees of the sun’s poles, where the
movement is so slow that it can only, by incredible refinements, be
dealt with successfully. The upshot was to emphasise the law of
slackening _angular_ speed detected by Carrington and confirmed by
Spoerer. From 25½ days at the Equator, the sun’s period of rotation was
found to become protracted to 38½ days at the seventy-fifth parallel of
latitude. Its investigation from photographs of faculæ has been lately
carried out by M. Stratonoff at Taschkent in Russia. The results of the
three methods are collected in the following little table.[10]

THE SUN’S ROTATION.
┌────────────────┬────────────────┬────────────────┬────────────────┐
│ │ Period from │ Period from │ Period from │
│ Mean Solar │ Faculæ. │ Spots. │ Spectroscopic │
│ Latitude. │ (Stratonoff.) │ (Spoerer.) │ Measures. │
│ │ │ │ (Dunér.) │
├────────────────┼────────────────┼────────────────┼────────────────┤
│ 0° │ 24^d·66 │ 25^d·09 │ 25^d·46 │
│ 15° │ 25 ·26 │ 25 ·44 │ 26 ·35 │
│ 30° │ 25 ·48 │ 26 ·53 │ 27 ·57 │
└────────────────┴────────────────┴────────────────┴────────────────┘

These facts, although so various, are not necessarily discordant. They
apply to different parts of the great solar machine, each one of which
may rotate with a certain independence. The spots drift, more or less
passively, _with_ the photosphere. The faculæ are elevated above it, and
appear to be everywhere accelerated relatively to its systematic
currents. The strata originating the Fraunhofer lines, to which alone
the spectroscope is applied, display, on the contrary, effects of
retardation. “This peculiar law of the sun’s rotation,” Professor Holden
remarks, “shows conclusively that it is not a rigid body, in which case,
every one of its layers in every latitude must necessarily rotate in the
same time. It is more like a vast whirlpool where the velocities of
rotation depend on the situation of the rotating masses, not only as to
latitude, but also as to depth beneath the exterior surface.”

Solar chemistry progresses by successive interpretations; and the
characters to be read are so multitudinous and so similar as to require
very delicate discrimination. The work, carried on simultaneously in the
sun and laboratory, becomes more arduous as it advances, and is still
far from complete. Indeed, the difficulties attending detailed
comparisons between the Fraunhofer lines and the innumerable components
of terrestrial spectra, would be insuperable but for the aid of
photography, here, as elsewhere, the versatile handmaiden of physical
astronomy.

Here is a list of 36 solar elements published by Professor Rowland of
Baltimore in 1891, and arranged according to the number of their
representative lines in the solar spectrum.

Iron (2000 +)
Nickel
Titanium
Manganese
Chromium
Cobalt
Carbon (200 +)
Vanadium
Zirconium
Cerium
Calcium (75 +)
Scandium
Neodymium
Lanthanum
Yttrium
Niobium
Molybdenum
Palladium
Magnesium (20 + )
Sodium (11 + )
Silicon
Hydrogen
Strontium
Barium
Aluminium (4)
Cadmium
Rhodium
Erbium
Zinc
Copper (2)
Silver (2)
Glucinium (2)
Germanium
Tin
Lead (1)
Potassium (1)

Only two of these substances, carbon and silicon, are non-metallic,
hydrogen ranking as a gaseous metal. Neither oxygen, nitrogen, nor
argon, have yet spoken their “Adsum,” but it is not impossible that they
may do so in the future. Negative evidence, at any rate, is, in
spectroscopic inquiries, absolutely inconclusive.

The spectra of sun-spots are, as might have been expected, characterised
by a great increase of absorption. There is a general darkening which
extends far up in the ultra-violet, and is modified, in the green and
blue, into remarkable dusky gratings made up of closely-set fine rays;
and some of the ordinary Fraunhofer lines are besides thickened and
blackened. The formation in spots of oxides is thought by Dr. Scheiner
to be possibly indicated by these symptoms; “if so,” he adds, “the
presence of oxygen in the sun would thus be indirectly suggested.”[11]
Bright lines, too, flash out in the immediate neighbourhood of
sun-spots, especially the “great twin brethren,” “H” and “K,” due to
calcium, which stand in imposing breadth and strength at the violet end
of the Fraunhofer spectrum, and are of corresponding importance as
indexes to solar phenomena. With this pair, brilliant hydrogen rays are
often associated, besides other “reversals,” by which, upon the
customary dark lines, flaming rays of identical wave-lengths are
superposed. But these signs of incandescence evidently belong to the
facular stratum high up above the spot-umbra.

So long ago as 1769, the observations of Dr. Wilson of Glasgow were
believed to have established, once for all, that spots are funnel-shaped
depressions in the photosphere. But the perspective effects from which
he argued are certainly not always, perhaps not very often, present. Mr.
Howlett, after thirty-five years—1859 to 1895—devoted to testing the
truth of the traditional conviction, has at last succeeded in shaking,
if not in overthrowing, it. Most solar observers now admit that spots
are of extremely various and extremely variable construction, so that
the obscure umbra, at times a sort of pit or crater, in which vapours,
cooled by expansion, well up from below, may, at another stage in the
life-history even of the same spot, represent an actual accumulation of
absorbent material above the brilliant solar cloud envelope. In any
case, a spotted area appears to be an area of elevation. This might be
due to a wide-spreading relief of pressure, or an accession of internal
heat. The fact emerged clearly from a series of measurements of the
sun’s diameter executed by M. Sykora at Charkow, Russia, in 1895.[12]

The intensity of the agitations connected with sun-spots can be most
fully appreciated from spectroscopic observations. Lines torn,
displaced, and _branching_, testify to velocities in the line of sight
of the matter surrounding or overlaying them up to three or four hundred
miles a second! These tumultuous uprushes and downrushes are not of a
systematic nature; they afford no insight, consequently, into the
formative laws of spots. Of these we are indeed far more ignorant than
Sir William Herschel supposed himself to be. Recent work on the sun has
provided a grand store of facts ascertained with surprising skill and
ingenuity. But they want _colligating_. No framework has yet been
constructed that will hold them, each in its proper place. It has been
truly said: “Considering the rapid progress which has been made in the
observational or practical side of solar physics, it must be confessed
that the theoretical side has been very imperfectly developed. Almost
every student of solar physics has his own theory, and usually he
himself is the only one who believes in it.”

Since Sir John Herschel propounded his “cyclonic theory” of sun-spots in
1847, there has been a marked tendency to assimilate solar to
terrestrial phenomena. But the circumstances of the two bodies are so
utterly unlike that such attempts can only prove misleading. The earth
is a solid globe warmed from without, hence, with hot tropical and
frigid polar regions. This disparity is the prime motor in the
circulation of its atmosphere and oceans; a circulation, essentially in
latitude, directed towards the equalisation of temperature. The sun, on
the contrary, is heated from within; there is no appreciable difference
of temperature between its poles and equator; and its circulation is of
the bodily kind belonging to fluid masses, and is carried on by vertical
currents effecting exchanges of heat between the surface and the
profundities beneath. Were these to stop, or even notably to slacken,
the sun would promptly cease to shine, and lapse into the condition of a
“dark star.” It is not then surprising that the drifting movements of
the photosphere are _along_, not _across_, parallels of latitude. Solar
meteorology, in a word, has almost nothing in common with terrestrial
meteorology; and explanatory schemes, based upon an analogy which does
not exist, must sooner or later be consigned to the limbo of vanities.

CHAPTER III.
THE SUN’S SURROUNDINGS.

“What we ordinarily call the sun,” wrote the late Mr. Ranyard, “is only
the bright spherical nucleus of a nebulous body.”[13] But it is only
when the interposing moon cuts off the dazzling rays of the nucleus that
we see directly anything of its nebular surroundings. Partial or annular
eclipses are of little or no use for this purpose; the revelation
belongs exclusively to the sombre, yet splendid moments of totality. No
sooner has the last glint of sunshine vanished than the corona starts
into view, encompassing the black lunar globe with a sort of “glory” of
silvery streamers. Its radiated shape suggests vacillation of form and a
flickering radiance; yet its immobility is absolute. The awe and wonder
of the sight tend, for the moment, to supersede scientific curiosity,
and they are enhanced by the perception, at the base of the corona, of
the serrated scarlet “chromosphere” fringing the moon’s circumference,
while the towering “prominences” that are usually seen to spring from it
produce the startling effect of a conflagration.

These marvellous appendages received no adequate notice until their
disclosure during the total eclipse of July 8, 1842. Even the
uninstructed crowds in the streets of Milan and Pavia shouted with
amazement at what they saw; while by solar students the recurrence of
similar opportunities has ever since been eagerly anticipated and
diligently turned to account. The question that first pressed for
solution related to the local habitation of prominences; for some
unwisely persisted in attaching them to the moon. A decisive answer was
given by photography at its first _effective_ application to eclipses on
July 18, 1860. From a comparison of negatives exposed at the beginning
and end of totality, it became clearly apparent that the moon had, in
the interval, moved _over_ the prominences, uncovering, to a small
extent, those on the west side and concealing those on the east.

Their solar connexion having thus been established by the camera, the
spectroscope was called upon to determine their physical and chemical
nature. An admirable opportunity for taking this further step was
presented by the Indian eclipse of August 18, 1868. The result was
decisive. The light of a huge spire of flame, 89,000 miles high, had no
sooner passed through a prism than its gaseous origin declared itself.
The spectrum consisted of several hydrogen lines, and one unknown line
in the yellow, slightly more refrangible than the sodium-pair D_{1}, and
D_{2}, and hence called D_{3}. “Je verrai ces lignes-là en dehors des
éclipses!” M. Janssen exclaimed, as they caught his eye; and on the
following morning, at Guntoor in the Neilgherries, he actually started
daylight spectroscopic work at the edge of the sun. He owed his success
to a perfectly simple principle. The ordinary invisibility of
prominences is due to the drowning of their light in reflected sunshine.
But sunshine, because it is continuous—that is, made up of beams of all
refrangibilities—can be weakened to almost any extent by dispersion,
while the detached prominence-rays lose nothing by being separated.
Hence, the result of passing the mixed light from near the solar limb
through a train of prisms is that the tell-tale bright lines stand out
distinctly from an _emaciated_ prismatic background. The method was
independently discovered by Mr. Norman Lockyer in England, and his and
Janssen’s communications on the subject were laid before the French
Academy of Sciences on the same day of October, 1868. It has proved of
inestimable value, and was further improved in 1869 by Dr. Huggins’s
device for viewing these objects in their proper shapes through an open
slit, instead of building them up in narrow sections by successive
observations through a narrow one. This was made possible by the
intensity of their light. They can be observed in variously coloured
images corresponding to the different rays they emit; but the least
refrangible of the hydrogen series—the blood-red C (alias Hκ)—is
generally chosen as being the most brilliant and best defined.

The unrecognised substance giving the yellow prominence-line was named
by Dr. Frankland “helium.” It evidently existed near the sun in enormous
quantities, and in close companionship with hydrogen. Yet no dark line
corresponding to its absorption was to be found in the Fraunhofer
spectrum, although it now and then emerged in spot-spectra. Conjectures
were rife as to its nature and relations. It was generally believed to
be specifically lighter than hydrogen, and some held it a product of its
dissociation, and so of a different elemental standing. Everything about
it, however, remained doubtful until, in March, 1895, Professor Ramsay
produced a sample for inspection close at hand, extracted by heat from
the rare mineral “clevite.” The recognition-mark was its emission, when
electrically excited, of the solar D_{3}, with which were associated
several other chromospheric rays previously registered as of unknown
origin, but now linked together as vibrations of the same molecules. A
sudden and entirely unlooked-for advance was thus made in the chemistry
of the sun’s surroundings.

Helium is a colourless gas of about twice the density of hydrogen. Its
peculiar qualities are shared only by argon, the new constituent of the
earth’s atmosphere. Both have unusual thermal relations; both are
chemically inert. They refuse to combine with any other element, and
thus stand apart from the round of multiform change involving the whole
material world. Helium is nevertheless distributed freely throughout the
universe. Hydrogen itself is scarcely more ubiquitous.

A considerable mass of information regarding the solar prominences was
rapidly collected by means of the Janssen-Lockyer invention. They were
at once divided into two classes. The “quiescent” kind occur in all
solar latitudes; they change their shapes very gradually; they have no
immediate relationship with spots. In form they resemble _pillared
clouds_ resting in banks like heavy cumuli, or floating, like expanses
of thin cirrus, high above the chromosphere with which they are
ordinarily connected by slender supports or conduit-pipes. But these are
at times invisible or non-existent. Father Secchi occasionally watched
isolated cloudlets form and grow spontaneously as if by condensation
from saturated air; and on October 13, 1880, Professor Young made a
confirmatory observation. About 11 A.M. he noticed a detached fiery mass
at an elevation of 67,500 miles above the limb. “It grew rapidly,
without any sensible rising or falling, and in an hour developed into a
large stratiform cloud, irregular on the upper surface, but nearly flat
beneath. From this lower surface pendent filaments grew out, and by the
middle of the afternoon the object had become one of the ordinary
stemmed prominences.”[14] The size of these formations is enormous. They
vary in height from about 10,000 to 100,000 miles; and ranges of them
450,000 miles in extent have been photographed during total eclipses.

[Illustration:

FIG. 3.—_Curves showing the development of Sun-spots and Prominences
during the period 1880 to 1891._ (Sidgreaves.)
]

The second class of prominences, known as “eruptive,” are obviously
manifestations of intense energy. In some of their forms they suggest
geyser-like spoutings of incandescent vapours. They represent swords and
scimetars, palms with twisted trunks composed of mounting flames,
igneous vegetation of sundry types. Their chemistry is much more complex
than that of the quiescent sort. Not only hydrogen and helium, but iron,
magnesium, sodium, and a number of other metals enter into their
composition. Belonging to the same order of disturbance with spots, they
are closely conjoined with them, both in time and space. They conform to
the sun-spot cycle, as well as to the “law of zones,” showing that
photospheric and chromospheric disturbances spring from a common cause.
Fig. 3 (from the _Observatory_ for March, 1893) embodies a comparison
between the “spotted area” as determined at Greenwich 1880–1891, and the
“profile area” of prominences (without distinction of kind) observed
spectroscopically at Stonyhurst during the years 1880–1892. The
agreement between the two curves is very striking; but the minimum of
solar activity in 1889 is decidedly better represented by the
prominence-tracing. Father Sidgreaves, director of the Stonyhurst
Observatory, adds the important remark that wide-spreading elevations of
the chromosphere attend spot-maxima, while depressions of equal extent
occur at minima.

The chromosphere is a solar envelope, but not a solar atmosphere. It
completely surrounds the sun to the depth of about 4,000 miles with a
close tissue of scarlet flames, their filamentous or tufted summits
swaying and intercrossing as if under the gusty sweep of fiery winds.
Any of these summits which attain an unwonted height become
“prominences,” but it is a mere matter of convention when the change of
nomenclature should take place. The chemical composition of the
chromosphere does not differ essentially from that of prominences. Its
permanent constituents were found by Professor Young to be hydrogen,
helium, “coronium,” and calcium, the last represented _only_ by “H” and
“K.” But disturbances never failed to be indicated by the blaze of
metallic lines, of which 273 in all have been determined by the same
authority. Their appearance signified, without doubt, the injection from
below of the corresponding vapours, chiefly those of iron, titanium,
sodium, magnesium, strontium, barium, and manganese. At moments the
reinforcement of the spectrum with bright rays was so extensive that it
seemed as if the entire “reversing layer” had been uplifted bodily into
the chromosphere.

The reversing layer lies quite close to the photosphere. It is scarcely
more than 300 miles deep, and is hence invisible except during about a
second at the beginning and end of total eclipses. Young was the first
to be favoured with a sight of it, on December 22, 1870. No sooner was
the direct solar spectrum intercepted by the moon, than “all at once, as
suddenly as a bursting rocket shoots out its stars, the whole field of
view was filled with bright lines, more numerous than one could count.
The phenomenon was so sudden, so unexpected, and so wonderfully
beautiful, as to force an involuntary exclamation.”[15] It was
afterwards frequently observed, and at last satisfactorily photographed
by Mr. Shackleton, a member of Sir George Baden-Powell’s expedition to
Novaya Zemlya, for the purpose of observing the total solar eclipse of
August 9, 1896. The permanent record then secured was of peculiar
importance as affording the means of confronting in detail the
components of the vario-tinted flash at the eclipsed sun’s limb with the
dusky legion of the Fraunhofer lines. The correspondence is striking,
and leaves no doubt that Young’s stratum is the actual locality where
the characteristic solar spectrum is produced. It may be described as an
universal solar ocean of glowing metallic vapours, the rays emanating
from which, although vivid when seen _off_ the sun, are thrown out in
dark relief by projection upon the white-hot photosphere. The existence
of just such a heterogeneous absorbing layer had been predicted, on
theoretical grounds, some years before it came into view.

The movements taking place in eruptive prominences are often of
portentous speed. They are betrayed, so far as they coincide with the
visual ray, by spectroscopic line-displacements; so far as they are
directed _across_ the visual ray, by immediate observation of the
spectroscopic images. Thus, the up-and-downrushes of flaming hydrogen
above spots on the disc reach velocities of 320 miles a second; and
solar tornadoes (detected by Mr. Lockyer more than a quarter of a
century ago) are often observed to whirl at rates which would be
incredible were they less well authenticated. Vertical explosions at the
limb, on the other hand, of still more unruly violence are rendered
manifest by displacements, not of the emitted lines, but of the
radiating substances themselves.

On September 19th and 20th, 1893, Father Fényi, director of the Kalocsa
Observatory in Hungary, witnessed the development and dissolution of a
pair of objects perhaps the most extraordinary in the astonishing record
of solar phenomena.[16] They broke out within nineteen hours of each
other, showed a close similarity of shape and structure, underwent
analogous changes, and, strangest of all, were situated at almost
diametrically opposite points of the solar limb. The first was already,
when first viewed at 2 P.M., 168,000 miles high; within half an hour, it
had sprung up to 224,000 miles (8′ 18″), and again subsided into a
commonplace flame of the modest dimension of 13,650 miles (30″). The
rate of ascent, directly measured (always necessarily through the medium
of the spectroscope), was 132 miles a second. This vast, though
transient construction, seemed to be formed of a multitude of distinct
fiery tongues, each leaping and flaring independently. As a whole, it
was also tongue-shaped, and “stood erect nearly in the direction of the
sun’s radius,” travelling, meanwhile, towards the earth at an average
rate of 186 miles a second.

The companion-prominence began to show at nine next morning, and, rising
with a velocity of 300 miles per second, attained in twelve minutes to a
height of 220,000 miles. This tremendous apparition was of the same
“ragged” texture as its predecessor, and shone, even in its loftiest
fragments, with the same intense glow. As might have been expected from
its opposite position, its radial movement was _from_ the earth. A
prominence measured by the same observer, July 15, 1895, was diminishing
its distance from the earth with the extraordinary velocity of 533 miles
a second; and on September 30 of the same year, a colossal object
resembling the bent and riven trunk of a great tree, was in the course
of half an hour flung upwards to a minimum altitude of 313,000 miles,
and had again faded out of sight. “The appearance,” Father Fényi wrote,
“of all the numerous great eruptions which I have observed has been such
as would be produced by a kind of explosion over a spotted region,
which, seizing upon a prominence already developed, hurls it upward from
the surface, tears it to pieces, and brings it to a speedy end.” The
matter thus acted upon is of enormous volume, but negligeable mass.

Photographs of prominence-spectra, obtained by Dr. Schuster during the
eclipse of May 17, 1882, brought out the remarkable predominance in
their light of the “H” and “K” emissions of calcium. It was
re-discovered by means of spectrographs of those objects, taken in 1891
without an eclipse, by Professor Hale at Chicago, and by M. Deslandres
in Paris. Both investigators promptly seized upon the advantage it
offered for their chemical delineation in full daylight. The lines in
question are dark and abnormally wide in the sun itself, bright and
sharp in prominences. Thus, at these particular parts of the spectrum,
the obliterating effects of scattered sunlight are non-existent. Just
here, too, photographic sensitiveness is at its maximum. Hence, by
working with either of these lines (K is preferable) nothing could be
easier than to get impressions of the brilliant forms of prominences
relieved against the background of solar absorption. (See Figures 4 and
5.) The thin, bright line is _sheltered_ from daylight glare by the
dusky, broad one. By the use of a “double slit,” the method was
completed. This, again, was simultaneously invented by Hale and
Deslandres, although they had, without suspecting it, been anticipated
by Janssen in 1869. The second slit is adjusted so as to exclude all but
a single ray of the spectrum formed by dispersing the light admitted
through the first. An unlimited power of selection is in this way
afforded as to the quality of light to be employed; but for general
purposes, K is not likely to be superseded.

In the Chicago spectroheliograph, two moveable slits, together with a
powerful diffraction spectroscope, are attached to a twelve-inch
refractor. With this instrument, monochromatic impressions of the sun
with its spots, faculæ, and flame-garland are obtained without
difficulty. To begin with, the solar disc is covered with a metal
diaphragm, then the first slit is caused to traverse the artificially
eclipsed image, the second following at such a rate that the K line
alone always falls upon the sensitive plate. The result is a complete
photographic record of the chromosphere and prominences. The diaphragm
having been then removed, the return journey of the slits is very
quickly made, so as to guard against the formidable actinic strength of
even that small element of direct sunlight contained in the K line. The
object of the second transit is to _insert_ an autographic print of the
sun itself into the space previously left blank to receive it. The
entire operation occupies less than one minute. Portrayed thus in
calcium light, the solar disc has a strange effect. It is entirely
overspread with a reticulation of irregular bright markings, greatly
emphasized over the spot-zones, and corresponding in general with the
positions of faculæ. According to Professor Hale, these masses and
wreathings of calcium vapour _are_ faculæ. M. Deslandres regards them
rather as gaseous formations connected with faculæ. Their extension and
intensity are at times so great that M. Deslandres has actually
succeeded, through the prevalence of their light, in photographing the
sun as a “bright-line star.” The double-slit method also affords the
means of studying the distribution of each element of the reversing
layer in the leisure of ordinary daylight, as M. Deslandres has shown by
some preliminary experiments.[17]

To this extent astronomers have made themselves independent of eclipses.
These momentous occurrences are, fortunately, not needed for researches
concerned with distinct coloured rays separable by dispersion from
diffuse sunshine. But with the corona it is different. For here we have
a white glory to deal with. Coronal light is derived from three sources:
from the original incandescence of solid or liquid particles, from
sunshine reflected by them, and from gaseous emissions. The most
conspicuous of these is a green ray of unknown chemical meaning. It
proceeds from every part of the corona, even from the dark rifts
separating its brilliant streamers, and the inconceivably tenuous
substance to which it owes its origin has, accordingly, received the
name of “coronium.” The coronal spectrum includes many other bright
lines, especially in the ultra-violet, photographed during eclipses; but
the hydrogen, helium, and calcium lines which accompany them probably
represent scattered chromospheric light.

[Illustration:

FIG. 4.—_Eruptive Prominence photographed by Professor Hale at the
Kenwood Observatory, March 24, 1895, at 22h. 40m. Chicago mean
time._ (_The photosphere is covered with a metallic disc._)
]

[Illustration:

FIG. 5.—_The same, 18m. later._

(From the _Astrophysical Journal_, May, 1896.)
]

The green coronal ray is much too faint to be isolated with the
spectroscope; but the continuous coronal spectrum has maxima of
intensity compared with ordinary daylight, which suggested to Dr.
Huggins, in 1882, a differential method of photographing the entire
structure apart from eclipses. It has however, as yet come to nothing,
and Hale and Deslandres have been equally unsuccessful with their
“double slit” apparatus. Hence, it is only by favour of the moon that
this wonderful appendage can be investigated, and the available moments
have not been allowed to pass in vain.

[Illustration:

FIG. 6.—_The Eclipsed Sun, photographed at Sohag in Egypt, May 17,
1882. A Comet is almost involved in the Corona._ (From
“Philosophical Transactions,” vol. clxxv.)
]

One result fully ascertained is that it changes in form concurrently
with the progress of the sun-spot period. The maximum coronal type is
entirely different from the minimum type, and reappears in unmistakable
connexion with vehement solar disturbance. This cyclical relation was
first pointed out by Mr. Ranyard. On July 29, 1878, a totality of 165
seconds was observed, under splendid conditions of weather, in the
Western States of North America. No prominences worthy of note were
visible, but the corona wore a most surprising aspect. A pair of
enormous equatorial streamers stretched east and west of the sun to a
distance of at least ten millions of miles. Indeed, they came to no
definite end. They were best seen with the naked eye, and made no show
on sensitive plates, but the application of low telescopic powers
disclosed, near the base of the effusions, a mass of delicate and
complex detail. The solar poles were as distinctively, although not so
strikingly, garnished as the solar equator. Each was the centre from
which diverged a dense brush of straight, electrical-looking rays. The
sun was at the time in a state of profound tranquillity; and it was
recalled that, at the previous minimum, in 1867, Grosch had delineated,
at Santiago, just the same equatorial extensions, and just the same
polar brushes. The connexion was emphasised during the maximum of
1882–4, by the substitution, when the moon covered the sun on May 17,
1882, and May 6, 1883, of a dazzling stellate formation for the winged
corona of 1878. In Fig. 6 is reproduced a photograph by Dr. Schuster of
the Sohag, or Egyptian corona, with the added embellishment of a comet
hurrying up to perihelion, conspicuous to the eye at the time, but never
seen again.

In 1889 the minimum type of corona reasserted itself. A drawing made by
Miss M. L. Todd during the eclipse of January 1, gave the characteristic
equatorial “fish-tails,” reaching out on the west to four solar
diameters.[18] And although the camera, owing to special difficulties,
has not yet been able to pursue them so far, Professor Barnard’s
exquisite picture (Fig. 7), taken at Bartlett’s Springs, California,
with an exposure of 4½ seconds, portrays the type to perfection, with
its suggested indefinite expansions, “the soft feathery details of the
inner corona, and the delicate fan-structures at the poles.” Two minute
notches mark the points where a couple of prominences have, by the
intensity of their actinic power, _eaten into_ the black circumference
of the lunar image.

[Illustration:

FIG. 7.—_The Corona of January 1, 1889, photographed by Professor E.
E. Barnard._
]

Nine negatives were secured by the artist, but at a considerable
personal sacrifice. “So impressive,” he wrote, “was the magnificent
spectacle upon the crowd that had gathered just outside our enclosure,
that not a murmur was heard. The frightened, half-whining bark of a dog,
and the click-click of the driving clock, alone were audible. When the
sun suddenly burst forth, an almost instantaneous and highly-surprised
cackling of the chickens, that had hastily sought their roosts at the
beginning of totality, would have been amusing could one have shaken off
the dazed feeling at the unexpectedly rapid termination of the
semi-darkness. My own feelings were those of excessive disappointment
and depression. So intent was I in watching the cameras and making the
exposures, that I did not look up to the sun during totality, and
therefore saw nothing of the corona.”

On April 16, 1893, at the height of the last sun-spot maximum, a
shadow-track crossed South America and Central Africa. Once more the
coronal type had changed. Not a trace remained of the equatorial
“wings”; not a trace of the polar “fans.” Instead, the “compass-card”
aureole of 1882 and 1883, shaped regardless of heliographic latitude,
reemerged from beneath the veil of daylight. That the sun’s filmy
“crown” follows, after its own inexplicable fashion, the general round
of solar vicissitudes, no longer admitted of a doubt. The fact is thus
stated by M. Deslandres, who observed the eclipse at Fundium, in the
Senegal district.

“The form of the corona,” he says, “undergoes periodical variations,
which follow the simultaneous periodical variations already ascertained
for spots, faculæ, prominences, auroræ, and terrestrial magnetism. This
important relation, indicated by preceding eclipses, is strongly
confirmed by the eclipse of 1893.”[19]

Professor Schaeberle’s photographs, taken on the same occasion at Mina
Bronces in Chili, marked a decided advance in coronal portraiture. The
sun’s disc measured four inches on his plates, exposed with a
photoheliograph forty feet in length; and the details of inner coronal
construction came out accordingly with unprecedented perfection. The
corona of August 9, 1896, reproduced the most striking features of the
corona observed August 29, 1886; and both corresponded to an
intermediate epoch of the spot-cycle. The polar brushes were present
without the equatorial extensions, while in both a protruding ray made
an angle of some thirty or forty degrees with the solar axis. This
distinctive trait imprinted itself with surprising emphasis on some of
Sir George Baden-Powell’s Novaya Zemlya photographs.

Researches, prosecuted under cover of eighteen eclipses, have greatly
strengthened the visible analogy between coronal streamers, auroral
coruscations, and comets’ tails. The persuasion that electrical
discharges in high vacua are concerned in all these phenomena is not
easily resisted. Repulsive forces such as are at work in Crookes’ tubes
perhaps come into play, on the vast solar scale, to produce the strange
and beautiful luminous forms revealed during eclipses. Their tenuity is
certainly extreme. They probably contain very much less matter, volume
for volume, than the incredibly exhausted tubes of modern physicists.
The unresisted passage of comets through the corona demands this
supposition, which is in complete accord with the fineness of the
Fraunhofer lines. The corona shows no increase of density downwards, and
the chromosphere very little. Hence neither can be a true solar
atmosphere, weighing freely upon the sun’s surface. For, under the
immense power of solar gravity, the accumulated pressure of the
superincumbent layers, even if there were only one hundred miles’
thickness of them, could not be intelligibly conveyed in figures; how
much less when the piling-up of the aerial strata is reckoned by
thousands of miles!

To recapitulate. Starting from the photosphere, we meet first an
envelope producing the _general_ absorption, by which sunlight is
enfeebled and reddened as if by the interposition of a slightly rufous
shade. Next comes the reversing layer composed of mixed incandescent
vapours, giving rise, by their _selective_ absorption, to the Fraunhofer
lines. No alterations in correspondence with the spot-cycle have yet
been determined in either of these couches, which, close as they lie to
the photosphere, remain, nevertheless, apparently indifferent to its
agitations. They are overspread by the chromosphere and prominences;
while above and beyond shines the mysterious corona; both chromosphere
and corona strictly conforming, by manifest changes, to the sun’s
periodicity. One other solar appendage remains to be noticed.

After sunset in spring, and before sunrise in autumn, a mass of soft
luminosity, often brighter than the Milky Way, may be seen tapering
upward from the horizon along an axis approximating to the line of the
ecliptic. Its more conspicuous visibility at those times just reverses
the case of the harvest moon. As a rule, the apex of the cone barely
reaches the Pleiades; but it does not really end here. Thrice during the
present century, by Brorsen, Backhouse, and Barnard, the zodiacal
“counterglow” has been independently discovered and studied. This is a
hazy, luminous patch, ten to fifteen degrees across, and exactly 180°
from the sun. It represents the _opposition aspect_ of the Zodiacal
Light, hence proved to be a formation in planetary space, extending
considerably beyond the earth’s orbit. Two plausible hypotheses as to
its nature have been proposed. Professor Searle[20] holds it to
represent the reflection of sunlight from “an infinite number of small
asteroids.” Professor Bigelow[21] considers it as an amassment in the
plane of the sun’s equator—“a place of zero potential”—of the particles
electrically expelled from the poles. The Light is then, if this view be
correct, an extension of the corona—a sort of “pocket or receptacle,
wherein the coronal matter is accumulated and retained as a solar
accompaniment.” A continuous spectrum is derived from it; no element of
original emission can be detected; so that the spectroscope “holds the
balance even” between the two theories. If, however, the latter were
true, the Zodiacal Light should spread out from the sun’s equator; if
the former, then its medial plane should deviate very slightly from that
of the ecliptic, to which the fundamental, or “invariable” plane of the
solar system is inclined only one and a half degrees. M. Marchand’s
observations from the Pic du Midi[22] appear to be decisive on the
point. During three years, he mapped down the limits assigned by his
observations night after night, to an emanation which, in that pure air,
was seen to compass the entire sphere. The eventual comparison of his
collected data showed its axis to be a great circle sensibly coincident
with the sun’s equator. All reasonable doubt as to the nature of the
Zodiacal Light has thus been removed. It is a reservoir for the sun’s
waste matter—the sink, into which are daily flung the particles rejected
through the agency of the aigrettes and streamers composing the
wonderful eclipse-vision of the corona.

CHAPTER IV.
THE INTERIOR PLANETS.

The Interior Planets are those which revolve within the earth’s orbit.
They are two in number—Mercury and Venus. Mercury, with a diameter of
three thousand miles, is the smallest of the eight principal planets. It
pursues a track, too, more eccentric and more highly inclined to the
ecliptic than any other planetary orbit. The zodiac had of old to be
made 16° wide in order to afford room for its excursions. These
irregularities are, however, quite innocuous as regards the stability of
the system, for the reason that they belong to a body of insignificant
mass. The successive approaches to it of Encke’s comet have afforded a
means of ascertaining its gravitative power; and, according to the
latest report from this filmy messenger, it is even less than had been
supposed. Mercury, it appears, weighs little more than one-ten-millionth
of the sun, or one-thirtieth of the earth. And since its volume is about
one-nineteenth the terrestrial, the matter of which it is composed must
be less dense in the proportion of 30 to 19. So that the planet would
turn the balance against one equal globe of granite, or three and a half
of water. We can hence easily calculate that gravity, at Mercury’s
surface, possesses less than one-fourth its power at the earth’s
surface. A man of sixteen stone transported thither, would find himself
relieved of fully three-quarters of his habitual burthen.

The plane of Mercury’s orbit makes an angle of 7° with the ecliptic, and
he traverses it with a speed varying from 23 to 35 miles a second. The
corresponding distances from the sun are 43½ and 28½ million miles,
while the mean distance, or semi-major axis of the ellipse, measures
just 36 millions. Independently then of what we call seasons, Mercury is
subject, in the course of its year of 88 days, to considerable
vicissitudes of temperature. At perihelion it receives nine times, at
aphelion only four times, more heat than is imparted by the sun to an
equal area of the earth.

The crucial point as regards the physical condition of a planet is the
presence or absence of an atmosphere. And there is decisive evidence
that Mercury is in this respect poorly provided. Certain luminous
phenomena, often observed during its transits across the sun, appear to
be of purely optical production, since they are less conspicuous with
good than with indifferent telescopes; while, on the other hand, genuine
refractive effects are absent. A corresponding indication is afforded by
the low “albedo,” that is, the slight reflective power of this planet.
Of the light flooding its surface only 17 per cent.[23] is returned; 83
per cent. is absorbed. Now the albedo of clouds is about 72; a
cloud-wrapt globe is little less brilliant than if it were covered with
fresh-fallen snow. Hence a high albedo accompanies a dense, vapour-laden
atmosphere; a low albedo indicates a transparent one. And since Mercury,
which sends back only about as much light as if it were made of grey
granite, has the lowest albedo of any of the principal planets, it may
be safely concluded to possess the thinnest aerial covering. Yet it is
not, apparently, a totally airless globe. Spots upon its surface have
been seen to become effaced as if by atmospheric veilings; and the
spectroscope hints (although doubtfully) at aqueous absorption.

Mercury is “new” when nearest to the earth, and “full” when most remote
from it. At both these periods, moreover, its position with regard to
the sun renders it ordinarily invisible; so that it is usually seen as
either gibbous or crescent shaped. The study of its phases has brought
out a noteworthy circumstance. It is easy to understand that geometrical
light changes will not proceed by the same gradations upon a smooth and
upon a rugged globe, where they are complicated by irregular shadows and
illuminations. The laws of variation are quite different in each case,
and their respective prevalence can be distinguished by steady
observation. There seems no reason to doubt that the latter are obeyed
by Mercury. After several years’ watching of its phases, Professor G.
Müller[24] of Potsdam concludes them to be such as characterise a broken
and uneven surface.

[Illustration:

FIG. 8.—_Map of Mercury, by Schiaparelli._ (From _Astronomische
Nachrichten_, No. 2944.)
]

Little or nothing was known about the rotation of Mercury when
Schiaparelli of Milan undertook its determination in 1882. His
observations were made in full daylight, in order to reduce atmospheric
disturbances to a minimum; and he executed, in the course of a few
months, a series of 150 Mercurian delineations upon which is founded the
planisphere exhibited in Fig. 8. The surface of the planet, coloured
light rose with a coppery tinge, was seen to be diversified by
brownish-red markings which became effaced towards the limb as if
through atmospheric absorption. Although evidently of a permanent
nature, their outlines escaped precise definition. The most remarkable
circumstance about them was that they showed no effects of rotation.
During several consecutive hours of watching, they remained sensibly
fixed in their places. The conclusion was finally arrived at that
Mercury rotates on a nearly upright axis in the same time that it
revolves round the sun. Its day, no less than its year, is equal to 88
of our days. Consequently it turns at all times substantially the same
face towards the sun; and the “terminator,” that is, the dividing-line
between darkness and light, only “librates,” without travelling right
round the globe. The librations of Mercury are, however, extensive in
proportion to the eccentricity of its orbit; hence, five-eighths of its
surface come in for some share of illumination during the Mercurian
year. Over the remaining three-eighths darkness reigns supreme.

“There is no light in earth or heaven,
But the cold light of stars.”

Satisfactory confirmation of this curious result was obtained by Mr.
Percival Lowell at the Flagstaff Observatory in Arizona during the
autumn of 1896.[25] In Schiaparelli’s map, the axis of rotation lies in
the plane of the paper, and the centre of the projected sphere thus
represents the point on Mercury’s surface where the sun is vertical at
perihelion and aphelion; A and B, 23° 41′ to the east and west of it
respectively, marking the places where the sun is vertical at the
libration-limits. That formidable luminary oscillates from the zenith of
A to the zenith of B and back in 88 days, occupying, in consequence of
the planet’s unequal motion, 51 in describing the arc from east to west
(left to right), but only 37 in retracing it from west to east.[26]

The effects of these arrangements upon climate must be exceedingly
peculiar. They cannot readily be traced in detail; but, thin as the
Mercurian atmosphere is, it must be to some extent operative in
modifying the contrast in temperature between the two hemispheres.
Except in a few favoured localities, the existence of liquid water must
be impossible in either. Mercurian oceans, could they ever have been
formed, should long ago have been boiled off from the hot side, and
condensed in “thick-ribbed ice” on the cold side.

Mercury is then, according to our ideas, totally unfitted to be the
abode of organic life. Nor can it at any time have been more favourably
circumstanced than at present. We need not hesitate to assert that its
rotation was reduced to its actual minimum rate by the power of tidal
friction. The brake was, moreover, applied by the sun. The attainment of
rapid gyration was prevented by the resistance of solar tides raised on
a plastic mass. Disruption was accordingly rendered impossible. The
planet was, by anticipation, deprived of satellites, and remained
undivided and solitary.

Venus, the earths nearest planetary neighbour, might be called its twin.
Its diameter being 7,700 miles, it is of nearly the same size; it is not
greatly inferior in mean density; gravity at its surface is of more than
four-fifths its terrestrial strength, and it is supplied with an
extensive atmosphere. Its movements are placid and well-regulated. In a
period of 225 days it revolves at the rate of 22 miles per second in an
almost circular track, deviating but slightly from the plane of the
ecliptic. Its distance from the sun is 67,200,000 miles; hence it
receives just twice as much heat and light as the earth. Moreover, it
reflects at least 65 per cent. of the light incident upon it. Viewed in
the same telescopic field with Mercury during a close conjunction in
1878, it shone, James Nasmyth reported, like burnished silver, while
Mercury appeared as dull as zinc or lead. Yet Mercury is illuminated, on
an average, three and a half times more intensely than its neighbour.

Atmospheric effects are conspicuous on Venus. At the beginning and end
of transits, the part of the little black disc off the sun, has
constantly been seen silver-edged through refraction; and when the
planet, at inferior conjunction, passes above or below the sun, its
whole circumference is not unfrequently bordered with a halo of solar
rays, bent inwards as if by the action of a lens. Just in the same way,
the _geometrical_ rising of the heavenly bodies is _visually_
anticipated, and their setting delayed on the earth, by the curvature of
the beams refracted in passing through its atmosphere—or rather, through
half of it; while we, as spectators of Venus from the outside, perceive
the entire effect. Made on equal terms, the comparison is greatly to the
disadvantage of the earth. Refraction, as directly measured on Venus,
considerably exceeds its terrestrial amount; and the measurable
refraction is only that produced in the higher part of the air
surmounting the shell of clouds which constitutes the planet’s visible
surface. Thus, at the cloud-level a barometer would, by the lowest
estimate, stand at 35 inches, while at the same altitude of, say, two
miles, the column of mercury would, on the earth, drop to 21 inches. It
is, indeed, very likely that the aerial envelope of Venus weighs twice
as much as our own.

The occasional visibility of the dark side of Venus is still
unexplained. The appearance is indistinguishable except in scale from
that of the “old moon in the new moon’s arms”; but illumination by
earthshine, which is fully competent to produce the lunar effect,
practically vanishes at the distance of Venus. The “ashen light,” as it
is called, ordinarily shows only when the planet figures as a narrow
crescent; but M. Brenner of the Manora Observatory, who has a knack of
being unprecedented, saw it in June, 1895,[27] during the gibbous phase.
The appearances of this pale gleam follow no traceable law. They occur
unsought; and are recalcitrant to vigilant expectation. Their closest
analogy is with our auroræ. The “phosphorescence” of the dark side of
Venus may quite reasonably be set down as of an electrical nature. But
it does not seem, like terrestrial auroræ, to follow the lines of a
magnetic system.

Distinct spectroscopic indications of aqueous absorption in the
atmosphere of Venus were perceived, during the transits of 1874 and
1882, by Tacchini, Riccò, and Young. They accord well with the
“snow-caps,” which are one of the many puzzling Cytherean features.
Since these can be resolved into groups of brilliant points, they
represent, in the opinion of the late M. Trouvelot, mountainous
formations penetrating the reflective stratum, and shining, lustrous
with snow, in the clear upper air. They might almost equally well be
cloud-like condensations of a permanent kind, called into existence by
topographical peculiarities, and hence, after a fashion, _rooted in the
soil_. On the other hand, Mr. Lowell questions their reality in any
form; and his drawings represent extraordinarily sure seeing.

[Illustration:

FIG. 9.—_Venus, from a drawing by Mascari._ (_Nature_, February 20,
1896.)
]

The only point regarding the planet’s rotation upon which astronomers
are agreed is that its axis is nearly perpendicular to the place of its
orbit. As to its period, the divergence is enormous. It reaches all the
way from 24 hours to 225 days. Bad as is the telescopic holding-ground
on Mercury, that afforded by Venus is worse still. The disc falls off
rapidly in brightness from the limb towards the terminator, and is
sometimes diversified by filmy and indefinite markings, obviously of
atmospheric origin (in Fig. 9 the shadings are much too pronounced).
Attempts to use them as fiducial points are foredoomed to failure. The
period, accordingly, of 23^h 21^m arrived at by forcing into artificial
agreement the observations of Cassini at Bologna, of Bianchini and De
Vico in Rome, obtained small credit. The subject lay, as it were,
dormant until Schiaparelli made, in 1890, the provisional announcement
that Venus rotates on the same plan as Mercury. A clamour of
contradiction was immediately raised, and a large amount of evidence on
both sides of the question has since been collected. It is curious to
notice that, setting aside the opposite conclusions of Terby and
Brenner, the Alps mark a dividing-line between the pros and the cons.
Schiaparelli’s period of 224·7 days (ratified by himself in 1895) is
supported by Perrotin’s observations both at Nice and Mont Mounier; by
Tacchini’s at Rome, Cerulli’s at Teramo, and Mascari’s at the
complementary establishments of Catania and Mount Etna; while Niesten,
Trouvelot, Villiger, Stanley Williams, and Flammarion, all under some
disadvantage as regards climate, aver that the debated gyration is
performed in “about” 24 hours. Now, in the first place, a period of 24
hours is in itself open to suspicion, since all delicate observations
are liable to be affected by diurnal atmospheric variations; in the
second, it is mainly, if not entirely, based upon supposed changes in
almost evanescent shadings, while the long period of 224·7 days has been
derived fundamentally, from the immobility relative to the terminator,
of definite and permanent topographical features. The perfect roundness
of the disc of Venus affords independent proof of extremely slow
rotation.

Spectroscopic evidence may before long become available. The quantity to
be measured by the exquisite method of line-displacements is, indeed, at
the most extremely small. The equatorial velocity of Venus would, with
the 24-hour period, but slightly exceed a quarter of a mile a second;
but this effect being doubled by reflexion from the planet, and doubled
again by juxtaposition of light from its east and west limbs, could
probably be made distinctly perceptible. In the negative case, the value
of the support lent to the long-period hypothesis can only be appraised
by the degree of refinement attained in the research.

The “long-period hypothesis” has, however, almost ceased to need such
support. Schiaparelli’s facts are inconsistent with any other; and they
are scarcely controvertible. They have besides, as in the case of
Mercury, been verified by Mr. Lowell’s recent observations. Assuming,
then, its truth, we may consider what it implies. Since the rotation and
revolution of Venus synchronise, she always looks inwards toward the
sun, perpetual day reigning on one hemisphere, perpetual night on the
other. And these regulations are much more strictly conformed to than on
Mercury. For the orbital motion of Venus is so nearly uniform that
libratory effects count for very little. The equatorial breadth of the
libration-zones, where light alternates with darkness, is only
thirty-three miles. On the other hand, the atmospheric diffusion of
sunshine is a powerful illuminating agency. The meteorology of the
planet presents great difficulties. Its conditions are so remote from
our experience that we can barely sketch out their results. The most
obvious of these is the vehement aerial circulation which must proceed
without ceasing between the hemisphere upon which the sun never rises
and the hemisphere upon which the sun never sets. We should expect it to
be accompanied by agitated conflicts of winds, and surgings of the
atmosphere from its lowest to its highest strata, betrayed by rendings
of the brilliant condensation-canopy, by the rapid transport of torn
scuds, and wheeling vortices of clouds. But nothing of all this is
telescopically visible. The aspect of the morning star suggests serenity
rather than interior tumult.

One of the most remarkable instances of persistent optical illusion
refers to a supposed satellite of Venus. It was first seen by Fontana at
Naples in 1645; it was last seen by Horrebow at Copenhagen in 1768; and
the intermediate observations were numerous, usually careful, and
apparently authentic. Yet the body, of which they affirmed the
existence, was purely fictitious; and it is a suggestive circumstance
that it never ventured into the field of view of an achromatic lens.

Comparing the two planets nearest to the sun, the first spontaneous
impression is of astonishment at their unlikeness. One travels in an
almost circular, the other in a highly eccentric orbit. One possesses a
dense and extensive atmosphere; the other is barely gauze-clad, and is
hence exposed to almost unmitigated extremes of temperature, while the
conformation of its solid surface is left open to telescopic scrutiny,
impeded only by the inconvenient glare of the sun. That surface is of a
reddish hue, and absorbs more than four-fifths of the light with which
it is flooded; the disc of Venus being, on the contrary, of a dazzling
whiteness, and little less reflective than a summer cloud. Yet these two
globes, so dissimilar individually, have apparently had the same destiny
prepared for them. Deprived of all but a remnant of their rotation by
the frictional resistance of sun-raised tides, they were debarred from
the production of satellites, and subjected to what we, in our
ignorance, might be apt to call fantastic climatal conditions. With due
reserve it may be added that they have thus apparently been rendered
unfit to be the abodes of highly developed organisms. Why this has been
so ordained we are unable to conjecture; we must wait to know.

CHAPTER V.
THE EARTH AND MOON.

The earth occupies a critical position in the solar system. Its greater
distance from the sun preserved it from the fate of Mercury and Venus.
The influence of solar tidal friction fell short of predominance over
the terrestrial future. All that it could do was to defer to the latest
possible moment (so to speak) the separation of the moon, the
comparatively large size of which was doubtless due to this
postponement. For a viscous body, such as the earth must then have been,
can bear much more rotational strain than a less coherent mass; but when
the strain comes to be relieved, the needful sacrifice of material is
proportionally greater. The process of fission, instead of being a mere
incident, becomes a catastrophe. The most violent explosions are
precisely those which are longest delayed.

Had the earth then been situated a few millions of miles nearer to the
sun there would have been, so far as we can see, no moon; and the
terrestrial day and year would have been of equal length. This
equalisation was rendered impossible by lunar influence.[28] We are
indebted to our satellite for the alternations of day and night which
make life possible. How this came about is quite clear upon some brief
consideration. Lunar tides are now about three times more effective than
solar tides, and at their origin the disproportion was enormous. Their
power might be called exclusive. Now, how was that power exercised?
Primarily, in compelling an agreement between the duration of the month
and day—that duration, to begin with, being of only a few hours. The day
might, and in the long run did, fall short, but it could not possibly
get ahead of the month. Hence the earth’s rotation was for ages
protected against the destructive agency of solar tidal friction. By the
time that the moon left it, as it were, to take care of itself, the
plastic stage, during which alone rapid change could take place, had
passed, and the earth was solid and secure.

Thus, the axial rotation of our planet in twenty-four sidereal hours is
the outcome of a delicate balance of relations established in the “deep
backward and abysm of time.” Its shape matches, or has accommodated
itself to the period, which has perhaps not varied much since the epoch
when interior fires were first banked in by the formation of a rigid
crust. The compression of rotating globes is so connected with the
quickness of their spinning that one can be calculated from the other;
and the earth’s theoretical compression, or ellipticity, is found to be
practically identical with its measured ellipticity of about ¹⁄₂₉₃. Its
mean diameter is 7,927 miles; the equatorial is 26 miles longer than the
polar diameter; so that the globe is belted with a protuberance, 13
miles high, corresponding to the excess of centrifugal force at the
Equator.

The heat by which it was originally maintained in a liquid condition is
still in process of dissipation. A small part escapes year by year, but
enough remains to keep the earth _alive_ for ages to come. Were the
supply exhausted, the oxygen of our air, and the water forming our
oceans, would be rapidly absorbed, chemically and mechanically, and with
them, vitality should disappear. Volcanic action, in some of its many
forms, is accordingly a condition of existence. One unmistakable symptom
of central fires still glowing is the increase of subterranean
temperature. It averages one degree Fahrenheit for fifty-five feet of
descent. Below two miles then, water can only remain liquid through the
compulsion of the overlying strata, the slightest relaxation of which
occasions it to flash explosively into steam; the devastating power of
“super-heated” water being one of the chief causes of volcanic
outbreaks. The growth of temperature downward cannot be supposed to
proceed indefinitely; otherwise, a fabulous thermal state would be
reached long before we got near the core of the globe; but the region of
maximum heat depends upon an unknown quantity—that is, the lapse of time
since the antique lava-globe began to crust over. Assuming it to be
fifty million years, Lord Kelvin showed that the limiting temperature of
about 5,400° F. is located not more than fifty miles from the surface.
But 5,400° approaches the temperature of the electric arc, at which
there is an all but universal vaporisation of material substances, and
rocks liquefy while comparatively cool. Diabase, for instance, a typical
basalt, is completely fluid at 2,200° F. On the other hand, the pressure
at 50 miles beneath the earth’s surface is of inconceivable power; and
it is employed in resisting the expansive tendency of heat. The
condition of matter subjected to these opposing and potent influences we
are unable to divine, and have no means of ascertaining. We do, however,
know from the results of various astronomical lines of enquiry that the
earth is effectively as rigid as steel. Its mean density is about five
and a half times that of water, the entire globe being more than twice
as heavy as if made of the ordinary surface rocks. This, however, is not
surprising, since oxygen enters largely into the composition of the
exterior strata, while the subjacent materials are likely to be in large
measure metallic.

The epoch of the earth’s superficial solidification has again, quite
lately, been under discussion. “The subject,” Lord Kelvin wrote, “is
intensely interesting. I would rather know the date of the
_Consistentior Status_ than of the Norman Conquest; but it can bring no
comfort in respect to the demand for time in palæontological geology.
Helmholtz, Newcomb, and another (Kelvin) are inexorable in refusing
sunlight for more than a score, or a very few scores of millions of
years.”[29]

Improved data having been substituted, the problem was solved anew, with
the result of very notably diminishing the “age of the earth.” It is for
the present fixed at twenty-four million years, and upon such strong
evidence as to “throw the burden of proof upon those who hold to the
vaguely vast age derived from sedimentary geology.”[30]

The earth is the largest of the terrestrial planets; and it is
specifically the heaviest of all the planets. Its compactness is more
likely to be a consequence of a particular relation between internal
temperature and pressure, than of a difference in chemical constitution.

The mass of its atmosphere can be directly determined. We have only to
look at a barometer in order to gain the information that our “cloud of
all-sustaining air” weighs as much as a universal ocean of mercury
thirty inches in depth. The corresponding depth of air, were it of the
same density throughout, would be nearly five miles. But it is _not_ of
the same density throughout. With each three and a half miles of ascent,
atmospheric pressure is halved; and the interval is lessened by making
due allowance for decrease of temperature upwards. To the succession of
these tenuous strata, no definite end can be assigned. The duration of
twilight shows that, above forty-five miles, they cease to reflect
light; yet meteors can be set ablaze at heights up to 120 miles, through
the resistance offered to their motion by air reduced to
1/250,000,000,000th its density at sea-level!

The cloud-bearing capability of the atmosphere has only of late been
fully recognised. Ordinary cirrus float about five miles high. On
December 4, 1894, an aeronaut, Dr. A. Berson, passed right through a
bank of them at an altitude of five and a half miles, and was able to
verify by actual contact their composition out of snow-flakelets.[31]
But since 1885, a still more delicate kind of floating formation has
come within our acquaintanceship. “Luminous night-clouds” were first
noticed by Ceraski; they have been systematically studied by O. Jesse of
Berlin.[32] They appear long after sunset, between May and July, and
derive their silvery radiance from the sun-rays which their elevated
situation enables them to intercept, while all below is wrapt in
darkness. Their height has been determined, from the comparison of
photographs taken simultaneously at different places, to average
fifty-one miles, and to range from fifty to fifty-four miles. They are
an entirely new order of phenomenon.

This globe upon which we dwell is a great magnet. Its directive action
upon the compass sufficiently proves the fact. But it is a magnet
probably only by virtue of the electric currents which course round it.
And since these currents originate from diverse interacting causes, the
laws of terrestrial magnetism are necessarily complex. They are
conditioned, yet not prescribed by the earth’s rotation. The magnetic
and geographical systems of co-ordinates approximate, but by no means
coincide. The former is, indeed, both complex and variable.[33] The
inclination, or “dip,” of the needle does not vary in the same way as
the declination, or horizontal position. There are two points on the
earth’s surface, called “poles of verticity,” where a magnetic needle,
freely swung, points vertically downward. One is situated in the arctic
peninsula Boothia, the other on the antarctic continent within a few
hundred miles of Mount Erebus. An intermediate line where the needle
poises itself horizontally, corresponds roughly with the geographical
equator. Each hemisphere contains besides two centres of maximum force,
by the joint action of which magnetic deviations from true north and
south are determined. Their mutual relations are highly intricate. The
North American focus is stationary, the Siberian focus oscillates. Their
relative and absolute intensity is probably also subject to
fluctuations. Hence the inconstancy of magnetic directive influences.
The variation of the compass varies.

It varies hour by hour, as well as year by year. The needle performs a
diurnal oscillation, reaching an eastward maximum about eight A.M., and
a corresponding westward maximum towards four P.M. Moreover, the range
of this vibration increases concordantly with the growth of spotted area
upon the sun, and falls off again as spots diminish (see Fig. 2). The
cosmical relations of terrestrial magnetism are emphasised by the
obvious connexion between a disturbed state of the sun and the
occurrence of “magnetic storms.” During these crises, the smooth
progression and regression of the needle are superseded by violent and
irregular movements. The photographic tracing in which they are recorded
presents only a series of lawless zigzags; earth-currents are set up;
telegraph-wires transmit messages without batteries; and the skies are
at night draped with auroral streamers.

Auroræ are possibly a survival of our planet’s original self-luminosity.
If so, their dependence upon the terrestrial magnetic system is highly
significant. They obey the magnetic period, they accompany magnetic
disturbances, they illuminate magnetic lines of force. That they are
immediately caused by electrical discharges in the high vacua of our
upper air is no longer doubtful. In these latitudes, the auroral arch
and crown are formed at a height of ninety to one hundred miles, in
(about) 1/1,000,000,000th of an atmosphere; but in the polar regions
they approach much nearer to the earth. There, indeed, they more usually
assume the form of a curtain, undulating in luminous folds, and
traversed by vertical electric currents. That they are so traversed is
demonstrated by the behaviour of the magnetic needle, the deviations of
which change their sign as the auroral drapery crosses the zenith.[34]
Auroræ seem to be confined to two zones of the earth, which, like the
sun-spot zones, approach the equator as the solar cycle advances. Their
frequency in temperate regions corresponds, accordingly, to a scarcity
in high latitudes. The auroral spectrum consists of a number of bright
rays, one of which is invariably present, and seems to be essential and
fundamental. Its origin is unexplained.

The velocity of the earth in its orbit exceeds more than sixty times
that of a cannon ball just leaving the muzzle of an eighty-ton gun. In
other terms, the third planet from the sun travels at an average rate of
18½ miles per second. Its albedo has been estimated—probably
under-estimated—at 0·30. This would leave 70 per cent. of the solar
emanations striking the upper surface of its atmosphere available for
interior consumption. Most of this supply is absorbed or scattered in
the atmosphere. The proportion sent back to space after reflection from
the actual terrestrial surface must be extremely small. Very little
topographical detail could be made out by telescopic scrutiny from the
moon or Venus. At the most, the trend of some great mountain ranges,
such as the Andes and Himalayas, and a dozen snow-clad peaks, could be
visible. No sign of the teeming organic life brought forth by mother
earth could be detected from without.

The more we know of the moon, the less inviting, from our point of view
as animated beings, it appears. It is a harsh and inhospitable world,
from which vital possibilities, if they were ever present, have plainly
long ago departed. The diameter of our satellite is 2,162 miles. Its
disc, so far as the most exact measurements tell, is perfectly round.
This in itself indicates a slow rotation; and even casual observations
suffice to show that they relate to only one lunar hemisphere. Rotation
and revolution here again synchronise. In 27 days 8 hours (nearly), the
moon executes one circuit of the earth, and one gyration on its axis.
The coincidence was brought about in remote ages by the power of
terrestrial tidal friction. The averted hemisphere does not, however,
remain wholly invisible. Two-elevenths of it are, by the effect of
librations, both in longitude and latitude, brought piecemeal into view.
But the additional “lunes,” thus thrown open to glimpses round the
corner, are greatly foreshortened.

The area of the moon is somewhat less than one-thirteenth that of the
earth. Yet room could be found there for the entire British Empire, with
six million square miles to spare. Its volume is ¹⁄₄₉th, its mass
¹⁄₈₂th, the volume and mass of the earth. Hence the lunar materials are
less dense than the terrestrial in the proportion of about three to
five. But this may be because they are under comparatively slight
pressure.

At the moon’s surface, gravity possesses only one-sixth its power here,
so that a stone thrown upward with equal force would reach a six-fold
height. Further, a projectile shot straight from our satellite with a
velocity of one and a half miles a second would never return, while a
speed of seven miles a second is just controllable by the earth, to say
nothing of the immense efficacy of her dense atmosphere in hindering
escape from her precincts. No terrestrial bomb, it may therefore be
safely asserted, has ever been hurled into space, although volcanic
ejecta may very well, in past ages, have made their way hither from the
moon.

But lunar volcanoes are no longer active. Only their remains stand as
records of a fiery past. In guiding a telescope across the scarred face
of our satellite we seem to traverse a volcanic charnel-house. The
evidence of ancient seismic action on the moon is overwhelming. Its
surface is pitted all over with cones and craters. Nearly 33,000 are
marked on Schmidt’s map, and the list is very far from being exhaustive.
The resulting chiaroscuro is obvious to the naked eye. Dante tried to
explain it in the “Divina Commedia”; Galileo detected its cause and
manner of composition. The chief facts about it are these.

[Illustration:

FIG. 10.—_Map of the Moon._ (From Fowler’s “Telescopic Astronomy.”)
]

1. Furnerius

2. Petavius

3. Langrenus

4. Macrobius

5. Cleomedes

6. Endymion

7. Altas

8. Hercules

9. Römer

10. Posidonius

11. Fracastorius

12. Theophilus

13. Piccolomini

14. Albategnius

15. Hipparchus

16. Manilius

17. Eudoxus

18. Aristotle

19. Cassini

20. Aristillus

21. Plato

22. Archimedes

23. Eratosthenes

24. Copernicus

25. Ptolemy

26. Alphonsus

27. Arzachel

28. Walter

29. Clavius

30. Tycho

31. Bullialdus

32. Schiller

33. Schickard

34. Gassendi

35. Kepler

36. Grimaldi

37. Aristarchus

A. Mare Crisum

B. Mare Fecunditatis

C. Mare Nectaris

D. Mare Tranquilitatis

E. Mare Serenitatis

F. Mare Imbrium

G. Sinus Iridum

H. Oceanus Procellarum

I. Mare Humorum

K. Mare Nubium

V. Altai Mountains

W. Mare Vaporum

X. Apennine Mountains

Y. Caucasus Mountains

Z. Alps

The general albedo of the lunar surface is 0·17; but portions of the
disc are as obscure as basalt or obsidian, while isolated spots glitter
like snow-peaks. The former are usually admitted to be the oldest of
conspicuous lunar formations, the latter to be comparatively recent. The
dusky spaces too, are dead levels, if not depressions; they were
formerly taken for seas, and retain the name of “Maria.” One “ocean,”
extending over two million square miles, is included amongst them. This
is the “Oceanus Procellarum” (see Fig. 10), which is five times larger
than its nearest rival, the “Mare Nubium.” The late Mr. Gwyn Elger
regarded the lunar “seas” as lava outflows, by which certain earlier
formations were all but obliterated. M. Suess explains them as areas
where the primitive thin “slag-crust” re-melted. To the same category
belong the vast “bulwark plains,” the ramparts enclosing which are of so
wide a sweep as to be, not merely “hull-down,” but completely invisible
to an imaginary spectator placed at their centres. Yet Pelions by the
dozen are tumbled upon Ossas for their construction, with here and there
an Olympus flung on the top. Typical examples are Ptolemæus, 115 miles
across; and Plato (near the Northern Pole), “sixty miles in diameter,
with its bright border and dark steel-grey floor.”[35]

The bottoms of lunar craters and “circuses” are nearly always
depressed—sometimes thousands of feet—below the general level. Thus, the
central peak of the great crater Copernicus towers to 11,300 feet above
the depressed plain from which it rises, but surmounts by only 2,600
feet the average level of the moon.

Successive stages of activity have left ineffaceable marks upon this now
stereotyped page. Groups of immense craters mutually encroach, and seem
to have been scooped out of each other’s flanks, like Kilauea from Mauna
Loa; craters occur within craters, as Vesuvius inside the broken rampart
of Somma; and the most recent are invariably the deepest and steepest.
Cup-shaped depressions or “crater-pits” are innumerable; they result,
according to Suess’s theory,[36] each from a single explosion, the
bursting of a “big bubble” of gas in a cooling lava-field. Mountain
ranges are profusely strewn with them. These lunar Alps and Apennines
appear to be as unmistakably igneous in their origin as Tycho or
Aristarchus. They are colossal slag-walls. There are apparently no
sedimentary deposits upon the moon. Aqueous action had no concern with
its geological history. Yet on the earth water is essential to the
production of volcanic phenomena. If they are to be developed without
it, M. Angelot concludes, it must be by explosive escapes from
solidifying materials, of gases absorbed by them when in a state of
fusion.

The mountains of the moon are much higher, proportionally, than the
summits of the Hindu-Kush, or of the Himalayas. Mount Everest, reduced
to the lunar scale, would be a modest elevation of 8,200 feet; while
pinnacles in the lunar Apennines spring up to 22,000 feet, and
crater-peaks of eighteen or twenty thousand abound. The disparity is
scarcely surprising when it is remembered that there the convulsive
throes of cooling were restrained by gravity reduced to one-sixth the
power it exerts here.

Among the puzzles of selenography are the objects termed respectively
“rills” and “rays” The former are very numerous. Considerably more than
a thousand of them have been mapped or photographed. They resemble the
cañons of Colorado. Some few run to 150 miles; most are a couple of
miles wide, and above a quarter of a mile deep. Their volcanic origin
cannot be doubted. The “rays” diverge in extensive systems from such
huge ring-craters as Tycho and Copernicus. They cast no shadows, and
come out best at full moon, circumstances suggestive of their being
immemorial lava-streams bleached by the chemical action of fumes from
the interior. The whiteness of Aristarchus has been similarly explained;
but accumulations of pumice and snow-like volcanic ashes perhaps enhance
the effect. The flashing back by this wonderful peak, of earthshine at
determinate angles of illumination, has often counterfeited the vivid
glow of actual eruptions. Their possibility, however, belongs to the
past. Nor have any of the rumoured alterations in lunar topography,
which from time to time excited interest and raised controversy, made
good their footing as solid facts. Agencies of change are certainly
there, in tidal strains and alternations of temperature, but they work
very slowly. There is no erosion by air or water; no grinding by ice; no
transport of materials. Repose reigns apparently undisturbed. Lunar
landscapes exhibit abrupt transitions from the blinding glare of crude
sunlight to the blackness of absolute shadow. Their aspect excludes any
but the thinnest possible atmospheric remnant To all intents and
purposes, the moon is an airless globe. Occultations of stars afford a
very refined test of this condition; and their instantaneousness alone
suffices to demonstrate its reality. Spectroscopic evidence is to the
same effect. Dr. Huggins watched, January 4, 1865, a _prismatic_
occultation of the small star, ε Piscium. Had there been the slightest
inequality of dispersion or absorption at the moon’s limb, it could not
have failed to be perceived. There was none. The spectrum remained
unaffected, and vanished abruptly, all the colours together. And
moonlight, analysed by the most powerful apparatus, varies not an iota
from sunlight. It is reflected without the smallest selective change.

The absence of water is equally well attested. There are no river-beds
to be seen, no rounded surfaces, no alluvial plains. A mosquito could
not find a moist corner to lay its eggs in. There is nothing to show
that this was otherwise in any past age, although it is not improbable
that the lunar rocks contain large volumes of oxygen once free. As
regards the earth, we can entertain no doubt that a goodly proportion of
its original atmosphere and oceans is now permanently lodged in its
bedded crust. But the geological histories of the earth and moon
probably diverged from the first.

Indeed water, as such, could probably not exist upon the moon’s surface.
It would promptly take the form of ice. Professor Langley has shown that
the temperature prevailing there, under vertical sunshine, is about that
of frost; while it sinks, during the moon’s long night of fourteen days,
almost to absolute zero. This frigid state is due to the absence of
atmospheric protection, leaving heat free to depart into space as fast
as it is received. Thus, of the small quantity of heat contained in
moonlight, nearly the entire comes to us by mere superficial reflection;
a minute residuum only is absorbed previously to being emitted. The
distinction is brought into view by comparing the solar and lunar
heat-spectra, when moonlight is found to contain longer invisible heat
waves than can be detected in sunlight Moreover, Professor Frank Very,
through his experimental demonstration that the equatorial are slightly
hotter than the polar regions, has established the fact of a slight
retention of heat by the moon’s substance. How slight the retention is,
has been proved by Dr. Boeddicker’s observations with the Rosse
three-foot speculum, showing that, during total eclipses, moon-heat
vanishes almost completely. Less than 1 per cent, survives. The thermal
phases are not, however, identical with the luminous phases.

The eclipsed moon, on June 10, 1816, is said to have been utterly lost
to sight; but, as a rule, with very few exceptions, our satellite
traverses visibly the densest part of the earth’s shadow. Even during
“black eclipses,” such as that of October 4, 1884, a dusky spot remains
as an index to its locality; while in “red eclipses,” the great craters
and bulwark plains can be easily distinguished with an opera-glass.
Occasionally, the moon seems turned to blood, and the people cry out in
the streets with fear. Such a phenomenon was witnessed by the writer at
Florence, February 27, 1877. Its explanation is not difficult The
refractive power of the earth’s atmosphere suffices to bring
illumination to the lunar disc at the very middle of the shadow-cone. It
is shut off from direct solar rays, not from those that are bent into
convergence by the lens of our air. That they must be reddened by the
process, sunset-effects on the earth tell plainly enough. But when the
air is vapour, or dust-laden, and consequently opaque, little light is
transmitted, and a scarcely mitigated eclipse ensues. That of 1884 is
believed to have been darkened by the outpourings from Krakatoa. A
photograph by Professor Barnard, of the totally eclipsed moon, September
3, 1895, is reproduced in Fig. 11. It was one of a _search-series_ for a
lunar satellite. None was found: but the question of its possible
existence was set at rest.

De la Rue’s and Rutherfurd’s plan of photographing the moon as a whole
is no longer followed. Bit by bit photography, on a large scale, has
superseded it. Splendid pictures of individual formations and separate
regions have in this way been obtained, both at the Paris and the Lick
Observatories; and their microscopic study has given some interesting
results; yet it is undeniable that the “chemical retina” cannot here
claim its usual superiority. “The best photograph of the moon ever
taken,” Professor W. H. Pickering avers,[37] “will not show what can be
seen with a six-inch telescope, under favourable atmospheric conditions.
For general outlines, for completeness of the coarser detail, and for
purposes of future testimony, the photograph evidently stands without a
rival; but as regards that which is really most interesting upon the
moon—the finer detail and more delicate features—the photograph does not
even hint at their existence.” One of the most successful specimens of
lunar photography forms the frontispiece to this volume. It was taken by
MM. Loewy and Puiseux, with the large Coudé equatorial, February 14th,
1894, at 7^h 27^m Paris time, and cannot easily be surpassed in
pictorial effect.

[Illustration:

FIG. 11.—_Photograph of the Totally Eclipsed Moon. By Professor
Barnard. Exposure, 3 Minutes._
]

Atmospheric agitations are one cause of imperfection in lunar
photographs. The eye can seize the instant of exquisite definition; the
camera must take what comes. Then the disparities of actinic intensity
in the various lunar formations are so wide that, in order to get an
ideal picture, a different length of exposure should be given to each.
What is enough for a plain—to take an example—is too much for the crater
rising from it, or for the rampart enclosing it. Minute irregularities
in the following motion of the telescope during the few seconds of
exposure occasion further difficulties. A momentary shifting, by half a
millimetre, of the image upon the sensitive plate, would suffice to blur
the negative seriously, if not fatally. For this, as for several other
lines of work, the instrument of the future may be of a type with which
the equatorial has little in common. Professor Pickering considers it
probable that “a horizontal telescope of three or four hundred feet
focus, and twelve to fifteen inches aperture, would give the most
satisfactory results. In such a case, it might be found best that the
mirror should remain fixed during the exposure, while the plate was
given an uniform motion by clock-work.”

The suggestion is one among many signs that a revolution in the mounting
of telescopes is at hand.

CHAPTER VI.
THE PLANET MARS.

The furthest terrestrial planet from the sun is Mars, the “star of
strength.” No other heavenly body, except the moon, is so well placed
for observation from our position in space. As a superior planet, it
does not merely, like Mercury and Venus, oscillate about the sun, but is
best seen when in opposition. It is then “full”; it crosses the meridian
at midnight, and is at its least distance from the earth. These
occasions recur every 780 days; but they are not all equally favourable.
The opposition distance of the planet varies, owing to the eccentricity
of its orbit, from thirty-five to sixty-one million miles; so that the
area of the disc is three times larger when a perihelion than when an
aphelion passage coincides with a midnight culmination. Under the best
circumstances it is of the apparent dimensions of a half-sovereign 2,000
yards from the spectator.

The diameter of Mars is 4,200 miles; its surface is equal to
two-sevenths, its volume to one-seventh those of the earth. But, in
consequence of its inferior mean density, nine such spheres would go to
make up the mass of our world. The superficial force of gravity on Mars,
compared with its terrestrial value, is as thirty-eight to a hundred. A
man could leap there a wall eight feet four inches in height with no
more effort than it would cost him here to spring over a two-foot fence.

The planet’s rotation is performed in 24 hours 37 minutes on an axis
deviating from the vertical by 240° 50′. Hence its seasons resemble our
own, except in being nearly twice as long, for the Martian year is of
687 days. They are modified, too, by the considerable elongation of the
ellipse traversed by Mars, causing a difference of 26½ millions of miles
in its greatest and least distances from the sun. These are respectively
155 and 128½ millions of miles, the mean distance being 141½ millions. A
polar compression of ¹⁄₂₂₀ is just what should be expected from its
rotatory speed. When at quadrature, it is plainly gibbous; but our
interior position with regard to it makes it impossible that it should
ever take the crescent form. Its albedo, according to Zöllner, is 0·26—a
figure intimating that sunlight is reflected from no cloud-canopy, but
by the soil itself. This atmospheric transparency leaves the door open
for researches into the condition of a very curious little world.

The disc of Mars is diversified with three shades of colour—reddish, or
dull orange, dark greyish-green, and pure white. The last shows mainly
in two diametrically opposite patches. Each pole is surrounded by a
brilliant cap, suggesting the deposition of ice or snow over the chilly
spaces corresponding to our arctic and antarctic regions. Nor is this
all. Each of the polar hoods shrinks to a mere remnant as the local
summer advances, but regains its original size when wintry influences
are again in the ascendant. Here, and nowhere else in the planetary
system, we meet evidence of seasonal change; and seasonal change is
associated with vital possibilities. Again, a globe upon which snow
visibly melts must contain water; hence the green markings cannot but
image to our minds seas and inlets sub-dividing continents, the blond
complexion of which may be caused by some native peculiarity of the
soil. It is in no way connected with vegetation, since it neither fades
nor flushes with the advent of spring; and an atmospheric origin is
excluded by the circumstance that it becomes effaced by a whitish haze
near the limb, just where the densest atmospheric strata are traversed
by the line of sight.

The spots on Mars are by no means so sharply defined as lunar craters
and _maria_; yet they are fundamentally permanent. Some can be
recognised from drawings made over two hundred years ago; and these
antique records have served modern astronomers to determine with minute
accuracy the rotation-period of the planet. There is accordingly no
doubt that “areography” has assured facts to deal with, although the
facts are not quite as “hard” as they might be. Continents are somewhat
vaguely outlined. Great tracts of them are of an uncertain and variable
hue, as if subject to inundations. This peculiarity, thoroughly
certified during the favourable opposition of 1892, makes a strong
distinction between Mars and the Earth. Terrestrial oceans keep within
the limits assigned to them. On the neighbouring planet—as M. Faye
observed in 1892—“Water seems to march about at its ease,” flooding,
from time to time, regions as wide as France. The imperfect separation
of the two elements recalls the conditions prevailing during the
terrestrial carboniferous era.

[Illustration:

FIG. 12.—_Chart of Mars on Mercator’s Projection._

(From Proctor’s “Old and New Astronomy.”)
]

The main part of the land of Mars is situated in the northern
hemisphere. It covers two-thirds of the entire globular surface. Rather
than land, indeed, it should be called a network of land and water. Fig.
12, from a chart by Schiaparelli, illustrates the remarkable fashion of
their intermixture. The great continental block—so its orange tint
declares it to be—is cut up in all possible directions by an intricate
system of what appear to be waterways, running in perfectly straight
lines—that is, along great circles of the globe—for distances varying
from 350 to upwards of 4,000 miles. They are frequently seen in
duplicate, strictly parallel companions developing thirty to three
hundred miles apart from the original formations. This mysterious
phenomenon is evanescent, or rather periodical. Canal-duplication is a
recurrent change, depending upon the Martian seasons, and becoming
obvious, according to Schiaparelli, chiefly near the equinoxes.

The canals invariably connect two bodies of water; hence they need no
locks or hydraulic machinery; their course is on a dead level. The
broadest of them are comparable with the Adriatic; those at the limit of
visibility, stretching like the finest spider-threads across the disc,
have a width of eighteen miles. “The canals,” Schiaparelli says, “may
intersect among themselves at all possible angles, but by preference
they converge towards the small spots to which we have given the name of
lakes. For example, seven are seen to converge in Lacus Phoenicis, eight
in Trivium Charontis, six in Lunae Lacus, and six in Ismenius
Lacus.”[38]

These “lakes” evidently form an integral part of the canal system. They
resemble huge railway-junctions; and the largest of them—the “Eye of
Mars” (Schiaparelli’s Lacus Solis)—seems, in Mr. Lowell’s phrase, like
the hub of a five-spoked wheel. It is depicted in Fig. 13 from a drawing
made by Professor Barnard with the great Lick refractor, September 3,
1894. Mr. W. H. Pickering in 1892, and Mr. Percival Lowell in 1894, were
amazed at their extraordinary abundance.

“Scattered over the orange-ochre groundwork of the continental regions
of the planet,” the latter wrote, “are any number of dark, round spots.
How many there may be it is not possible to state, as the better the
seeing, the more of them there seem to be. In spite, however, of their
great number, there is no instance of one occurring unconnected with a
canal. What is more, there is apparently none which does not lie at the
junction of several canals. Reversely, all the junctions appear to be
provided with spots.”

[Illustration:

FIG. 13.—_The “Eye of Mars,” drawn by Prof. Barnard with the great
Lick Refractor. The southern snow-cap is visible much shrunken by
melting._
]

Most of these foci are about 120 miles in diameter, and appear most
precisely circular when most clearly seen. “Plotted upon a globe,” Mr.
Lowell continues, “they and their connecting canals make a most curious
network over all the orange-ochre equatorial parts of the planet, a mass
of lines and knots, the one marking being as omnipresent as the other.
Indeed, the spots are as peculiar and distinctive a feature of Mars as
the canals themselves.”

Like the canals, too, they emerge periodically, and in the same but a
retarded succession. They “are therefore, in the first place, seasonal
phenomena, and, in the second place, phenomena that depend for their
existence upon the prior existence of the canals.”[39]

Mr. Lowell terms them “oases” (see Fig. 14), and does not shrink from
the full implication of the term.

The most important result of the numerous observations of Mars, made
during the oppositions of 1892 and 1894, was the recognition of a
regular course of change dependent upon the succession of its seasons.
Schiaparelli had long anticipated this result; he is commonly in advance
of his time. These changes, moreover, when closely watched, are really
self-explanatory. The alternate melting of the northern and southern
snow-caps initiates, and to some extent determines them. As summer
advances in either hemisphere, the wasting of the corresponding white
calotte can be followed in every minute particular. “The snowy regions
are then seen to be successively notched at their edges; black holes and
huge fissures are formed in their interiors; great isolated fragments
many miles in extent stand out from the principal mass, dissolve, and
disappear a little later. In short, the same divisions and movements of
these icy fields present themselves to us at a glance that occur during
the summer of our own arctic regions.”[40]

Indeed, glaciation on Mars is much less durable than on the earth. In
1894, the southern snow-cap vanished to the last speck 59 days after the
solstice; and the remnant usually left looks scarcely enough to make a
comfortable cap for Ben Nevis. An immense quantity of water is thus set
free. The polar seas overflow; gigantic inundations reinforced,
doubtless, from other sources, spread to the tropics; Syrtis regions of
marsh or bog deepen in hue, and become distinctly aqueous; canals dawn
on the sight, and grow into undeniable realities. We seem driven to
believe that they discharge the function of flood-emissaries.

Mr. Lowell does not hesitate to pronounce them of artificial formation,
and, on that large assumption, the purpose of their connexion with his
“oases” becomes transparently clear. They bring to these Tadmors in the
wilderness the water supply by which they are made to “blossom as the
rose.” The junction-spots, we are told, do not enlarge when the vernal
freshet reaches them; they only darken through the sudden development of
vegetation. These circular “districts, artificially fertilised by the
canal system,” are strewn broadcast over vast desert areas, the
orange-ochreous sections of Mars, covering the greater part of its
surface, but deep buried in the millennial dust of disintegrated red
sandstone strata.

“Here, then,” Mr. Lowell remarks,[41] “we have an end and reason for the
existence of canals, and the most natural conceivable—namely, that the
canals are constructed for the express purpose of fertilising the oases.
When we consider the amazing system of the canal lines, we are carried
to this conclusion as forth-right as is the water itself; what we see
being not the canal itself, indeed, but the vegetation along its banks.”

[Illustration:

FIG. 14.—_The Oases of Mars. Drawn by Percival Lowell._

(From “Popular Astronomy,” April, 1895.)
]

The idea that we see the water only by its effects along the shores of
these prodigious troughs, originated with Professor W. H. Pickering. It
is strikingly illustrated by the aspect of rivers from a balloon. Thus
the Rhine, as M. Flammarion attests,[42] seen from a perpendicular
altitude of 8,000 feet, shows like a green thread drawn in the midst of
a ribbon of meadow. The Martian canals, it is suggested, correspond to
the “ribbon of meadow.”

The hypothesis is seductive, but should not be hastily adopted. It gives
no account of the doubling of the canals, yet the process takes place on
a grand scale, at determinate epochs, and under fairly well ascertained
conditions. It undoubtedly belongs to the series of vernal changes going
forward upon the planet, and is accomplished with amazing rapidity. A
single canal may be transformed into a double canal within twenty-four
hours, and that simultaneously along its whole course. The two stripes,
so curiously substituted for one, “run straight and equal with the exact
geometrical precision of the two rails of a railroad.”[43] The tendency
is shared by the lakes or “oases.” “One of these,” we learn from the
same authority, “is often seen transformed into two short, broad dark
lines parallel to one another, and traversed by a yellow line.”

This singular principle of subdivision offers at present no hold for
profitable speculation. Schiaparelli trusts to the “courtesy of nature”
for some ray of light by which, in the future, to penetrate the mystery;
but wisely deprecates recourse being had to the intervention of
intelligent beings. Such arbitrary modes of dealing with perplexing
problems constitute, as he says, a grave obstacle to the acquisition of
just notions concerning them. They raise prepossessions by which the
progress of genuine research is impeded.

The proportion of water to land is much smaller on Mars than on the
earth. Only two-sevenths of the disc are covered by the dusky areas, and
of late the aqueous nature of some, if not all of these, has been
seriously called in question. Professor Pickering was convinced by his
observations, in 1892 and 1894, “that the permanent water area upon
Mars, if it exist at all, is extremely limited in its dimensions.”[44]
He estimated it at about half the size of the Mediterranean. Professor
Schaeberle is similarly incredulous. If the dark markings are seas, he
asks, how explain the irregular gradations of shade in them?[45] How,
above all, explain their apparent intersection by well-marked canals?
Professor Barnard, observing with the Lick thirty-six inch in 1894,
discerned on the Martian surface an astonishing wealth of detail, “so
intricate, small, and abundant, that it baffled all attempts to properly
delineate it.”[46] It was embarrassing to find these minute features
belonging more characteristically to the “seas” than to the
“continents.” Under the best conditions, the dark regions lost all trace
of uniformity. Their appearance resembled that of a mountainous country,
broken by cañon, rift, and ridge, seen from a great elevation. These
effects were especially marked in the “ocean” area of the hour-glass
sea.

Evidently the relations of solid and liquid in that remote orb are
abnormal; they cannot be completely explained by terrestrial analogies.
Yet a series of well-attested phenomena are intelligible only on the
supposition that Mars is, in some real sense, a terraqueous globe. Where
snows melt there must be water; and the origin of the Rhone from a great
glacier is scarcely more evident to our senses than the dissolution of
Martian ice-caps into pools and streams.

The testimony of the spectroscope is to the same effect. Dr. Huggins
found, in 1867, the spectrum of Mars impressed with distinct traces of
aqueous absorption, and the fact, although called in question by
Professor Campbell of Lick, in 1894, has been re-affirmed both at Tulse
Hill and at Potsdam. That clouds form and mists rise in the thin Martian
air, admits of no doubt. During the latter half of October, 1894, an
area much larger than Europe remained densely obscured. Whether or no
actual rain was at that time falling over the Maraldi Sea and the
adjacent continent, it would be useless to conjecture. We only know that
with the low barometric pressure at the surface of Mars, the boiling
point of water must be proportionately depressed (Flammarion puts it at
115° Fahrenheit), which implies that it evaporates rapidly, and can be
transported easily.

If the Martian atmosphere be of the same proportionate mass as that of
our earth, it can possess no more than one-seventh its superficial
density. That is to say, it is more than twice as tenuous as the air at
the summits of the Himalayas.[47] The corresponding height of a
terrestrial barometer would be four and a half inches. Owing, however,
to the reduced strength of gravity on Mars, this slender envelope is
exceedingly extensive. In the pure sky scarcely veiled by it, the sun,
diminished to less than half his size at our horizons, probably exhibits
his coronal streamers and prominences as a regular part of his noontide
glory; atmospheric circulation proceeds so tranquilly as not to trouble
the repose of a land “In which it seemeth always afternoon”; no cyclones
traverse its surface, only mild trade-winds flow towards the equator to
supply for the volumes of air gently lifted by the power of the sun, to
carry reinforcements of water-vapour north and south. Aerial movements
are, in fact, by a very strong presumption, of the terrestrial type, but
executed with greatly abated vigour.

Brilliant projections above the terminator of Mars were first distinctly
perceived at the Lick Observatory in 1890. They have been re-observed at
Nice, Arequipa, and Flagstaff (Mr. Lowell’s Observatory), coming into
view, as a rule, when circumstances concur to favour their visibility.
They strictly resemble lunar peaks and craters, catching the first rays
of the sun, while the ground about them is still immersed in
darkness;[48] and Professor Campbell[49] connects them with “mountain
chains lying _across_ the terminator of the planet,” and in some cases
possibly snow-covered. He calculates their height at about ten thousand
feet. Their presence was unlooked-for, since a flat expanse is a
condition _sine quâ non_ for the minute intersection of land by water,
which seems to prevail on Mars.

Although the sun is less than half as powerful on Mars as it is here,
the Martian climate, to outward appearance, compares favourably with our
own. Polar glaciation is less extensive and more evanescent, and little
snow falls outside the arctic and antarctic regions. Yet the theoretical
mean temperature is minus 4°C., or 61° of Fahrenheit below freezing.
This means a tremendous ice-grip. The coldest spot on the earth’s
surface is considerably warmer than this cruel average. Fortunately, it
exists only on paper. Some compensatory store of warmth must then be
possessed by Mars, and it can scarcely be provided by its attenuated
air. Possibly, internal heat may still be effective, and we see
exemplified in Mars the geological period when vines and magnolias
flourished in Greenland, and date-palms ripened their fruit on the coast
of Hampshire.

The climate of Mars, according to Schiaparelli,[50] “must resemble that
of a clear day upon a high mountain. By day a very strong solar
radiation hardly at all mitigated by mist or vapour; by night a copious
radiation from the soil towards celestial space, and hence a very marked
refrigeration; consequently, a climate of extremes, and great changes of
temperature from day to night, and from one season to another. And as on
the earth, at altitudes of from 17,000 to 20,000 feet, the vapour of the
atmosphere is condensed only into the solid form, producing those
whitish masses of suspended crystals which we call cirrus-clouds, so in
the atmosphere of Mars it would be rarely possible to find collections
of cloud capable of producing rain of any consequence. The variation of
temperature from one season to another would be notably increased by
their long duration, and thus we can understand the great freezing and
melting of the snow, renewed in turn at the poles at each complete
revolution of the planet round the sun.”

But the anomalies in the Martian domestic economy cannot thus easily be
removed, and the only safe conclusion is Flammarion’s, that “the general
order of things is very different on Mars and on the earth.”

The German astronomer, Mädler, searched in 1830 for a Martian satellite,
and although his telescope was of less than four inches aperture, he
satisfied himself that none with a diameter of as much as twenty-three
miles could be in existence. As it happened, he was right. The pair of
moons detected by Professor Asaph Hall with the Washington twenty-six
refractor, August 11 and 17, 1877, are unquestionably below that limit
of size. Neither of them can well be more than ten miles across. Their
names, “Deimos” and “Phobos,” are taken from the _Iliad_, where Fear and
Panic are introduced as attendants upon the God of War. Deimos revolves
in 30 hours and 18 minutes at a distance of 14,600 miles from the centre
of Mars. And, since the planet rotates in 24 hours 37 minutes, the
diurnal motion of the sphere from east to west is so nearly neutralised
by the orbital circulation of the satellite from west to east that
nearly 132 hours elapse between its rising and its setting. During the
interval, it changes four times from new to full, and _vice versâ_.
Professor Young estimates that Mars receives from it when full only
¹⁄₁₂₀₀th of full moonlight.

Phobos is more effective in illumination, both because it is larger, and
because it is less distant. At the Martian equator, its brightness is
equal to ¹⁄₆₀th that of our moon, but beyond 69° of latitude it is
permanently shut out from view by the curvature of the globe. This
exclusion is an effect of its uncommon closeness to its surface, the
interspace being only 3,700 miles, while its distance from the centre is
5,800. Moreover, the period of Phobos being only 7 hours 39 minutes, or
less than ⅓ the time of rotation of its primary, it rises in the west,
sets in the east, and courses across the heavens in 11 hours, during
which interval it accomplishes one entire cycle of its phases, and gets
through half another. This is an unique phenomenon, and points to an
unique origin for the little moon. No other known satellite revolves
more quickly than its primary rotates, and the discovery of the fact has
dealt a fatal blow to Laplace’s method of planetary evolution. Were
Phobos capable of raising any appreciable tide on Mars, its frictional
effects would hence be of an opposite character to those of other tidal
waves; and instead of being pushed outward, it would be drawn inward,
and finally precipitated upon the planet. But it derives safety, on the
one hand, from its small mass; on the other, from the insensibility of
Mars to tidal action. The satellite is incapable of exerting the
required influence; the planet is not in a state to respond to it, were
it exerted. For the configuration of land and water upon its surface is
such as effectually to prevent the flow of tides, were the compulsive
power a thousand-fold that possessed by its pair of diminutive
satellites.

CHAPTER VII.
THE ASTEROIDS.

Between the orbits of Mars and Jupiter is interposed a huge gap. On one
side of it lie the terrestrial planets; on the other, the “major
planets”—orbs belonging to a different order, both as to magnitude and
as to constitution. The hiatus marks a change of front in planetary
development, and its existence gravely compromises the symmetry of the
solar system. Its inconsistency with Bode’s law of planetary distances
long troubled investigators. A member of the series had somehow dropped
out; it was sought for under the form of a planet, and found,
apparently, as its disintegrated constituents. The discovery of Uranus
nearly at the distance indicated for it by the law roused astronomers to
the necessity for a systematic chase; but before their organisation had
got into full working order, the missing occupant of the vacant zone
presented itself spontaneously. This was Ceres, the first asteroid,
discovered by Piazzi at Palermo, January 1, 1801, the opening day of the
present century.

A series of surprises followed. While watching its path, Dr. Olbers,
March 28, 1802, came across an associated body. He named it Pallas, and
it was at once proved by the calculations of Gauss to revolve
practically at the same distance from the sun as Ceres. _Both_ occupied
nearly the position required by Bode’s law. This double fulfilment was
more than was bargained for; it was unprecedented and perplexing; but
the anomaly was temporarily removed by Olbers’ daring hypothesis of an
exploded planet. The prediction based upon it that the acquaintance made
with two specimen-products of the catastrophe would be followed by an
introduction to many more, was strikingly verified by Harding’s
discovery of Juno, September 1, 1804, and by Olbers’ of Vesta, March 29,
1807. By a further coincidence, both were at the time situated in the
positions suggested as the most promising for a successful search—that
is, near the line of intersection which should necessarily be common to
orbits described by fragments of a single original mass.

The four asteroids received for many years no accession to their
numbers. They were found to deviate, in several respects, from the
example set them by the planets, properly so-called. They revolve,
indeed, from west to east, thus following the current of systemic
movement; but their paths are considerably eccentric and highly tilted.
Each one of the quartette transgresses the zodiacal limits; and Pallas
travels at an angle of no less than thirty-five degrees to the plane of
the ecliptic.

Vesta, the brightest asteroid, can occasionally be seen with the naked
eye; but the natural inference that it is the largest has lately been
disproved. No trustworthy measurements of the real _discs_ of the
asteroids had been made until Professor Barnard in 1894 successfully
performed the feat with a power of 1000 on the Lick refractor. The
upshot has been to substitute Ceres for Vesta as the leading member of
the group. Its diameter proved to be 485 miles, Pallas coming next with
304, while those of Vesta and Juno are respectively 243 and 118 miles.
Now, Professor Edward Pickering, by comparing the brightness of the same
bodies, and assuming for all indiscriminately an albedo equal to that of
Mars, had arrived at a diameter for Vesta of 319, for Pallas of 169
miles. The disparity between his results and Barnard’s can be reconciled
only on the supposition of marked differences in reflective power. Their
reality was established by G. Müller’s photometric observations at
Potsdam.[51] Thus Ceres is large and dull, Vesta comparatively small,
but exceedingly bright—almost incredibly bright, indeed, since its
albedo is estimated at 0·72, which represents a lustre midway between
those of white paper and fresh-fallen snow. Ceres, on the other hand, is
as obscure as Mercury, while Pallas throws back proportionately somewhat
less, and Juno considerably more light than Mars.[52] The phases of
these last two bodies progress besides in such a manner as to show that
they are superficially uneven, and at quadratures flecked with profound
shadows.

The facts thus arrived at are disconcerting to the views previously
entertained. Few expected to meet with so much individuality in the
asteroids. They were looked upon rather as loaves from the same batch.
But now we find among them bodies as physically unlike as Venus and the
moon. Ceres must be composed of rugged and sombre rock, unclothed
probably by any vestige of air. Vesta displays a brilliant shell of
clouds. And from Vesta alone among the asteroids, Vogel derived in 1873
some uncertain indications of atmospheric action upon the sun-rays
reflected by it. There is, nevertheless, great difficulty in supposing a
body of no more than one-thousandth the mass of Mars endowed with a
dense atmosphere. Yet it must be dense and extensive in order to
maintain the heavy cloud-layer implied, so far as our present knowledge
goes, by an unusually high albedo. The difficulty is this. All gases
tend, by their nature, to become indefinitely diffused through space.
They can be restrained within a sphere of finite radius only through the
exertion of some force capable of holding their elasticity in check.
This force is gravity; none other suitable for the purpose is known. It
acts as a counterpull to the translational velocities of the gaseous
particles which, according to the dynamical theory of gases, constitute
their elasticity. But if the confining power be insufficient, the roving
particles will dart away, each on its own account, and will cease to
form an atmosphere. This condition was adverted to some years ago by Dr.
Johnstone Stoney, and he calculated the mass needed to secure to a
heavenly body the lasting possession of an aerial envelope. It differs
naturally for different gases; the lightest particles being affected by
the swiftest movements, and hence being the readiest to escape. The
earth, on this view, is impotent to retain hydrogen; since the critical
velocity at its surface is seven miles a second, and hydrogen-molecules
can, now and again, attain 7·4 miles, so that they would dribble away,
one after another, until the whole original supply was exhausted. Mars
(a projectile fired from which, with a speed exceeding three miles a
second, would depart irrevocably), can but just hold oxygen, nitrogen,
and water-vapour, all with more massive and sluggish molecules than
those of hydrogen; while the moon has long ago been forsaken by whatever
gaseous substances primitively belonged to it. The mass of Vesta,
however, is only ¹⁄₃₁₂ the lunar mass (supposing their mean densities
the same); hence, if the relation just described holds good under all
circumstances, its surface _ought_ to be as bare and dry as any lunar
volcano. The albedoes of the asteroids raise, then, questions of
fundamental importance in planetary physics.

Endeavours to add to the asteroidal group, after having been
relinquished for over a score of years, were resumed, in 1830, by a
retired Prussian post-master named Hencke. His watch was rewarded with
the discoveries of Astraea, December 8, 1845, and of Hebe eighteen
months later. Since then, every year has regularly brought its quota of
detections. About forty astronomers devoted themselves systematically to
the search, and some of them reckoned their trophies by the score. No
less than eighty-five were credited, in 1893, to Palisa of Vienna;
Peters of Clinton (N.Y.), whose career closed in 1890, owned
forty-eight; Watson, another American professor, made testamentary
provision for his twenty-two clients, lest, for lack of computational
care, they should relapse into their former outcast condition. The task
is, indeed, a heavy one of keeping guard over some hundreds of minute
objects threading their way through a maze of orbits, amid throngs of
stars, from which they are indistinguishable except by continuous
observation, and the question, _Cui bono?_ has been asked, and has only
with hesitation been answered. But the business has, up to the present,
been kept going; the registry and inquiry asteroidal office remains open
at Berlin, and the almost overwhelming mass of calculations, necessary
for identification, is punctually dealt with.

The work and responsibilities of this department have, of late, been
alarmingly augmented. Until five years ago the telescope was the sole
implement of research in connection with it, but on December 22, 1891,
Professor Max Wolf of Heidelberg, discovered No. 323, afterwards named
Brucia, on a sensitive plate exposed with a six-inch portrait lens, of
thirty inches focus, and a field of seventy square degrees. Before the
year 1892 had closed, his photographic discoveries of the same kind
numbered eighteen, and they had, in January, 1897, run up to fifty-six,
of which five were recorded on the same night. He picked up, besides,
several “lost” or strayed asteroids. M. Charlois of Nice immediately
adopted Wolf’s method, and emulated his success. About ninety of these
objects have already fallen to his share by telescopic and photographic
means. In either case they are discriminated from stars solely by their
motion; but on sensitive plates its effects are directly visible, fixed
objects being represented by round dots, travelling objects by lines,
the length of which is proportionate to the amount of displacement
during the hour, or hours, of exposure.

About 440 asteroids are now established members of the solar system. It
has long been thought that numerical identification is as much as they
can properly claim; but the old and inconvenient system of mythological
nomenclature is still pursued. Indeed, the supply of goddesses is
running out, and has to be reinforced by apotheosis or invention.
Already, to some extent, as Professor Holden remarks, the asteroidal
catalogue “reads like the Christian names at a girls’ school.” Needless
to say that the brightness of the objects annually registered is in
steady course of decline. Very few of those now drawn to shore in the
photographic net are likely to exceed twenty miles in diameter. Yet
although mere planetary shreds, they are probably large compared with
the grains of planetary dust, numberless as the sands of the seashore,
which indiscernably revolve round the sun under analogous conditions.

Their aggregate mass is very small. Leverrier assigned for its superior
limit one-fourth that of the earth, but the limit, we may rest assured,
is very far from being attained. M. Niesten of Brussels estimated that
the first 216 asteroids, including all the larger ones, amounted to
¹⁄₁₀₀₀th the earth’s volume, and we may add, since they are beyond doubt
specifically lighter, to about ¹⁄₈₀₀₀th the earth’s mass. Mr. Roszl
finds for the mass of 311 asteroids one-fortieth that of the moon.[53]
Still later, M. Gustave Ravené has attempted to account for the
superfluous movement of the perihelion of Mars by the gravitational
influence of these bodies.[54] He computes the required mass to be
two-thirds that of the moon. In other words, he assumes the group to be
fairly represented by 500 globes as large as Juno (124 miles in
diameter), and of terrestrial density. But he obviously puts some
constraint on nature in order to secure the desired agreement.

The distribution of these dwarfed globes is not without significant
features. It is such, at any rate, as absolutely to negative Olbers’s
hypothesis of their origin through the explosion of an already formed
planet. They represent, on the contrary, the materials of a planet that
never was, and never will be formed. They follow paths curiously
intertwined. D’Arrest noticed forty-five years ago, as a proof of the
intimate relation subsisting among the members of what was then a small
group, “that, if their orbits are figured under the form of material
rings, these rings will be found so entangled that it would be possible,
by means of one among them taken at hazard, to lift up all the rest.”
They are not, however, scattered at random over the wide zone
appropriated to them which, at its extreme limits, measures three times
the radius of the earth’s orbit. It includes blank spaces which seem as
if cleared by some expulsive agency. That agency, as Professor Kirkwood
divined in 1866, is the disturbing power of Jupiter. For the blank
spaces occur where there would be commensurability of periods, and
whence, accordingly, revolving particles should be ejected by
accumulated perturbations. The clearing power was not exerted once for
all; it is still active. But its effectiveness in modifying distribution
is now perceived to be less complete than it seemed when our
acquaintance with the bodies in question was more limited. It has
produced in general only partial vacancies. M. Parmentier[55] analysed
in 1895 the arrangement in space of 390 orbits, with the result of
finding that some of the originally noted gaps had ceased to exist. The
mean distances, for instance, corresponding to periods two-sevenths and
three-sevenths the Jovian period, are fairly well frequented; while, on
the other hand, there is an unmistakable thinning out where five
revolutions are performed while Jupiter accomplishes two. He found again
that no asteroid circulates either in half, or in one-third the same
dangerous period. Yet, even since he wrote, No. 401 has been detected
occupying the former of these prohibited spaces. But this apparent
breach of rule may turn out to result from a miscalculation, as in the
case of Menippe, which has in consequence never been recaptured since
she first presented herself in 1878, and was erroneously assigned a
period two-fifths that of Jupiter. There is no doubt that the asteroids
are collected most densely about the mean distance 2·8 of the earth’s,
just where conformity to Bode’s law would place them. Nor is it less
certain that Kirkwood’s “rule of commensurability” has fundamentally
influenced their distribution.

He further discerned among them groups of two or three moving in
closely-related orbits. Additional examples of this sort of connexion,
which is far too close to be casual, have been pointed out by M.
Tisserand and Mr. Monck, and eighty asteroids are at present known to
have companions, their actual ties with which indicate, as Kirkwood
held, original identity. Each group consists of fragments of a primitive
nebular mass torn asunder by the unequal attraction of Jupiter shortly
after its detachment from the great parent sphere eventually condensed
to form the sun. As an example, we may take Juno and its twin Clotho.
Both revolve at a mean distance from the sun 2·67 times that of the
earth, in orbits of sensibly the same eccentricity, and of nearly the
same inclination to the ecliptic, their major axes diverging, however,
to the extent of ten degrees, obviously through unequal perturbations.
As surely as corresponding scars on opposite cliffs vouch for their
antique disruption, do these concurrent paths attest the primitive unity
of the pair of planetules traversing them. And bodies similarly
connected occur not in pairs only, but in triplets as well.

From whatever point of view the “planetary cluster” composed by the
asteroids is regarded, the influence of Jupiter is perceived as dominant
in the background. The manner of planetary production underwent a marked
change subsequently to the separation of his mighty mass. No interval of
repose followed; but a constant shredding off of chips and shavings.
This may safely be attributed (in accordance with Professor Kirkwood’s
surmise) to the tide-raising power of Jupiter at close quarters, by
which strain in the central rotating mass was almost prevented, through
the facility with which it was relieved. Hence the parent nebula long
remained incapable of parting with any appreciable portion of its
substance, and never resumed planet-making on the ancient scale. The
asteroids then came into existence under Jupiter’s auspices; they were,
while still in an inchoate state, subdivided, or even pulverised by his
disruptive influence, and scattered over the zone allotted to them under
the compulsion of his perturbing power.

CHAPTER VIII.
THE PLANET JUPITER.

Jupiter is by far the most important member of the solar family. The
aggregate mass of all the other planets is only two-fifths of his, which
316 earths would be needed to counter-balance. His size is on a still
more colossal scale than his weight, since in volume he exceeds our
globe 1,380 times. His polar and equatorial diameters measure
respectively 84,570 and 90,190 miles,[56] giving a mean diameter of
88,250 miles, and a polar compression of ¹⁄₁₆th. The corresponding
equatorial protuberance rises to 2,000 miles, so that the elliptical
figure of the planet strikes an observer at the first glance. This at
once indicates rapid axial movement; and Jupiter’s rotation is
accordingly performed in nine hours and fifty-five minutes, with an
uncertainty of a couple of minutes. The cause of this uncertainty will
presently appear.

The numbers just given imply that this great planet is of somewhat
slight consistence, and its mean density is in fact, a little less than
that of the sun. The sun is heavier than an equal bulk of water in the
proportion 1·4 to 1, Jupiter in the proportion of 1·33 to 1. The earth
is thus more than four times specifically heavier than the latter globe.
Three Jupiters would keep in equipoise four equal globes of water, while
the earth would turn the scale against five and a half aqueous models of
itself. This low density, an unfailing characteristic of all the giant
planets, is charged with meaning. It at once gives us to understand
that, in crossing the zone of asteroids, we enter upon a different
planetary region from that left behind. The bodies revolving there are
on an immensely larger scale of magnitude than those on the hither side;
they are of solar, rather than terrestrial, density; they rotate much
more rapidly, and are in consequence of a more elliptical shape; they
display, and most likely possess, no solid surface; they are attended by
retinues of satellites.

Jupiter circulates round the sun in 11·86 years, in an orbit deviating
by less than one and a half degrees from the plane of the ecliptic, but
of thrice the eccentricity of the ellipse traced out by the earth. With
a mean distance from the sun of 483 millions of miles, it accordingly
approaches within 462 at perihelion, and withdraws to 504 millions of
miles at aphelion. And since the heat and light received from the sun
are inversely as the squares of these numbers, it follows that Jupiter
is better warmed and illuminated when at the near than when at the far
extremity of its orbit, in the proportion of 109 to 100. Seasons it has
none worth mentioning; nor could they be of much effect even if they
were better marked. At its mean distance of 5·2 “astronomical
units”—that is, radii of the earth’s orbit—the sun’s potency is reduced
to ¹⁄₂₇th what it is here; we might accordingly have expected to meet in
this planet the conditions of a frozen world. But this anticipation has
been singularly falsified.

Under propitious circumstances Jupiter comes within 369 million miles of
the earth. These occur when he is in opposition nearly at the epoch of
his perihelion passage. His maximum opposition distance, on the other
hand, is 411 million miles. He is then at aphelion. Thus, at the most
favourable opposition, he is 42 million miles nearer to us than at the
least favourable. The effect on his brightness is evident to the eye.
When his midnight culmination takes place in October, he in fact sends
us one and a half times more light than when the event comes round to
April. We need only recall the unusual splendour of his appearance in
September and October, 1892, when his lustre was double that of Sirius.
His opposition period, as we may call it, is 399 days.

The intrinsic brilliancy of his surface is surprising, especially when
we consider that it is somewhat deeply tinged with colour. According to
Müller’s determination (relative to Mars), it actually returns 78 per
cent. of the incident light. But this would imply self-luminosity, the
presence of which is negatived by trustworthy evidence. Hence Zöllner’s
absolute albedo of 0·62 seems preferable. In either case, Jupiter does
not fall far short of being as reflective as white paper.

The minimum diameter of the visible disc considerably exceeds the
maximum of that of Mars. The latter never measures more than 25″;
Jupiter at conjunction, when (in round numbers), 600 million miles
distant from us, presents a surface 32″ in diameter, widened at a
favourable opposition to 50″. Even with a low power it thus makes a
beautiful and interesting telescopic object Its distinctive aspect is
that of a belted planet, the belts varying greatly in number and
arrangement. As many as thirty have, on occasions, been counted,
delicately ruling the disc from pole to pole. They are always parallel
to the equator, but are otherwise highly changeable, and cannot be too
closely studied as an index to the planet’s physical constitution. Two
in particular are remarkable. They are called the north and south
equatorial belts, and enclose a lustrous equatorial zone. The poles are
shaded by dusky hoods.

This general scheme of markings, however, when viewed with one of the
great telescopes of the world, is so overlaid with minor particulars as
sometimes to be scarcely recognisable. One cannot see the wood for the
trees. Lovely colour-effects, too, come out under the best circumstances
of definition and aerial transparency. The tropical belts may be
summarily described as red; but they are of complex structure, and their
subordinate features and formations are marked out, under the sway of a
ternating and tumultuous activities, by strips and patches of vermilion,
pink, purple, drab and brown. The intermediate space is divided into two
bands by a line, or narrow riband, pretty nearly coinciding with the
equator, and rosy, or vivid scarlet in hue. The polar caps are sometimes
of a delicate wine-colour, sometimes pale grey.

Professor Keeler made an elaborate study of the planet with the Lick
36-inch in 1889, and executed a series of valuable drawings, one of
which we are privileged to reproduce (Fig. 15). With a power of 320, the
disc, he tells us, “was a most beautiful object, covered with a wealth
of detail which could not possibly be accurately represented in a
drawing.” Most of the surface was then “mottled with flocculent and
irregular cloud-masses. The edges of the equatorial zone were
brilliantly white, and were formed of rounded, cloud-like masses, which,
at certain places, extended into the red belt as long streamers. These
formed the most remarkable and curious feature of the equatorial
regions. They are the cause of the double or triple aspect which the red
belts present in small telescopes.”[57]

Near their starting-points the streamers were white and sharply defined,
but became gradually diffused over the ruddy surface of the belts. When
at all elongated, they invariably flowed backward _against_ the
rotational drift, and were inferred to be cloud-like masses expelled
from the equatorial region, and progressively left behind by its
advance. This hypothesis was confirmed by the motion of some bright
points, or knots, on the streamers. “The portions of the equatorial zone
surrounding the roots of well-marked streamers were somewhat brighter,”
Professor Keeler continues, “than at other places, and it is a curious
circumstance that they were almost invariably suffused with a pale
olive-green colour, which seemed to be associated with great
disturbance, and was rarely seen elsewhere.”

[Illustration:

FIG. 15.—_Jupiter, October 3, 1890. Drawn by Professor Keeler with the
great Lick Refractor. The Red Spot is visible._
]

Now, if the material of the streamers had been simply a superficial
overflow, it should have carried with it into higher latitudes an excess
of linear rotational speed, and should hence have pushed its way onwards
as it proceeded north and south. But, instead, it fell behind; its
velocity was less, not greater than that of the belts with which it
eventually became incorporated. What are we to gather from this fact?
Evidently that the currents issuing north and south were of eruptive
origin. Their motion, in miles per second, was slow, because they
belonged to profound strata of the planet’s interior. Their backward
drift measured the depth from which they had been flung upward.

The spots, red, white, and black, constantly visible on the Jovian
surface, excite the highest curiosity. They are of all kinds and
qualities, and their histories and adventures are as diverse as they are
in themselves. Some are quite evanescent; others last for years. At
times they come in undistinguished crowds, like flocks of sheep, then a
solitary spot will acquire notoriety on its own account. White spots
appear in both ways; black spots more often in communities; and it is
remarkable that the former frequent distinctively, though not
exclusively, the southern, the latter the northern hemisphere. Red
spots, too, develop pretty freely; but the attention due to them has
been mainly absorbed by one striking specimen.

The Great Red Spot has been present with us for at least nineteen years;
and it is a moot point whether its beginnings were not watched by
Cassini more than two centuries ago. Its modern conspicuousness,
however, dates from 1878. Then of a full brick-red hue, and
strongly-marked contour, it measured 30,000 by nearly 7,000 miles, and
might easily have enclosed three such bodies as the earth. It has since
faded several times to the verge of extinction, and partially recovered;
but there has never been a time when it ceased to dominate the planet’s
surface-configuration. More than once it has been replaced by a bare
elliptical outline, as if through an effusion of white matter into a
mould previously filled with red matter; and just such a sketch was
observed by Gledhill in 1870. The red spot is attached, on the polar
side, to the southern equatorial belt. It might almost be described as
jammed down upon it; for a huge gulf, bounded at one end by a jutting
promontory, appears as if scooped out of the chocolate-coloured material
of the belt to make room for it. Absolute contact, nevertheless, seems
impossible. The spot is surrounded by a shining aureola, which seemingly
defends it against encroachments, and acts as a _chevaux de frise_ to
preserve its integrity. The formation thus constituted behaves like an
irremovable obstacle in a strong current. The belt-stuff encounters its
resistance, and rears itself up into a promontory or “shoulder,”
testifying to the solid presence of the spot, even though it be
temporarily submerged. The great red spot, the white aureola, and the
brownish shoulder are indissolubly connected.

The spot is then no mere cloudy condensation. Yet it has no real fixity.
Its period of rotation is inconstant. In 1879–80, it was of 9 hours, 55
minutes, 34 seconds; in 1885–86, it was longer by 7 seconds. The object
had retrograded at a rate corresponding to one complete circuit of
Jupiter in six years, or of the earth in seven months.[58] It is not
then fast moored, but floats at the mercy of the currents and breezes
predominant in the strange region it navigates. A quiescent condition is
implied by the approximate constancy of its rotation-period during the
last ten years. With the paling of its colour, its “proper motion”
slackens or ceases. This must mean that, at its maxima of agitation, it
is the scene of uprushes from great depths, which, bringing with them a
slower linear velocity, occasion the observed laggings. It is not
self-luminous, and shows no symptom of being depressed below the general
level of the Jovian surface. A promising opportunity was offered in 1891
of determining its altitude relative to a small dark spot on the same
parallel, by which, after months of pursuit, it was finally overtaken.
An occultation appeared to be the only alternative from a transit; yet
neither occurred. The dark spot chose a third. It coasted round the
obstacle in its way, and got damaged beyond recognition in the process.
Its material, as Mr. Stanley Williams observed, “was diverted and forced
bodily southwards, and obliged to pass round the southern side of the
red spot as if it were an island projecting above a stream.”

Jupiter has no certain and single period of rotation. Nearly all the
spots that from time to time come into view on its disc are in relative
motion, and thus give only individual results. The great red spot has
the slowest drift of all (with the rarest exceptions), while the black
cohorts of the northern hemisphere outmarch all competitors. Mr. Stanley
Williams,[59] as the upshot of long study, has delimitated nine
atmospheric surfaces with definite periods. They are well marked, and
evidently have some degree of permanence, yet the velocities severally
belonging to them are distributed with extreme irregularity. Thus, two
narrow, adjacent zones differ in movement by 400 miles an hour. This
state of things must obviously be maintained by some constantly acting
force, since friction, if unchecked, would very quickly abolish such
enormous discrepancies. The rotational zones are unsymmetrically placed;
there is no correspondence between those north and south of the Jovian
equator; and, although the equatorial drift is quicker than that of
either tropic, it is outdone in 20° to 24° north latitude. The stability
of this anomalous mode of rotation was remarkably illustrated by Dr.
Rambaud’s measurements of the “Garnet Spot” of October, 1895. Its
movement proved to be strictly conformable to that of the zone in which
it was situated (10° to 20° north latitude), and to agree, moreover,
within a fifth of a second with the value deduced by Schröter in 1787
for that of a spot in the same “zenographical” district.[60]

Jupiter’s equatorial rotation, as indicated by observations of spots, is
accomplished in 9 hours 50 minutes; but Bélopolsky’s and Deslandres’
spectrographic determinations gave rates of approach and recession
falling somewhat short of the corresponding velocity.[61] Possibly the
spots forge ahead in the medium that sustains them; or it may be, as M.
Bélopolsky suggests, that the planetary sphere itself has been measured
too large, owing to refraction in its atmosphere.

However this be, the rotation of the great planet, albeit ill-regulated
(if the expression be permissible), is distinctly of the solar type. It
is itself a “semi-sun,” showing no trace of a solid surface, but a
continual succession of cloud-like masses belched forth from within.
Each series, in fact, of certain classes of markings, such as the
equatorial “port-holes,” plainly owes its origin to the rhythmical
activity of a solitary, deep-buried focus.[62] Jupiter’s low mean
density, considered apart from every other circumstance, suffices to
demonstrate the primitive nature of his state. Under the enormous
pressure reigning in his interior, the same materials should be vastly
more massive, specifically, than within our own small globe; their
fourfold expansion gives us to understand the intensity of that heat by
which pressure has been so much more than neutralised. Moreover, the
agitations due to the cooling of a fluid globe make their mark on its
turbulent surface. On a solidified body like the earth, circulation is
kept up by heat received from without, and is purely atmospheric, and
essentially horizontal. In a sun-like body, the circulation is bodily
and vertical. That the processes going on in Jupiter are of this kind is
beyond question. Exchanges of hot and colder substances are effected,
not by surface-flows, but by up and down rushes. The parallelism of his
belts to his equator makes this visible to the eye. An occasional
oblique streak[63] betokens a current in latitude, but it is
exceptional, and might be called out of character.

Jupiter’s true atmosphere encompasses the disturbed shell of vapours
observed telescopically. Its general absorptive action upon light is
betrayed by the darkening of the planet’s limb—another point of
resemblance to the sun; while its special, or selective, absorption can
only be detected with the spectroscope. The arresting effect of
water-vapour was early noticed by Huggins and Vogel, and they measured a
strong line in the red of unknown origin, but contained in banded star
spectra. Atmospheric absorption is strongest above the ruddy equatorial
belts, which are hence concluded to be placed at a lower level than the
white surface.

Planetary photography was set on foot by Dr. Gould of Boston, in 1879,
when he obtained some promise of success with Mars, Jupiter, and Saturn;
and Dr. Lohse prosecuted the subject in 1883. The actinic power of
Jupiter’s light is very remarkable. It surpasses that of moonlight nine
times, and that of Mars twenty-four times. Dr. Lohse further ascertained
that the southern hemisphere is twice as chemically effective as the
northern.[64] This superiority is doubtless connected with the greater
physical agitation of the same region. A series of photographs of
Jupiter, taken in 1891 with the great Lick refractor, were the first of
any value for purposes of investigation. Each is one inch in diameter;
the image of the planet having been enlarged eight times before being
received upon the plate. Mr. Stanley Williams found them full of
interesting detail. Figure 16 shows an enlargement of a striking
photograph taken by Professor E. C. Pickering.

Jupiter’s satellites were the first trophies of telescopic observation.
They are, indeed, bright enough for naked eye perception, could they be
removed from the disc which obscures them with its excessive splendour;
and the first and third have actually been seen, in despite of the
glare, by a few persons with phenomenally good eyesight. The
mythological titles of the Galilean group—Io, Europa, Ganymede, and
Calypso (proceeding from within outward) have been superseded by prosaic
numbers. The change was unlucky, but is now probably irremediable.

The Jovian family presents an animated and attractive spectacle. The
smallest of its original members (No. II.) is almost exactly the size of
our moon; the largest (No. III.), with its diameter of 3,550 miles,
considerably exceeds the modest proportions of Mercury. Satellite I.
revolves in 42½ hours at the same average distance from Jupiter’s
surface that our moon does from that of the earth. No. II. has a period
of 3 days 13 hours, and its distance from Jupiter’s centre is 415,000
miles. Both these orbits are sensibly circular; and Nos. III. and IV.
travel in ellipses of very small eccentricity, the one at a mean
distance of 664,000, the other at 1,167,000 miles, in periods
respectively of 7 days 4 hours, and 16 days 16½ hours. All four revolve
strictly in the plane of Jupiter’s equator.

[Illustration:

FIG. 16.—_Photograph of Jupiter. Exposure, 87 seconds._

(From _Knowledge_, November, 1889.)
]

They constitute a system bound together by peculiar dynamical relations,
in consequence of which they can never be all either eclipsed, or seen
aligned at one side of their primary, at the same time. They can all,
however, be simultaneously hidden behind it, or in its shadow; although
this moonless condition is looked out for as a telescopic rarity.

The varied phenomena of eclipses, occultations, and transits, offer the
interest, not only of predictions fulfilled, but sometimes of
discrepancies detected. The three inner satellites plunge through the
huge neighbouring shadow-cone at every revolution; the fourth, owing to
its greater distance, escapes eclipse when the shadow makes an
appreciable angle with the plane of its orbit. When Jupiter is in
opposition or conjunction, occultations, but no eclipses, of his moons
take place; at other periods, the two kinds of obscuration merge into,
or succeed each other. “Time cannot stale their infinite variety.”

From observations of the eclipses of Jupiter’s satellites, Olaus Römer
gathered, in 1675, the first intimations of the finite velocity of
light. He noticed that their visibility was alternately retarded and
accelerated as the earth withdrew from, and approached the scene of
their occurrence; and he designated half the extreme difference, or the
time occupied by light in travelling from the earth to the sun, the
“equation of light.” Its value is 500 seconds; and until recently, no
other measure was available of that fundamental constant of nature—the
rate of luminous transmission.

The transits of the satellites across the Jovian disc present many
curious appearances, due to complicated and changeable effects of light
and shade both upon the planetary background, and upon the little
circular objects self-compared with it. These, in the ordinary course,
show bright while near the dusky limb, then vanish during the central
passage, and re-emerge again bright at the opposite side. But, instead
of duly vanishing, they now and then darken even to the point of
becoming indistinguishable from their own shadows, by which they are
preceded or followed. This difference of behaviour cannot be attributed
wholly to varieties of lustre in the sections of the disc transited;
otherwise, it could be predicted. But this has never been attempted;
“black transits” come when least expected. The third and fourth
satellites are those chiefly subject to these phases; the second has
never been known to exhibit them; and they but slightly affect the
first. A drawing by Professor Barnard of one of its bright transits with
an attendant shadow that Peter Schlemyl might have envied, is reproduced
in Figure 17. Its belted appearance, detected by that eminent observer,
will be noted. Indeed, all the satellites, except perhaps No. II. are
striped or spotted; and this leads to seeming deformations in their
shape, as well as fluctuations in their brightness, the markings being
evidently of atmospheric origin, and hence changeable. Their distinct
and accurate perception has been made possible by the excellence of the
Lick thirty-six inch refractor.

[Illustration:

FIG. 17.—_Transit of Jupiter’s first Satellite, with Shadow, drawn by
Prof. Barnard, November 19, 1893._ (From _Monthly Notices_, January,
1894.)
]

Jupiter’s moons seem to resemble him in constitution. The three first
possess the same high reflective power. No. II. is as bright as the
planet’s brightest parts, so that its albedo cannot fall short of 0·70.
And even No. IV. (formerly designated “Calypso” in reference to its
frequent obscurations) exactly matches, during its darkest phases, the
blue-grey polar hoods of its primary. On an average, too, the satellites
seem to be of about the same mean density as Jupiter, No. I. being
considerably the lightest for its bulk; and their spectra, according to
Vogel’s observations in 1873, are composed of solar rays modified in
precisely the same way as those reflected by the planet. Nothing is
known quite certainly about their rotation-periods. Sir William Herschel
concluded them to be of the same length with their periods of
revolution; but recent work throws some doubt upon the reality of this
agreement.

The discovery, September 9, 1892, of Jupiter’s “fifth satellite” was one
of the keenest astronomical surprises on record. An accession to a
system so symmetrically arranged, so complete, to our judgment, as it
stood, appeared superfluous, and, considering the eager scrutiny devoted
to it during 282 years, well-nigh incredible. But the extra member was
in truth out of reach until it was found; original discovery being, as
every one knows, a greatly more arduous feat than subsequent
verification. Nor could it have been casually detected. Professor
Barnard seized the opportunity, lent by the specially favourable
opposition of 1892, to rummage the system for novelties. Keeping the
telescopic field dark by means of a metallic bar placed so as to occult
the gorgeous planetary round, he sought, night after night, for what
might appear. At length, on September 9, he caught the glimmer he
wanted, and made sure, September 10, that it truly intimated the
presence of a new satellite.

This small body revolves in a period of 11 hours, 57 minutes, 23
seconds, at a mean distance of 112,160 miles from Jupiter’s centre, or
67,000 from his bulged equatorial surface. Hence, it should by right be
called “No. I.” instead of “No. V.” The major axis of the ellipse in
which it circulates advances so rapidly, owing to the disturbance caused
by Jupiter’s spheroidal figure, as to complete a revolution in five
months. The implied eccentricity of its orbit, as M. Tisserand has
shown,[65] very slightly exceeds that of the orbit of Venus, yet it has
been made obvious by Barnard’s observations of the differences between
its east and west elongations. Its orbital velocity of 16½ miles a
second far surpasses that of any other satellite in the solar system.
Close vicinity to a mass so vast as Jupiter’s demands counter-balancing
swiftness. Its period of revolution being, however, longer by one hour
than Jupiter’s period of rotation, it so far conducts itself normally as
to rise in the east and set in the west. On the other hand, since its
progress over the sphere is measured by the difference between the two
periods, it spends five Jovian days in journeying from one horizon to
the other, running, in the meantime, four times through all its phases.
Yet it never appears full. Jupiter’s voluminous shadow cuts off sunlight
from it during nearly one-fifth of each circuit.

It is an exceedingly elusive telescopic object. There is no chance of
catching a glimpse of it except with a powerful and perfect telescope at
its “elongations,” or furthest excursions of about eight seconds of arc
on either side of the planet For the most part, it lurks within the
blaze as closely as Teucer behind the shield of Ajax. It is far too
small to be discerned in projection upon the disc, which, viewed from it
in mid-transit, is _full_ with a diameter of 42° 2′, and an area 6,440
times that of our moon. Yet, since its intrinsic lustre is less in the
proportion of 2 to 15, the light shed by Jupiter upon the “fifth
satellite” equals the joint radiance of no more than 860 full moons.

The new satellite is indistinguishable in aspect from a star of the
thirteenth magnitude. And its neighbour No. I. being of 5·6 magnitude,
we receive from it 910 times more light than from the stranger. If both
be equally reflective, the diameter of the latter is ¹⁄₃₀th the diameter
of the former, or, approximately, 80 miles. But its albedo is unlikely
to exceed that of Mars. By a rough estimate, therefore, this interesting
object measures 120 miles across, and 9000 such miniature globes would
go to the making of one full-sized Jovian attendant. Instead of being a
late addition to the system, or, so to speak, an afterthought, it may be
presumed, from the perceptible eccentricity of its path, to be the
senior member of the family. But the subject of its origin is not yet
ripe for discussion.

CHAPTER IX.
THE SATURNIAN SYSTEM.

Nearly twice as far from the sun as Jupiter revolves a planet, the
spacious orbit of which was, until 1781, supposed to mark the uttermost
boundary of the solar system. The mean radius of that orbit is 886
millions of miles; but in consequence of its eccentricity, the sun is
displaced from its middle point to the extent of 50 million miles, and
Saturn is accordingly 100 million miles nearer to him at perihelion than
at aphelion. The immense round assigned to the “saturnine” planet is
traversed in 29½ years, at the tardy pace of six miles a second. His
seasons are thus twenty-nine times more protracted than ours, and are
nominally more accentuated, since his axis of rotation deviates from the
vertical by 27°. But solar heat, however distributed, plays an
insignificant part in his internal economy. In the first place, its
amount is only ¹⁄₉₁th its amount on the earth; in the second, Saturn,
like Jupiter—even more than Jupiter—is thermally self-supporting. The
bulk of his globe comparatively to its mass suffices in itself to make
this certain. The mean diameter of Saturn is 71,000 miles, or nine times
(very nearly) that of the earth; if of equal density, its mass should
then be nine cubed, or 729 times the same unit The actual proportion,
however, is 95; hence the planet has a mean density of only ⁹⁵⁄₇₂₉, or
between ⅐th and ⅛th the terrestrial, and being thus composed of matter
as light as cork, would float in water. Professor G. H. Darwin has
moreover demonstrated, from the movements of its largest satellite, that
its density gains markedly with descent into the interior, so that its
surface-materials must be lighter than any known solid or liquid.

When at its nearest to the earth, Saturn is as large as a sixpence held
up at a distance of 210 yards.[66] But instead of being round like a
sixpence, it is strongly compressed—more compressed even than Jupiter.
The spectra of the two planets are almost identical. Both are impressed
with traces of aqueous absorption, and include the “red star line.”
About the albedo of Saturn there is some uncertainty. Zöllner made it
0·50, a very probable value; Müller of Potsdam determined it at 3·3
times that of Mars, the unit of his scale. For the value of the unit,
the only authority is Zöllner, who found Mars to give back 0·26 of the
light dispensed to him. Multiplying then 0·26 by 3·3 we get for the
albedo of Saturn 0·86, an impossible number for a non-luminous body, the
albedo of “untrodden snow” being, as already stated, 0·78.

Saturn resembles to the eye a large, dull star; its rays are entirely
devoid of the sparkling quality which distinguishes those of Jupiter.
But it shows telescopically an analogous surface-structure. Its most
conspicuous markings are tropical dark belts of a greyish or greenish
hue; the equatorial region is light yellow, diversified by vague white
spots; while the poles carry extensive pale blue canopies. The apparent
tranquillity of the disc may be attributed in part to the vast distance
from which it is viewed; yet not wholly. For lack of fiducial points, no
attempt was made to determine the planet’s rotation until 1794, when the
elder Herschel, by following an identified irregularity in a complex
banded formation, arrived at a period of 10 hours 16 minutes. The first
possibility of checking this result offered itself to Professor Hall of
Washington, after fourteen years of vain expectation, in the emergence
of a white spot just north of the equator, the movement of which gave
for the length of the Saturnian day, 10 hours, 14 minutes, 24 seconds.
In 1891–2, Mr. Stanley Williams made observations upon a good many such
objects; and their discussion by Mr. Denning afforded a mean period two
seconds longer than Hall’s. Individual variations, however, to the
extent of 14 seconds were brought out by it, proving that Saturnian,
like Jovian, spots have “proper motions,” and cannot be depended upon to
give the true rotation of the planet. Its compound nature may be
suspected, but has not yet been proved.

From measures executed by Barnard in 1895, it appears that the
equatorial diameter of Saturn is 76,470, its polar diameter 69,770
miles, giving a mean diameter of 74,240, and a compression of about
¹⁄₁₂. Gravity, at its surface, is only one-fifth more powerful than on
the earth.

Thus, Saturn not only belongs to the same celestial species as Jupiter,
but is a closely-related individual of that species. There is no
probability that either is to any extent solid. Both exhibit the same
type of markings; both betray internal tumults by eruptions of spots
which, by their varying movements, supply a measure for the profundity
of their origin; both possess identically constituted atmospheres, and
are darkened marginally by atmospheric absorption.

[Illustration:

FIG. 18.—_Saturn and its Rings. Drawn by Prof. Barnard, July 2, 1894._
]

Saturn is, however, distinguished by the possession of an unique set of
appendages. Nothing like them is to be seen elsewhere in the heavens;
and when well opened (as in Fig. 18) they form, with the globe they
enclose, and the retinue of satellites in waiting outside, a strange and
wonderful telescopic object. The rings, since they lie in the plane of
Saturn’s equator, are inclined 27° to the Saturnian orbit, and 28° to
the ecliptic. The earth is, however, comparatively to Saturn, so near
the sun, that their variations in aspect, as viewed from it, may in a
rough way be considered the same as if seen from the sun. They
correspond exactly with the Saturnian seasons. At the Saturnian
equinoxes, the rings are illuminated edgewise, and disappear, totally or
approximately; at the Saturnian solstices, sunlight strikes them nearly
at the full angle of 27°, first from _below_, then from _above_. At
these epochs, we perceive the appendage expanded into an ellipse about
half as wide as it is long. Two concentric rings (generally called A and
B) are then very plainly distinguishable, the inner being the brighter.
The black fissure which separates them is called “Cassini’s division,”
because that eminent observer was, in 1675, the first to perceive it. A
chasm known as “Encke’s division,” in the outer ring (A), is a thinning
out rather than an empty space; and temporary gaps frequently appear in
A, while B is entirely exempt from them. There are then two definite and
permanent bright rings, and no more; but with them is associated the
dusky formation discovered by W. C. Bond, November 15, 1850, and
described by Lassell as “something like a crape veil covering a part of
the sky within the inner ring.” It is semi-transparent the limb of
Saturn showing distinctly through it.

The exterior diameter of the ring-system is 172,800, while its breadth
is 42,300 miles.[67] The rings A and C are each 11,000 miles wide; while
B measures 18,000, Cassini’s division 2,270, and the clear interval
between C and the planetary surface somewhat less than 6,000 miles. Each
ring, C included, is brightest at its outer edge; but there is no gap
between the shining and the dusky structures, B shading by insensible
gradations up to C, yet maintaining distinctness from it. The earliest
exact determinations of the former were made by Bradley in 1719, since
when they have been affected by no appreciable change.[68] The
theoretically inevitable subversion of the system is progressing with
extreme slowness.

The thickness of the rings is quite inconsiderable. They are flat
sheets, without (so to speak) a third dimension. For this reason, they
disappear utterly in most telescopes, when their plane passes through
the earth, as it does twice in each Saturnian year. Only under
exceptional conditions, a narrow, knotted, often nebulous, streak
survives as an index to their whereabouts. On October 26, 1891,
Professor Barnard,[69] armed with the Lick refractor, found it
impossible to see them projected upon the sky, notwithstanding that
their shadow lay heavily on the planet It was not until three days
later, that “slender threads of light” came into view. The corresponding
thickness of the formation was estimated at less than fifty miles. The
phenomenon of the disappearance of the rings will not recur until July
29, 1907.

The constitution of this marvellous structure is no longer doubtful. It
represents what might be called the fixed form of a revolving multitude
of diminutive bodies. This was demonstrated by Clerk Maxwell in the
Adams Prize Essay of 1857. His conclusion proved irreversible. The
pulverulent composition of Saturn’s rings is one of the acquired truths
of science. An incalculable number of tiny satellites, revolving
independently in distinct orbits, in the precise periods prescribed by
their several distances from the planet, are aggregated into the
unmatched appendages of Galileo’s _tergeminus planeta_. The local
differences in their brightness depend upon the distribution of the
component satelloids. Where they are closely packed, as in the outer
margins of rings A and B, sunlight is copiously reflected; where the
interspaces are wide, the blackness of the sky is barely veiled by the
scanty rays thrown back from the thinly scattered cosmic dust. The
appearance of the crape ring as a _dark_ stripe on the planet results—as
M. Seeliger has pointed out—not from the transits of the objects
themselves, but from the flitting of their shadows in continual
procession across the disc.

The albedo of these particles is so high as to render it improbable that
they are of an earthy or rocky nature, such as the meteorites which
penetrate our atmosphere. The rings they form are, on the whole, more
lustrous than Saturn’s globe; but this superiority is held to be due to
the absence of atmospheric absorption. Their spectrum is that of
unmodified sunlight.

An eclipse of Japetus, the eighth Saturnian moon, by the globe and
rings, November 1, 1889, was highly instructive as to the nature of the
dusky appendage. The satellite was never lost sight of during its
passage behind it; but became more and more deeply obscured as it
travelled outward; then, at the moment of ingress into the shadow of
ring B, suddenly disappeared. Certainty was thus acquired that the
particles forming the crape ring are most sparsely strewn at its inner
edge—which is, nevertheless, perfectly definite—and gradually reach a
maximum of density at its outer edge. Yet, while there is not the
smallest clear interval, a sharp line of demarcation separates it from
the contiguous bright ring. Professor Barnard was the only observer of
these curious appearances. The distribution of the ring-constituents,
like that of the asteroids, was governed by the law of commensurable
periods, Saturn’s moons replacing Jupiter as the perturbing and
regulating power. Kirkwood showed in 1867, that Cassini’s division
represents a region of peculiarly strong disturbance; since a body
revolving there would have a period connected by a simple relation with
the periods of no less than _four_ satellites. Encke’s division, too, as
Dr. Meyer has indicated, and other lines of scanty occupation and
occasional vacancy, coincide with districts of space where similar
combinations occur.

The “satellite-theory” of Saturn’s rings has received confirmation from
apparently the least promising quarters. Professor Seeliger of Munich
showed, from photometric experiments in 1888, that their constant lustre
under angles of illumination ranging from 0° to 30° was proof positive
of their composition out of discrete small bodies.[70] And Professor
Keeler of Alleghany, by a beautiful and refined application of the
spectroscopic method, arrived at the same result in April, 1895.[71]
“Under the two different hypotheses,” he remarked, “that the ring is a
rigid body, and that it is a swarm of satellites, the relative motion of
its parts would be essentially different.” The former would necessarily
involve increasing velocity _outward_, the latter, increase of velocity
_inward_, just for the same reason that Mercury moves more swiftly than
the earth, and the earth than Saturn; while the sections of a solid
body, which could have but one period of rotation, should move faster,
_in miles per second_, the farther they were from the centre of
attraction. The line of sight test is then theoretically available; but
it was an arduous task to render it practically so. The difficulties
were, however, one by one overcome; and a successful photograph of the
spectra of Saturn and its rings gave the required information in
unmistakable shape. From measurements of the inclinations of five dusky
rays contained in it with reference to a standard horizontal line, rates
of movement were derived of 12½ miles per second for the inner edge of
ring B, and of 10 miles for the outer edge of ring A. The agreement with
theory was, as nearly as possible, exact; the components of the rings
were experimentally demonstrated to be moving, each independently of
every other, under the dominion of Kepler’s laws.

For the globe of Saturn, Professor Keeler obtained, by the same
exquisite method, a rotational period of 10 hours, 14 minutes, 24
seconds, in precise accordance with that indicated by the white spot of
1876, which thus seems to have had no proper motion, but to have floated
on the ochreous equatorial surface as tranquilly as a water-lily upon a
stagnant pool. The result, so far as it goes, hints that Saturn may be
really, as well as apparently, less ebullient than Jupiter.

Seers into the future of the heavenly bodies consider that the rings of
Saturn, like the gills of a tadpole, are symptomatic of an early stage
of development; and will be disposed of before he arrives at maturity.
They cannot be regarded otherwise than as abnormal excrescences. No
other planet retains matter circulating round it in such close relative
vicinity. It was proved by Roche of Montpellier that no secondary body
of importance can exist within less than 2·44 mean radii of its primary;
inside of that limit, it would be rent asunder by tidal strain. But the
entire ring-system lies within the assigned boundary; hence, being
_where_ it is, it can only exist _as_ it is—in flights of discrete
particles. Will it, however, always remain where it is?

“Clerk Maxwell,” wrote Mr. Cowper Ranyard,[72] “used to describe the
matter of the rings as a shower of brickbats, amongst which there would
inevitably be continual collisions. The theoretical results of such
impacts would be a spreading of the ring both inwards and outwards. The
outward spreading will in time carry the meteorites beyond Roche’s
limit, where, in all probability, they will, as Professor Darwin
suggests, slowly aggregate, and a minute satellite will be formed. The
inward spreading will in time carry the meteorites at the inner edge of
the ring into the atmosphere of the planet, where they will become
incandescent, and disappear as meteorites do in our atmosphere.”

Yet it may be that collisions are infrequent in this conglomeration of
“brickbats.” There is the strongest presumption that they all circulate
in the same direction, in orbits nearly circular, and scarcely deviating
from the plane of the Saturnian equator. Those pursuing markedly
eccentric tracks must long ago have been eliminated. Thus, encounters
can only occur through gravitational disturbances by Saturn’s moons, and
they must be of a mild character, depending upon very small differences
of velocity. The first sign of a “spreading outwards” should be the
formation of an exterior “crape ring,” of which no faintest trace has
yet been perceived.

Saturn’s rings are entirely invisible from its polar regions, but
occasion prolonged and complex eclipse-effects in its temperate and
equatorial zones. They have been fully treated of from the geometrical
point of view by Mr. Proctor in “Saturn and its System.”

Of this planet’s eight satellites, the largest, Titan (No. VI.), was
discovered first (by Huygens in 1655), and the smallest, Hyperion (No.
VII.), last (by Lassell and Bond in 1848). The five others were detected
by J. D. Cassini and William Herschel. Titan, alone of the entire group,
equals our moon in size. It measures, according to Professor Barnard,
2,720 miles across. Its period of revolution is nearly sixteen days, its
distance from Saturn’s centre, 771,000 miles. The orbit of Japetus (No.
VIII.) is the largest, and its period the longest of any secondary body
in the solar system. It circulates in 79⅓ days at a distance of
2,225,000 miles, equal to 59½ of Saturn’s equatorial radii. Hence its
path is of about the same _proportional_ dimensions as that of our moon.
Japetus is remarkable for its variability in light. It is capable of
tripling or quadrupling its minimum lustre. Sir William Herschel noticed
that these maxima coincided with a position on the western side of the
planet, and inferred rotation of the lunar kind. “From the changes in
this body,” he argued in 1792,[73] “we may conclude that some part of
its surface, and this by far the largest, reflects much less light than
the rest; and that neither the darkest nor the brightest side is turned
towards the planet, but partly one and partly the other, though probably
less of the bright side.”

This explanation, however, he admitted to be incomplete. There was, and
is, outstanding variability, which seems to intimate the presence of an
atmosphere and the formation of clouds. But no positive knowledge has
yet been gained regarding the physical state of Saturn’s moons. We may
nevertheless conjecture that, since tidal friction has destroyed the
rotation (as regards Saturn) of the remotest member of the family, it
has not spared those more exposed to its grinding-down action. All
presumably rotate in the same time that they revolve.

The five inner satellites move in approximately circular orbits; the
three outer in ellipses about twice as eccentric as the terrestrial
path. All, Japetus only excepted, keep strictly to the plane of the
rings. And since this makes an angle of 270 with the planet’s orbit,
eclipses are much less frequent here than in the Jovian system. They can
only occur when Saturn is within a certain distance (different for each)
from the node of the satellite-orbit. Even Mimas (No. I.), although it
wheels round the ring at an interval of only 34,000 miles, often slips
outside the obliquely-projected shadow-cone. Its distance from Saturn’s
centre is 118,000 miles, and it completes a circuit in 22½ hours.
Perpetually wrapped in the glare of its magnificent primary, it is a
very shy object, only to be caught sight of in its timid excursions by
the very finest telescopes. Like all the Saturnian moons, except Titan,
and, by a rare conjuncture, Japetus, it is far too much contracted to be
visible in transit across the disc.

The movements of these bodies have been carefully studied, and their
mutual perturbations to some extent unravelled. They have proved
exceedingly interesting to students of celestial mechanics. Titan has,
in this department, chiefly to be reckoned with. He exercises in the
Saturnian system a similar overpowering influence to that wielded by
Jupiter in the solar system. Mr. Stone finds its mass to be ¹⁄₇₆₀₀th
that of Saturn, showing that its density is nearly equal to that of our
moon. This seems to indicate an advanced stage of cooling. On the other
hand, its albedo is evidently very high. The other satellites appear in
the largest telescopes as mere stellar points.

CHAPTER X.
URANUS AND NEPTUNE.

The four giant planets, closely allied as they are, and strongly
distinguished in physical constitution from the terrestrial planets,
divide again of themselves into two sub-groups. Jupiter and Saturn have
much more in common than either has with Uranus or Neptune; while Uranus
and Neptune present peculiar analogies. Conclusions concerning one may
almost be said to apply to the other. Their enormous distance, it is
true, tends to efface minor differences; yet it is insufficient to
obliterate similarities of a peculiar kind.

Uranus is a globe 32,000 miles in mean diameter, and decidedly
elliptical in shape. Mädler and Schiaparelli agreed in assigning to it a
compression of ¹⁄₁₁; Barnard, in 1894, uninformed of their results,
noticed the disc to be more oval than Saturn’s. The indicated rotational
movement must be very swift; and a lucid spot watched by MM. Perrotin
and Thollon at Nice in 1884, seemed to fix it at about ten hours. This
was, however, only a vague estimate. Faint equatorial belts, too, have
with difficulty been seen. Remembering, indeed, that the object they
diversify is just large enough to be _annularly eclipsed_ by a cricket
ball two miles off, there is little cause for surprise at the
indistinctness of its surface-markings. They probably consist, like
those of Jupiter and Saturn, in dusky polar hoods, a brilliant
equatorial zone, and obscure intermediate bands. The last were seen as
“the merest shades on the planet’s surface,” and under a somewhat
deformed aspect, by the Lick observers in 1890 and 1891.[74] By
Professor Young in 1883, on the other hand, and by the MM. Henry at
Paris in 1884, they were observed to be symmetrically placed, parallel
one to the other, and of what might be called the normal type for great
planets. That they constitute, with the bright space they enclose, an
equatorial scheme of marking, was proved by Barnard’s comparison of the
trend (or position angle), determined for them by Young, with the
direction of the shortest axis of the little disc they traverse.[75]
Their considerable foreshortening in 1894 was, doubtless, the reason why
Barnard, with his acute vision, was compelled to rely upon earlier
observations, brought up to date by computation. Unless, indeed, the
markings are intrinsically variable.

This was suspected at Nice in 1889, when a thirty-inch refractor was
available for their scrutiny.[76] Dusky rulings were obvious on a
strongly compressed spheroid; and they ran parallel to the major axis of
the spheroid—that is, to the planet’s equator. But their appearance
varied, and their width seemed irregular. At the same establishment, but
with a fourteen-inch telescope, Uranus was observed, under particularly
favourable circumstances, March 18, 1884.[77] An unexpected resemblance
to Mars was apparent. The ordinarily sea-green disc was divided into a
sombre north-western and a bluish-white south-eastern hemisphere. Dark
spots were visible, and a conspicuous white one at the limb simulated a
snow-cap. But ulterior observations resolved the spots into belts, and
showed the shining patch to be, not polar, but equatorial. It was
presumably of an eruptive nature.

The axis upon which Uranus rotates is very much bowed towards the plane
of its orbit. Its seasons are hence abnormal; but their vicissitudes can
scarcely be sensible at a distance from the sun more than twice that of
Saturn. This, as Mr. Proctor noticed, is the only case in which the
ratio of one to two is exceeded in the radii of two adjacent planetary
orbits. The radius of the Uranian track, pursued at the leisurely pace
of 4⅕ miles a second, is 1,782 millions of miles, or more than 19
astronomical units. It consequently receives from the sun 370 times less
warmth and light than the earth does. Area for area, it is true, the sun
shines with the same intensity there as here; the difference lies in its
apparent size. Instead of the broad eye of day to which we are
accustomed, the luminary of Uranus presents a surface only 2¼ times that
of Jupiter, as seen from the earth at an _unfavourable_ opposition; and
although Uranus is 166 millions of miles nearer to the sun at perihelion
than at aphelion, no conspicuous difference would mark the passage from
one to the opposite point. This is accomplished in 42, the entire round
in 84 years.

In point of size, as Professor Young remarks, Uranus compares with the
earth very much as the earth compares with the moon. For its surface
exceeds the terrestrial surface about sixteen times, and its volume
amounts to sixty-six times the terrestrial volume. Its mass, however, is
less than fifteen times that of the earth, whence its density is
represented (in round numbers) by the fraction ¹⁵⁄₆₆. The large globe is
then nearly five times less dense than the small one, its materials
exceeding the weight of an equal bulk of water by only one-fifth.
Gravity is actually less at its surface than at the sea-level on the
earth. Every ton of coal, for instance, delivered in that remote globe
would fall short by two hundred pounds. The albedo of Uranus differs
little from that of Jupiter; if anything, it is somewhat higher, and is
nearly represented by the brilliancy of white paper.

The spectrum of Uranus indicates an emphatic departure from the
planetary conditions so far met with. This body is obviously surrounded
by a powerfully absorptive atmosphere, of a constitution foreign to our
experience. The greenish hue of the light which has traversed some of
its strata gives a preliminary indication of the manner in which it has
been affected. This its spectrum, first inspected by Secchi in 1869,
expounds in detail. He noticed a number of heavy dark bands in the red,
while the green and blue sections remaining open gave to the planet its
characteristic colour. A couple of years later, Huggins and Vogel
executed concordant measurements of six pronounced bands, besides some
faint streaks; and on June 3, 1889, the former obtained, with two hours’
exposure, a beautiful spectrographic impression extending far up into
the ultra-violet. A corroborative, though less comprehensive, photograph
was taken by Mr. Frost at Potsdam, April 23, 1892. Both included many
Fraunhofer lines, the presence of which demonstrates that the light of
Uranus, although more powerfully stamped with original absorption than
that of the rest of the planets, consists essentially of reflected solar
rays. Professor Keeler’s admirable series of visual observations with
the Lick refractor were undertaken in 1889 to test the truth of a
suggestion that this peculiar spectrum consisted of bright bands upon a
dark ground, and not of dark bands upon a bright ground. His decision in
favour of the latter alternative was without appeal.

Of the six principal dark bands representing the arresting action upon
light of the planetary atmosphere, four are quite distinctive; the fifth
is the “red star line” common to the spectra of Jupiter and Saturn; the
sixth is the hydrogen “F” (Hβ)—not definite and narrow as it is seen in
the solar spectrum, but hazy, and graduating in darkness towards the
middle, an undoubted outcome of native absorption.[78] Now, this is a
fact that implies a great deal. It gives direct evidence of a very high
temperature. Free hydrogen ceases to be present in a body upon which
water can form—given, of course, the presence of oxygen, which it would
be in the highest degree arbitrary to exclude. At one epoch of its
development, the earth must have been surrounded by immense volumes of
hydrogen. But with the diminution of heat, union with oxygen became
possible, and the gas vanished to reappear in the form of liquid oceans,
with their related hydrographic and cloud-systems. Uranus is
presumably—almost certainly—still too hot to permit the combination of
hydrogen and oxygen; and the absence from its spectrum of the slightest
trace of aqueous absorption strengthens this inference. Doubtless, the
time will come when the two elements will no longer be held at arms’
length; their affinities will come into play; the familiar,
all-important terrestrial liquid will be formed, and the geological
history of Uranus will begin.

Uranus is attended by four moons. They are named Ariel, Umbriel, Titania
and Oberon. Titania—the third in order of distance from the primary—is
the brightest of the group, and has a diameter of possibly one thousand
miles. Oberon is slightly inferior. Both were detected by Herschel in
1787. Ariel and Umbriel, captured by Lassell at Malta in 1851, are
insignificant bodies in themselves—their dimensions probably differing
but slightly from those of Hyperion, the seventh and least Saturnian
moon, estimated to measure five hundred miles across. They are among the
most difficult of telescopic objects, since they circulate about as
close to Uranus as Mimas and Enceladus do to Saturn, are physically
smaller, and more than twice as remote from the earth. Both were
believed variable by Lassell, and Newcomb obtained in 1875 plausible,
though not convincing, evidence that Ariel, at any rate, is subject to
light changes in the period of its orbital circulation, showing that,
here again, tidal friction has done its work of synchronising rotation
and revolution.[79] None of the four orbits are appreciably eccentric;
they all lie in the same plane, and are described in periods ranging
from 2½ to 13½ days.

The position of that plane is, however, exceedingly remarkable. It is
tilted at an angle of 98° to the ecliptic. This means that the
satellites move _backward_, against the succession of the zodiacal
signs. For direct becomes retrograde motion automatically, so to speak,
by turning the plane in which it is performed beyond the limit of the
vertical. The same fact is merely expressed in two different ways by
saying that the bodies in question travel from west to east at an angle
of 98°, or from east to west at an angle of 82° to the ecliptic. The
planes of the ecliptic and of the Uranian orbit deviate, it should be
mentioned, by only two-thirds of a degree. The disturbance by which the
Uranian system was set topsy-turvy did not in the least affect the
motion of Uranus itself.

Another unusual circumstance about that system is that the
satellite-plane departs widely from the equatorial plane. Our own moon,
it is true, is similarly circumstanced; but, on the Uranian scale, it is
nearly eight times farther from its primary than Ariel, and 2·6 times
farther than Oberon; while the enormous equatorial protuberance of
Uranus almost seems to impose conformity upon bodies revolving so close
to it. Conformity, none the less, is absent. The direction taken by the
equator of Uranus, as we have seen, is indicated in a two-fold manner:
first, by the trend of the belts; secondly, by the lie of the major
axis. And these indications agree. Supposed discrepancies between them
have been reconciled by improvements in the conditions of observation.
But with the equatorial line the plane of satellite-revolution cannot be
brought to coincide. The angle of divergence is uncertain, but may be
put roughly at 20°. This would give 78° for the inclination of the
Uranian equator, so that the rotation of the planet is likely to be
direct. If so, the extraordinary anomaly is here met with of a
satellite-system circulating in a direction opposite to that of its
primary’s rotation.

Uranus can at times be perceived with the naked eye. Indian traditions
of an eighth “dark” planet have been thought to refer to it, and its
slow course among the stars had been noted by savage tribes long before
Herschel singled it out from them by its tiny disc. It is about three
times brighter than Vesta; and Mr. Proctor stated that “in the summer of
1887 they were comparable under favourable conditions,” when both, in
the transparent skies of Florida, were “quite conspicuous without
telescopic aid.” Twenty chances of discovering Uranus were missed before
it came to Herschel’s turn. So many times it had been located or
catalogued as a fixed star by astronomers far from indifferent to
immortal fame.

Neptune is much nearer to the sun than it ought to be. Both Leverrier
and Adams assumed that Bode’s law would hold good for the planet still
below the horizon of knowledge; they could do no otherwise; yet the rule
played them false. Some have even asserted paradoxically that the planet
found was not the planet sought. In point of fact, the distance of the
theoretical Neptune is thirty-eight, that of the real Neptune thirty
astronomical units. The mean radius of its orbit measures 2,792 million
miles. Hence the sun is reduced to ¹⁄₉₀₀th its terrestrial brilliancy,
and could be replaced by 687 full moons. “As seen from Neptune,”
Professor Young remarks, “the sun would look very much like a large
electric arc lamp at a distance of a few feet. It would give about
forty-four millions the light of a first-magnitude star.”[80]
Accordingly, Neptune does not circulate by any means in outer darkness.
His orbit, although very slightly eccentric, brings him at perihelion
fifty millions of miles nearer to the sun than at aphelion. It makes an
angle of less than 2° with the ecliptic, and is traversed, at the rate
of 3⅓ miles a second, in a period of 165 years.

Neptune, being fainter than the eighth stellar magnitude, is quite
inaccessible to unaided vision. But a good telescope at once displays
the seeming star in the guise of a small planetary nebula with a
diameter of 2″·433. This mean value, reduced to the mean distance of the
planet from the sun, was afforded by Barnard’s measures in 1895 with a
power of 1,000 on the Lick refractor.[81] It corresponds to a linear
diameter of 32,900 miles. Neptune accordingly, although only 17 times
more massive than the earth, is 72 times more bulky, and composed of
materials 4·2 times specifically lighter. Gravity at its surface has
almost precisely its terrestrial power. The albedo of Neptune, combining
Zöllner’s with Müller’s results, is 0·65; and its spectrum appears
identical with that of Uranus. It may be inferred that this planet also
is too hot to contain water.

Its satellite is believed to be of about the size of the moon; but since
it is 12,000 times more distant, it can be distinguished only with the
most powerful telescopes as a star of the fourteenth magnitude. The
radius of its orbit measures 225,000, that of our moon 238,000 miles;
but Neptune’s attendant completes a circuit in 5 days 21 hours; and it
is through this rapidity of movement that the large mass of its primary
has been learned. It resembles the moon besides in being solitary, so
far as can be ascertained by the most diligent researches; and it is
beyond doubt that if any companion-bodies exist they are comparatively
small or obscure. That they do exist, appears probable on the face of
it.

The one Neptunian satellite emphasises the problems set by the Uranian
four. These problems are concerned with the origin and early mechanical
relations of the solar system. Here, at its utmost verge, we encounter a
decided reversal in the direction of systemic motion—a reversal prepared
for, as it might seem, by the nearly vertical position of the Uranian
plane of satellite-revolution. This diversity is in no sense
“accidental,” as some have unwisely asserted, invoking impacts of
comets, and such like futile devices, to account for it; it belongs
fundamentally to the design of planetary evolution. Laplace’s scheme has
no room for it; Faye’s, constructed expressly to include it, requires
that Uranus and Neptune, instead of being the first, should have been
the latest formed of all the solar train. And their obviously
rudimentary condition favours the suggestion. Neptune’s satellite
revolves from east to west in a quasi-circular path, inclined to the
ecliptic at an angle of 35°; or, putting it otherwise, it revolves from
west to east at an angle of 145°.

As the only member of the solar system exempt from perturbations by a
third body (the sun being too remote to cause perceptible deflections),
it seemed admirably fitted to discharge the functions of a standard
celestial clock, greatly needed, but nowhere to be found in our
system.[82] But in 1886 Mr. Marth drew attention to certain divagations
of this “ideal time-keeper” resulting from conspicuous changes in the
position and plane of its orbit. They were explained almost
simultaneously in 1888 by M. Tisserand,[83] late director of the Paris
Observatory, and by Professor Newcomb.[84] The disturbance, which, in
its mode of production, is analogous to the precession of the equinoxes,
results from the polar compression of the Neptunian globe combined with
a deviation of the satellite’s motion from its equatorial plane. By the
action of the protuberant girdle, a slow gyration of the secondary
body’s orbital plane is produced, its inclination to the primary’s
equator remaining unchanged. Viewed under a different aspect, the same
phenomenon may be described as a retrograde movement, in a period of at
least five hundred years, of the pole of the satellite’s orbit round the
pole of the planet’s equator. The radius of the circle described cannot
be less than 20°, implying a flattening of the Neptunian globe of
¹⁄₈₅th, and may easily amount to 30°, with which an ellipticity of ¹⁄₁₁₅
should be associated. But before the centre of this circle—that is, the
pole of Neptune’s axial movement—can be satisfactorily located, several
centuries must elapse. At present we may affirm with reasonable
certainty: first, that the rotation in question is retrograde, like the
satellite’s revolution; secondly, basing the inference upon the
comparatively slight ellipticity of Neptune’s figure, that it is much
slower than the vertiginous spinning of Jupiter, Saturn, and Uranus.

Uranus and Neptune are, as has been said, companion globes. In bulk and
density they differ very slightly; their albedoes are virtually the
same, their spectra indistinguishable. They seem perfectly alike in
chemical and physical constitution, and to be situated at precisely the
same stage of development. Both govern retrograde systems. In Uranus the
peculiarity appears as if in an incipient form; in Neptune, strongly
accentuated.

Viewed from the position of Neptune, all the planets are morning and
evening stars. They are tethered to the chariot-wheels of the sun,
instead of having the run of the sky. “The four terrestrial planets,”
Professor Young writes, “would be hopelessly invisible, unless with
powerful telescopes, and by carefully screening off sunlight. Mars would
never reach an elongation of three degrees from the sun; the maximum
elongation of the earth would be two, and that of Venus about one and a
half degrees. Jupiter, attaining an elongation of about ten degrees,
would probably be easily seen somewhat as we see Mercury. Saturn and
Uranus would be conspicuous, though the latter is the only planet of the
whole system that can be better seen from Neptune than it can be from
the earth.”[85]

To a spectator retreating with the velocity of light, all the planetary
cortège would in a few hours disappear, and the sun would shine alone.
No sign would remain that his office is purely ministerial—that he
exists only to enlighten, rule, and vivify the relatively minute globes
shred from his mass in the beginning, maintaining by his attractive
power the adjusted movements of the complicated piece of mechanism they
constitute. The skies perhaps hold millions of his stamp; every solitary
star telescopically visible may be the centre of a planetary scheme like
our own; or, on the other hand, our own may, quite conceivably, have no
counterpart in the wide universe.

CHAPTER XI.
FAMOUS COMETS.

In the fourth year of the 101st Olympiad (373 B.C.), the Greeks were
startled by a celestial portent. They did not, at that time, draw fine
distinctions, and posterity would have remained ignorant that the
terrifying object was a great comet but for the description of it left
by Aristotle, who saw it as a boy at Stagira. It was mid-winter when it
flared up from due west at sunset, its narrow, definite tail running
“like a road through the constellations” over a third of the heavens.
Diodorus relates that it cast shadows like the moon, which implies a
very unusual, yet not impossible, degree of brightness. The prompt
engulfment by an earthquake and its attendant tidal wave of the Achaean
towns, Helice and Bura, justified the apprehensions it aroused. It never
came back to retrieve its reputation. During at least two thousand
subsequent years, such objects lay under the ban of popular
superstition; and the counts upon which they were accused of malefic
influence were so many and so vague that acquittal was impossible. Their
respect of persons was notorious; nor were they consistent in their
dealings with the great, to whom alone they paid individual attention. A
comet marked the apotheosis of the great Julius; a comet announced the
death of Constantine; a comet illuminated the cradle of Napoleon.

The very word “comet” takes us back to the Stagyrite; for it is derived
from the Greek word κόμη, hair, and signifies a _hirsute_ star.
Shakspeare’s “crystal tresses” represent what we now, in homely fashion,
call the “tail,” while the “nucleus” and “coma” make up the “head.” The
nucleus, in great comets, shines like a star of the first magnitude,
sometimes indeed surpassing the brilliancy of Jupiter. It is usually of
measurable dimensions, often of granular texture. The planetary disc,
round which the filmy appendages of the comet of December 1618 were
displayed, was observed by Cysatus, a Jesuit astronomer at Ingolstadt,
to become transformed into the semblance of a star cluster; Hevelius
noticed a double nucleus in the comet of 1652; and modern instances of
the same kind abound. There is indeed no likelihood that substantial
globes are ever included in the construction of comets.

The coma is of immense volume, and extreme tenuity. The rays of faint
stars traverse, undimmed and unrefracted, strata of it tens of thousands
of miles in thickness. Yet strong lines of structure develop in it
through the influence of forces emanating from the sun. As they approach
our system out of the depths of space, comets are scarcely
distinguishable from round nebulæ, and they relapse into a similar
quiescent condition on leaving it. Their temperature must then be very
near the absolute zero of cold, since they cannot be supposed either to
contain stores of native heat, or to retain stores of borrowed heat.
Thus the rapidly augmenting power of solar radiation, as they rush with
accelerated velocity nearer and nearer to its source, produce upon them
stupendous effects. The nucleus blazes out into a coruscating star; the
coma, violently driven off from it, forms multiple envelopes like thin
gauze veils, one outside the other, flung round the nucleus on the side
next the sun, separated by intervening dark spaces, and diversified by
brilliant jets and sectors. The tail is the outcome of a double
repulsion. Matter expelled by the nucleus towards the sun is, at a
certain point, thrown back to form an immense, oppositely directed
appendage, usually convex on the forward side. Some tails resemble
hollow cones, being bright at the edges, and dark within: others are
traversed by a shining _backbone_; many, perhaps all, are composite. The
magnificent object first seen by Klinkenberg at Haarlem, December 9,
1743, was supplied with six, varying in length from 30° to 44°, each,
according to the extant representations, being separately _rooted_ in
the head. Grouped into a lustrous fan, they presented a very beautiful
and surprising appearance, not again to be displayed until the world and
humanity have undergone some unlooked-for changes. For the period of the
comet was computed to be one hundred thousand years! Tails, less
obviously and splendidly multiplex, are rather the rule than an
exception. Or rather, closer observations, chiefly photographic, have
made it manifest that the single efflux of nebulous stuff generally
designated as a comet’s tail can be analysed into bundles of fibres,
into straight rays and curved plumes of light, or into knotted and
branching emanations. Homogeneous outflows, such as are seen in
drawings, do not really exist. Tails pointing _towards_ the sun have
also been occasionally noticed; but they are always feeble. Olbers
recorded, however, that, during eight days of January, 1824, the comet
then visible had a solar tail of 7°, while its anti-solar tail was only
3½° long.

The great comet of 1680 will always be memorable for having had its
orbit calculated by Newton on gravitational principles. It was not
unworthy of the distinction. Approaching the sun almost in a straight
line, it penetrated the corona at the rate of 370 miles a second, and
passing within 140,000 miles of the photosphere, escaped by means of its
extraordinary velocity from those perilous precincts. Resulting internal
commotions became evident through the rapid development of a tail more
than a hundred million miles in length. Newton calculated that particles
from the head reached its extremity in two days. He assigned to the
comet a highly elliptical orbit traversed in six centuries. But, since
its speed might be called parabolic, millenniums may be nearer the mark
than centuries. It cannot, therefore, be identified with any earlier
apparition.

The comet of 1682 was Halley’s, the predicted return of which, in 1759,
was unprecedented and memorable. At its apparition in 1835, valuable
observations of a physical kind were made upon it by Bessel at
Königsberg, and by Sir John Herschel at the Cape. They were facilitated
by the circumstance that this far-travelling body, the perihelion
distance of which is 55 million miles, and the aphelion-distance 2½
times that of Neptune, approached the earth on this occasion within 4½
million miles. It was remarkable for singular and sudden changes of
aspect. To Bessel the nucleus seemed like a burning rocket. Divergent
flames issued from it towards the sun, and he took especial note of a
blazing “sector,” which swung like a pendulum to and fro, in a period of
4⅗ days. These emanations, accumulating at the surface where the solar
balanced the cometary repulsive force, were then swept back, as if by a
tempestuous wind, to form a tail, which, on October 15, measured at
least 24°. The conviction was forced upon him that the body in which
these wonderful processes were going on was affected by opposite
polarities; and he fully concurred with Olbers in the opinion that
tail-production was a purely electrical phenomenon.

During some time before and after its perihelion passage on November 16,
the comet wore the disguise of a star. All its hairy appendages had
vanished. On the 23rd of January, 1836, it was sharply stellar;
twenty-four hours later it had acquired, besides a twenty-fold increase
of light, a disc like that of the planet Neptune, enclosed in a nebulous
sheath of about fourfold breadth. Later in its career, Sir John
Herschel[86] observed the nucleus under the form of “a miniature comet,
having a nucleus, head, and tail of its own, perfectly distinct, and
considerably exceeding in intensity of light the nebulous disc or
envelope” containing it, which was, properly speaking, the “head” of the
comet. At last, on May 5, through the progress of distension, the last
thin shred of its substance melted into the sky. The next return of
Halley’s comet, somewhat accelerated by Jupiter’s influence, is looked
for in the year 1910.

The “vintage comet” lingered in northern skies during 510 days—from
March 26, 1811, until August 17, 1812. It was attentively observed by
Sir William Herschel, who gathered from it the then new truth that
comets are self-luminous bodies. “The quality of giving out light,” he
acutely remarked, “is immensely increased by an approach to the sun.”
But he failed to persuade his contemporaries or successors. His
inference had to wait for spectroscopic demonstration. The nucleus of
the comet of 1811 he found to measure 428 miles. It showed a ruddy hue,
and was eccentrically placed within a greenish-blue “planetary body”
127,000 miles in diameter. This was again enclosed in a shining
atmosphere about four times as wide, round which was flung an envelope
of a yellow tint, forming a thin hemispherical shell on the side next
the sun, and continued indefinitely away from the sun as the hollow cone
of the tail. Owing to this mode of construction, the space between the
head and the hemispherical sheath, as well as the central part of the
tail, appeared dark. The latter extended, in October, over 100 million
miles of space, and was 15 million miles broad. Its soft radiance
resembled that of the Milky Way, side by side with which it ran on
November 9, 1811. The comet’s path lay entirely outside the earth’s
orbit, and Argelander assigned to it a period of 3,065 years. The
restriction was needless. Between a period of infinite length, and one
of 3,000, or 1,000 years, no valid distinction can, where comets are in
question, be drawn. The short sections of their tracks observable from
the earth might belong equally well to parabolas or to the
far-stretching ellipses which such protracted periods imply.

The apparition of 1811 suggested to Olbers the “electrical theory” of
comets’ tails. The uncommon impressiveness with which it displayed not
uncommon phenomena, was perhaps a result of its considerable distance
from the sun, owing to which the _interior_ force obtained an advantage
over the _exterior_, and the locus of equilibrium between solar and
cometary repulsion was pushed back further than usual from the
nucleus.[87] He calculated that the materials of the tail spent 11
minutes in the journey from its root to its tip, indicating ejection by
a force greatly more powerful than the opposing force of gravity. Olbers
anticipated the modern view that chemical differences determine the
shapes of comets’ tails, the various species of matter being diversely
acted upon by electrical repulsion. The long, straight ray, for
instance, issuing from the comet of 1807, must, he perceived, have been
composed of particles much more energetically repelled than those
aggregated in the inflected plume with which it was associated. The
curvature of these appendages, in fact, depends upon the relation
between the orbital velocity of the comet and the velocity of ejection
imparted to their constituent molecules. It has to be borne in mind,
however, that while curved tails may appear straight in projection,
straight tails can never appear curved

Olbers’ classification of comets is still of great significance. He
divided them into:

(1.) Comets which develop no matter subject to solar repulsion. These
are without tails, and may be regarded as simple nebulosities devoid of
solid nuclei.

(2.) Comets showing no trace of nuclear, while subject to solar
repulsion. They throw out no matter _towards_ the sun; the heads are
consequently left bare of envelopes, and are of simple structure. The
comet of 1807 was of this kind.

(3.) Comets manifesting the effects of both species of action. They are
characterised by the presence of a dark hoop round the head, and of a
dark rift in the tail, by which it may be judged to be a hollow conoid.

On February 28, 1843, a “short, dagger-like object” blazed out at an
interval of only fifty-two minutes of arc from the sun’s limb. It was
viewed with amazement in various parts of the world; and spectators in
Italy, by shielding their eyes from the direct mid-day glare, were able
to discern a tail already several degrees long. The proportions of the
appendage rapidly grew. On March 3, it measured twenty-five degrees; on
March 11, an adjunct to it shot out, within twenty-four hours, to nearly
twice the apparent length of the main structure, conveying, as Sir John
Herschel said, “an astounding impression of the intensity of the forces
at work.” It was first seen in this country after sunset on March 17, as
“a perfectly straight, narrow band of white cloud, thirty degrees in
length, and about one and a half in width.” On the following night, Sir
John identified this “luminous appearance” as the tail of a grand comet,
stretching over an extent of space (as it afterwards proved) of no less
than two hundred millions of miles.

The movements of this body were as surprising as its aspect. It rushed
past perihelion with a speed of 366 miles a second, leaving an interval
of 100,000 miles between its centre and the sun’s surface, and swinging
through two right angles in two hours and eleven minutes. The northern
part of its course was finished in two hours and a half; hence, it was a
“southern” comet. Very curiously, it seems to have remained obscure
throughout its journey towards the sun, reserving its outburst for the
day _after_ perihelion. Periods were assigned to it ranging from seven
to six hundred years.

Strangest of all, it turned out to be but one member of a whole family
of similarly-conditioned bodies. The “great southern comet” of February,
1880, seemed like its ghost. It had no perceptible nucleus, but an
inordinately extended train, which rapidly faded; and it scarcely
deviated by a hair’s breadth from the track of its predecessor. That is
to say, so far as could be ascertained; for the object was so indefinite
as to elude exact observation. Its period could not even be conjectured.
The nature of the relationship between the comets was thus left
uncertain.

But after the lapse of two years and a half, the question was reopened
by the appearance of the leading constituent of the group. Like the
comet of 1843, the “great September comet” of 1882, was first seen close
beside the sun. At Ealing, shortly before noon, on September 17, Dr.
Common was struck with the astonishing spectacle of a brilliant comet
hurrying up to perihelion. A transit was evidently imminent, but clouds
veiled the scene. Its completion was, however, fortunately witnessed six
thousand miles away by Mr. Finlay and Dr. Elkin at the Cape Observatory.
The comet was watched by them “right into the boiling of the limb,”
which it had no sooner touched, than it utterly disappeared. This cannot
have been through the absence of contrast; for although its intrinsic
brilliancy was excessive, it must either have shown bright against the
sun’s dusky margin, or dark when projected upon his dazzling centre.
Since neither effect was produced, it can only be inferred that the
object was translucent owing to insubstantiality. That it had not passed
_behind_ the sun was later fully ascertained. During three subsequent
days the “blazing star near the sun” drew popular attention in the
southern hemisphere, and many parts of Europe. Nothing quite so
extraordinary had ever been seen before. The spectacle of 1843 was
renewed, but outdone.

Meanwhile, an astonished public hung on the dicta of perplexed
astronomers. The speculation which obtained most currency was that the
three successive southern comets were accelerated returns of the same
body, destined, after a few short, spiral circuits, to make fiery
shipwreck in the glowing solar ocean. The effects upon terrestrial life
were unwarrantably described as likely to prove disastrous; but only an
abortive panic ensued. Data, however, to serve as the basis of a
determinate conclusion, were on this occasion collected in abundance.
The comet of 1882 was not lost sight of until June 1, 1883, when its
distance from the earth was more than five astronomical units—the
greatest at which any previous comet except that of 1729 had been
observed. Hence the general character of its orbit became thoroughly
known. It proved to deviate somewhat from the tracks pursued by the
comets of 1843 and 1880; it gave the sun a slightly wider berth; above
all, its period had unmistakably a duration of several centuries. There
could then be no further question of its being a return of either, or
both of those bodies, although its close connexion with them was
assured. This can be most rationally explained by supposing them to have
primitively constituted a single body. According to Professor Kreutz’s
able and exhaustive research, the period of the September comet is 772,
that of the comet of 1843, between five and six hundred years; and the
relative situation of their orbits indicates that the supposed
catastrophe of their disruption took place at perihelion, where a large
incoherent mass could scarcely fail to yield to the strain of the sun’s
unequal attraction at the excessively close quarters it was brought into
by the conditions of its movement. The comet of 1880 is another splinter
from the same trunk; and yet one more fragment presented itself to M.
Thome at Cordoba, January 18, 1887, when he observed literally a “nine
days’ wonder” in the guise of a shadowy ray, thirty-five degrees in
extent, following the lead of the other “southern comets,” and taking
rank (so far) as the last and least of their company.

A tendency to still further disaggregation was evident in the comet of
1882. It did not pass with impunity through the fiery ordeal of its
visit to the sun; internal agitations supervened; abnormal appendages of
rarefied texture, but prodigious dimensions, issued from it sunward; the
nucleus broke up into six spherules like strung pearls; and it was
noticed in October to be surrounded by detached nebulous masses, just
launched perhaps on independent cometary careers. The tail was two-fold.
It consisted of a dim, straight ray which temporarily attained a length
of a couple of hundred millions of miles, and a massive forked
appendage, strongly luminous and unusually permanent. Fig. 19 shows one
of a series of photographs of this comet taken with an ordinary portrait
lens under Dr. Gill’s direction in October, 1882. The observations of
its transit proved to be of great importance. Having been made just
before perihelion, they availed to demonstrate that no loss of motion
had been suffered in its plunge through the corona. This
incontrovertible fact implies an inconceivable degree of rarity in the
solar surroundings.

[Illustration:

FIG. 19.—_Great Comet of September, 1882. Photographed at the Royal
Observatory, Cape of Good Hope._ (From Clerke’s “History of
Astronomy,” 3rd ed.)
]

So long ago as 1831, Clausen pointed out that many comets are grouped
together after the manner incomparably exemplified later by the southern
comets. An analogous system, composed of only two known members, is
formed by the comet of 1807, and Tebbutt’s comet of 1881. The former,
made by Bessel the subject of a masterly investigation, was not again
due at perihelion until the remote epoch 3346 A.D., so that the
announcement of a reappearance so exceedingly premature was startling.
But when the new comet was also found to have a period of several
thousand years, it became clear that no return had been observed, but
only a companion recognised. Tebbutt’s comet was a beautiful object. Its
head, adorned with interlacing arcs of light, was an overmatch for
Capella, while so translucent that a star of the seventh magnitude
seemed rather to gain than to lose brightness by shining centrally
through it. As the upshot of these singular experiences, the difficulty
of identifying comets has been increased tenfold. Their aspects were
always perceived to be well-nigh interchangeable, but their movements
were held to be distinctive; now their very orbits are found to be, to a
considerable extent, common property.

A small, glimmering nebulosity descried at Florence by Donati, June 2,
1858, gave little promise of coming splendour. Yet few more picturesque
celestial effects have been witnessed than it presented, October 5, when
Arcturus blazed undimmed through the denser part of the tail, in
brilliant conjunction with the equal splendour of the nucleus. The
ineffable grace with which the comet spread its luminous plumage was set
off by the juxtaposition, as if for the purpose of determining the
amount of its curvature, of a long, perfectly straight ray. The aspect
of this beautiful object on October 3, is represented in Fig. 20; some
idea of its rapid development in size and brilliancy can be gathered
from an inspection of the Frontispiece to this Section. The apparition
lasted, to the naked eye, for 112 days, and will not again be visible
for 2,000 years. So that Donati’s comet may be reckoned an “irrevocable
traveller.”

[Illustration:

FIG. 20.—_Donati’s Comet, October 3, 1858._ (From Langley’s, “New
Astronomy.”) _The Star to the left of the Comet’s head is Arcturus._
]

Twice during the present century the earth has traversed, with impunity,
the tail of a comet. First, on June 26, 1819, when a comet passed
invisibly between us and the sun, sending its tail our way. Again on
June 30, 1861. The sun had scarcely set that evening when a yellowish
disc became apparent at the horizon, from which issued an enormous
double train, enclosing our planet within its folds. The closing-up and
withdrawal of the “outspread fan” to which they were compared was
accomplished in a few hours. The head of the comet had as many envelopes
as a Chinese puzzle.

The first recognised “short-period” comet approached within one and a
half million miles of the earth, July 1, 1770. Had it possessed ¹⁄₅₀₀₀th
the mass of the globe which rushed by it with entire indifference, a
perceptible lengthening of the year should have ensued; and its
gravitational insignificance was confirmed by the fact that it passed,
in 1779, right through the Jovian system without troubling the mutual
relations of its members. Lexell (with whose name it has continued to be
associated) fixed its period of revolution at five and a half years; yet
it had never been seen before. Astronomers, in fact, caught it on its
trial trip along a fresh orbit to which it had been transported in 1767
by the disturbing power of Jupiter, and whence it was removed by the
same influence in 1779. An intermediate return in 1776 had doubtless
occurred; but circumstances precluded its observation. Further
encounters with the giant planet may, however, bring back the vagrant,
and the possibility was thought to have been realised when the history
of a comet discovered by Mr. Brooks of Geneva, N.Y., July 6, 1889, came
to be inquired into. Its return about the predicted time in 1896
afforded an opportunity for revising the laborious inquiry, with the
result of disproving the case for identity.

A comet, lost under very different circumstances, was picked up February
27, 1826, by an Austrian officer, Wilhelm von Biela. His calculations
led him to the unlooked-for discovery that it travelled in an orbit with
a period of 6½ years, and had already been observed in 1772 and in 1805.
On its return in 1832, when it had become reduced to the status of a
telescopic object, Sir John Herschel watched its conjunction with a knot
of minute stars, the rays of which traversed it without the smallest
obstruction. It had neither tail nor nucleus; its aspect was that of the
commonest type of nebula. On December 29, 1845, however, a curious
change was seen to have affected it. The comet had split into two, each
of which immediately assumed the characteristic cometary shape, by
providing itself with a tail and bright nucleus. Thus divided and
regenerated, the pair advanced side by side, 157,000 miles apart,
without the least trace of mutual action through gravity, but displaying
vivid interchanges of brightness, reasonably attributed to the play of
electrical forces.[88] They re-visited the sun in 1852, but have never
since, and most probably will never again, be seen. Their end came
through senile decay. It was that predicted by Newton for all such
bodies. _Diffundi tandem et spargi per universos cœlos._

The most rapidly-revolving comet of our acquaintance was investigated in
1819 by Johann Franz Encke, of the Seeberg Observatory, who assigned to
it a period of 3½ years, and predicted its return in May, 1822. It was
punctually recaptured at Sir Thomas Brisbane’s Observatory in New South
Wales. Encke traced back its appearances to 1786, and identified it with
a comet detected by Caroline Herschel in 1795. At its last return in
1894–5, it was just at the limit of naked eye visibility. It fluctuates,
however, considerably, at successive apparitions. M. Berberich[89] has
sought to associate these perplexing changes with solar vicissitudes;
but his arguments are not entirely convincing. Encke’s comet, even if
45,000 billion times less dense than air at atmospheric pressure—the
consistence attributed by Babinet to cometary matter—would still weigh
twelve hundred tons.[90] Its excessive rarefaction is a matter of ocular
proof. On October 21, 1881, Barnard observed a central passage of this
comet, then more than usually bright and condensed, over a ninth
magnitude star, which “remained so remarkably distinct during the entire
progress of occultation, that it formally impressed me with the idea of
a transit of the star _across_ the comet—a pearly point floating between
me and the bright mass of vapour.”[91]

This object signally exemplifies the cometary peculiarity of contracting
near perihelion, and re-expanding after the critical point has been
passed. Thus, it measured 312,000 miles across, October 28, 1828, when
135 million miles from the sun, but only 14,000 on December 24, when its
distance had been reduced to 50 millions; and in passing perihelion,
December 17, 1838, at an interval of 32 millions, its diameter had
shrunk to 3,000 miles. It fulfils, as regards Mercury, the function of
spying upon the planets, assigned to comets by Airy; for, only through
the Mercurian disturbances of its motion has the Mercurian mass been at
all definitely ascertained; and a residual acceleration, which, at each
circuit, brings it back to perihelion a couple of hours before the
appointed time, has long been regarded as an index to the condition of
planetary space. Encke explained this shortening of period by the action
of an hypothetical “resisting medium” augmenting in density towards the
sun; but accumulated facts have swept it out of existence. The southern
comets performed for our benefit, one after the other, an _experimentum
crucis_ in the matter. The chief of them, on September 17, 1882, swept
through a region where Encke’s medium should be _two hundred thousand_
times denser than it is at the perihelion distance of Encke’s comet; yet
suffered no appreciable loss of motion. Nor has the comet itself of late
complied with the requirements of the theory it suggested. At its return
to the sun in 1868, the acceleration had fallen to one-half its
customary, and until then, constant value. And the change has proved to
be permanent. But the influence of the postulated medium is evidently
incapable of diminution. Thus, the movements of Encke’s comet still
remain problematical.

CHAPTER XII.
NATURE AND ORIGIN OF COMETS.

Comets reflect sunlight, and also emit light of their own. But the
combination was scarcely thought of as possible until the spectroscope
gave its verdict. The first analysis of cometary rays was made by Donati
at Florence, August 5, 1864. They were dispersed by his prisms into a
yellow, a green, and a blue band, with wide intervals between. Their
chemical interpretation was afforded by Dr. Huggins in 1868. The subject
of his experiments was Winnecke’s comet, an insignificant object with a
period of five and a half years. He found it to be composed—at least in
part—of acetylene, or some other hydro-carbon gas. The coloured bands
agreed precisely in position with those in the spectrum of the blue
light at the base of a candle-flame, or of a gas-jet. The spectra of the
immense majority of comets is of this pattern, with more or less of
continuous light added. A portion of this is borrowed, a portion
inherent. A photograph of the spectrum of Tebbutt’s comet (1881, III.),
taken by Dr. Huggins, June 24, 1881, demonstrated by its distinct
impression with several Fraunhofer lines the presence of solar radiance;
the association of which with native emissions of the continuous sort
has been made evident in various comets by sudden outbursts of white
light.

Comets do not then consist entirely of carbon-compounds; but their
remaining constituents make no distinctive show in their spectra unless
when sun-raised agitation is particularly vehement. Thus, an approach
within five million miles of the sun evoked in comet Wells (1882, I.),
sodium-luminosity, detected by Dr. Copeland at Dunecht, June 17, 1882.
The blaze was so vivid that a crocus-tinted image of the entire head
with the beginning of the tail was visible, like a solar prominence,
through the open slit of the spectroscope. The same observer witnessed
an outbreak of both sodium and iron lines in the September comet (1882,
II.). In both cases, the newly-kindled emissions effaced the old, and,
after a time, were replaced by them. This mode of procedure is
characteristic of electrical action, and combines with other symptoms to
assure us that cometary illumination is produced by interior electrical
disruptive discharges due to solar induction.

Olbers’s felicitous conjecture has been developed into a plausible
theory of comets’ tails by M. Bredichin, late director of the Pulkowa
Observatory. He divided them into three “types,” distinguished by the
values of the repulsive forces employed severally in their production.
Those belonging to type I. imply the exertion of a counter-influence
fourteen times stronger than gravity. They are long, straight rays, the
constituent particles of which are carried, in a torrent too swift to be
deflected, to the observed extraordinary distances. Their outward
velocity of five miles a second to start with is, we must remember,
constantly accelerated, and finally becomes enormous. Halley’s comet and
the great comets of 1811 and 1861 had tails of this type. Donati’s great
plume exemplified the second, in which the average strength of repulsion
exceeds that of gravity one and a half times. Tails of the third type
correspond to a ratio varying from three-tenths to one-tenth. Solar
attraction is, in them, only partially neutralised. They are short,
strongly-bent, brush-like appendages, seldom seen apart from those of a
more striking kind.

These three types have a physical meaning of great interest. The
attractive force of gravity varies as the mass, the repulsive force of
electricity as the surface of the molecules they sway; hence the ratio
of repulsion is inversely as the ratio of molecular weight, the lightest
particles being the most violently driven away from the sun. Assuming
them to be hydrogen-molecules, Bredichin found that the atomic weights
of hydro-carbon gases and iron would correspond fairly well with the
speed of projection signified respectively by the curvatures of the
second and third types of tail. Materials of other kinds are not
excluded; their presence is, indeed, demanded by the width of these
appendages, which obviously consist of bundles of emanations differently
influenced, and presumably of a different chemical nature. Bredichin’s
theory works admirably from a geometrical point of view. All the
varieties of cometary trains can be constructed by strict calculation
from the basis it supplies. Yet there are spectroscopic difficulties in
the way of accepting it unreservedly. No evidence is at present
forthcoming of any connexion between the chemistry of tails and their
shapes; and hydrogen rays are conspicuously absent from cometary
spectra.

“Short period,” or “planetary” comets may be defined as those revolving
in periods of less than eight years. They have much more in common,
however, than the quickness of their successive returns to the sun. All
move from west to east; they show some preference for the plane of the
ecliptic; and none of their orbits are excessively elongated. Thus, they
tend towards conformity with the regular ordinances of the solar system,
which its less accustomed visitants completely ignore. All, too, have a
_used-up_ appearance. This is easily understood. They have wasted their
substance spinning out nebulous appendages—_sicut bombyces filo
fundendo_, as Kepler said—at their frequent returns to perihelion. They
are thus visibly effete bodies. Before long, they will drop out of
individual existence, and survive obscurely, reduced to the “dust of
death.” Yet the supply is not likely to become exhausted. Discovery
proceeds faster than disappearance.

“Lost comets” belong, without exception, to this class. Two typical
instances have already been mentioned in the disaggregation of Biela’s,
and the removal of Lexell’s comet. The fate of Biela may have been
shared by Brorsen’s, a comet with an established period of five and a
half years, which has, nevertheless, remained submerged since 1879. It
is believed by Dr. Lamp to have exploded through internal forces in
1881, and he recognises as one of its fragments a faint comet detected
by Mr. Denning at Bristol, March 26, 1894. The adventures of displaced
comets, such as Lexell’s can be traced only by arduous and delicate
inquiries. They depend upon a single cause. Unsettled comets are those
which pass near Jupiter’s orbit, and are subject to encounters with his
mighty mass. And since they must necessarily return to the point of
disturbance, the series of their vicissitudes can come to an end only by
their being driven off finally from the solar system along a hyperbolic
path.

The condition of these bodies might be described by saying that, in the
regular course of things, they revolve round the sun disturbed by
Jupiter; while, during brief but energetic crises, they revolve round
Jupiter disturbed by the sun. Their abnormal condition results from the
situation of their aphelia close to the Jovian track. This is the case,
in a minor degree, with many comets of comparatively settled habits.
They escape eviction and exile, and suffer only disquietment. Such are
Winnecke’s, D’Arrest’s, Faye’s comets, which, having been continuously
observed during half a century, are, as Mr. Plummer expresses it, “well
under control.”[92]

Short-period comets, with the solitary exception of Encke’s, appear to
be inevitably connected with Jupiter. The peculiarity is rendered more
significant by the circumstance that the other great planets are also
provided with cometary clients. The Jovian group is the largest; it
includes more than two dozen recognised individuals. Saturn claims nine,
Uranus eight, and Neptune five. Halley’s comet belongs to the Neptunian
family. Another of its members was discovered by Pons in 1812, and
re-discovered by Brooks in 1883, so that it has a period of 71 years.
And the reappearance in 1887 of a comet first seen by Olbers in 1815,
bore reassuring testimony to the regularity with which Neptune’s comets
conduct themselves during their long periods of invisibility.

The nature of these planetary relationships was at once conjectured. It
seemed an open secret that the comets had been taken prisoners by the
attractive force of the great globes they flitted past on their way to
the sun. But astronomers can take nothing for granted; and preliminary
mathematical inquiries served rather to discredit the first and easy
surmise. The case had to be thoroughly sifted; and it was only through
the profound researches of Tisserand, Callandreau, and Newton of Yale,
that the “capture-theory” has taken its place as a highly probable
truth. With an unstinted allowance of time and _comets_, it can perform
all that is required of it. “Captures” are not effected all at once; the
lasso is thrown many times over the escaping body before it is
definitively secured. Moreover, at each such effort, the chances are
even of its being made in the wrong direction. We observe only the
outcome of the hits; the misses are beyond our reckoning. A multitude of
happy accidents have led to the domestication in our system of Faye’s,
Tuttle’s, Winnecke’s, D’Arrest’s comets. Mr. Plummer has adverted to the
likelihood that we are indebted to some slight but well-directed pulls
from Mercury for the permanent addition of Encke to the solar company;
and Neptune exerted itself ages ago with similar success as regards
Halley’s comet, yet under great difficulties, since retrograde comets,
and those with highly inclined orbits are, as a rule, exempt from
capture. This is one of the reasons why short-period comets show some
degree of conformity to planetary modes of motion.

These investigations remove all doubt as to the foreign origin of
comets. Those that are in the solar system are not of it. They assuredly
remained unaffected by the gradual processes of its development. Yet
they, as well as the multitude of parabolic comets, belong to it in a
wider sense. That is to say, they accompany its march through space.
Otherwise, as M. Fabry has demonstrated, most of their orbits should be
strongly hyperbolic; and no such cometary orbits are known. They should,
besides, if casually encountered, present themselves chiefly along the
line of the sun’s way; they arrive, on the contrary, indifferently from
all quarters of the heavens. They are then subject to the same
mysterious influences which govern his motion, and drift with the cosmic
current which bears the solar family along, we know not how or whither.

[Illustration:

FIG. 21.—_Photograph of Swift’s Comet. Taken by Prof. Barnard, April
6, 1892. Exposure, 1h. 5m._
]

[Illustration:

FIG. 22.—_Photograph of Swift’s Comet. Taken by Prof. Barnard 24h.
later. Exposure, 50m._
]

Comet-photography became possible only through the introduction of
highly-sensitive gelatine plates; and even with them, exposures of an
hour and upwards are necessary in order to obtain the desired results.
But these results are of such importance as to deserve the closest
attention. For investigating either the forms or the spectra of comets,
the camera is unrivalled. Its systematic employment for these purposes
dates from 1892. It can also serve as an engine of discovery. On October
12, 1892, a comet so faint that, had it not been photographed, it would
most likely never have been seen, appeared as a nebulous trail on a
plate exposed by Professor Barnard to the Milky Way in Aquila. It proved
to be one of Jupiter’s dependents, pursuing, in a period of 6·3 years, a
track so closely resembling the orbit of Wolf’s comet in 1884, that
Schulhof regarded them as the offspring of one parent body.

In the year 1892, seven comets were detected; and all, by one of those
picturesque coincidences with which nature loves to entertain her
devotees, were, towards its close, visible in the sky together. One of
them was first noticed by Lewis Swift—a specialist in that line—and
passed perihelion April 6.[93] The head competed in brightness with a
third-magnitude star; the tail was 20° long, and came out, in a
photograph taken by Mr. Russell at Sydney, on March 22, self-analysed
into eight perfectly distinct rays. _No such structure could be seen
with the telescope._ Figs. 21 and 22 reproduce two pictures of this
object obtained by Professor Barnard, April 6 and 7 respectively. During
the interval, a striking change had occurred. In the first photograph,
the tail is sharply separated into two branches, and shows traces of
further indefinite subdivisions. The uneven, knotty texture of the main
stream is obvious. The matter composing it seems as if it had rushed in
a torrent over a rocky bed, whirling and foaming round the obstacles it
encountered. Twenty-four hours later, this powerful emanation left
scarcely a trace on the plate. Its dwindled remnant had split up into
two faint streaks, while the almost negligeable offset of the previous
night had sprung into unlooked-for prominence. A unique feature was
added in the apparent development of a secondary comet two degrees
behind the head. The anomalous enlargement brightened gradually inwards,
and can readily be seen upon the plate to be the centre of an entirely
new system of tails.[94]

Owing to moonlight and clouds, the autobiography of this planetary _bud_
unfortunately remained a fragment; and since Swift’s comet has an
indefinitely long period, it will never again exhibit for our benefit
any of its caprices of change.

[Illustration:

FIG. 23.—_Photograph by Prof. Barnard of Holmes’ Comet near the
Andromeda Nebula._
]

On November 8, 1892, Professor Barnard secured a very perfect
representation (shown in Fig. 23) of a peculiar-looking comet grouped
with the great Andromeda and its attendant nebula. Discovered only two
days previously by Mr. Edwin Holmes of London, it presented a great
round disc with definite edges visible to the naked eye. This contained
a tail in embryo, which subsequently opened out into a feeble brush, the
head being then pear-shaped, and granulated like a remote star
cluster.[95] A strictly continuous spectrum was derived from it. “Its
appearance,” Professor Barnard wrote, “was absolutely different from
that of any comet I had ever seen. It was a perfectly circular and
clean-cut disc of dense light, almost planetary in outline. There was a
faint, hazy nucleus.”[96] A photograph taken by him, November 10,
showed, distant about one degree to the south-east, “a large irregular
mass of nebulosity covering an area of one square degree or more, and
noticeably connected with the comet by a short, hazy tail.”

This object underwent extraordinary vicissitudes of aspect. From a
seeming planet it quickly degenerated by distension into the thinnest of
nebulosities; then suddenly, on January 16, 1893, gathered itself
together into an ill-defined star of the eighth magnitude. This
evanescent outburst was simultaneously observed in several parts of the
world. After some minor rallies and relapses, the comet finally, on
April 6, 1893, melted into the sky-ground. Jupiter is responsible for
its introduction into the solar system, and it will again be due at
perihelion in May, 1899. Yet its reappearance is considered doubtful.

It was perhaps caught sight of during a temporary crisis of internal
agitation, which may not recur. Certainly it could not, if as bright as
when discerned by Mr. Holmes, have remained many nights unnoticed.
Nevertheless, it had passed the sun five months previously. Its orbit is
more nearly circular than that of any previously observed comet, and it
revolves wholly within the asteroidal zone. That is to say, its
perihelion lies outside the orbit of Mars, its aphelion inside that of
Jupiter. Hence, it ought to be visible like a planet, at every
opposition. Professor Barnard, however, sought vainly for it, when thus
situated. The apparition was in many ways enigmatical.

A comet discovered by Brooks, October 16, 1893, was photographed by
Barnard three nights later, when a tail was disclosed, 3½° long, and
flowing off in two branches with a spine-like ray attached to each. A
series of impressions were fortunately taken, and that of October 21
(reproduced in Fig. 24) proved to be of peculiar interest. Since the
night before, the tail had apparently met with an accident. It imprinted
itself upon the plate shattered, deformed, and affected by a double
curvature. A collision with some external body was at first suggested as
the cause of this untoward state of things; but, knowing all that we do
about the violent interior paroxysms of comets, it seems more rational
to attribute it to extreme irregularities in the quantity and direction
of effluences from the nucleus. The following night’s photograph gave
evidence of a partial return to normal conditions. Yet the appendage
still looked badly damaged; and an elliptical fragment, wrenched from it
during the convulsion, showed no tendency towards reunion. At the time
of this incident, Brooks’ comet was situated well outside the orbit of
the earth.

The facts already collected by the photographic study of comets are
concordant, and easily interpreted. One obvious inference from them is
“that the matter of a comet’s tail is driven away from the nucleus in a
very irregular and spasmodic manner.”[97] At certain crises, outflows
are only accomplished by convulsions, compared by Mr. Ranyard to the
explosions of terrestrial volcanoes, or solar prominences. Moreover,
capricious as cometary forms are to the eye, they are still more
inconstant as recorded chemically. “The appearance one day,” Professor
Hussey says, “affords no indication as to what it may be the next. The
most radical changes of form have been observed in almost every
reasonably bright comet that has been photographed; and they sometimes
take place so rapidly as to become conspicuous in an hour or two.”[98]

[Illustration:

FIG. 24.—_Brooks’ Comet, photographed by Prof. Barnard, October 21,
1893. Exposure, 35m._
]

Comets’ tails appear very different in structure photographically and
visually. On the sensitive plate, they are perceived to be composed of
innumerable, distinct filaments, sometimes tied up, as it were, into
sheaves. The filaments, or streamers may, however, according to the same
authority, “leave the coma in a single compressed bundle, or they may
spring from it in widely divergent and loosely connected groups; they
may be smooth, and straight, and distinct, or they may be lumpy,
crooked, interlacing, and spirally twisted; or again, they may be broken
into fragments, and scattered as though they were smoke driven by the
wind.” And these effects often swiftly succeed each other in the same
comet.

In photographs of Swift’s and Rordame’s comets in 1892 and 1893 (taken
by Barnard and Hussey respectively), the effects of a spiral outward
movement in the grouped streamers of the tail can be plainly recognised.
They are indistinguishable from “the twisted forms produced by an
electrical discharge in a magnetic field.”[99] Another much more common
peculiarity of such appendages brought into prominence by chemical
portraiture, is the occurrence upon them of knots, or condensations.
These are evidently accumulations of outflowing matter. Again, in most
of the comets recently photographed, the tails start directly from the
nuclei, which appear destitute of genuine envelopes. This is the precise
criterion of Olbers’ first cometary division, in which solar repulsion
acts alone, nuclear repulsion being ineffective, or non-existent. It
comes out remarkably in Barnard’s photographs of Gale’s comet in 1894.

We may now resume in a few words what we have learned about comets. To
begin with, they are of such small mass that no gravitational effects
from their closest vicinity have ever yet been detected. Their bulk, on
the other hand, is enormous. The great comet of 1811 comprised a
nebulous globe 2½ times larger than the sun, with a tail many thousand
times more voluminous. Hence the extraordinary tenuity of such bodies.
They must indeed contain solid matter; otherwise they could not hold
together even in the imperfect way that they do; but it is probably in a
state of very loose aggregation. Their permeability to light may thus be
accounted for. The visibly granular texture of their nuclei is
confirmatory of the supposition. If, then, the nuclei of comets are
essentially “meteor-swarms,” all the constituent particles must revolve
round the centre of gravity of the whole, in a common period, but with a
velocity directly proportional to distance from the centre—that is,
increasing outward. And the joint mass being so small, the utmost speed
attained would perhaps rarely exceed a couple of hundred yards a second.
Moreover, towards the centre, where the components of the swarm would
crowd most closely together, motion would become so slow as to be
scarcely perceptible. Hence collisions would be infrequent and of slight
effect; while the probability of their occurrence should diminish with
the comet’s approach to the sun, which, by its unequal attraction, would
draw the revolving particles asunder, and amplify their allowance of
space. Internal collisions may then fairly be left out of the account in
considering the phenomena of comets. The expansion of their nuclear
parts, due to tidal forces, is, however, usually disguised by the
contraction, near perihelion, of their nebulous surroundings. The latter
effect can be explained by the immense predominance at that conjuncture
of solar over cometary electrical repulsion.

That the light-emissions of comets are largely of electrical origin is
no longer doubtful; so that the present rush-ahead in this branch of
knowledge cannot but help to elucidate many of the still mysterious
circumstances connected with these strange visitants from the uttermost
verge of the sun’s empire. The tie of allegiance hangs loosely there;
but by the persevering efforts of the great planets it is sometimes
drawn closer, with the result of domiciling under their control a train
of dilapidated comets, verging towards dissolution.

Carbon, sodium, and iron, are the only substances directly known to
exist in these bodies. Spectroscopic evidence also suggests the presence
of nitrogen or hydrogen; and a number of chemical elements which make no
show in their light doubtless enter into their composition. The state of
comets when remote from the sun can only be surmised. Their gaseous
constituents may be solidified by cold. They can, in any case, scarcely
be other than obscure and inert bodies.

CHAPTER XIII.
METEORITES AND SHOOTING STARS.

At Madrid, on the morning of February 10, 1896, the sunshine was at 9.30
overpowered by a vivid flash of bluish light, succeeded by a violent
explosion. Much glass was broken, and other devastation of a minor kind
wrought; above all, some hundreds of thousands of people were thoroughly
frightened. The origin of the commotion was visible in a white cloud
rushing across the sky, and leaving behind a dusty train. Of this
débris, scattered from a height of fifteen miles, some fragments were
picked up and analysed. They were composed of silicates of magnesia and
iron, with very small quantities of aluminium, nickel, and calcium.
These specimens were strictly “aerolites,” a term used to designate any
solid meteoritic matter that reaches the earth.

Equally conspicuous apparitions of the sort are not always equally
clamorous. There are silent, as well as detonating fire-balls. The cause
of the difference cannot certainly be assigned. It resides, perhaps, in
the diverse constitution of the exploding bodies; it is, beyond doubt,
unconnected with their height in the atmosphere. Thus, a remarkable
meteor was seen, but not heard, by Dr. Rambaud, the astronomer-royal for
Ireland, at Dunsink, February 8, 1894. The object, he says, “suddenly
burst into view with an intense brilliance, and shone out against the
cloudless blue sky with a greenish metallic lustre. It fell in a
vertical direction until it disappeared behind some trees. In shape it
resembled a very elongated pear, like most fire-balls of the sort. It
emitted no visible sparks, and disappeared quite noiselessly.” When
first observed, it was at a height of about 87 miles above the Irish
Channel; then crossing Lancashire, it descended so rapidly on its way,
probably, to engulfment in the North Sea, that, when last noticed, it
was scarcely, if at all, higher above the earth’s surface than the
Madrid meteorite at the moment of its formidable disruption. Astonished
rustic beholders at Kingswood and Dudley averred that it burst “in the
next field”; but this is a common illusion. Professor Langley relates
that some witnesses of a marvellously swift meteor at a presumable
elevation of some fifty miles, sallied out of their houses next day to
make sure that it had not struck their chimneys.

Such phenomena are tolerably frequent, and have been recorded from the
remotest antiquity. Homer lends a meteoric aspect to Athene, when she
descends from Olympus to take the war-path by the shore of Scamander.
Chronicles abound with accounts substantially identical with the
telegrams supplied by Reuter’s Agency on February 10, 1896. The fall of
the “Crema meteorite” has a special interest as having been depicted by
Raphael in his “Madonna di Foligno.”[100] A multitude of stones were
discharged by it on the banks of the Adda, six of which weighed each one
hundred pounds and upwards; the sulphurous smell characteristic of
fresh-fallen aerolites is mentioned in contemporary accounts of the
event, which occurred September 4, 1511; and it is further said that
“sheep were killed in the fields, birds in the air, and fishes in the
streams.” No specimen of this sky-volley is known to exist. In elder
times, objects of this class were worshipped; and Professor Newton[101]
has collected many curious facts about the meteoric cult traceable in
classical history. To this day, indeed, the central sanctuary of
Mahometanism—the Kaaba—owes its sacredness to the embedment in its
masonry of a blackened aerolite.

Until the beginning of the present century, only the ignorant believed
it possible that stones could come from heaven; philosophers regarded
them as generated in the clouds. They were at last convinced that the
popular view was correct by Biot’s investigation of the meteoric tempest
which broke over L’Aigle, in the department of the Orne, April 26, 1803.
He estimated at two thousand the number of fragments scattered over an
area six by two and a half miles, one of which, weighing five pounds, is
now in the South Kensington Museum. And at Pultulsk, January 30, 1869,
one hundred thousand stones were reported to have been showered upon the
earth. It is not often, indeed, that largesse from space is so lavishly
made. Yet all meteors (with the rarest exceptions) rendered luminous by
the resistance of its atmosphere, become, in one way or another,
incorporated with its mass. Their materials are no doubt often reduced
to fine dust and gas; yet six or seven hundred solid masses per annum
are computed to reach the surface of sea or land, for the most part
“unrecked-of and in vain.” Of late, the scientific demand for them has
grown keen, and their enhanced value has raised the legal question of
their ownership. The decision of the American courts is that aerolites
are not “wild game,” but “real estate,” and, as such, belong to the
owner of the land upon which they fall.

No wonder they should be at a premium, those blackened and wasted
samples of immeasurably distant globes. The velocities with which they
entered our atmosphere alone suffice to prove their cosmical origin. Had
it not trapped them, many, circuiting the sun in a hyperbolic curve,
would have escaped for ever from our system. Their primitive
disconnexion from it is implied by their swift motions, which
considerably exceed, on an average, those of comets, and point to
interstellar space as their proper habitat. The earth’s orbital pacing
has, however, to be added or subtracted as the case may be; so that the
actual rate of encounter varies from ten to forty-five miles a second.
Most of this is spent before the earth’s surface is reached. Only
considerable masses travelling at express speed bring any sensible
proportion of it with them to the ground. But what is lost as motion
reappears in other forms of energy, as light, heat, and sound. In front
of the rushing body, the air—despite its inconceivable tenuity at
elevations of fully one hundred miles—is suddenly compressed and raised
to an exceedingly high temperature, while a corresponding vacuum behind
gives rise to violent reactive currents. Professor Dewar calculated, by
way of example, in 1887, that a body, three feet in diameter, moving
eighteen miles a second at an altitude of twenty-three miles, where
barometric pressure is reduced to one-fifth of an inch, would compress
the air in its path 5,600 times, the resistance offered to its passage
thus equalling that of thirty-seven atmospheres. The abrupt increase of
heat accompanying compressions of this order amounts to thousands of
degrees, and tends to rend in pieces a body arriving from frigid abysses
where matter can only exist in a stark and, so to speak, lifeless state.
Explosions of occluded gases ensue; vaporised and incandescent particles
are blown behind in a luminous train; and, at the most, some shattered
solid remnants tumble to our continents, or plunge into our oceans. The
few that are rescued for examination look much the worse for their final
adventure. The signs of the furnace and the hurricane (both
self-created), are visible in their jetty and fused surfaces,
“thumb-marked,” probably through the continual and irregular changes in
the pressure exerted upon them. The crust is, however, a mere varnish,
the interior, which is usually of a greyish hue, being entirely
unaffected by heat. It remains, on the contrary, sunk in the depths of
cold. Agassiz compared the aerolite which fell at Dhurmsala in India, in
1860, to the Chinese _chef d’œuvre_, a “fried ice”;[102] and a large
fragment of it, which fell in moist earth, was found coated with
ice.[103]

Aerolites, or meteorites, as they may equally well be called, are
roughly divided into “stones” and “irons”; the former being composed of
various and peculiar minerals, the latter of iron, with a considerable
percentage of nickel.[104] All show a more or less distinctive
crystalline structure. Meteoric chemistry includes about thirty of the
seventy or so terrestrial elements. The chief of them are: iron, nickel,
carbon, oxygen, silicon, magnesium, sulphur, aluminium, phosphorus, with
smaller quantities of chromium, cobalt, tin, copper, titanium,
manganese, antimony, arsenic, lithium, hydrogen, nitrogen, argon, and
helium. Argon and helium were expelled by heat from a piece of meteoric
iron picked up in Augusta County, Virginia, the former coming off nearly
a hundred times more plentifully than the latter. As the light of argon
makes no show in the spectrum of any heavenly body, the proof of its
cosmical diffusion thus obtained by Professor Ramsay is of great value.
Besides argon and helium, hydrogen, carbonic acid, and carbonic oxide
gases are found included in meteorites. They seem, as it were, to
hybernate in the stony or metallic enclosures from which they can only
be _boiled out_.

Although these wind-falls from space contain no strange elements, the
manner of their composition is special to themselves. Their study
constitutes a separate branch of mineralogy. They are certainly of
igneous origin. They show no sign of water-action, and but little of
oxidation. The nearest affinities of the minerals aggregated in them are
with volcanic products from great depths. Thus meteorites seem broken up
fragments of the interior parts of globes like our own. A few among them
contain solid carbon, either amorphous, or in the shape of graphite, or
even crystallised into minute diamonds. In the Cañon Diablo siderite, or
meteoric iron, all three varieties occurred together, some of the
translucent particles proving, when put to the test of actual
combustion, to be indeed “gems of purest ray serene,” dwelling incognito
in a strange environment!

The thin streaks of light called “shooting stars” differ in several
respects from explosive meteorites. In the first place, they—probably
without exception—form systems. Innumerable multitudes of them travel in
the same paths round the sun. Moreover, those paths resemble cometary
orbits; they are very elongated ellipses, inclined at all angles to the
plane of the ecliptic, and traversed indifferently in either direction.
Their velocities are thus sensibly parabolic, while fire-balls commonly
attain hyperbolic speed. Finally, they are soundless. They slide by in
ghostly silence. Most of them are probably not larger than a pea, yet
were the shield of its atmosphere withdrawn, the earth would be rendered
well-nigh uninhabitable by their pelting. Incredible numbers of them are
encountered. They come by the million daily to be burnt, visibly to the
naked eye, in the thin upper air. Kleiber’s allowance is eleven,
Newton’s twenty millions; and these figures should be multiplied a score
of times to include telescopic fire-specks. Now, the combined mass of
all these particles goes to reinforce the mass of the earth; but it is
relatively so small that ages must elapse before the contribution can
become sensible. Our defeated meteoric assailants surrender to us also
the heat of their arrested motion; which is, however, only as a spark
added to the furnace of our supply from the sun.

Shooting stars, as we have seen, move in closed orbits. They are, then,
a periodical phenomenon. Not that we ever see the same individual twice;
its visibility implies its dissolution, but its companions are as the
sands of the seashore. Their association is recognised by their
agreement in direction and date. Unless their orbits intersected that of
the earth, nothing could be known of them terrestrially; they come to
our notice only through actual encounters, and encounters are possible
only at the time of year when our planet is passing through the node.
This is the given rendezvous, different, speaking generally, for each
system; although, speaking particularly, many meteoric streams are so
wide that the earth takes days, even weeks, to cut its way through them,
and so may be overtaken by fresh onsets before the original one is
exhausted. Each community is distinguished by the lie of its orbit—that
is, by the point in the sky from which the flying arrows of light seem
to diverge. This is known as the “radiant-point” of the system, and is
its special characteristic.

The August meteors are a familiar example of such an association. Their
annual recurrence is no new discovery. Long ago, in mediæval times, they
were called the “tears of Saint Lawrence,” because never looked for
vainly on the 10th of August. But they are so far from being limited to
that particular night, that Mr. Denning has picked up skirmishers and
stragglers from the main body all the way from July 8 to August 22. They
are distributed with tolerable evenness along an immensely long ellipse,
traversed in 120 years; and, because they radiate from near the star η
Persei, are known to science as the “Perseids.”

The scattering of the November meteors—or “Leonids,” since their point
of emanation is marked by ζ Leonis—is on the same plan, with a
difference: the Perseids might be compared to a plain gold ring; the
Leonids, to a ring with a gem on it They send us some shots every year
on the 13th and 14th of November; but three times in a century they open
fire for a regular bombardment. An early Leonid display took place in
902 A.D., noted in old chronicles as “the year of the stars.” All night
long on October 19—the node advances 14½ degrees in a thousand
years—while the tyrant Ibrahim lay dying “by the judgment of God” before
Cosenza, beholders far and near viewed with consternation the stars
precipitating themselves from the sky. Recurrences of the phenomenon
every thirty-three years received curiously little attention until
Humboldt described, and insisted on the periodic nature of the meteoric
tempest witnessed by him at Cumana on the morning of November 12, 1799.
One scarcely less violent broke over Europe and Asia in 1832, and the
American continent in 1833. From the Gulf of Mexico to Halifax the stars
were seen to fall as silently as snow-flakes, and almost as thickly, yet
after a less undirected fashion. Rather they darted and swooped, like
falcons, with a purpose; and it was noticed that the lines of their
flight could, with essential invariability, be traced back to one point,
or small area in the heavens. This remark gave the clue to their nature.
They were perceived to be necessarily cosmical bodies. For since the
focus of the meteors remained unaffected by the earth’s rotation, they
showed themselves plainly extraneous to its domestic arrangements. “A
new planetary world,” exclaimed Arago, “has been disclosed to us!”

The anticipated repetition, in 1866, of the November shower of 1833,
came off with _éclat_. Many still remember the amazing spectacle
presented by the heavens in the early morning of November 14, in that
year. In 1867, when the earth came round again to the same point of its
orbit, the star-rain was still falling heavily; and even in 1868 it
amounted to a fair sprinkle. Thus the swarm was, thirty years ago,
already so extended that it spent three years in sweeping past the node,
at the rate of twenty-seven miles a second. “The meteors themselves,”
according to Dr. Johnstone Stoney,[105] “are probably little pebbles,
the larger about an ounce, or perhaps two ounces, in weight, and spaced
in the densest part of the swarm at intervals of one or two miles
asunder every way. The thickness of the stream is about 100,000 miles,
which, however, is a mere nothing compared with its enormous length. The
width is such that the earth, when it passes obliquely through the
stream, is exposed to the downpour of meteors for about five hours.”
Each “pebble” revolves round the sun, and suffers planetary
perturbation, in complete independence of its fellows, their orbits
being only alike, not identical. The next full encounter with them will
take place November 14, 1899; but avant-couriers may be looked for at
the critical dates in 1897 and 1898, as well as a strong rear-guard in
1900.

The orbit of the November meteors is roughly bounded by the orbits of
the earth and of Uranus. They pass perihelion very near our
meeting-place with them; and since they run counter to the earth’s
motion, the velocity of collision is nearly equal to the sum of the two
orbital velocities, or forty-four miles a second. They are almost the
swiftest shooting stars of our acquaintance.

The successful calculation of meteoric orbits by Adams, Schiaparelli,
and Leverrier, promptly led to a discovery as important as it was
unexpected. Late in 1866, Schiaparelli announced that the August meteors
follow precisely the same track with a bright comet (1862, III.)
discovered in 1862 by Tuttle, an American astronomer; and the reality of
this singular relationship was, in the following year, verified by the
detection of three similar examples. The Leonids, with a period of 33¼
years, proved to be close associates of Tempel’s comet (1866, I.); a
meteoric stream flowing down upon the earth annually on April 20, from
the direction of the constellation Lyra, was perceived to move in the
vast ellipse traced out in 415 years by the comet 1861, I.; finally a
star-drift, first noticed December 6, 1798, was rightfully claimed as an
appurtenance of Biela’s comet.

Thus the fact of a close connexion between comets and meteors was at
once rendered patent; and as to the nature of the connexion, the history
of Biela’s comet is particularly instructive. Since its disappearance,
the meteor-swarm sharing its orbit has received a notable accession. The
comet seems to have broken up into meteors. And this, we can scarcely
doubt, is what has really occurred. Hence, when the earth passes
moderately, near where the comet _would_ have been, had it survived in
cometary shape (a conjuncture happening once in thirteen years), a
vehement outburst of shooting stars is observed. On November 27, 1872,
the “Bielids,” or “Andromedes,” came in tens of thousands from near γ
Andromedæ, the very point whence the track of the disaggregated comet
intersects the earth’s orbit at an angle of twelve degrees. Their
movements were leisurely; for they came up with our globe, instead of,
like the Leonids, rushing to meet it. They seemed to sail, rather than
shoot, across the sky. The calculated position of the originating body
was, at this date, two hundred millions of miles _in advance_ of the
node, and it was three hundreds of miles _behind_ the same point when
the display was renewed in 1885. It is then certain[106] that at least
five hundred millions of miles of Biela’s route are densely strewn with
meteoric fragments. The entire multitude, moreover, necessarily
separated from the comet subsequently to an episode of disturbance by
Jupiter in 1841. This is plainly shown by the fact that the members of
the associated company pursue the modified track. The perturbation of
1841 was exerted upon them no less than upon the comet, with which,
accordingly, they must then have formed one mass.

Biela’s comet has thus taught us that such bodies meet their end by
getting pulverised into meteoric particles; and further, that the
particles disperse with extraordinary rapidity along the length of their
orbits. Solar and planetary _differential_ action produce this kind of
effect, although they hardly explain its amount. Subordinate swarms are
also created by disturbance. Such an one met the earth November 23,
1892, when Professor Young estimated that at least 30,000 Andromedes
furrowed the sky at Princeton. Heavy star-showers, however, are
perishable phenomena. They thin out with comparative rapidity into a
continuous drizzle. At each recurrence, diffusion is seen to have made
progress, until at last the “gem on the ring” has vanished. With the
Perseids this is already the case. The stream flows without material
interruption over a bed a hundred times wider than that of the Leonids.
These meteors, too, will no doubt eventually reach a similar condition.
In the course of a couple of centuries, their thirty-three year period
will be completely effaced. In 1799, the main body of them crossed the
node in less than a year; at the close of the present century, the earth
will probably make her annual round at least four times, before the
march-past comes to an end. Obviously, it is about to become perennial.
Leverrier concluded from his researches that the Leonid comet and the
Leonid meteors, which then made part of its substance, were “captured”
by Uranus in 126 A.D., and so introduced into the solar domain. The
truth of the supposition may still be tested; should it be established,
this remarkable system affords yet another example of the rapidity with
which cometary materials become disintegrated and scattered.

The number of meteoric radiants now distinctly known is estimated by Mr.
Denning at about three thousand; and we need not hesitate to ascribe to
all these streams a cometary origin. It is true that the three thousand
generating comets have, all but three, “gone over to the majority.” But
we have witnessed the obsequies of Biela, and it seems only logical to
infer that those of its 2996 congeners were, in old times, celebrated
after the same fashion, and are still kept in mind by the annual blaze,
in their honour, of a few representative sky-rockets.

No component of a star-burst has so far _undoubtedly_ come to the
ground. The fire-works shown are of the most innocuous kind. Two
_possible_ exceptions are, however, on record. On April 4, 1095, a
shower of Lyraids was visible in Western Europe. The stars, according to
the Saxon Chronicle,[107] crowded “so thickly that no man could count
them.” And in France, one of the throng fell so accessibly that a
bystander, having noted the spot, “cast water upon it, which was raised
in steam with a great noise of boiling.” But, unless the aerolite came
from the same radiant as the stars, their simultaneous arrival was an
unmeaning coincidence. It implied no connexion, physical or dynamical,
between them. The same coincidence was renewed during the Andromede
shower of November 27, 1885. Just before it began, a “ball of fire”
struck the ground at Mazapil in Mexico, and proved to be a substantial
piece of iron containing nodules of graphite. It weighed eight pounds.
Yet here again that essential circumstance, the direction of its fall,
remained unknown. We must then, for the present, suspend our judgment as
to whether aerolites may be regarded, like shooting stars, as actual
cometary débris.

Mr. Denning’s patient watch of thirty years has led him to the singular
discovery of “stationary radiants.” The direction in which meteors
appear to approach the earth is determined by the combination of theirs
with the earth’s movements. The effect is strictly analogous to the
aberration of light. Meteoric radiants ought accordingly to shift on the
sphere just as the heavenly bodies change their apparent places by the
prescribed measure of aberration. And most do in this respect conform to
theory, the Perseid radiant notably. On the other hand, certain
well-known radiants continue fixed night after night in seeming
independence of the earth’s orbital advance; and there are a good many
points in the sky whence shooting stars continue to _dribble_ without
sensible interruption during many months of each year. The fact is
undeniable, although inexplicable.

The future progress of meteoric astronomy depends largely upon the
introduction of the photographic mode of observation. Only by its aid
can the precise determination of radiant-points be effected; and this is
the chief desideratum. Its realisation before the close of the century
may safely be predicted. Dr. Elkin, director of Yale College
Observatory, had a “meteorograph” constructed for the purpose in 1894,
and hopes to use it for the registration of the Leonids now hastening to
meet us. Hitherto, only casual fire-balls have printed their tracks on
sensitive plates. Success in obtaining permanent records of shooting
stars diverging from a radiant will mark a turning-point in meteoric
investigations.

ASTRONOMY

[Illustration:

NEBULA IN ANDROMEDA. 31 MESSIER.

(_From a Photograph, by Dr. Roberts._)
]

SECTION IV.—THE SIDEREAL HEAVENS.

BY J. E. GORE, F.R.A.S.

CHAPTER I.
THE STARS AND CONSTELLATIONS.

The study of the sidereal heavens is one of surpassing interest, and
tends to raise our minds above the sordid things of time and the petty
affairs of the little planet on which we dwell,—a globe absolutely
large, of course, when compared with objects around us, but relatively
very small in comparison with the vast stellar universe which surrounds
us on all sides, a universe so vast that even the largest telescopes can
only partially fathom its immeasurable depths.

For the study of the sidereal heavens, as revealed to us by the giant
telescopes of modern times, it will be advisable to begin by a
consideration of the starry sky as seen by the naked eye, without
optical assistance of any kind. On a clear and moonless night, when the
vault of heaven is spangled over with shining points of light, some
bright, others fainter, and many more barely perceptible to the unaided
vision, we are inclined to imagine that the stars visible to the naked
eye are innumerable, and that any attempt to count them would be a
hopeless task. This idea, however, is quite a mistake, and, indeed,
merely an optical illusion, due partly to the scintillation or twinkling
of the brighter stars, and stars near the limit of vision, and partly to
their irregular distribution over the surface of the heavens. As a
matter of fact, the stars visible to the naked eye can be easily
counted; and they have been counted and catalogued. As every book in the
catalogue of a large library can be identified, so every star visible to
the unaided vision—and thousands even fainter, and only visible in
telescopes—have been mapped, and their exact positions are as well known
to astronomers as those of every town and village in Great Britain are
known to geographers. The number of stars which can be seen with
ordinary eyesight is, in fact, very limited, and does not exceed the
number of inhabitants in a small town. Some years ago, a German
astronomer, Heis, who was gifted with excellent eyesight carefully
mapped down all the stars visible to his eye without optical aid, and
found the total number visible in the middle of Europe to be only 3,903.
A similar work was undertaken for the Southern Hemisphere by Behrmann,
another German astronomer, and the total number distinctly seen by both
astronomers in both hemispheres of the star sphere is 7,249. Of course,
at any given time and place only one half the star sphere is visible,
the other half being below the horizon. It follows, therefore, that
about 3,600 stars are visible at one time from any point on the earth’s
surface. As, however, everyone does not possess the keen vision of the
astronomers referred to above, we may safely say that not more than
3,000 stars are, on the average, visible at a time to ordinary eyesight.
On the other hand, persons gifted with exceptionally keen vision may
possibly see even more than Heis and Behrmann did; but even to such
eyes, the total number distinctly visible on a clear night without a
moon would probably not exceed 5,000. We may easily satisfy ourselves as
to the truth of this statement by taking a portion of the sky, and
counting the number of stars which can be steadily seen. Everybody knows
the Great Bear, sometimes called the “Plough,” or “Charles’ Wain.” Four
of the well-known stars in this remarkable group form a four-sided
figure. Well, let the reader look carefully at this figure, and see how
many stars can be detected within the space formed by imaginary lines
joining the bright stars. Probably surprise will be felt at the small
number which can be distinctly seen. Heis, with his keen vision, only
shows eight on his map, and of these, four are very faint, and near the
limit of even good eyesight. Probably very few eyes will see more than
eight, and perhaps most persons will fail to see so many. As the whole
hemisphere is roughly five hundred times larger than this spot, the
number seen by Heis in the quadrilateral of the Plough would give a
total of 4,000 stars visible at one time. Of course, some portions of
the sky are much richer in stars than the spot selected; but, on the
other hand, others are much poorer, so that perhaps this may be taken as
a spot of average richness. From this single example it will be seen
that the idea of countless multitudes of stars visible to the naked eye
is a mistake. Probably the effect of a great number is partly due to our
catching glimpses by “averted vision” of still fainter stars, which
cannot, however, be seen steadily when the eye is turned directly
towards them.

[Illustration:

FIG. 1.—_Stars visible in the Northern Hemisphere._

(From “Visible Universe.”)
]

In speaking of stars visible to the naked eye, we do not, of course,
include the stars in the Milky Way, that arch of cloudy light which
spans the heavens; for although this wonderful zone is composed of faint
stars, these stars are not individually visible without a telescope.

Notwithstanding the limited number of the visible, or lucid, stars, as
they are called, the aspect of the starry sky still presents a spectacle
of marvellous beauty and interest, and may be viewed with pleasure and
profit even without a telescope. There are many interesting objects
which may be seen without optical assistance of any kind. Look at the
middle star of the three forming the “tail” of the Great Bear, or
“handle” of the Plough. This star was called Mizar by the old Arabian
astronomers. Close to it, good eyesight will see a small star, known as
Alcor. This little star was called by the Arabians Alsuha, which means
“the neglected small star.” The name Alcor means the “test,” and is
supposed to indicate that the old astronomers considered it a test for
keen vision; but the Arabians had a proverb, “I show him Alsuha, and he
shows me the moon,” a saying which seems to imply that it could be
easily seen by these old astronomers. The faintest star of the seven,
the one at the root of the tail, was called Megrez by the Arabian
astronomers. This star is supposed to have diminished in brightness
since ancient times, as it was rated of the third magnitude by Ptolemy,
and of the second by Tycho Brahé, while at present it is not much above
the fourth magnitude. It may possibly be variable in its light, like
many other stars in the heavens.

[Illustration:

FIG. 2.—_Stars visible in the Southern Hemisphere._

(From “Visible Universe.”)
]

Here it may be mentioned that the stars were divided into magnitudes or
classes according to their brightness by the ancient astronomers, all
the brightest stars being placed in the first magnitude, those
considerably fainter being called second magnitude, those fainter still
third magnitude, and so on to the sixth magnitude, or those just visible
to ordinary eyesight. This classification has been practically retained
by modern astronomers, but, of course, there are stars of all degrees of
brightness from Sirius down to the faintest stars visible in the largest
telescopes. Sirius is the brightest star in the heavens, and is equal to
about six average stars of the first magnitude, such as Altair or
Aldebaran. According to the Harvard photometric measures, the following
are the brightest stars in the heavens in order of magnitude:—(1)
Sirius, (2) Canopus, (3) Arcturus, (4) Capella, (5) Vega, (6) Alpha
Centauri, (7) Rigel, (8) Procyon, (9) Achernar, (10) Beta Centauri, (11)
Betelgeuse (slightly variable), (12) Altair, and (13) Aldebaran. Of
these Canopus, Alpha, and Beta Centauri, and Achernar, do not rise above
the horizon of London. Of those brighter than the second magnitude, the
following are north of the Equator: Alpha Cygni, Pollux, Castor, Eta
Ursæ Majoris, Gamma Orionis, Beta Tauri, Epsilon Ursæ Majoris, Alpha
Ursæ Majoris, Alpha Persei, and Beta Aurigæ; and south of the Equator:
Alpha Crucis, Fomalhaut, Antares, Spica, Beta Crucis, Gamma Crucis,
Epsilon Orionis, Zeta Orionis, Epsilon Canis Majoris, Beta Carinæ,
Epsilon Carinæ, Lambda Scorpii, Alpha Triangulum Australis, Gamma Argûs,
Alpha Gruis, Epsilon Sagittarii, Alpha Hydræ, Theta Scorpii, and Delta
Velorum. Of those below the second magnitude, and brighter than the
third, there are about 34 in the Northern Hemisphere, and 61 in the
Southern. As the brightness decreases, the numbers increase rapidly.
Indeed, the increase is in geometrical progression, the number in each
class of magnitude being about three times as many as those in the class
one magnitude brighter. The exact magnitudes of all stars visible to the
naked eye in both hemispheres have now been determined by the aid of
photometers. These instruments are described in Section II. of the
present work, Chapter XVII.

The stars were divided by the ancient astronomers into groups called
constellations. Some of these were formed in the earliest ages of
antiquity. Orion and the Pleiades are mentioned in Job (Chapter
XXXVIII.), which is believed to be one of the oldest books in existence.
Josephus ascribes the division of the stars into constellations to the
family of Seth, the son of Adam; and according to the Book of Enoch the
constellations were already known and named in the time of that
patriarch. The brightest stars of each constellation are designated by
the letters of the Greek alphabet, which were assigned to them by Bayer
in the year 1603, Alpha generally denoting the brightest star, Beta the
next in lustre, and so on. This is not, however, invariably the case,
and Bayer seems in many cases to have followed the outline of the
imaginary figure from which the constellation derives its name, rather
than the relative brightness of the stars composing the constellation.
For example, the seven stars in the Plough are known as Alpha, Beta,
Gamma, Delta (the faint one), Epsilon, Zeta, and Eta, beginning with the
northern of the two in the square farthest from the tail, thus evidently
following the shape of the figure, and not the order of relative
brightness. When the letters of the Greek alphabet are exhausted,
recourse is had to numbers, those in Flamsteed’s catalogue being usually
employed. Those only visible in telescopes are known by their numbers in
various catalogues. The exact positions of the stars are fixed by
determining their right ascensions and declinations, terms which on the
celestial sphere correspond to longitude and latitude on the earth.

The stars Alpha and Beta of the Plough are called “the pointers,”
because a line drawn from Beta through Alpha points nearly to a star of
the second magnitude, called the Pole Star, which lies near the pole of
the celestial sphere, or the point round which the whole star sphere
seems to rotate, owing to the rotation of the earth on its axis, in
twenty-four hours. The distance from Alpha to the Pole Star is about
five times the distance between Alpha and Beta.

If we draw an imaginary line from the star Epsilon through the Pole
Star, and produce it to about the same distance on the opposite side of
the Pole, it will pass through a well-known group called Cassiopeia’s
Chair. This consists of five fairly bright stars arranged in the form of
an irregular W. A sixth star, much fainter than the others, forms with
three of them a quadrilateral figure. It was near this faint star—known
to astronomers as Kappa—that the famous “new,” or temporary, star of
Tycho Brahé, sometimes called the “Pilgrim Star,” suddenly appeared in
November, 1572, of which more hereafter.

If we continue the curve formed by the three stars in the tail of the
Great Bear, it will pass near a very bright star of an orange colour.
This is Arcturus, one of the brightest stars in the sky. If we can rely
on the measures of distance which have been made of this brilliant star,
it must be one of the largest bodies in the universe, much larger than
our sun, which, placed at the distance assigned to Arcturus, would only
shine as a small star, quite invisible indeed to the naked eye.

Returning again to the Great Bear, if we draw a line from Gamma to Beta
and produce it, it will pass near a bright star of a yellow colour. This
is Capella. It was called by the Arabian astronomers the “Guardian of
the Pleiades.” It is the brightest star of the constellation Auriga or
“the Charioteer,” referred to by Tennyson in the lines:

“And the shining daffodil dies, and the Charioteer
And starry Gemini hang like glorious crowns
Over Orion’s grave low down in the West,”

evidently referring to the disappearance of Orion below the western
horizon in the evening sky of April. “Starry Gemini” is marked by two
bright stars, Castor and Pollux, which may be found by drawing a line
from Delta to Beta of the Great Bear, and producing it. Another line
drawn from Delta to Gamma, and produced towards the south, will pass
near a bright star called Regulus, the brightest star in the well-known
“Sickle” in Leo or the Lion. Again, a line drawn from Regulus to Gamma
in the Great Bear, and produced, will pass near another bright star,
Vega in the Lyre. This is one of the brightest stars in the Northern
Hemisphere, the three, Arcturus, Capella, and Vega, being nearly equal
in brightness. The name Vega seems to be a corruption of the Arabic name
_vaki_, or _al-nasr al-vaki_, “the falling eagle,” the wings of the bird
being represented by the stars Epsilon and Zeta Lyræ, which form, with
Vega, a small triangle, called by the Arabians _al-alsafi_, “the
trivet.” But what relation exists between a “falling eagle” and the
musical instrument known as the Lyre (Persian _al-lûra_) is not very
obvious. Possibly, however, as suggested by Schjellerup, the Arabic
word, _al-schalzâk_ “a goose,”—also applied to the constellation—refers
to the resemblance in shape between a plucked goose and a Greek lyre.
The Greeks called the constellation χέλυς, a tortoise, which also
somewhat resembles a lyre in shape.

Of the two stars which form a triangle with Vega, the northern, Epsilon,
is a double star, which is said to have been seen double with the naked
eye by several astronomers, but, probably, most people would fail to see
it as anything but a single star, as the component stars are very close.
An opera-glass will, however, show it distinctly. Each of the components
is again double, so that the object forms a most interesting quadruple
star when viewed with a good telescope.

To the east of Vega lies Cygnus, or the Swan, one of the finest of the
constellations. It may be distinguished by the long cross formed by the
principal stars which are known to astronomers as Alpha, Beta, Gamma,
Delta, and Epsilon; Alpha, or Deneb, being the brightest and most
northern of the five, and Beta the most southern and faintest. The name
Deneb is derived from the Arabic word _dzanab al-dadjâdja_, or “the tail
of the hen,” referring to its position in the ancient figure, which
represents a hen or swan flying towards the south.

To the south-east of Cassiopeia’s Chair, we find the well-known festoon
of stars which marks the constellation Perseus. Its brightest star is
sometimes called Mirfak, a name derived from the Arabic word _marfik_,
the elbow, referring, perhaps, to its position in the curved line of
stars. South of Perseus, and the nearest bright star to Mirfak in that
direction, is Algol, the famous variable star. Further south, we come to
the constellation of Taurus, or the Bull, with the well-known groups of
the Pleiades and Hyades. The Pleiades form a remarkable cluster, and
when once recognised can never be mistaken. To ordinary eyesight six
stars are visible, but those having keener vision can see more. A little
south of the Pleiades is a V-shaped figure, the Hyades, with a bright
star of a reddish colour. This is Aldebaran, a name derived from the
Arabic _al-dabarân_, the attendant or follower, because it appears to
follow the Pleiades in the diurnal motion. It was also called _aïn
al-tsaur_, “the eye of the bull,” and by several other names such as
_al-fanîk_, “the great camel,” the other smaller stars forming the
Hyades being called _al-kilas_, “the young camels!”

South of Taurus and Gemini comes the magnificent constellation of Orion,
perhaps the most splendid collection of stars in the sky. This brilliant
asterism contains many fine objects. Looking at it when it is visible in
the winter sky, we notice a large quadrilateral figure formed by four
conspicuous stars. The upper one to the left is called Betelgeuse, and
is decidedly reddish in colour—very much resembling Aldebaran both in
tint and brightness. Its name is derived from our Arabic word meaning
the shoulder, because it is situated on the right shoulder of the giant
Orion on the old celestial globes. The upper one to the right is called
Bellatrix, or the female warrior! The real significance of some of those
old names is sometimes difficult to understand. Of the lower stars, the
one on the right is a fine white star of the first magnitude known as
Rigel. It is situated on the left foot of the ancient figure of Orion,
and its name is derived from the first part of the compound Arabic name
_ridjl-al-djauzâ_, “the leg of the giant.” The lower star on the left is
known to astronomers by the Greek letter Kappa.

In the middle of the four-sided figure referred to above are three stars
of the second magnitude, nearly in a straight line, forming “Orion’s
Belt.” The upper one of the three is slightly fainter than the others,
and has been suspected of being slightly variable in its light, but the
variability is doubtful. South of these three conspicuous stars are
three fainter stars, forming a nearly vertical line. This is “the Sword
of Orion.” The middle star of the three marks the position of “the great
nebula in Orion,” one of the finest objects in the heavens, of which
more hereafter. To some eyes a nebulous glow is visible round this star.
Even in a small telescope the nebula is an interesting object. On a very
clear night the southern star of the three may be seen double with good
eyesight. The stars forming Orion’s Belt were called by the Arabian
astronomers _mintakat al-djauza_, “the Belt of the Giant”; and the stars
forming the “sword,” _al-lakat_, the “gleaned ears of corn,” and also
_saif-al-djabbâr_, “the Sword of the Giant.” Perhaps the latter word is
the origin of the name Algebar, formerly applied to Rigel.

The three bright stars in Orion’s Belt nearly point (to the south-east)
to Sirius, the brightest star in the heavens. This is a splendid white
star, and is so much brighter than any other fixed star that its
identity cannot be mistaken.

If we draw a line from the star Gamma in the Plough to the Pole Star,
and produce it, it will pass through a somewhat similar four-sided
figure, but of much larger size, and the stars rather fainter. This is
known as “the Square of Pegasus.” The upper stars are known as Beta
Pegasi (the one to the right) and Alpha Andromeda. To the east of Alpha
Andromedæ is a star of the third magnitude, Delta, and to the east of
Delta, a star of the second magnitude called Beta Andromedæ. A little
north of Beta are two small stars, Mu and Nu, nearly in a line with
Beta, and to the north of Nu is the famous “nebula in Andromeda” “the
queen of the nebulæ,” as it has been termed. It is just visible to the
naked eye as a hazy spot of light, and it may be well seen in a good
opera-glass or binocular. Even in a small telescope it is a really
splendid object. The reader should fix its exact position carefully, as
it has been frequently mistaken for a comet by observers whose knowledge
of the heavens is not very accurate.

The following alignments may be found useful by beginners in the study
of the starry sky:—

Castor and Pollux, already mentioned, nearly point south to the star
Alpha Hydræ, an isolated reddish star of the second magnitude. It is
also called Alphard, from the Arabic _al-fard_, “the solitary one,”
because there is no other bright star near it. It is described by
Al-Sûfi, the Persian astronomer, as red in the tenth century. In the
Chinese annals it is called “the Red Bird.”

An isosceles triangle is formed by Castor (at the vertex), Alphard and
Sirius. Procyon is nearly in the centre of this triangle. Two other
roughly isosceles triangles are formed, having Aldebaran at the vertex
of each, namely: Aldebaran, Castor, and Procyon, and Aldebaran, Procyon,
and Sirius.

Castor, Alpha, Delta, and Beta Orionis are nearly in a straight line;
also Beta Pegasi, Alpha Pegasi and Fomalhaut. A right-angled triangle is
formed by Arcturus, Spica, and Regulus, Spica being at the right angle.

In the Southern Hemisphere, the most remarkable group of stars is the
well-known Southern Cross. It consists of four stars, known as Alpha,
Beta, Gamma and Delta—Gamma being at the top of the cross, and Alpha at
the bottom. These stars are popularly supposed to be of great
brilliancy, but this is a mistake; their magnitudes, according to recent
photometric measures, being Alpha, first magnitudes, Beta 1½, Gamma,
second magnitude, and Delta, third magnitude. A little south of Delta is
Epsilon, a star of the fourth magnitude, which rather spoils the
symmetry of the cross-shaped figure. A little to the east of the
Southern Cross are Alpha and Beta Centauri, two of the brightest stars
in the sky. Another fine group of stars is Scorpio, or the Scorpion, of
which the brightest star is Antares, a reddish star of about magnitude
1½, which is visible near the southern horizon in the months of June and
July in England.

When the positions of the principal stars are known, it will be easy to
find any other required object by means of star maps.

CHAPTER II.
DOUBLE, MULTIPLE, AND COLOURED STARS.

Many of the stars when examined with a good telescope are seen to be
double, some triple, and a few quadruple, and even multiple. These when
viewed with the naked eye, or even a powerful binocular, seem to be
single, and show no sign of consisting of two components. These
telescopic double stars should be carefully distinguished from those
which appear very close together with the naked eye, and which in
opera-glasses or telescopes of small power might be mistaken for wide
double stars by the inexperienced observer. These latter stars, such as
Mizar—the middle star in the tail of the Great Bear, and its small
companion, Alcor, referred to in the last chapter—have been called
“naked eye doubles,” but they are not, properly speaking, double stars
at all. Telescopic double stars are far closer, and even the widest of
them could not possibly be seen double without optical aid, even by
those who are gifted with the keenest vision. Of these so-called “naked
eye doubles,” we may mention Alpha Capricorni, which on a very clear
night may be seen with the naked eye to consist of two stars. On a very
fine night two stars may be seen in Iota Orionis, the most southern star
in Orion’s Sword. The star Zeta Ceti has near it a fifth magnitude star,
Chi, which may be easily seen with the unaided vision. The star Epsilon
Lyræ (near Vega), is, as mentioned in the last chapter, a severe test
for naked eye vision. Bessel, the famous German astronomer, is said to
have seen it when thirteen years of age. Omicron Cygni (north of Alpha
and Delta Cygni) forms another naked eye double, and other objects of
this class may be noticed by a sharp-eyed observer.

The star Mizar, already referred to, is itself a wide telescopic double,
and it seems to have been the first double star discovered with the
telescope (by Riccioli in 1650). It consists of two components, of which
one is considerably brighter than the other. It will give an idea of the
closeness of even a “wide” telescopic double when we say that the
apparent distance between Mizar and Alcor is nearly forty times the
distance which separates the close components of the bright star. From
this it will be seen that even a powerful binocular field-glass would
fail to show Mizar as anything but a single star. The components may,
however, be well seen with a 3-inch telescope, or even with a good
2-inch. The colours of the two stars are pale green and white. Between
Mizar and Alcor is a star of the eighth magnitude, and others fainter.
Mizar was the first double star photographed by Bond.

The Pole Star has a small companion at a little greater distance than
that which separates the components of Mizar, but owing to the faintness
of this small star, the object is not so easy as Mizar. A telescope with
a good 3-inch aperture should, however, show it readily. Dawes saw it
with a small telescope of 1³⁄₁₀-inch aperture, and Ward, who has
wonderful vision, with only 1¼-inch.

The star Beta Cygni is composed of a large and small star, of which the
colours are described as “golden-yellow and smalt-blue.” This is a very
wide double, and may be seen with quite a small telescope. Another fine
double star is that known to astronomers as Gamma Andromedæ. The
magnitudes of the components are about the same as those of Mizar, but a
little closer. Their colours are beautiful (“gold and blue”). This is
one of the prettiest double stars in the heavens. It is really a triple
star, the fainter of the pair being a very close double star; but this
is beyond the reach of all but the largest telescopes. The star Gamma
Delphini is another beautiful object, the components being a little more
unequal in magnitude, but the distance between them about the same as in
Gamma Andromedæ. I have noted the colours with a 3-inch telescope as
“reddish-yellow and greyish-lilac.” Gamma Arietis, the faintest of the
three well-known stars in the head of Aries, is another fine double
star, a little closer than Gamma Delphini. This is an interesting
object, from the fact that it was one of the first double stars
discovered with the telescope—by Hooke, in 1664, when following the
comet of that year. He says:—“I took notice that it consisted of two
small stars very near together, a like instance of which I have not else
met with in all the heaven.” Eight years previous to this, however, in
1656, Huygens is said to have seen three stars in Theta Orionis, the
well-known multiple star in the Orion nebula; and in 1650, Riccioli, at
Bologne, saw Zeta Ursæ Majoris (Mizar) double, as already stated.

Another beautiful double star is Eta Cassiopeiæ, the components being
about equal in brightness to those of Gamma Delphini, but the distance
less than one half, so that a higher magnifying power will be required
to see them well. The colours are, according to Webb, yellow and purple;
but other observers have found the smaller star garnet or red. This is a
very interesting object, the components revolving round each other, and
forming what is called a binary star.

Another fine double star is Castor, which is composed of two nearly
equal stars separated by a distance about half that between the
components of Gamma Andromedæ. This is also a binary or revolving double
star, but the period is long. Gamma Virginis is another fine double
star, with components at about the same distance as those of Castor, and
the colours very similar. It is also a remarkable binary star, and
further details respecting it will be given when we come to speak of the
binary stars.

Among double stars of which the components are closer than those
mentioned above, but which are within the reach of a good 3-inch
telescope—a common size with amateur observers—the following may be
noticed:—Alpha Herculis, colours, orange or emerald green; the light of
this star is slightly variable. Gamma Leonis, another binary star with a
long period; colours, pale yellow and purple. Epsilon Boötis, a lovely
double star, the colours of which Secchi described as “most beautiful
yellow, superb blue.” This has been well seen with a 2¼-inch achromatic.

For observers in the Southern Hemisphere, the following fine double
stars may be seen with a 3-inch telescope:—Alpha Centauri; this famous
star, the nearest of all the fixed stars to the earth, is also a
remarkable binary; its period, as recently computed by Dr. See, is 81
years, and the component stars are now at nearly their greatest distance
apart, the distance being greater than that between the components of
Mizar, so that any small telescope will show them. Theta Eridani is a
splendid pair, but closer than Alpha Centauri. It is, however, an easy
object with a 3-inch telescope, and with a telescope of this size I
noted the colours in India as light yellow and dusky yellow. The star
known as _f_ Eridani is a very similar double to Theta, but the
components are fainter. I noted the colours in India as yellowish-white
and very light green. There are, of course, many other double stars in
both hemispheres within the reach of small telescopes; but those
described above are perhaps the finest examples.

In addition to these comparatively wide double stars, there are many of
which the components are so close that they are quite beyond the reach
of a 3-inch or even a 4-inch telescope. Some, indeed, are so excessively
close as to tax the highest powers of the largest telescopes yet
constructed.

Of triple, quadruple, and multiple stars, there are several which may be
well seen with a small telescope. Of these may be mentioned Iota
Orionis, the lowest star in the Sword of Orion, which consists of a
bright star accompanied by two small companions. In Theta Orionis, the
middle star of the Sword, four stars may be seen forming a quadrilateral
figure, known to observers as the “trapezium.” I have seen these in
India—where the star is higher in the sky than in this country—with a
3-inch refractor reduced by a “stop” over the object-glass to 1½ inch.
There are two fainter stars in this curious object, which lie in the
midst of the Orion nebula, but a somewhat larger telescope is required
to see them. Within the trapezium are two very faint stars, which are
only visible in the largest telescopes. In Sigma Orionis—a star closely
south of Zeta, the lowest star in Orion’s Belt—six stars may be seen
with a 3-inch telescope. Indeed, Ward has seen ten with a slightly
smaller telescope. Epsilon Lyræ may be seen double with a low power, and
each star of the pair again double with a high power; but this is more
difficult than the other close stars mentioned above.

When carefully examined, many of the stars show differences in colour.
Among the brightest stars it will be noticed that Sirius, Rigel, and
Vega, shine with a white or bluish-white light; Capella is distinctly
yellowish; Arcturus yellow or orange; and Aldebaran and Betelgeuse have
a well-marked reddish hue. There are no stars of a decided blue colour
visible to the naked eye, at least in the Northern Hemisphere. The third
magnitude star, Beta Lyræ, is said to be greenish, but its colour is not
conspicuous. Betelgeuse is perhaps the ruddiest of the brighter stars,
and its reddish tint contrasts strongly with the white light of Rigel,
in the same constellation. Aldebaran, which lies not far from
Betelgeuse, is of nearly the same hue. But the reddest star visible to
the naked eye in the Northern Hemisphere is the fourth magnitude star,
Mu Cephei. It is not, however, sufficiently bright to enable its colour
to be well seen without optical aid, but with an opera-glass its reddish
hue is beautiful and striking when compared with other stars in its
immediate vicinity. It was called by Sir William Herschel the “garnet
star,” and its colour is certainly remarkable. Like so many of the red
stars, it is variable in light, but numerous observations by the present
writer seem to show that there is no regular period, and its light often
remains for many weeks with little or no perceptible change.

Among other stars visible to the naked eye, the reddish colour is also
conspicuous in Antares, Alphard, Eta, and Mu Geminorum, Mu and Nu Ursæ
Majoris, Beta Ophiuchi, Gamma Aquilæ, and others in the Southern
Hemisphere· Alphard was noted as red by the Persian astronomer, Al-Sûfi,
in the tenth century, and it was called “the Red Bird,” by the old
Chinese observers.

Ptolemy, in his catalogue, calls the following stars “fiery red”:
Arcturus, Aldebaran, Pollux, Antares, Betelgeuse, and, curious to say,
Sirius, which is now white. There is some little doubt as to the reality
of this change of hue in Sirius, but Al-Sûfi distinctly describes the
variable star, Algol, as red, whereas it is now white, or only slightly
yellowish.

The finest examples of red stars are, however, found among those only
visible with a telescope. Of these may be mentioned the star numbered
713 in Espin’s edition of Birmingham’s “Catalogue of Red Stars,” which
Franks describes as “orange vermilion,” and the star Birmingham 248,
which Espin notes as “magnificent blood-red.” Another very fine red star
is the variable R Crateris, which Sir John Herschel described as
“scarlet, almost blood colour,” Birmingham “crimson,” and Webb “very
intense ruby.” Observing it in India with a 3-inch telescope, I noted it
as “full scarlet.” It has near it a star of the ninth magnitude of a
pale bluish tint. No. 4 of Birmingham’s “Catalogue” is described by
Espin as of an “intense red colour, most wonderful.” The variable star U
Cygni is very red, and is described by Webb as showing “one of the
loveliest hues in the sky.” Another red star is the remarkable, variable
R Leonis, whose fluctuations in light will be described in the chapter
on Variable Stars. Hind says: “It is one of the most fiery-looking
variables on our list—fiery in every stage from maximum to minimum, and
is really a fine telescopic object in a dark sky about the time of
greatest brilliancy, when its colour forms a striking contrast with the
steady white light of the sixth magnitude, a little to the north.”

In the Southern Hemisphere there are some fine red stars. Epsilon
Crucis, one of the stars of the Southern Cross, is said to be very red,
and so are Mu Muscæ and Delta Gruis, the southern star of a naked eye
double. Pi Gruis is also a wide double star, and Dr. Gould describes one
of the pair as “deep crimson,” while the other is “conspicuously white.”
The variable R Sculptoris is another fine red star, which Gould
describes as “intense scarlet,” and Miss Clerke says it “glows like a
live coal in the field,” a good description of these telescopic red
stars. With reference to a small star in the field of view with Beta
Crucis, one of the brightest stars in the Southern Cross, Sir John
Herschel says: “The fullest and deepest maroon-red, the most intense
blood-red of any star I have seen. It is like a drop of blood when
contrasted with the whiteness of Beta Crucis.”

Among the double stars there are numerous examples of coloured suns. Of
these may be mentioned Alpha Herculis, the components of which are
orange and emerald, or bluish-green, and described by Smith as “a lovely
object, one of the finest in the heavens”; Epsilon Boötis, of which the
colours are described by Secchi as “most beautiful yellow, superb blue”;
Beta Cygni, “golden-yellow and smalt-blue”; Beta Cephei, “yellow and
violet”; Delta Cephei, “yellow and blue”; Gamma Andromedæ, “gold and
blue”; and Beta Piscis Australis, of which the colours were noted by the
present writer in India as white and reddish-lilac.

It has been found that the red stars are most numerous in or near the
Milky Way, and one portion of the Galaxy—between Aquila, Lyra, and
Cygnus—was called by Birmingham “the red region in Cygnus.” Yellow and
orange stars seem to be most abundant in the constellations, Cetus,
Pisces, Hydra, and Virgo, and the white stars in Orion, Cassiopeia, and
Lyra.

CHAPTER III.
THE DISTANCES AND MOTIONS OF THE STARS.

The determination of the distances of the stars from the earth has
always formed a subject of great interest to astronomers. The earlier
observers appear to have thought that the problem was an insoluble one.
The famous Kepler, judging from what he called the “harmony of
relations,” came to the conclusion that the distance of the fixed stars
should be about 2,000 times the distance of Saturn from the sun. Saturn
was then the outermost planet of the solar system. The distance of even
the nearest star, as now known, is about 14 times greater than that
supposed by Kepler. Huygens thought the determination of stellar
distance by observation to be impossible, but made an attempt at a
solution of the problem by a photometric comparison between Sirius and
the sun. By this method, he found that Sirius is probably about 28,000
times the sun’s distance from the earth, but modern measures show that
this estimate is far too small, the distance of Sirius being probably
over 500,000 times the sun’s distance, or about 18 times greater than
Huygens made it.

When the Copernican theory of the earth’s motion round the sun was first
advanced, it was objected that, if the earth moved in a large orbit, its
real change of place should produce an _apparent_ change of position in
the stars nearest to the earth, causing them to shift their relative
position with reference to more distant stars. Copernicus replied to
this objection—and we now know that his reply was correct—by saying that
the distance of even the nearest stars was so great that the earth’s
motion would have no perceptible effect in changing their apparent
position in the heavens; in other words, the diameter of the earth’s
orbit round the sun would be almost a vanishing point if viewed from the
distance of the nearest stars. This explanation of Copernicus was at
first ridiculed, and even the famous astronomer, Tycho Brahé, could not
accept such a startling conclusion. This celebrated observer failed
indeed to detect by his own observations any annual change of place in
the stars, but he fancied that the brightest stars showed a perceptible
disc, like the planets, a fact which, if true, would imply that, if the
distance of the stars was so great as Copernicus supposed, their real
diameter must be enormous. The invention of the telescope, however,
dispelled this delusion of Tycho Brahé, and showed that even the
brightest stars showed no perceptible disc. This was proved by Horrocks
and Crabtree, who noticed that, in occultations of stars by the moon,
the stars disappeared instantaneously, a fact which proved that the
apparent diameter of the stars must be a very small fraction of a second
of arc.

Galileo suggested that possibly the distance of the nearer stars might
be determined by careful measures of double stars, on the assumption
that the brighter star of the pair—if the difference in brilliancy is
considerable—is nearer the earth than the fainter star. He says (in his
“_Opere di Galileo Galilei_”), “I do not believe that all the stars are
scattered over a spherical superficies _at equal distances from a common
centre_, but I am of opinion that their distances from us are so various
that some of them may be two or three times as remote as others, so that
when some minute star is discovered by the telescope close to one of the
larger, and yet the former is highest, it may be that some sensible
change might take place among them.” Acting on this idea, Sir William
Herschel, at the close of the eighteenth century, made a careful series
of measures of certain double stars. He did not, however, succeed in his
attempt, as his instruments were not sufficiently accurate for such an
investigation, but his labours were rewarded by the great discovery of
binary or revolving double stars, most interesting objects, which will
be considered in the next chapter.

Numerous but unsuccessful attempts were made by Hooke, Flamsteed,
Cassini, Molyneux, and Bradley, to find the distance of some of the
stars. Hooke, in the year 1669, thought he had detected a parallax of 27
to 30 seconds arc in the star Gamma Draconis, but we now know that no
star in the heavens has anything like so large a parallax. It must be
here explained that to find the distance of any star from the earth, we
must first measure its “parallax,” which is the apparent change in its
place due to the earth’s motion round the sun. As the earth makes half a
revolution in six months, and as the earth’s mean distance from the
sun—or the radius of the earth’s orbit—is about 93 millions of miles,
the earth is, at any given time, about 186 millions of miles distant
from the point in its orbit which it occupied six months previously. The
apparent change of position in a star’s place, known as parallax, is
_one-half_ the total displacement of the star as seen from opposite
points of the earth’s orbit. In other words, it is the angle subtended
at the star by the sun’s mean distance from the earth. The measured
parallax of a star may be either “absolute” or “relative.” An “absolute
parallax” is the actual parallax. A “relative parallax” is the parallax
with reference to a faint star situated near a brighter star, the faint
star being assumed to lie, as suggested by Galileo, at a much greater
distance from the earth. As, however, the faint star may have a small
parallax of its own, the “relative parallax” is the difference between
the parallaxes of the two stars. Indeed, in some cases a “negative
parallax” has been found, which, if not due to errors of observation,
would imply that the faint star is actually the nearer of the two. From
the observed parallax, the star’s distance in miles may be found by
simply multiplying 93 millions of miles by 206,265 and dividing the
result by the parallax. To find the time that light would take to reach
us from the star—the light journey as it is called—it is only necessary
to divide the number 3·258 by the parallax.

In attempting to verify the result found by Hooke for the parallax of
Gamma Draconis, Molyneux and Bradley found an apparent parallax of about
20 seconds of arc, thus apparently confirming Hooke’s result, but
observations of other stars showing a similar result, Bradley came to
the conclusion that the apparent change of position was not really due
to parallax, but was caused by a phenomenon now known as the “aberration
of light,” an apparent displacement in the positions of the stars, due
to the effect of the earth’s motion in its orbit round the sun combined
with the progressive motion of light. The result is that “a star is
displaced by aberration along a great circle, joining its true place to
the point on the celestial sphere towards which the earth is moving.”
The amount of aberration is a maximum for stars lying in a direction at
right angles to that of the earth’s motion. The existence of aberration
is an absolute proof that the earth does revolve round the sun, for were
the earth at rest—as some paradoxes contend—there would be no aberration
of the stars. This effect of aberration must, of course, be carefully
allowed for in all measures of stellar parallax. To show that
“aberration” could not possibly be due to “parallax,” it may be stated
that aberration shifts the apparent place of a star in one direction,
while parallax shifts it in the opposite direction.

From photometric comparisons, the Rev. John Mitchell, in the year 1767,
concluded that the parallax of Sirius is less than a second of arc; a
result which has been fully confirmed by modern measures. He considered
that stars of the sixth magnitude are probably 20 to 30 times the
distance of Sirius, and judging from their relative brilliancy alone,
this result would also be nearly correct. But recent measures have shown
that some of the fainter stars are actually nearer to us than some of
the brighter, and that the brightness of a star is no criterion of its
distance.

The first stars on which observations seem to have been made with a view
to a determination of their distance seem to have been Aldebaran and
Sirius. From observations made in the years 1792 to 1804 with a vertical
circle and telescope of 3 inches aperture, Piazzi found for Aldebaran an
“absolute” parallax of about 1½ seconds of arc. O. Struve and Shdanow,
in 1857, using a refractor of 15 inches aperture, found a “relative”
parallax of about half a second. This was further reduced by Hall with
the 26-inch refractor of the Washington Observatory to about one-tenth
of a second, and Elkin, with a heliometer of 6 inches aperture, finds a
relative parallax of 0″·116, or about 30 years’ journey for light For
Sirius, Piazzi found, in 1792–1804, an absolute parallax of four
seconds, but this was certainly much too large. All subsequent observers
find a much smaller parallax, recent measures giving a relative parallax
of 0·370″ by Gill, and 0·407″ by Elkin. In the years 1802–1804, Piazzi
and Cacciatori found an absolute parallax of 1′·31 for the Pole Star;
but this has been much reduced by other observers. Pritchard, by means
of photography, found a relative parallax of only 0·073″, which agrees
closely with some other previous results, and indicates a “light
journey” of about 44 years!

For the bright star Procyon, Piazzi found a parallax of about three
seconds, but this is also much too large, a recent determination by
Elkin giving 0·266″, a figure in fair agreement with results found by
Auwers and Wagner. For the bright star Vega, Calandrelli, in the years
1805–6, found an absolute parallax of nearly four seconds, but this has
also been much reduced by modern measures; Elkin, from observations in
the years 1887–88, finding a relative parallax of only 0·034″. Brinkley
found a parallax of over one second for Arcturus, but Elkin’s result is
only 0·018″. If this minute parallax can be relied on, Arcturus must be
a sun of vast size.

Owing to the large “proper motion” of the star known as 61 Cygni, its
comparative proximity to the earth was suspected, and in 1812, Arago and
Mathieu found, from measures made with a repeating circle, a parallax of
over half a second. Various measures of its parallax have since been
made, ranging from about 0·27″ to 0·566″. Sir Robert Ball, at Dunsink,
Ireland, found 0·468″, and Pritchard, by means of photography with a
13-inch reflector, found 0·437″. We may, therefore, safely assume that
the parallax of 61 Cygni is about 0·45″. This implies a distance of
458,366 times the sun’s distance from the earth, or about 42 billions of
miles, and a “light journey” of about 7¼ years.

It is usually stated that 61 Cygni is the nearest star to the earth in
the Northern Hemisphere, but for the star known as Lalande 21,185,
Winnecke found 0·511″, and afterwards 0·501″. This has, however, been
reduced by Kapteyn (1885–1887) to 0·434″; and recently a parallax of
0·465″ has been found by the photographic method for the binary star,
Eta Cassiopeiæ. 61 Cygni is a wide double star, but it seems doubtful
whether the components are physically connected, although several orbits
have been provisionally computed.

Nearer to us than 61 Cygni is the bright southern star Alpha Centauri,
which, so far as is known at present, is the nearest of all the fixed
stars to the earth. The first attempt to find its distance was made by
Henderson in the years 1832–33, using a mural circle of 4 inches
aperture and a transit of 5 inches. He found an “absolute” parallax of
about one second of arc, which subsequent measures have shown to be
rather too large. Measures in recent years range from 0·512″ to 0·976″,
but probably the most reliable are those made with a heliometer of 4½
inches aperture by Dr. Gill (1881–82), who found a “relative” parallax
of 0·76″, and by Dr. Elkin, using the same instrument, 0·671″. Gill’s
result would place the star at a distance of 271,400 times the sun’s
distance from the earth, or about 25 billions of miles, a distance which
light, with its great velocity of 186,300 miles a second, would take
over 4¼ years to traverse.

It will be understood that the parallaxes found for even the nearest
fixed stars are so small that their exact determination taxes the powers
of the most perfect instruments and the skill of the most experienced
observers. One thing, however, seems certain, that the brightest stars
are not necessarily the nearest, and that comparatively faint stars may
be actually nearer to the earth than some of the brightest gems which
deck our midnight sky. Indeed, from a discussion of the observed
parallaxes and “proper motions” of 11 stars, Gylden finds a mean
parallax of only 0·083″ for stars of the first magnitude. This agrees
closely with the value 0·089″ found by Dr. Elkin.

In old times the stars were supposed to be absolutely fixed in the
celestial vault, that is to say, that their relative positions did not
change. This was a very natural conclusion, for before the invention of
the telescope it would have been impossible to detect any “proper
motion”—as it is called—by naked eye observations. Hence the term “fixed
stars,” used to distinguish the stars from the planets, which are always
shifting their positions in the heavens. The existence of proper motion,
in some at least of the stars, seems to have been discovered by Halley,
who found from his observations in 1715 that the bright stars, Sirius,
Arcturus, and Aldebaran, had apparently shifted their positions since
the date of the earliest observations. This discovery was confirmed by
James Cassini in 1738. He found that Arcturus had apparently moved
through some five minutes of arc in 152 years, or about two seconds a
year, a result which agrees fairly well with more exact modern measures.

This interesting discovery of stellar motion has been fully confirmed by
modern observations, and we now know that, far from the stars being
“fixed,” most of them have an apparent motion on the celestial vault.
These motions are, however, very slow, and can only be detected by
accurate measurements and a careful comparison of their positions after
the lapse of a number of years. The largest proper motion hitherto
detected is that of a star known as 1830 of Groombridge’s catalogue, a
small star of about 6½ magnitude, which lies in the constellation Ursa
Major. This star has an apparent motion of seven seconds per annum,
which, though relatively large, is of course absolutely small, as the
observed motion would only suffice to carry it through a space equal to
the moon’s apparent diameter in about 266 years. Assuming a parallax of
about one-sixth of a second found by Kapteyn, this apparent motion would
indicate a real motion of about 128 miles a second at right angles to
the line of sight. As, however, there may be also motion _in_ the line
of sight, the above velocity would be a minimum—if the parallax can be
relied upon—and the actual motion may be considerably more. From its
rapidity, 1830 Groombridge has been called by Prof. Newcomb “the runaway
star.”

Next in order of rapidity of motion comes the southern star known as
Lacaille 9352, which lies in the constellation Piscis Australis, a
little south of Fomalhaut. This seventh magnitude star has an apparent
motion of 6·9 seconds, which, with a parallax of 0·285″ found by Gill,
indicates a velocity of 71 miles per second. Next comes 61 Cygni, with a
velocity of 30 miles, and Epsilon Indi—another southern star—with a
velocity of nearly 68 miles a second. These velocities are, however,
exceeded by other stars if the measured parallaxes are correct. Thus the
star Mu Cassiopeiæ, with a proper motion of 3·7 seconds, has, according
to Pritchard’s photographic measures, a parallax of only 0·036″, which
would indicate a velocity of no less than 302 miles a second! and the
small parallax found by Elkin for Arcturus would imply the startling
velocity of 376 miles a second!

It is a remarkable fact that the eight stars with the largest proper
motions are all below the fourth magnitude in brightness, and as a large
proper motion probably indicates proximity to the earth, the conclusion
seems evident that the brightest stars are not as a rule the nearest. Of
twenty-five stars, with proper motions greater than two seconds of arc,
there are only two—Arcturus and Alpha Centauri—whose magnitude exceeds
the third. Indeed, more than half the stars with motions greater than
one second are invisible to the naked eye!

Many stars have proper motions of less than a second of arc per annum.
Very small proper motions have also been detected, which only reveal
themselves after the lapse of a great number of years, and it seems
probable that there are no really “fixed stars” in the heavens. For
stars of the sixth magnitude, M. Ludwig Struve finds an average motion
of only eight seconds in a hundred years, or about one-twelfth of a
second per annum. If we assume that stars of the sixth magnitude are, on
the average, of the same size and brightness as stars of the first
magnitude, their distance from the earth would be ten times greater.
Consequently, stars of the first magnitude should have an average proper
motion of about eighty seconds in one hundred years. This, however, is
not the case. The twenty brightest stars show an average motion of only
sixty seconds in a hundred years. And the motion of stars of the second
magnitude is relatively still slower. Instead of an average motion of
fifty seconds in a hundred years—which they should have if the
brightness were inversely proportional to the distance—it has been found
that twenty-two stars of the second magnitude show an average motion of
only seventeen seconds. This result seems to show that the brighter
stars are not so near us as their brilliancy would lead us to suppose, a
conclusion which has been already proved by actual measures of their
distance.

From a consideration of the results found for stellar parallax, Mr.
Thomas Lewis, F.R.A.S., of the Greenwich Observatory, comes to the
following conclusions[108]:—

“(1) Leaving out a few of the brightest stars, the parallaxes are
constant down to 2·70 magnitude.

“(2) After 2·70 mag. is reached, the parallaxes are doubled, and remain
practically constant to 8·40 mag.

“(3) Up to the 3rd mag. the velocities are very small, averaging about 9
miles per second, while after the 3rd mag. the velocity is 38 miles per
second.

“Hence we may fairly deduce—

“(1) That there are a few stars (about 8) of exceptional brilliancy in
our immediate neighbourhood, and scattered about amongst these a number
of small stars (at present about 40 are known).

“(2) Stars of mag. 1·0 to 3·0 are, as a class, far outside this inner
space, and have very small velocities.

“(3) The small stars here dealt with have apparently large velocities
across the line of sight.

“These results show that the generally received idea that parallaxes are
to be sought for in stars with large proper motion is correct, and we
may add that this holds good, no matter what may be the star’s
magnitude.”

The “proper motion” of a star only indicates its motion at right angles
to the line of sight—that is, its motion on the surface of the celestial
vault—and gives us no information as to whether the star is approaching
to or receding from the earth. This motion “in the line of sight” cannot
be detected by micrometrical measures with an ordinary telescope, and
would probably have remained for ever unknown had the spectroscope not
been invented. Dr. Huggins was the first to show that motions in the
line of sight could be determined by measuring the displacement of the
spectral lines caused by the approach or recession of the source of
light, the lines being slightly shifted towards the blue end of the
spectrum when the star is approaching the earth, and towards the red end
when it is receding from us. The effect would, of course, be exactly the
same if the star were at rest and the earth in motion. By carefully
measuring this observed displacement of the spectral lines, the velocity
in the line of sight can be easily computed. Dr. Huggins’ observations
were fully confirmed by Dr. Vogel.

The earlier determinations of motion in the line of sight were made by
eye measurements with a micrometer, and owing to the difficulty and
delicacy of these measures, the results were very discordant. The method
has recently been much improved by photographing the spectra and
measuring the positions of the lines on the photograph. Both methods
agree in showing that the following stars, among others, are certainly
_approaching_ the earth: Arcturus, Vega, Procyon, Pollux, Altair, Spica,
Alpha Cephei, Alpha Persei, Alpha Arietis, 61 Cygni, and the Pole Star;
and the following are certainly _receding_: Capella, Rigel, Betelgeuse,
Aldebaran, and Regulus.

Measures of photographic stellar spectra have yielded much more accurate
results than the old method. Some of the velocities found in this way by
Dr. Vogel—who has given especial attention to this subject—are very
considerable. For the bright star Rigel he finds a velocity of recession
of about 39 miles a second, for Aldebaran 30 miles, and for Capella 15
miles. He finds that the Pole Star is approaching the earth at the rate
of 16 miles a second, and Procyon about 7 miles.

Dr. Bélopolsky has recently investigated the _absolute_ velocity in
space of the brighter component of 61 Cygni—that is, the motion across
the line of sight combined with the motion _in_ the line of sight.
Assuming a parallax of half a second and a proper motion of 5·2 seconds,
he finds that the motion across the line of sight, corrected for the
sun’s motion in space, is about 22½ miles per second. The motion _in_
the line of sight, also corrected for the sun’s motion, he finds, from
photographs taken at Pulkova, to be about 27 miles a second towards the
earth. Combining these motions, he finds the absolute velocity of the
star in space to be about 35 miles a second, or nearly double the
velocity of the earth in its orbit

This method of measuring velocities in the line of sight has also been
applied to the nebulæ. Mr. Keeler has observed and measured a
displacement of the line known as the chief nebular line in several
planetary nebulæ, and finds considerable motion in the line of sight.
For example, in the nebula numbered 6790 in the “New General Catalogue,”
he finds a motion of recession of about 38 miles a second. Some of these
motions may possibly be due, in part at least, to the sun’s motion in
space, carrying the earth with it, a motion which will now be
considered. The method has also led to the discovery of the so-called
“spectroscopic binary stars,” a most interesting class of objects, which
will be considered in the next chapter.

The proper motions of the stars long since suggested the idea that
possibly the observed motion may be—to some extent, at least—merely
apparent, and due to the real motion of the sun and solar system through
space. The first investigation of this interesting question was made by
Sir William Herschel in 1783, and he came to the conclusion that the sun
is moving towards a point near Lambda Herculis, a result not differing
widely from modern determinations. The reality of Herschel’s result has
been fully confirmed by subsequent investigations, and Argelander placed
it beyond doubt by a comparison of the positions of a large number of
stars determined at Abo with those found by Bradley in 1752. The
accuracy of Argelander’s result was confirmed by Otto Struve. According
to the elder Struve, the results arrived at by Argelander, O. Struve,
and Peters, is to place the point towards which the sun is moving,
between the stars Pi and Mu Herculis, “at a quarter of the apparent
distance of these stars from Pi Herculis,” and they estimated the annual
motion at about 33½ million miles geographical. The general accuracy of
this conclusion has been verified by modern researches, although the
results found by different astronomers vary to some extent. The
accompanying diagram shows some of the different positions found by
various computers. The later determinations seem to place the “apex of
the solar motion,” as it is termed, not far from the bright star Vega,
or further to the east than Herschel placed it. The velocity of the
sun’s motion in space has not been so well determined as its direction.
L. Struve’s computations would indicate a velocity of about 14 miles a
second; but other results give a much smaller velocity.

[Illustration:

FIG. 3.—_Diagram showing “Solar Apex,” and the different Positions
found by various Computers._

(From “Visible Universe.”)
]

From a recent investigation of the nature of the sun’s motion in space
by Mr. G. C. Bompas,[109] he considers that the various positions of the
sun’s “apex” show a tendency to a drift along the edge of the Milky Way,
and that this drift “seems to point to a plane of motion of the sun
nearly coinciding with the plane of the Milky Way, or, perhaps, more
nearly with the plane of that great circle of bright stars first
described by Sir Wm. Herschel as inclined about 20° to the galaxy, and
which passes through Lyra, in or near which constellation the solar apex
lies,” and he concludes, from the motion of the nearer stars, “that the
sun moves in a retrograde orbit from east to west, and in a plane
inclined a few degrees to that of the Milky Way.” With reference to this
very interesting conclusion, which may, perhaps, be confirmed by further
observations, Mr. Bompas quotes the following passage from “The Visible
Universe,” p. 197, by the present writer:—“With reference to a possible
motion of the stars in some general system, M. Rancken has found, from
an examination of 106 stars, a tendency to drift along the course of the
Milky Way from Aquila towards Cygnus and Cassiopeia, and past Capella
through Orion to Argo. The _larger_ motions, shown in Proctor’s map of
‘proper motions,’ exhibit this tendency in a marked degree between
Cygnus and Capella, and less clearly on the Sirius, but the smaller
motions not so well,” and Mr. Bompas points out that this apparent drift
of the stars in the Milky Way, from west to east, “is just such as would
be occasioned by a real motion of the sun in that plane, in a contrary
direction from east to west.”

CHAPTER IV.
BINARY STARS.

Double and multiple stars may be either optical or real. Optical double
stars are those in which the component stars are merely apparently close
together, owing to their being seen in nearly the same direction in
space. Two stars may _seem_ to be close together, while, in reality, one
of them may be placed at an immense distance behind the other. Just as
two lighthouses at sea may, on a dark night, appear close together when
viewed from a certain point, whereas they may be really miles apart. In
the case of double stars it is, of course, always difficult to determine
whether the apparent closeness of the stars is real or merely optical.
But when, from a long series of observations of their relative position,
we find that one is apparently moving round the other, we know that the
stars must be comparatively close, and linked together by some physical
bond of union. These most interesting objects are known to astronomers
as binary or revolving double stars. The probable existence of such
objects was predicted from abstract reasoning by Mitchell in the
eighteenth century; but the discovery of their actual existence was made
by Sir William Herschel, while engaged on an attempt to determine the
distance of some of the double stars from the earth. “Instead of
finding, as he expected, that annual fluctuation to and fro of one
component of a double star with respect to the other—that alternate
increase and decrease of their distance and angle of position, which the
parallax of the earth’s annual motion would produce—he observed, in many
cases, a regular progressive change; in some cases bearing chiefly on
their distance, in others on their position, and advancing steadily in
one direction, so as clearly to indicate a real motion of the stars
themselves,” and measurements made during the subsequent 25 years fully
proved the truth of the illustrious astronomer’s discovery. It was found
that in many double stars an orbital motion round each other was evident
after a number of years of careful observation of their relative
positions. Unlike the planetary orbits, which are nearly circular, at
least those of the larger planets of the solar system, it was found that
the orbits of these double stars differ, in many cases, widely from the
circular form, in some cases, indeed, approaching in shape more the
orbit of a comet than a planet.

The binary stars are among the most interesting objects in the heavens.
The number now known probably amounts to nearly one thousand. In most of
them, however, the motion is very slow, and in only about seventy cases
has the change of position, since their discovery, been sufficient to
enable an orbit to be computed. In most cases the plane of the real
orbit, or ellipse, described by the companion round the principal star,
is inclined to the line of sight. We therefore see the orbit
foreshortened into a more elongated ellipse.

The relation of the apparent ellipse—or the ellipse we see described by
one star round the other—to the real ellipse will be easily understood
by the following illustration. Suppose a cylinder or rod of an
elliptical, not circular, section to be cut across obliquely to its
axis. This oblique section will represent the _real_ orbit of a binary
star, and the section at right angles to the axis, the _apparent_ orbit.
The angle between these two sections will represent the inclination of
the real orbit to the plane of projection, or background of the sky. In
the apparent orbit, the primary star, which is assumed to be situated in
one of the foci of the real ellipse, does not lie in the focus of the
apparent ellipse, and from its observed position in this latter ellipse
we can deduce, mathematically, the particular angle at which the oblique
section must be made to agree with the observed place of the primary
star, and other details respecting the real ellipse.

Savary, in 1830, was the first astronomer who attempted to compute the
orbit of a binary star, namely, the star Xi Ursæ Majoris. This
remarkable pair was discovered by Sir William Herschel in 1780, and as
the period of revolution is about 61 years, a considerable portion of
the ellipse had been described in 1830, when it was attacked by Savary.
Since that year, orbits have been computed for a number of binary stars
by several computers, among whom may be mentioned Sir R. Ball, Behrmann,
Casey, Celoria, Doberck, Dunér, Elkin, Fritsche, Glasenapp, Sir J.
Herschel, Hind, Jacob, Mädler, Mann, Schur, See, Thiele, Villarceau, and
the present writer. The computation of a double star orbit is a matter
of considerable trouble and difficulty, and cannot be described here. An
account of the principal results arrived at by astronomers in this
interesting branch of sidereal astronomy may, however, prove of interest
to the general reader.

We will first consider the binary stars with short periods of
revolution, which are, of course, the most interesting, and those whose
orbits can be computed with greater accuracy than binaries having
periods of considerable length. The binary star with the shortest period
known at present seems to be the fourth magnitude star Kappa Pegasi. It
was discovered as a wide double star by Sir William Herschel in 1786,
the companion star being of the ninth magnitude. In August, 1880, Mr.
Burnham, the famous American double star observer, examining the star
with the 18½ inch refractor of the Dearborn Observatory, found the
brighter star to be a very close double, with a distance between the
components of only a quarter of a second of arc. A few years’
observations showed that this pair were in rapid motion round each
other, and from measures up to the year 1892, Burnham finds a period of
11·37 years. A later determination by Dr. See makes the period 11·42
years, so that we may conclude that the orbit is now pretty accurately
determined. The plane of the orbit is highly inclined to the line of
sight. Dr. See makes the inclination 81°.

Another binary star, with a period of about the same length, is Delta
Equulei, which was discovered to be a close double by Otto Struve in
1851. As in the case of Kappa Pegasi, the orbit is highly inclined to
the line of sight. In the year 1887, Wrublewsky, the Russian computer,
found a period of about 11½ years, with an orbit nearly circular. A new
orbit was published in 1895 by Dr. See, who finds a period of 11·45
years, and an orbit agreeing fairly well with that of Wrublewsky, the
orbit differing little from the circular form, and inclined to the line
of sight at the high angle of 79 degrees. Burnham found only a “slight
elongation” in the star with the great 36-inch telescope of the Lick
Observatory in July, 1889. The distance between the components does not
at any time exceed half a second of arc, so that it is always beyond the
reach of all but the largest telescopes.

Next in order of shortness of period comes the southern binary star Zeta
Sagittarii, for which an orbit was first computed in the year 1886 by
the present writer, who found a period of 18·69 years. The orbit was
re-computed in 1893, with the aid of recent measures by Mr. J. W.
Froley, who finds a period of 17·71 years. The orbit of this star will,
I think, require still further revision, but the period of about 18
years is probably not far from the truth.

Another remarkably rapid binary star is 85 Pegasi, for which Schaeberle
computed a period of 22·3 years, but a later orbit by Prof. Glasenapp
makes the period 17½ years, and Burnham thinks it will certainly be less
than 20 years. Dr. See, however, finds a period of 24 years. The primary
star is about the sixth magnitude, and the companion only the eleventh,
a difference of five magnitudes, which implies that the larger star is
one hundred times brighter than the companion.

Next in order of rapidity of motion we have the southern binary star 9
Argûs. For this pair, Burnham finds a period of 23·3 years, and Dr. See
22 years, the other elements of the orbit being also in close agreement.
In this case also the orbit plane is highly inclined to the line of
sight.

The star 42 Comæ Berenices has a period of about 25¾ years, according to
Otto Struve. The orbit is remarkable from the fact that its plane passes
through or nearly through the earth, and is, therefore, projected into a
straight line, the companion star oscillating backwards and forwards on
each side of its primary. I find that the plane of the orbit is at right
angles to the general plane of the Milky Way.

The star Beta Delphini—the most southern of the four stars in the
“Dolphin’s Rhomb”—is also a fast-moving binary, discovered by Burnham in
1873, for which periods have been computed of 22·97 years by Glasenapp,
26·07 years by Dubjago, 27·66 years by Dr. See, and 30·91 years by the
present writer. Burnham thinks the period will prove to be about 28
years. The spectrum of the light of Beta Delphini is similar to that of
our sun, so that the two bodies should be comparable in intrinsic
brilliancy. From my orbit of the pair, the “hypothetical parallax” is
0·052″—that is, this is the parallax the star would have on the
supposition that the combined mass of its components is equal to the
mass of the sun. Now, assuming the value of the sun’s stellar magnitude
which I have recently computed (_Knowledge_, June, 1895)—namely, 27·15—I
find that the sun, if placed at the distance indicated for Beta
Delphini, would be reduced to a star of 5·84 magnitude. As the star was
measured 3·74 at Harvard, we have a difference of 2·1 magnitude,
denoting that the binary—if of the same mass as the sun—must be about
seven times brighter. As the spectrum is of the same type, this seems
improbable, and we must conclude that the star’s parallax is more than
0·052″.

Another remarkable binary star with a comparatively short period is Zeta
Herculis. This pair have now performed three complete revolutions since
their discovery in 1782 by Sir William Herschel. Several orbits have
been computed, but Dr. See’s period of 35 years is probably the best The
companion is now not far from its maximum distance (1½ seconds) from the
primary star, and is within the reach of moderate-sized telescopes. The
companion is, however, rather faint, being only 6½ magnitude, while the
primary star is of the third. When at their nearest, some observers have
spoken of an “occultation” of one star by the other, but no real
occultation ever takes place, the components never approaching within
half a second of arc. The companion merely disappears owing to its
faintness in telescopes of moderate power. An occultation of one
component of a binary star by the other cannot take place except—as in
the case of 42 Comæ—when the plane of the orbit passes through the
earth.

[Illustration:

FIG. 4.—_Apparent Orbit of Zeta Herculis._ (From “Worlds of Space.”)
]

In the case of the binary star, Eta Coronæ Borealis, it was, some forty
years ago, uncertain whether its period was 43 or 66 years, but now that
two complete revolutions have been performed since its discovery by Sir
William Herschel in 1781, the question has been finally decided in
favour of the shorter period. Numerous orbits have been computed, but
these by Dr. Doberck and Dr. Dunér are probably the best. Those give a
period of about 41½ years. The components are nearly equal in
brightness, but at their present distance are not within the reach of
small telescopes.

The brilliant star Sirius is also an interesting binary star. The
companion, which is relatively very faint—about tenth magnitude,—was
discovered by Alvan Clark in 1862. The existence of some such disturbing
body was previously suspected by astronomers, owing to observed
irregularities in the proper motion of Sirius. Several orbits, giving
periods of about 50 years, have been computed. Some measures in recent
years, however, seemed to show that this period was somewhat too short,
but a period of about 58½ years, computed by the present writer in 1889,
will probably prove too long. Some few years ago, Burnham found the
companion an easy object with the 36-inch refractor of the Lick
Observatory, but towards the end of the year 1890 it passed beyond the
power of even this giant telescope. It will probably, however, emerge
very soon now from the rays of its brilliant primary.[110] Burnham finds
a period of about 52 years, but the German astronomer, Auwers, who has
carefully investigated the observed irregularities in the proper motion
of Sirius, adheres to a period of about 49½ years. The great brilliancy
of Sirius, the brightest star in the heavens, naturally suggests a sun
of great size. Recent investigations, however, do not favour this idea.
Assuming a parallax of 0″·39 (about a mean of the results found by Elkin
and Gill), Auwers finds the mass of the system to be about three times
the mass of the sun, the mass of the companion being about equal to the
sun’s mass. Placed at the distance of Sirius, the sun would, I find, be
reduced to a star of about 1½ magnitude. As Sirius is about 1 magnitude
brighter than the zero magnitude—that is, about 2 magnitudes brighter
than a standard star of the first magnitude—it follows that it is about
2½ magnitudes, or about ten times brighter than the sun would be in the
same position. Its spectrum is, however, of the first type, and the star
is therefore not comparable with the sun in brilliancy. The above result
would indicate that stars of the first or Sirian type are intrinsically
brighter than our sun.

Sirius is about 11 magnitudes brighter than its faint companion. This
makes the light of Sirius about 25,000 times the light of the small
star. If, therefore, the two bodies were of the same intrinsic
brilliancy, their diameters would be in the ratio of 158·5 to 1, and if
of the same density, the mass of Sirius would be nearly five million
times the mass of the companion! But, according to Auwers’ calculations,
the companion’s mass is about one-half that of its primary. The two
bodies must, therefore, be differently constituted, and, indeed, the
companion must be nearly a dark body. It has been suggested that the
companion may possibly shine by reflected light from Sirius; but this I
have shown elsewhere to be quite impossible.[111] Even with a diameter
equal to that of the sun, I find that with reflected light only it would
be quite invisible in all parts of its orbit, even with the great Lick
telescope. It must, therefore, shine with inherent light of its own, and
it seems probable that it is a large body, cooling down and approaching
the complete extinction of its light. If Sirius has any planets
revolving round it—like those of our solar system—they must for ever
remain invisible in our largest telescopes. This remark, of course,
applies to all the fixed stars, single and double. They may possibly
have attendant families of planets, like our sun, but if so, the fact
can never be ascertained by direct observation. I find that the plane of
the orbit of Sirius is at right angles to the general plane of the Milky
Way.

[Illustration:

FIG. 5.—_Apparent Orbit of the Companion of Sirius._

(From “Old and New Astronomy.”)
]

The star Zeta Cancri is a well-known triple star, the close pair
revolving in a period of about 60 years. Nearly two revolutions have now
been completed since its discovery by Sir William Herschel in 1781. All
three stars probably form a connected system, but the motion of the
third star round the binary pair is very slow and irregular. The motion
of this interesting system has recently been investigated by Professor
Seeliger, and he comes to the conclusion that, to make the observations
agree with calculation, it is necessary to assume that the third star is
in reality a very close double, the components of which revolve round
their centre of gravity in about 17½ years, and both round the known
binary pair. If this be so, we have here a remarkable quadruple pair;
but it must be added that all efforts with large telescopes to see the
companion star double have failed, and that the existence of the fourth
star rests only on theory. Burnham, in 1889, using a power of 1500,
failed to see any other component.

Another interesting binary star is Xi Ursæ Majoris. As already stated,
this was the first pair for which an orbit was computed. More than a
complete revolution has now been performed since its discovery by Sir
William Herschel in 1780. The period has, therefore, been well
determined, and seems to be about 60 years. Although the components are
not near their maximum distance at present, they are still within the
reach of moderate telescopes, the distance being about 1¾ seconds, and
the magnitudes of the components, not very unequal, about 4 and 5.

The bright southern star, Alpha Centauri, the nearest of all the fixed
stars to the earth, so far as is known at present, is also a remarkable
binary star. It seems to have been first noticed as a double star by
Richaud in 1690. Several orbits have been computed, ranging from about
75 to 88½ years, but recent calculations by Mr. A. W. Roberts and Dr.
See make the period about 81 years, which agrees closely with Dr.
Elkin’s period of 80⅓ years. Combining Dr. Gill’s parallax of 0″·76 with
Elkin’s elements, I find the sum of the masses nearly twice the mass of
our sun, and the mean distance between the components about 23 times the
earth’s distance from the sun, or somewhat greater than the distance
between the sun and Uranus. Dr. Doberck finds a period of about 79
years, and assuming a parallax of 0″·75, he finds the mean distance
between the components 24·6 times the earth’s distance from the sun; and
he points out that if we suppose that their diameter does not differ
much from that of our sun, each component “would appear from the other
as a mere star to unaided vision, the distance being too great to show a
disc.”[112] From a recent investigation of the proper motion and
position of Alpha Centauri, Mr. A. W. Roberts finds that the masses of
the components are nearly equal, and the combined mass equal to twice
the mass of our sun, a conclusion in close agreement with the result
found above from the orbit. According to Dr. Gill, the difference in
brightness of the two components is 1·25 magnitude, and Professor Bailey
makes their photometric magnitudes 0·50 and 1·75. As this difference
would make the brighter component over three times brighter than the
companion, it follows that its surface must be much brighter, and Mr.
Roberts concludes that the companion has proceeded “some distance on the
down track from a sun to an ordinary planet.” Assuming my value of the
sun’s stellar magnitude (about 27), I find that the sun, if placed at
the distance of Alpha Centauri, would appear of about the same
brightness as the star does to us. As, according to Professor Pickering,
the spectrum of Alpha Centauri is of the second or solar type, it would
seem that in mass, brightness, and physical condition, the star closely
resembles our sun.

We next come to another very interesting binary star, known to
astronomers as 70 Ophiuchi. It is a very fine double star, the
magnitudes of the components being about 4 and 6, and the colours yellow
and orange. More than a complete revolution has now been described by
the components since its discovery by Sir William Herschel in 1779.
Numerous orbits have been computed with periods ranging from 73¾ to 98
years. An orbit computed by the present writer, in 1888, gave a period
of 87·84 years, and this was confirmed in 1894 by Burnham, who found a
period of 87·85 years. A subsequent investigation by Schur gives a
period of 88·356 years. My orbit, combined with Krüger’s parallax of
0″·162, give for the combined mass of the components 2·777 times the
mass of the sun, and the distance between them 27·777 times the earth’s
distance from the sun, or somewhat less than the distance of Neptune
from the sun. Schur has, however, recently found a parallax of 0″·286,
which would reduce the mass of the system, and also the distance between
the components. Recent observations show that the companion is now in
advance of the theoretical position indicated by Schur’s orbit, and Dr.
See thinks that the observed irregularities in the orbital motion of the
pair indicate the existence of a third body, and that either the primary
star or the companion, probably the latter, is a very close binary star.
Careful search, however, for a third body, made with large telescopes,
have failed to reveal its existence, and so the matter remains in
suspense. Placed at the distance indicated by Krüger’s parallax, I find
that our sun would be reduced to a star of about magnitude 3½, which
shows that the sun and star are of about equal brightness. The spectrum
is of the solar type, according to Vogel. I find that the plane of the
orbit is at right angles to the plane of the Milky Way.

The star Gamma, in Corona Borealis, is a close and difficult binary
star. Dr. Doberck finds a period of 95½ years, and Celoria about 85¼. As
in the case of 42 Comæ, the plane of the orbit nearly passes through the
earth, and the apparent orbit is, consequently, nearly a straight line.
I find that the plane of the orbit is at right angles to the plane of
the Milky Way.

The star Xi Scorpii is a remarkable triple star, like Zeta Cancri, the
magnitudes of the components being about 4½, 5, and 7½. The components
of the close pair have described a complete revolution since their
discovery by Sir William Herschel in 1780. Dr. Doberck finds a period of
about 96 years, and Schorr 105 years. The real orbit is nearly circular,
but owing to its high inclination, about 70°, the apparent orbit is a
very elongated ellipse. All three stars have a common proper motion
through space, and, probably, form one system, but the motion of the
third star is very slow, and its period of revolution must be several
hundred years.

[Illustration:

APPARENT ORBIT OF 70 OPHIUCHI, COMPUTED BY J. E. GORE (1888).

(_Showing positions of companion star in
different years._)

(From “The Scenery of the Heavens.”)
]

The star ο^2, or 40 Eridani, is another interesting object. It is a star
of about 4½ magnitude, with a distant ninth magnitude companion, which
is a double and binary star. It is sometimes stated that the bright star
is the binary, but this is quite incorrect; the large star is single—at
least, as far as is known at present. An orbit for the binary pair was
computed, in 1886, by the present writer, who found a period of 139
years; but Burnham, using later observations, finds a period of 180
years. A physical connexion may possibly exist between the binary pair
and the bright star, as both have the same common motion through space,
but the angular motion, if any, is very slow. Professor Asaph Hall found
a parallax of about one-fifth of a second of arc, and this, combined
with Burnham’s orbit, gives the combined mass of the binary pair about
two-thirds of the sun’s mass, a result which seems remarkable, for the
sun, placed at the distance indicated by Hall’s parallax would, I find,
shine as a star of about the third magnitude, or considerably brighter
than the principal star of 40 Eridani. Owing to the faintness of the
binary pair, the nature of its spectrum has not been determined.
Computed by a well-known formula, its “relative brightness”—that is, its
brightness compared with that of other binaries—is very small.

A very famous binary star is that known to astronomers as Gamma
Virginis. Its history is a very interesting one. It lies close to the
celestial equator, about one degree to the south and about fifteen
degrees to the north-west of the bright star Spica (Alpha of the same
constellation), with which it forms the stem of a Y-shaped figure,
formed by the brightest stars of the constellation Virgo, or the Virgin,
Gamma being at the junction of the two upper branches. The brightness of
Gamma Virginis is a little greater than an average star of the third
magnitude. Photometric measures made at Oxford and Harvard Observatories
agree closely, and make its brightness about 2·7 magnitude—that is to
say, rather nearer the third than the second magnitude. Variation of
light has, however, been suspected in one or both components, and this
question of light variation will be considered further on. The Persian
astronomer, Al-Sûfi, in his description of the heavens, written in the
tenth century, rates it of the third magnitude, and describes it as “the
third of the stars of _al-auvâ_, which is a mansion of the moon,” the
first and second stars of this “mansion” being Beta and Eta Virginis,
the fourth star Delta, and the fifth Epsilon, these five stars forming
the two upper branches of the Y-shaped figure above referred to. Gamma
was called _Zawiyah-al-auvâ_, “the corner of the barkers!” perhaps from
its position in the figure, which formed the thirteenth Lunar Mansion of
the old astrologers. It was also called _Porrima_ and _Postvarta_ in the
old calendars. These ancient names of the stars are curious, and their
origin doubtful.

The fact that Gamma Virginis really consists of two stars very close
together seems to have been discovered by the famous astronomer,
Bradley, in 1718. He recorded the position of the components by stating
that the line joining them was then exactly parallel to a line joining
Alpha and Delta of the same constellation. This was, of course, only a
rough method of measurement, and the position thus found by Bradley
being probably more or less erroneous, has given much trouble to
computers of the orbit described by the component stars round each
other, or, rather, round their common centre of gravity. Bradley does
not give the apparent distance between the component stars; but we may
conclude from the orbit, which is now well determined, that they were
then at nearly their greatest possible distance apart. It is curious
that between Bradley’s time and 1794, the star was on several occasions
occulted by the moon; but none of the observers refer to its duplicity.
It was again measured by Cassini in 1720, by Tobias Mayer in 1756, and
by Sir William Herschel in 1780. These measures showed that the distance
between the components was steadily diminishing, and that the position
angle of the two stars was also decreasing. This decrease in the
position angle—measured from the north round by the east, south, and
west, from 0 to 360°—shows that the apparent orbital motion is what is
called retrograde, or in the direction of the hands of a clock, direct
or “planetary motion” being in the opposite direction. The star was
again measured by Sir John Herschel and South in the years 1822–38, by
Struve in the same years, and by Dawes and other observers from 1831 to
the present time. The recorded measures are very numerous, and have
enabled computers to determine the orbit with considerable accuracy. The
rapid decrease in the apparent distance from 1780–1834 indicated that
the apparent orbit is very elongated, and that possibly the two stars
might “close up” altogether, and appear as a single star even in
telescopes of considerable power. This actually occurred in the year
1836, or, at least, the stars were then so close together that the most
powerful telescopes of that day failed to show Gamma Virginis as
anything but a single star. Of course, it would not have been beyond the
reach of the giant telescopes of our day. From the year 1836 the pair
began to open out again, and at present the distance is again
approaching a maximum. It is now within the reach of small telescopes,
and forms a fine telescopic object with a moderate-sized instrument.

The general character of the orbital motion may be described as
follows:—In 1718, at the time of Bradley’s observation, the companion
star was to the north-west of the primary star; it then gradually moved
towards the west and south, and in 1836, when at its minimum distance,
it was to the south-east. From that date it again turned towards the
north, and at present it is north-west of the primary star, and not far
from the position found by Bradley in 1718.

The first to attempt a calculation of the orbit described by this
remarkable pair of suns was Sir John Herschel, who in the year 1831
found a period of about 513 years. In 1833, he re-calculated the orbit,
and found nearly 629 years. We now know that both these periods are much
too long; but the data then available were insufficient for the
calculation of an accurate orbit. From these results Herschel predicted
that “the latter end of the year 1833, or the beginning of the year
1834, will witness one of the most striking phenomena which sidereal
astronomy has yet afforded, _viz._, the perihelion passage of one star
round another, with the immense angular velocity of between 60° and 70°
per annum, that is to say, of a degree in five days. As the two stars
will then, however, be within little more than half a second of each
other, and as they are both large and nearly equal, none but the very
finest telescopes will have any chance of showing this magnificent
phenomenon. The prospect, however, of witnessing a visible and
measurable change in the state of an object so remote, in a time so
short, may reasonably be expected to call into action the most powerful
instrumental means which can be brought to bear on it.” This prediction
was not verified until the year 1836, when the pair “closed up out of
all telescopic reach,” except at the Dorpat Observatory, where a
magnifying power of 848 still showed an elongation in the telescopic
disc of the star. The orbit found by Sir John Herschel was a tolerably
elongated ellipse, with its longer axis lying north-east and south-west.
This was not quite correct, for we now know that this axis lies
north-west and south-east, and that the apparent orbit is much more
elongated than Sir John Herschel at first supposed. This was soon
recognised by Herschel himself, and he came to the conclusion that he
and other computers had been misled by Bradley’s observation in 1718. He
then rejected this early, and evidently faulty, observation, and using
the measures up to 1845, he found a period of about 182 years, which we
now know to be near the truth. The orbit was also computed by the famous
German astronomer, Mädler, who found periods of 145, 157, and 169 years;
by Hind, 141 years; by Henderson, 143 years; by Jacob, 133½, 157½ and
171 years; by Adams, 174 years; by Flammarion, 175 years; and by Admiral
Smyth, 148 and 178 years. All these periods, we now know, are too small.
Fletcher found 184½ years, and Thiele 185 years. Two orbits were
computed by Dr. Doberck, in recent years, with periods of 180½ and 179½
years; but very recently (1895) the orbit has been re-computed by Dr.
See, and he finds a period of 194 years. A comparison of the observed
and computed positions shows, he thinks, that his elements are the most
exact yet determined for any binary star.

The apparent orbit of the pair is a very elongated ellipse, and as
Admiral Smyth said, “more like a comet’s than a planet’s.” The real
ellipse has a very high eccentricity, nearly 0·9—indeed, the greatest of
all the known binary stars, and not much less than that of Halley’s
comet

As I said above, the variability of the light of one or both components
of Gamma Virginis has been strongly suspected. So far back as 1851 and
1852, O. Struve paid particular attention to this point. His
observations in these years show that sometimes the component stars were
exactly equal in brilliancy, and sometimes the southern star—the one
generally taken as the primary—was from 0·2 to 0·7 magnitude brighter
than the other. There seems to be little doubt that some variation
really takes place in the relative brightness of the pair. This is
clearly indicated by the measures of position angle. For example, in the
year 1886, Professor Hall recorded the position as 154·9, evidently
measuring from the northern star as the brightest of the two; while, in
1887, Schiaparelli gives 334°·2—or about 180° more—thus indicating that
he considered the _southern_ star as the primary, or brighter, of the
pair. Burnham found 153°·4 in 1889, and Dr. See 332°·50 in 1891. This is
also shown by earlier measures, for Otto Struve found the southern star
half a magnitude brighter than the other on April 3, 1852, while on
April 29 of the same year he found them “perfectly equal.” He thought
the variation was about 0·7 of a magnitude, but that the climate of
Poulkova, where he observed, was not suitable for such observations.
This variation is very interesting, and the question should be
thoroughly investigated with a good telescope.

As the distance of Gamma Virginis from the earth has not been
determined, it is not possible to calculate the actual dimensions of the
orbit and the mass of the system. If we assume that the combined mass of
the components is equal to the sun’s mass, I find from Dr. See’s orbit
that the “hypothetical parallax” would be 0·119″, implying a distance of
1,733,319 times the sun’s distance from the earth. If, however, we
suppose that the mass of each of the components is equal to the sun’s
mass, or the mass of the system double that of the sun—perhaps a more
probable supposition—I find that the parallax would be about one-tenth
of a second, denoting a distance of 2,062,650 times the sun’s distance
from the earth. Placed at this last distance, the sun would, I find, be
reduced to a star of about 4½ magnitude, or about 1¾ magnitudes fainter
than Gamma Virginis appears to us. This difference implies that,
supposing each of the component stars of the binary to have a mass equal
to the sun’s mass, their combined light is about five times greater than
the sun would emit if placed at the same distance, and as the components
are nearly equal in brightness, each of them would be 2½ times brighter
than the sun. According to Vogel, the star’s light gives a spectrum of
the first or Sirian type, but according to the Draper “Catalogue of
Stellar Spectra,” the spectrum is of the solar type. If the spectrum is
of the first type, its brilliancy is easily explained; for, as I have
shown elsewhere, the Sirian stars, are intrinsically much brighter in
proportion to their mass than those of the solar type. But if its
spectrum is of the solar type, it is not so easy to explain its
brilliancy. Computing by a well-known formula, I find its relative
brightness is nearly five times greater than that of Xi Ursæ Majoris,
the spectrum of which is of the solar type. If, to account for its
brilliancy, we assume that the star is nearer to the earth than the
parallax assumed above would imply, then the mass of the system must be
less than the mass of our sun. As we have seen above, doubling the
supposed mass increased the distance; so, on the other hand, if we
diminish the distance, we must diminish the mass also. Thus, if we
reduce the distance to one-half, we must reduce the mass to one-eighth
of the sun’s mass. A distance of one-third would give a mass of ¹⁄₂₇th,
and a distance of one-fourth would imply a mass only ¹⁄₆₄th of the sun’s
mass. To reduce the sun to the same brightness as Gamma Virginis, it
should be removed to a distance indicated by a parallax of one-tenth of
a second multiplied by the square root of five, or 0·223″. If, however,
the star’s parallax were so much as this, it is probable that it would
have been detected and measured long ago. In the case of the binary star
Castor, I find from the orbit and a small parallax found by Johnson
(about one-fifth of a second) that its mass is only ¹⁄₁₉th of the sun’s
mass, but in this case the spectrum is of the Sirian type, and stars of
this type are very bright in proportion to their mass. The colours of
the components of Gamma Virginis, which are very similar to those of
Castor—white or pale yellow—would suggest that they may belong to the
same type.

Another interesting binary star is Eta Cassiopeiæ. The components are
about 4 and 7½ magnitude, and the pair have described a considerable
portion of their orbit since its discovery in 1779 by Sir William
Herschel, the distance diminishing from about 11 seconds to 4¾. Periods
ranging from 149 to 222½ years have been found by different computers.
The most recent computation makes it about 196 years. Assuming a
parallax of 0·154″ found by Struve, the mass of the system will be from
5¾ to 10¾ times the mass of the sun, according to the length of the
period we assume. A much larger parallax of 0″·3743 was, however, found
by Schweizer and Socoloff, which would considerably reduce the mass, and
recently a still larger parallax of 0″·465 has been found by
photography, which, with Grüber’s elements of the orbit, would reduce
the mass of the system to ⅙th of that of the sun.

The bright star Gamma Leonis, situated in the well-known “Sickle in
Leo,” is also a binary star, but only a small portion of the orbit has
been described since its discovery by Sir William Herschel in 1782. Dr.
Doberck finds a period of 407 years. It is remarkable for its very high
“relative brightness,” which is curious, as its spectrum is of the solar
type. This pair forms a fine object for a small telescope.

The star known as 12 Lyncis is a triple star, the components being 5, 6,
and 7½ magnitude. The close pair form a binary system, for which an
orbit has been computed by the present writer, who finds a period of
about 486 years. Sir John Herschel predicted in 1823 that the angular
motion of the pair would “bring the three stars into a straight line in
57 years.” This prediction was fulfilled in 1887, when measures by
Tarrant showed that the stars were then exactly in a straight line.

[Illustration:

FIG. 7.—_Triple Stars._

(From “Scenery of the Heavens.”)
]

The bright star Castor is a famous double star, and has been known since
the year 1718, when it was observed by Bradley and Pond. It was also
observed by Maskelyne in 1759, and frequently by Sir William Herschel
from 1799 to 1803. Numerous orbits have been computed, with periods
ranging from 199 years by Mädler, and 1,001 years by Doberck. Wilson
found a period of about 983 years, and Thiele about 997 years, so that
the longest period would seem to be nearest the truth. According to a
somewhat doubtful parallax found by Johnson, the distance of Castor from
the earth is about double that of Sirius. With this distance, and
Doberck’s elements of the orbit, I find that the mass of the system of
Castor is only ¹⁄₁₉th of the sun’s mass, a result which would imply that
the components are masses of glowing gas! The spectrum of Sirius is of
the first, or Sirian, type, another example of the great brilliancy of
stars of this type. Quite recently (1896), Dr. Bélopolsky has found,
with the spectroscope, that the brighter component is a close binary
star with a dark companion, like Algol. The period of revolution is
about 3 days, and the relative orbital velocity about 20¾ miles a
second. Dr. Bélopolsky’s observations show that the system is receding
from the earth at the rate of about 4½ miles per second. Assuming the
bright and dark companion to be of equal mass, and hence the absolute
orbital velocity of each one half the relative velocity found by
Bélopolsky, I find that, if the orbit is circular, the distance between
the components is about 85,400 miles, or slightly less than the sun’s
diameter, and their combined mass about ¹⁄₈₇th of the sun’s mass. This
result would imply a still smaller mass for the whole system of Castor
than that found from the orbit of the two bright components, but tends
strongly to confirm the opinion already expressed, that the components
of this remarkable system are merely masses of glowing gas. Assuming
that all three components are of equal mass, the combined mass of the
system would be ¹⁄₅₈th of the sun’s mass. From this result we can easily
compute the stars’ parallax, which, from Dr. Doberck’s orbit, I find to
be 0″·2873, a quantity which might be measured by the photographic
method.

With reference to the colours of the components of binary stars, the
following relation between colour and relative brightness has been
established[113]:—

(1.) When the magnitudes of the components are equal, or approaching
equality, the colours are generally the same, or similar.

(2.) When the magnitudes of the components differ considerably, there is
also a considerable difference in colour.

A new class of binary stars has been discovered within the last few
years by means of the spectroscope. These have been called
“spectroscopic binaries,” and the brighter component of Castor, referred
to above, is an example of the class. They are supposed to consist of
two component stars, so close together that the highest powers of the
largest telescopes fail to show them as anything but single stars.
Indeed, the velocities indicated by the spectroscope show that they must
be so close that the components must for ever remain invisible by the
most powerful telescopes which could ever be constructed by man. In some
of these remarkable objects, the doubling of the spectral lines
indicates that the components are both bright bodies, but in others, as
in Algol, the lines are merely shifted from their normal position, not
doubled, thus denoting that one of the components is a dark body. In
either case, the motion in the line of sight can be measured by the
spectroscope, and we can, therefore, calculate the actual dimensions of
the system in miles, and thence its mass in terms of the sun’s mass,
although the star’s distance from the earth remains unknown. Judging,
however, from the brightness of the star, and the character of its
spectrum, we can make an estimate of its probable distance from the
earth.

Let us first take the case of Algol. This famous variable star has,
according to the Draper catalogue, a spectrum of the Sirian type. It
may, therefore, be comparable with that brilliant star in intrinsic
brightness and density. Assuming the mass of Sirius at 2·20 times the
mass of the sun, as found by Auwers, and that of the brighter component
of Algol at four-ninths of the sun’s mass, as given by Vogel,[114] I
find that for the _same distance_ Sirius would be about 2·8 times
brighter than Algol. But photometric measures show that Sirius is about
22 times brighter than Algol, from which it follows—since light varies
inversely as the square of the distance—that Algol is 2·77 times further
from the earth. Assuming the parallax of Sirius at 0·39″, this would
give for the parallax of Algol O·14″, or a journey for light of about 23
years. From the dimensions of the system, as given by Vogel—about
3,230,000 miles from centre to centre of the components—this parallax
would give an apparent distance between the components of less than
¹⁄₂₀₀th of a second, a quantity much too small to be visible in our
largest telescopes, or probably in any telescope which man can ever
construct From a consideration of irregularities in the proper motion of
Algol and in the period of its light changes, Dr. Chandler infers the
existence of a third dark body and a parallax of 0·07″. As this is
exactly one-half the parallax found above, it implies a distance just
double of what I have found, and would, of course, indicate that Algol
is intrinsically four times brighter than Sirius. This greater
brilliancy would suggest greater heat, and would agree with its small
density, which, from its diameter, as given by Vogel—1,061,000 miles—I
find to be only one-third of that of water.

Let us now consider the case of Beta Aurigæ, which spectroscopic
observations show to be a close binary star with a period of about four
days, and a distance between the components of about eight millions of
miles. This period and distance imply that the mass of the system is
about five times that of the sun. As in this case the spectral lines are
doubled at regular intervals of two days, and not merely shifted, as in
the case of Algol, we may conclude that both the components are bright
bodies, and we may not be far wrong in supposing that they are of equal
mass, each having 2½ times the mass of the sun. As the spectrum of Beta
Aurigæ is of the same type as Sirius, we may compare it with that star,
as we did in the case of Algol. Assuming the same density and intrinsic
brightness for both Beta Aurigæ and Sirius, I find that Beta Aurigæ
should be about twice as bright as Sirius. Now, according to the Oxford
photometric measures, Sirius is 2·89 magnitudes, or 14·32 times brighter
than Beta Aurigæ. Hence it follows that the distance of Beta Aurigæ
should be about 5½ times greater than the distance of Sirius. Hence,
assuming the parallax of Sirius at 0″·39, that of Beta Aurigæ should be
about 0″·061. From actual measures of the parallax of Beta Aurigæ, made
by the late Prof. Pritchard at Oxford, he found, from two companion
stars, a mean parallax of 0″·062, a result in remarkably close agreement
with that computed above from a consideration of the star’s mass and
light, compared with that of Sirius. As the actual distance between the
components of Beta Aurigæ is equal to the sun’s diameter divided by
11·625, we have the maximum angular separation between the components
equal to 0″·062 divided by 11·625, or about ¹⁄₂₀₀th of a second, or
nearly the same as in the case of Algol.

The bright star Spica has also been found by the spectroscope to be a
close binary star. Vogel finds a period of four days with a distance
between the components of about 6¼ millions of miles, and assuming that
the components have equal mass and are moving in a circular orbit, he
finds the mass of the system about 2·6 times the mass of our sun. This
would give each of the components 1·3 times the mass of the sun, and it
follows that the light of Spica—which gives a spectrum of the Sirian
type—should, for equal distances, exceed that of Sirius about 1·4 times.
Now, the photometric measures at Oxford show that Sirius is 1·91
magnitude, or 5·8 times brighter than Spica. Hence it follows that the
distance of Spica should be 2·85 times the distance of Sirius. This
would make the parallax of Spica about 0″·137. So far as I know, a
measurable parallax has not yet been found for this star. Brioschi, in
1819–20, observing with a vertical circle of four inches aperture, found
a negative parallax, which would imply that its parallax is too small to
be measurable. Still, the above result would seem to indicate that its
parallax might be measurable by the photographic method. The parallax
found above would imply that the maximum distance between the components
of Spica would not exceed ⅒th of a second, a quantity much too small to
be detected by the most powerful telescopes. In addition to its orbital
motion, Vogel finds that Spica is approaching the sun at the rate of
over 9 miles per second.

We now come to Zeta Ursæ Majoris (Mizar), which has also a spectrum of
the Sirian type, and which the spectroscopic measures indicate is a
close binary star with a period of about 104 days, and a combined mass
equal to forty times the mass of the sun. Proceeding as before, we find
that the light of Mizar should be about 8·7 times that of Sirius. But
the photometric measures show that Sirius is about three magnitudes, or
about sixteen times brighter than Mizar. Hence the distance of Mizar
should be nearly twelve times the distance of Sirius. This gives for the
parallax of Mizar about 0″·033. Klinkerfues found a parallax of 0″·0429
to 0″·0477, which does not differ widely from the above result. As the
velocity of the orbital motion shown by the spectroscope indicates a
distance between the components of about 143 millions of miles, or about
the distance of Mars from the sun, it follows that the maximum distance
between the components would be 0″032, multiplied by 1½ or 0″·048, a
quantity beyond the reach of our present telescopes.

The well-known variable star, Delta Cephei, has recently been added to
the list of “spectroscopic binaries.” From observations with the great
30-inch refractor of the Pulkowa Observatory in the summer of 1894, M.
Bélopolsky finds that the star is probably a very close double, the
companion being a nearly, or wholly, dark body, as in the case of Algol,
and the orbit a very eccentric one. The observed variation of light
indicates, however, that there is no eclipse, as occurs in Algol, so
that the fluctuations in the light of Delta Cephei are probably due to
some other cause. The spectrum of the star is of the solar type, so that
in this respect it differs from the other spectroscopic binaries
referred to above. The observations show that the system is approaching
the sun at the rate of about 15 miles a second. Spectroscopic
observations also suggest that the well-known variable star Beta Lyræ
may also consist of two close companions. Further details respecting
these observations will be given in the next chapter.

From a recent investigation of the proper motion of the star Tau
Virginis, Dr. Fritz Cohen thinks it is probably a close binary, the
companion star of which has not yet been detected.

It should be mentioned that in the case of Beta Aurigæ, Spica, Zeta Ursæ
Majoris, and Castor, as there is no variation of light, as in Algol, the
plane of the orbit is probably inclined to the line of sight. This would
have the effect of increasing the computed mass of the system, and thus
diminishing the calculated parallax. As the above calculations have been
made on the assumption that the plane of the orbit passes through the
earth, it follows that the computed parallax is a maximum, and that
these remarkable objects may be really further from the earth than even
the minute parallaxes found above would indicate. As the parallaxes of
the nearest stars, such as Alpha Centauri, 61 Cygni, Sirius, and some
other stars, are considerably greater than those found above, it would
seem that our solar system is not situated in a region of binary stars,
and that these wonderful objects lie beyond our immediate neighbourhood.
It is also remarkable that, with the exception of Delta Cephei, they
have all spectra of the Sirian type, including those Algol variables
whose spectra have been examined.

By the aid of the parallaxes computed above, we can easily calculate the
relative brightness of the sun compared with that of the spectroscopic
binaries. Assuming that the sun is 27 magnitudes brighter than the Zero
magnitude, or 28 magnitudes brighter than a standard star of the first
magnitude, and taking the parallax of Algol as 0″·07, I find that the
sun, placed at the distance indicated by this parallax, would be reduced
to a star of 5·35 magnitude, or about three magnitudes fainter than
Algol, which implies that Algol is about 15½ times brighter than our
sun. In the case of Beta Aurigæ, if the sun were placed at the distance
indicated by the parallax of 0″·061, it would be reduced to a star of
5·65 magnitude, or about 3·7 magnitudes fainter than Beta Aurigæ, which
would imply that Beta Aurigæ is about thirty times brighter than the
sun. In the case of Spica we have the sun reduced to a star of about the
fourth magnitude, or about three magnitudes fainter than Spica,
indicating that Spica is, like Algol, about 15½ times brighter than the
sun, although the mass of Spica is only 2·6 times the mass of the sun.
Finally, in the case of Mizar, we have the sun reduced to a star of
about the seventh, or about five magnitudes fainter than Mizar,
indicating that Mizar is no less than one hundred times brighter than
our sun. These results show the great relative brilliancy of stars with
a Sirian spectrum, when compared with that of the sun, a consideration
which has already been arrived at from other considerations.

CHAPTER V.
VARIABLE AND TEMPORARY STARS.

To ordinary observers, the light of the stars seems to be constant. Even
to those who are familiar with the constellations, the stars appear to
maintain their relative brilliancy unchanged. To a great extent this is,
of course, true; the great majority of the stars remaining of the same
brightness from day to day, and from year to year. There are, however,
numerous exceptions to this rule. Many of the stars, when carefully
watched, are found to fluctuate in their light, being sometimes
brighter, and sometimes fainter. These are known as “variable stars”—one
of the most interesting class of objects in the heavens. Some of these
have been known for a great number of years, and their variations having
been carefully watched, the laws governing their light changes have been
well determined.

We will first consider the variable stars with long periods of
variation, as these generally show the largest fluctuations of light.
Among these, the first star in which variation of light seems to have
been noticed is the extraordinary object, Omicron Ceti, popularly known
as Mira, or the “wonderful” star. It appears to have been first noticed
by David Fabricius in the year 1596. He observed that the star now
called Omicron, in the constellation Cetus, was of the third magnitude
on April 13 of that year, and that in the following year it had
disappeared. Bayer saw it again in 1603, when forming his maps of the
constellations, and assigned to it the Greek letter Omicron, but does
not seem to have noticed the fact that it was the same star which had
been observed by Fabricius seven years previously. No further attention
seems to have been paid to it until 1638 and 1639, when it was observed
at Francker by Professor Phocylides Holwarda to be of the third
magnitude in December, 1638, invisible in the following summer, and
again visible in October, 1639. From 1648 to 1662 it was carefully
observed by Hevelius, and in subsequent years by several observers. Its
variations are now regularly followed from year to year, and it forms
one of the most interesting objects of its kind in the heavens. Its
light varies from about the second magnitude to the ninth, but its
brightness at maximum is variable to a considerable extent. Heis found
its _average_ brightness at maximum in the years 1840–58 to be about the
third magnitude, but on November 6, 1799, Sir William Herschel found it
but little inferior to Aldebaran. On the other hand, at the maximum of
1868, November 7, Heis found it only of the fifth magnitude, and fainter
than he had seen it for twenty-seven years. Sawyer also observed a
maximum of about the fifth magnitude (4·9) on November 10, 1887. M.
Dumenel finds (1896) that in the last twelve periods the magnitude at
maximum varied from 2·5 to 4·7.[115]

It is stated in several books on astronomy, on the authority of
Hevelius, that in the years 1672–76 Mira was invisible at the epoch of
maximum. This is, however, quite a mistake, for it was long since (1837)
pointed out by Bianchi that the supposed non-appearance of Mira in those
years can be simply accounted for by the fact that the star was near the
sun at the time of maxima, and could not be observed. If the star
happens to be at a maximum in April or May, it will be too near the sun
to be seen, and as the mean period is about 331 days, this occurs every
ten years. For this reason the maxima seems to have passed unobserved in
the years 1852, 1853, and 1854, and again in 1883. The star will be very
favourably placed for observation in the year 1897, and some following
years. It has also been stated that Mira wholly disappears at the
maximum, but this is another error, for the star never becomes fainter
than 9½ magnitude at any time, and always remains visible in a 3-inch
telescope. The colour of the star is decidedly reddish, but this hue
seems to be more marked at minimum than at maximum. The spectrum is a
remarkable one of the third type, in which bright lines have been seen
by Espin, Maunder, and Secchi. At the minimum of February, 1896, the
spectrum was photographed by Professor Wilsing, and he found it very
similar to a photograph taken by Professor Pickering some years
previously. The recent photograph shows the lines of hydrogen broad and
bright. There seems to be no other bright lines except those of
hydrogen. The blue end of the spectrum is very similar to that of our
sun, but towards the red end there are “dark flutings, fading towards
the red.” The bright hydrogen lines have only been seen at maximum, but
the instruments used by Professor Wilsing were not sufficiently powerful
to show whether they are also visible at minimum.[116] Professor
Pickering thinks that “probably most of the stars of long period give a
spectrum resembling that of ο Ceti, and having the hydrogen lines G,
_h_, α, β, γ, and δ, bright about the time of maximum. When the
photographic spectrum is faint, only the brighter lines, G and _h_, are
visible.” Within the last few years, Mrs. Fleming, while examining the
photographs of stellar spectra taken for the Henry Draper Memorial, has
detected a number of variable stars of long period by the presence of
bright lines in their spectra. These are mostly telescopic stars.

Although the average period of Mira is about 331 days, it is subject to
marked irregularities, which Argelander has attempted to represent by an
elaborate formula. In recent years, however, the epochs of maxima have
deviated considerably from the dates computed from this formula, and at
the maximum of February, 1896, the star did not reach its maximum light
until nearly two months after the predicted time.

Perhaps the long period variable star next in order of interest—at least
to observers in the Northern Hemisphere—is that known as Chi Cygni. It
was discovered by Kirch in 1686. A mistake is often made about the
identity of this remarkable object It is sometimes confused with the
neighbouring star, 17 Cygni of Flamsteed’s catalogue. At the time of
Flamsteed’s observation, the variable star—which is the true Chi Cygni
of Bayer’s map (made in 1603)—happened to be faint, and Flamsteed, not
being able to find Bayer’s star, affixed the Greek letter χ to his No.
17. It was proposed by Struve to call Flamsteed’s star χ^1, and the
variable χ^2; but there seems to be no necessity to perpetuate
Flamsteed’s error, which has been frequently pointed out. All
authorities on the variable stars now give this variable its proper
designation—χ Cygni. The star varies at maximum from 4 to 6½ magnitude,
and at the minimum it sinks to below the thirteenth magnitude. At some
maxima, therefore, it is easily visible to the naked eye, and at others
it is just below the limit of ordinary vision. At the maximum of 1847,
it was visible to the naked eye for a period of 97 days. The average
period is about 406 days; but, according to Schönfeld—a well-known
authority on the variables—observations indicate a small lengthening of
the period. Observations in recent years show that the minimum occurs
about 185 days before the maximum. This gives 221 days for the fall from
maximum to minimum, and illustrates a feature common to many of the
variable stars, namely, that the increase of light is more rapid than
the decrease. This peculiarity is especially marked in the short period
variables, which will be considered further on. Chi Cygni is said to be
“strikingly variable in colour.” Espin’s observations in different years
show it “sometimes quite red, at others only pale orange-red.” In the
spectroscope, its light shows a splendid spectrum of the third type (or
banded spectrum, very characteristic of these long period variables), in
which bright lines were observed by Espin in May, 1889. One of these
bright lines seems to be identical with the coronal line D_{3}, the
characteristic line of helium.

R Leonis is another remarkable variable star, which is sometimes visible
to the naked eye at maximum. It lies closely south of the star known as
19 Leonis. It was discovered by Koch in 1782. At the maximum, its
brightness varies from 5·2 to 7 magnitude, and at minimum it fades to
about the tenth magnitude. The mean period is about 313 days; but this
is subject to some irregularities, and Chandler finds “good evidence of
cyclical variation of period, with a long term.” The star is red in all
phases of its light, and forms a fine telescopic object. Close to it are
two small stars, which form, with the variable, an isosceles triangle.
The spectrum is a fine one of the third type, a type very characteristic
of these long period variables. Espin finds that the bright bands of the
spectrum are brighter when the star is increasing in light, and fainter
when decreasing. At the maximum of 1889, he found bright lines in its
spectrum.

Another long period variable star which is visible to the naked eye at
maximum is R Hydræ—the Upsilon Hydræ of Bayer—but it is rather too far
south to be well observed in this country. Its variability was discerned
by Maraldi in 1704; but the star was also observed by Hevelius in 1672.
Its light at maximum varies from 3½ to 5½ magnitude, and at minimum it
fades to nearly the tenth magnitude. The period has diminished
considerably since the year 1708, when it was about 500 days. This had
decreased to about 487 days in 1785, to 461 days in 1825, and to 437
days in 1870, and it seems to be still diminishing. Formulæ have been
computed by Gould and Chandler, but do not agree. Schmidt found that the
minimum occurs about 200 days before the maximum. The star is very
reddish, and the spectrum is a fine one of the third type, which Dunér
describes as of “extraordinary beauty,” the typical bands of this type
of spectrum being very large, and perfectly black. At the maximum of
1889, Espin observed a bright line in its spectrum, and finds—as in R
Leonis—that the bright bands are brighter when the star is increasing in
light, and fainter as it decreases.

There is a very remarkable variable star in the Southern Hemisphere
known as Eta Argûs. It lies in the midst of the great nebula in Argo,
and the history of its fluctuations in light is very interesting.
Observed by Halley in 1677 as a star of the fourth magnitude, it was
seen of the second magnitude by Lacaille in 1751. After this, it must
have again faded, for Burchell found it of only the fourth magnitude
from 1811 to 1815. From 1822 to 1826, it was again of the second
magnitude, as observed by Fallows and Brisbane; but on Feb. 1, 1827, it
was estimated of the first magnitude by Burchell. It then faded again,
for on Feb. 29, 1828, Burchell found it of the second magnitude. From
1829 to 1833, Johnson and Taylor rated it of the second magnitude; and
it was still of this magnitude, or a little brighter, when Sir John
Herschel commenced his observations at the Cape of Good Hope in 1834. It
does not seem to have varied much in brightness from that time until
December, 1837, when Herschel was astonished to find its light “nearly
tripled.” He says:[117] “It very decidedly surpassed Procyon, which was
about the same altitude, and was far superior to Aldebaran. It exceeded
α Orionis, and the only star (Sirius and Canopus excepted) which could
at all be compared with it was Rigel, which, as I have already stated,
it somewhat surpassed.”

From this time its light continued to increase. On the 28th December it
was far superior to Rigel, and could only be compared with α Centauri,
which it equalled, having the advantage of altitude, but fell somewhat
short of it as the altitudes approached equality. The maximum of
brightness seems to have been obtained about the 2nd January, 1838, on
which night, both stars being high and the sky clear and pure, it was
judged to be very nearly matched, indeed, with α Centauri, sometimes the
one, sometimes the other, being judged brighter; but, on the whole, a
was considered to have some little superiority. After this, the light
began to fade. Already on the 7th and 15th January, α Centauri was
unhesitatingly placed above, and Rigel as unhesitatingly below, it. On
the 20th, it was “visibly diminished—now much less than α Centauri, and
not _much_ greater than Rigel. The change is palpable.” And on the 22nd,
Arcturus (the nearest star in light and colour to α Centauri which the
heavens afford), when only 10° high, surpassed η, the latter being on
the meridian; η was still, however, superior to β Centauri, α Crucis,
and Spica, and continued so (and even superior to Rigel) during the
whole of February, nor was it until the 14th April, 1838, that it had so
far faded as to bear comparison with Aldebaran, though still somewhat
brighter than that star. In 1843, it again increased in brightness, and
in April of that year it was observed by Maclear to be brighter than
Canopus, and nearly equal to Sirius! It then faded slightly, but seems
to have remained nearly as bright as Canopus until February, 1850, since
which time its brilliancy gradually decreased. It was still of the first
magnitude in 1856, according to Abbott, but was rated a little below the
second magnitude by Powell in 1858. Tebbutt found it of the third
magnitude in 1860; Abbott a little below the fourth in 1861. Ellery
rated it fifth magnitude in 1863, and Tebbutt sixth magnitude in 1867.
In 1874 it was estimated 6·8 magnitude at Cordoba, and only 7·4 in
November, 1878. Tebbutt’s observations from 1877–86 show that it did not
rise above the seventh magnitude in those years, and in March, 1886, it
was rated 7·6 magnitude by Finlay at the Cape of Good Hope. This seems
to have been the minimum of light, for in May, 1888, Tebbutt found that
it “had increased fully half a magnitude” since April, 1887, and might
“be rated as a star of 7·0 magnitude.” From photometric measures made
with the meridian photometer in Peru in the years 1889–91, Professor
Bailey found its mean magnitude to be 6·32, so that probably the star is
now slowly rising to another maximum. Bailey found the hydrogen lines
Hβ, Hγ, and Hδ, bright in the spectrum of its light. Wolf suggested a
period of 46 years, and Loomis, 67; but Schönfeld thought that a regular
period is very improbable. The star is very reddish in colour.

There are many other variables of long period, but they are too numerous
to be described in detail in a work of this character. Particulars
respecting some of them will be found in “The Scenery of the Heavens,”
by the present writer.

We will now consider the variables of short period, which are
particularly interesting objects, owing to the comparative rapidity of
their light changes. The periods vary in length from about 17¼ days down
to a few hours. Perhaps the most interesting of these short period
variables, at least to the amateur observer, is the star Beta Lyræ,
which is easily visible to the naked eye in all phases of its light. It
can be readily identified, as it is the nearest bright star to the south
of the brilliant Vega, and one of two stars of nearly the same
magnitude, the second being Gamma Lyræ. The variability of Beta Lyræ was
discovered by Goodricke in the year 1784. The period is about 12 days,
21 hours, 46 minutes, 58 seconds. At maximum the star is about 3·4
magnitude, and there are two minima, one of magnitude 3·9, and the
other—the chief minima—of 4·5 magnitude. That is, the star has at
maximum 2¾ times the light of the chief minimum, and 1·6 times the light
of the secondary minimum. In other words, if we represent the light of
the star at maximum by 27 candles, placed at a suitable distance from
the eye, the secondary minimum will be represented by 17 candles, and
the chief minimum by 10 candles. These fluctuations, although not very
great, can be easily recognised with the naked eye by comparison with
the neighbouring star Gamma Lyræ. Professor Pickering thought that this
variation in the light of Beta might be explained by supposing that the
star rotated on its axis in the period indicated by the variation, that
the ratio of the axis of the rotating spheroid is as 5 to 3, and that
there is a darker portion at one of the ends, which is “symmetrically
situated as regards the longer axis.” Recent observations with the
spectroscope, however, render this explanation doubtful, and indicate
rather that the star is a very close double or “spectroscopic binary,”
although it does not seem certain that an actual eclipse of one
component by the other takes place, as in the case of Algol. Bright
lines were detected in the star’s spectrum by Secchi so far back as
1866. In 1883, M. Von Gothard noticed that the appearance of these
bright lines varied in appearance, and from an examination of
photographs taken at Harvard Observatory in 1891, Mrs. Fleming found
displacements of bright and dark lines in a double spectrum, the period
of which agreed fairly well with that of the star’s light changes.
Professor Pickering thence concluded that the star consists of two
components, one stellar and the other gaseous, but this conclusion has
been somewhat modified by subsequent investigations. M. Bélopolsky, from
photographs taken with the great 30-inch telescope at the Pulkowa
Observatory, confirms the periodical displacement in the bright spectral
lines “in a period identical with that of the star’s usual double
fluctuation,” but Keeler and Vogel agree that the observed displacements
are incompatible with the supposed occurrence of eclipses. Vogel,
however, is “convinced that Beta Lyræ represents a binary or multiple
system, the fundamental revolutions of which, in 12 days 22 hours, in
some way control the light change, while the spectral variations,
although intimately associated with the star’s phases, are subject,
besides, to complicated disturbances running through a cycle perhaps
measured by years.”[118] The helium line, D_{3}, is visible in the
spectrum.

Another interesting star of short period is Delta Cephei, which is one
of three stars forming an isosceles triangle a little to the west of
Cassiopeia’s Chair, the variable being at the vertex of the triangle,
and the nearest of the three to Cassiopeia. Its variability was also
discovered by Goodricke in 1784. It varies from 3·7 to 4·9 magnitude,
with a period of 5 days, 8 hours, 47 minutes, 40 seconds. The amount of
the variation is, therefore, the same as in the case of Algol, the
star’s light at maximum being about three times its light at minimum.
The period and light curve, however, show, according to Schönfeld, some
irregularities, the computed times of maxima and minima being sometimes
in error to the extent of over an hour. These are, however, small, and,
on the whole, the star seems to be very uniform in its fluctuations.
From seven years’ observations, Argelander found no deviation from
perfect uniformity. The curve representing the light variations is not,
however, very smooth, particularly during the decrease of light, when a
nearly stationary period seems to occur from 16 to 24 hours after the
maximum. The rise from minimum to maximum occupies about one-third of
the period, another example of the feature so characteristic of variable
stars, namely, that the increase of light is quicker than the decrease.
As already stated (Chapter IV.), observations of the spectrum recently
made by M. Bélopolsky, with the great Pulkowa telescope, show that, like
Beta Lyræ, the star is probably a close binary, the period of the
observed fluctuations in the positions of the spectral lines agreeing
with that of the star’s light changes. In this case, however, the lines
are not doubled, as in Beta Lyræ, but merely displaced from their normal
position, indicating that, as in the case of Algol, one of the
components is a dark body. There are, however, no indications that any
eclipse of the bright star by its dark companion takes place. Indeed,
the nature of the light changes, which are continuous and not confined
to a few hours, as in Algol, are inconsistent with the occurrence of an
eclipse. We must, therefore, conclude that the fluctuations of light are
caused in some way by physical disturbances produced by the approach and
recession of the two component bodies in an elliptic orbit round their
centre of gravity. The observations indicate that the component stars,
when furthest apart in their orbital revolution, are separated by a
distance three times as great as when at their point of nearest
approach. The observations also show that Delta Cephei is approaching
the earth at the rate of about 8¾ miles a second. Its spectrum is of the
second or solar type, differing in this respect from the other
spectroscopic binaries, which show a spectrum of the first or Sirian
type. The colour of the star is yellow, and it has a distant bluish
companion of about the fifth magnitude, which may possibly have some
physical connexion with the brighter star, as both stars have a common
proper motion through space.

Another remarkable star of short period is Eta Aquilæ, the variability
of which was discovered by Pigott in 1784. It varies from magnitude 3·5
to 4·7, with a period of 7 days, 4 hours, 14 minutes, but Schönfeld
found marked deviations from a uniform period. It will be seen that the
amount of the light change, 1·2 magnitude, is the same as that of Delta
Cephei. Its colour is yellow, and its spectrum, like that of Delta
Cephei, of the second or solar type. The minimum takes place about three
days before the maximum.

Zeta Geminorum is another variable star with a comparatively short
period. It varies from about 3·7 to 4·5 magnitude, with a period of 10
days, 3 hours, 41½ minutes. Here the variation of light is only 0·8 of a
magnitude, or, in other words, the light at maximum is about double the
light of minimum, as in the case of the Algol type variable, Lambda
Tauri. Its light curve, unlike that of Delta Cephei and Eta Aquilæ, is
nearly symmetrical; that is, the period occupied in the increase of
light is about the same as that of the decrease. Prof. Pickering thinks
that Zeta Geminorum is possibly a “surface of revolution,” one side of
the rotating star being about four-fifths of the brightness of the
other; but Prof. Lockyer finds it to be a “spectroscopic binary,” like
Beta Lyræ and Delta Cephei.

Among variables with very short periods may be mentioned the southern
star R Muscæ, which is close to Alpha Muscæ. It varies from 6·6 to 7·4,
and goes through all its changes in the short period of 21 hours 20
minutes. The minimum takes place about nine hours before the maximum. It
was discovered at the Cordoba Observatory, and Dr. Gould remarks that
“its average brightness is so near the limit of ordinary visibility in a
clear sky at Cordoba, that the small regular fluctuations of light place
it every few hours alternately within or beyond this limit.”

A remarkable variable star of short period was discovered in 1888 by Mr.
Paul in the southern constellation Antlia. It varies from magnitude 6·7
to 7·3, with the wonderfully short period of 7 hours, 46 minutes, 48
seconds, all the light changes being gone through no less than three
times in twenty-four hours! It was for some years believed that the
variation was of the Algol type, but recent measures made at the Harvard
College Observatory show that it belongs to the same class as Delta
Cephei and Eta Aquilæ.

A telescopic variable with a wonderfully short period was discovered by
Chandler in 1894. It lies a little to the west of the star Gamma Pegasi,
and has been designated U Pegasi. It varies from magnitude 8·9 to 9·7,
and was first supposed to be of the Algol type with a period of about
two days, but further observations showed that the period was much
shorter, and only 5 hours, 31 minutes, 9 seconds. The light curve is
quite different from the Algol type, and also from that of Delta Cephei
and other short period variables, the times of increase and decrease of
light being about equal, as in the case of Zeta Geminorum. This fact,
combined with the remarkable rapidity of its light changes, which are
gone through four times in less than twenty-four hours, makes this
remarkable star a most interesting object. Possibly there may be other
stars in the heavens with a similar rapidity of variation which have
hitherto escaped detection.

Several southern variables of short period have been discovered in
recent years by Mr. A. W. Roberts at Lovedale in South Africa.

Unlike the variable stars of long period which seem scattered
indifferently over the surface of the heavens, the great majority of the
short period variables are found in a zone which nearly coincides with
the course of the Milky Way. The most notable exceptions to this rule
are W Virginis with the comparatively long period of 17¼ days, and U
Pegasi, above described, which has the shortest known period of all the
variable stars. Another peculiarity is that most of them are situated in
what may be called the following hemisphere, that is between 12 hours
and 24 hours of right ascension. The most remarkable exception to this
rule is Zeta Geminorum. The above rules do not apply to variables of the
Algol type, which we will now proceed to consider.

Algol, or Beta Persei, is a famous variable star, and the typical star
of the class to which it belongs. Its name, Algol, is derived from a
Persian word, meaning the “demon,” which suggests that the ancient
astronomers may have detected some peculiarity in its behaviour. The
real discovery of its variation was, however, made by Montanari in 1667,
and his observations were confirmed by Maraldi in 1692. Its fluctuations
of light were also noticed by Kirch and Palitzsch, but the true
character of its variations was first determined by the English
astronomer, Goodricke, in 1782. Its fluctuations of light are very
curious and interesting. Shining with a constant, or nearly constant,
brightness for a period of about 59 hours as a star of a little less
than the second magnitude, it suddenly begins to diminish in brightness,
and in about 4½ hours it is reduced to a star of about magnitude 3½. In
other words, its light is reduced to about one-third of its normal
brightness. If we suppose three candles placed side by side at such a
distance that their combined light is merged into one, and equal to the
usual brightness of Algol, then if two of these candles are
extinguished, the remaining candle will represent the light of Algol at
its minimum brilliancy. It is stated in several books on astronomy that
Algol varies to the extent of two magnitudes, but this is quite
incorrect, as a change of two magnitudes would imply that the light at
maximum is over six times the light at minimum, which is more than
double the star’s real variation. The star remains at its minimum, or
faintest, for only about 15 minutes. It then begins to increase, and in
about 5 hours recovers its normal brightness, all the light changes
being gone through in a period of about 10 hours out of nearly 69 hours,
which elapse between successive minima. These curious changes take place
with great regularity, and the exact hour at which a minimum of light
may be expected can be predicted with as much certainty as an eclipse of
the sun.

Goodricke, comparing his own observations with one made by Flamsteed in
the year 1696, found the period from minimum to minimum to be 2 days, 20
hours, 48 minutes, 59½ seconds, and he came to the conclusion that the
diminution in the light of the star is probably due to a partial eclipse
by “a large body revolving round Algol.” This hypothesis was fully
confirmed in the years 1888–89 by Professor Vogel with the spectroscope.
As no close companion to Algol is visible in the largest telescopes, we
must conclude that either the satellite is a dark body, or else so close
to the primary that no telescope could show it. As has been stated in
Chapter III., the motion of a star in the line of sight can be
ascertained by measuring displacements in the positions of the spectral
lines. Now, if the diminution in Algol’s light is due to a dark body
revolving round it, and periodically coming between us and the bright
star, it follows that both components will be in motion, and both will
revolve round the common centre of gravity of the pair. A little before
a minimum of light takes place, the dark companion should therefore be
approaching the eye, and, consequently, the bright companion will be
receding. During the minimum there will be no apparent motion in the
line of sight, as the motion of both bodies will be at right angles to
the visual ray. After the minimum is over, the motion of the two bodies
will be reversed, the bright one approaching the eye, and the dark one
receding. Now, this is exactly what Vogel found. Before the diminution
in the light of Algol begins, the spectroscope showed that the star is
receding from the earth, and after the minimum, that it is approaching
the eye. That the companion is dark and not bright, like the primary, is
evident from the fact that the spectral lines are merely shifted from
their normal position and not doubled, as would be the case were both
components bright, as in the case of some of the “spectroscopic
binaries”—for example, Beta Aurigæ—which has been considered in the
chapter on binary stars (Chapter IV.). Vogel found that before the
minimum of light, Algol is receding from the earth with the velocity of
24½ miles a second, and after the minimum it is approaching at the rate
of 28½ miles a second. The difference between the observed velocities
indicates that the system is approaching the earth with a velocity of
about 2 miles a second. Knowing, then, the orbital velocity, which is
evidently about 26½ miles a second, and assuming the orbit to be
circular, it is easy, with the observed period of revolution, or the
period of light variation, to calculate the diameter of the orbit in
miles, although the star’s distance from the earth remains unknown.
Further, comparing its period of revolution and the dimensions of the
orbit with that of the earth round the sun, it is easy to calculate, by
Kepler’s third law of motion, the mass of the system in terms of the
sun’s mass, and the probable size of the component bodies. Calculating
in this way, Vogel computes that the diameter of Algol is about
1,061,000 miles, and that of the dark companion 830,300 miles, with a
distance between their centres of 3,230,000 miles, and a combined mass
equal to two-thirds of the sun’s mass, the mass of Algol being
four-ninths, and that of the companion two-ninths, of the mass of the
sun. Taking the diameter of the sun as 866,000 miles, and its density as
1·44 (water being unity), I find that the above dimensions give a mean
density for the components of Algol of about one-third that of water, so
that the components are probably gaseous bodies, as Hall has already
concluded.

From the recorded observations of minima in past years, it has been
found that the period of variation of Algol’s light has been slowly
diminishing since Goodricke’s time, and Dr. Chandler finds the present
period is about 2 days, 20 hours, 48 minutes, 51 seconds, or about 8½
seconds less than Goodricke made it. Chandler thinks that this variation
in the length of the period is cyclical, and that it has now about
reached its smallest value, and will soon begin to increase again. He
believes that this variation is probably due to the orbital revolution
of the pair round a third body in a period of about 130 years. M.
Tisserand, however, explains the irregularities by supposing an
elliptical orbit, and a slight flattening or polar compression in the
primary star. Professor Boss is inclined to favour Chandler’s
hypothesis.

It is a curious fact that Al-Sûfi, the Persian astronomer, in his
“Description of the Heavens,” written in the tenth century, speaks
distinctly of Algol as a red star (_étoile, brillant; d’un éclat,
rouge_), while at present it is white, or at the most, of a yellow
colour. A similar change of colour is supposed to have taken place in
the case of Sirius, but the change in Algol seems more certain, as
Al-Sûfi’s descriptions are generally most accurate and reliable.

Stars of the Algol type of variable are very rare objects, only a dozen
or so having been hitherto discovered in the whole heavens. Those
visible to the naked eye, when at their normal brightness, are: Algol,
Lambda Tauri, Delta Libræ, R Canis Majoris, and U Ophiuchi. The
variation of Lambda Tauri was discovered by Baxendell in 1848. It varies
from magnitude 3·4 to 4·2, and its period from minimum to minimum of
light is about 3 days, 22 hours, 52 minutes, 12 seconds. Its
fluctuations have not been so well studied as those of Algol, but it is
known that the “period is subject to marked inequalities,” sometimes
amounting to 3 hours. The variation of light is less than that of Algol,
the light at maximum being only twice the light at minimum. Two candles
at a suitable distance would therefore represent the maximum light, and
one candle the minimum brightness. All the light changes take place in a
period of about 10 hours. The star is white like Algol.

The variability of Delta Libræ was discovered by Schmidt in 1859. It
varies from magnitude 4·9 to 6·1, with a period of 2 days, 7 hours, 51
minutes, 22·8 seconds. The period is, however, according to Schönfeld,
subject to some irregularities. The variation of light is about the same
as that of Algol, the light at maximum being about three times the light
at minimum. The variation takes about 12 hours, of which the decrease
occupies 5½ hours. The star is white like Algol.

The variability of R Canis Majoris was detected by Sawyer in 1887. The
variation is from 5·9 to 6·7 magnitude, or about equal in amount to that
of Lambda Tauri, and the period 1 day, 3 hours, 15 minutes, 55 seconds.

U Ophiuchi was also discovered by Sawyer in 1881. Its variation is from
magnitude 6·0 to 6·7, or slightly less than that of Lambda Tauri, and
the period 20 hours, 7 minutes, 41·6 seconds, but subject to an apparent
diminution. The maximum brightness lasts for about 16 hours, and all the
fluctuations of light take place in the short period of 4 hours. Its
colour is white, like most stars of the Algol type.

U Cephei is a very interesting variable of the Algol type, discovered by
Ceraski in 1880. It varies from 7·1 to 9·5, with a period of 2 days, 11
hours, 49 minutes, 45 seconds. Here the variation of light is greater
than that of Algol, the light at maximum being nearly seven times the
light at minimum. Its rapidity of variation is very great, sometimes
exceeding a magnitude in an hour. The light variations occupy about 6
hours, and the minimum lasts for about an hour and a half, Professor
Pickering thinks that the variation of light is, as in the case of
Algol, caused by an eclipsing satellite, but that in this case the
eclipse may possibly be total, the light at minimum being that due to
the satellite, which may have some inherent light of its own. Lord
Crawford examined the star with the spectroscope, and found that at the
minimum the blue end of the spectroscope faded, and the red was
intensified, which seems to suggest that the light of the star in that
phase shines through a gaseous medium, and that the eclipsing body may
be surrounded with an atmosphere.

Another interesting Algol variable is that known as Y Cygni, which was
discovered by Chandler in 1886, while using it as a comparison star for
the short period variable X Cygni. It varies from 7·1 to 7·9 magnitude,
or about the same amount as Lambda Tauri, with a period of 1 day, 11
hours, 56 minutes, 48 seconds. It has alternate bright and faint minima,
which suggest, according to Dunér, that the star consists of two
_bright_ components, one of them being brighter than the other, and both
revolving round their common centre of gravity in an elliptic orbit,
with a period double that of the light variation. Yendell, who has
carefully observed the star’s fluctuations, fully concurs in Dunér’s
views, and says “the substantial corrections of his fundamental
assumption appears to be proved beyond the possibility of a cavil.”

The variability of the star known as S Cancri was discovered by Hind in
1848. It varies from 8·2 to 9·8, or it is said, at some minima, to 11·7,
with the comparatively long period of 9 days, 11 hours, 37 minutes, 45
seconds. The variations of light occupy about 21½ hours. If the minimum
of 11·7 is correct, we have a variation of no less than 3½ magnitudes,
which implies that the normal light of the star is 25 times its light at
a faint minimum. If this be so, the eclipse must be nearly total.
Argelander found that after the minimum the light increases very
rapidly, and he thinks that the descent from the maximum is even more
rapid.

Some interesting examples of the Algol type of variable have been
discovered in recent years. One detected by Chandler, in 1894, and now
known as Z Herculis, varies from about the seventh to the eighth
magnitude, and has a period of 3 days, 23 hours, 48½ minutes. Faint and
very bright minima alternate in periods of 47 and 49 hours, the ratios
of the light at maximum and minima being 3, 2, and 1. These Professor
Dunér considers, indicate that the star consists of two revolving
components of equal size, one of which is twice as bright as the other,
and he computes that the components revolve round their common centre of
gravity in an elliptic orbit, the plane of which is in the line of
sight, and the semi-axis major about six times the diameter of the
stars. If we assume that the diameter of each component is equal to the
diameter of our sun, I find, from the above data, that the combined mass
of the system is about 1½ times the mass of the sun.

Another remarkable example of the Algol type was discovered by Miss
Wells in 1895. The star lies a little north of the “Dolphin’s rhomb,”
and at its normal brightness is about magnitude 9½. The period of
variation is about four days. The variation somewhat resembles that of U
Cephei. Professor Pickering says: “For nearly two hours before and after
the minimum it is fainter than the twelfth magnitude. It is impossible
at present to say how much fainter it becomes, or whether it disappears
entirely. It increases at first very rapidly, and then more slowly,
attaining its full brightness, magnitude 9·5, about five hours after the
minimum. One hundred and thirty photographs indicate that, during the
four days between the successive minima, it does not vary more than a
few hundredths of a magnitude. The variation may be explained by
assuming that the star revolves round a comparatively dark body, and is
totally eclipsed by it for two or three hours, the light at minimum, if
any, being entirely that of the dark body.”[119] This seems to be an
unique object, and it should be carefully followed through its minimum
with a large telescope.[120]

With reference to the Algol type of variable stars, Chandler finds that
“the shorter the period of the star, the higher the ratio which the time
of oscillation bears to the entire period.” Thus, in U Ophiuchi, with a
period of about 20 hours, the light changes occupy five hours, or
one-fourth of the period, while in S Cancri, which has a period of 227½
hours, the fluctuations of light take up 21½ hours, or only about
one-tenth of the period. In all cases in which the Algol type variables
have been examined with the spectroscope, the spectrum has been found to
be of the first or Sirian type, and they seem to be the only stars with
spectra of the Sirian type whose light is variable. It should be noted,
however, that, on the eclipse theory, the variation of light in these
stars is due merely to an occultation of one star by another, and not to
any physical change in the star itself. The bright star Spica, although
shown by the spectroscope to be a close binary star, like Algol, is not
variable, because, in this case, the plane of its orbit is inclined to
the line of sight, and hence the comparison star does not transit the
disc of its primary. Seen from some other point in space, it would
probably be an Algol variable.

A remarkable peculiarity about the variable stars in general is that
none of them have any considerable proper motion. As a large proper
motion is generally considered to indicate proximity to the earth, we
may conclude, with great probability, that the variable stars, as a
rule, lie at a great distance from our system. In other words, it
appears that the sun does not lie in a region of variable stars, and,
with the exception of Alpha Cassiopeiæ and Alpha Herculis, a measurable
parallax has not yet been found, so far as I know, for any known
variable star.

Plotting the known variables on star charts, I find a marked tendency to
cluster into groups. Thus, in and near the constellation, Corona
Borealis, there are five; near Cassiopeia’s Chair, five. In Cancer there
are four in a limited area. Near Eta Argûs there are several, and in a
comparatively small region in the northern portion of Scorpio there are
no less than fifteen variable stars.

We now come to the interesting and mysterious class of objects known as
“new” or “temporary” stars. These phenomena are of very rare occurrence,
and but few undoubted examples of the class are recorded in the annals
of astronomy. Possibly in some cases they have been merely variable
stars, of irregular period and fitful variability; but others may have
been due to a real catastrophe, such as the collision of two dark bodies
in space, or, possibly, the passage of a bright or dark body through a
gaseous nebula.

The earliest temporary star of which we have any reliable information
seems to be one which is recorded in the Chinese annals of Ma-tuan-lin,
as having appeared in the year 134 B.C. in the constellation Scorpio.
Its position seems to have been somewhere between the stars Beta and Rho
of Scorpio. Pliny informs us that it was the sudden appearance of a new
star which induced the famous astronomer Hipparchus to form his
catalogue of stars, the first ever constructed. As the date of
Hipparchus’ catalogue is 125 B.C., it seems highly probable that the new
star referred to by Pliny was the same as that recorded by the Chinese
astronomer as having appeared nine years previously.

A new star is said to have appeared in the year 76 B.C. between the
stars Alpha and Delta in the Plough, but the accounts are vague.

In 101 A.D., a small “yellowish-blue” star is said to have appeared in
the “sickle” in Leo, but its exact position is not known. In 107 A.D., a
new star is mentioned near Delta, Epsilon and Eta in Canis Major, three
bright stars south-east of Sirius. In 123 A.D., another new star is
recorded by Ma-tuan-lin to have appeared between Alpha Herculis and
Alpha Ophiuchi.

The Chinese annals record that on Dec. 10, 173 A.D., a brilliant star
appeared between Alpha and Beta Centauri in the Southern Hemisphere. It
remained visible for eight months, and is described as resembling “a
large bamboo mat!”—a curious description. There is at present close to
the spot indicated, a known variable star—R Centauri—of which the period
seems to be long and the variation of light irregular. Possibly an
unusually bright maximum of this variable star formed the star of the
Chinese annals, or perhaps the variable star is the remnant of the
outburst which took place in the first century. The variable is a very
reddish star, and at present varies from about the sixth to the tenth
magnitude

A new star is recorded in the year 386 A.D. as having appeared between
Lambda and Phi Sagittarii. Near the position indicated, Flamsteed
observed a star, No. 65 of his catalogue, which is now missing; and it
has been conjectured that the star seen by Flamsteed may possibly have
been a return of the star mentioned in the Chinese annals.

Cuspianus relates that a star as bright as Venus appeared near Altair in
389 A.D., during the reign of the Emperor Honorius, and that he had
himself seen it. There is some doubt, however, about the exact date, as
other accounts give the year 388 or 398. The star seems to have
disappeared in about three weeks.

In the year 393 A.D., another strange star is recorded in the tail of
Scorpio. An extraordinary star is said to have been seen near Alpha
Crateris in 561 A.D. Here again a known variable and red star—R
Crateris—is close to the position indicated by the ancient records.

The Chinese annals record a new star in 829 A.D., somewhere in the
vicinity of the bright star Procyon, and in this locality there are
several known variable stars.

The Bohemian astronomer, Cyprianus Leoviticus, mentions the appearance
of new stars in Cassiopeia in the years 945 A.D. and 1264, and it has
been conjectured that perhaps these were apparitions of Tycho Brahé’s
famous star of 1572 (to be presently described), forming a variable star
with a period of over 300 years. Lynn and Sadler, however, have shown
that the supposed stars of 945 and 1264 were, in all probability,
comets.

Extraordinary stars are recorded near Zeta Sagittarii in 1011 A.D., near
Mu Scorpii in 1203, and near Pi Scorpii on July 1, 1584. It is
remarkable how many of these objects seem to have appeared in this
portion of the heavens.

A very brilliant star is mentioned by Hepidannus as having appeared in
Aries in May, 1012. He describes it as “dazzling the eye.” Other
temporary stars are mentioned in 1054 A.D., near Zeta Tauri, and in
1139, near Kappa Virginis; but the accounts of these are very vague, and
it seems by no means certain that they were really new stars.

No possible doubt, however, can be entertained with reference to the
appearance of the object which suddenly blazed out in Cassiopeia’s Chair
in November, 1572. It was called the “Pilgrim Star,” and was observed by
the famous astronomer, Tycho Brahé, who has left us a very elaborate
account of its appearance, position, etc. Although usually spoken of as
Tycho Brahé’s star, it seems to have been really discovered by Cornelius
Gemma on the evening of November 9. That its appearance was very sudden
may be inferred from Cornelius Gemma’s statement, that it was not
visible on the preceding night in a clear sky. Tycho Brahé’s attention
was first attracted to it on November 11. His description of the new
star is as follows—as quoted by Humboldt:[121]—“On my return to the
Danish islands from my travels in Germany, I resided for some time with
my uncle, Steno Bille, in the old and pleasantly situated monastery of
Herritzwadt, and here I made it a practice not to leave my chemical
laboratory until the evening. Raising my eyes, as usual, during one of
my walks, to the well-known vault of heaven, I observed with
indescribable astonishment, near the zenith in Cassiopeia, a radiant
fixed star of a magnitude never before seen. In my amazement, I doubted
the evidence of my senses. However, to convince myself that it was no
illusion, and to have the testimony of others, I summoned my assistants
from the laboratory, and inquired of them, and of all the country people
that passed by, if they also observed the star that had thus suddenly
burst forth. I subsequently heard that in Germany, waggoners and other
common people first called the attention of astronomers to this great
phenomenon in the heavens—a circumstance which, as in the case of
non-predicted comets, furnished fresh occasion for the usual raillery at
the expense of the learned. This new star I found to be without a tail,
not surrounded by any nebula, and perfectly like all other fixed stars,
with the exception that it scintillated more strongly than stars of the
first magnitude. Its brightness was greater than that of Sirius, α Lyræ,
or Jupiter. For splendour, it was only comparable to Venus when nearest
to the earth (that is, when only a quarter of her disc is illuminated).
Those gifted with keen sight could, when the air was clear, discern the
new star in the day-time, and even at noon. At night, when the sky was
overcast, so that all other stars were hidden, it was often visible
through the clouds, if they were not very dense (_nubes non admodum
densas_). Its distances from the nearest stars of Cassiopeia, which
throughout the whole of the following year I measured with great care,
convinced me of its perfect immobility. Already, in December, 1572, its
brilliancy began to diminish, and the star gradually resembled Jupiter,
but by January, 1573, it had become less bright than that planet.
Successive photometric estimates gave the following results: for
February and March, equality with stars of the first magnitude
(_stellarum affixarum primi honoris_—for Tycho Brahé seems to have
disliked Manilius’ expression of _stellæ fixæ_); for April and May, with
stars of the second magnitude; for July and August, with those of the
third; for October and November, those of the fourth magnitude. Towards
the month of November, the new star was not brighter than the eleventh
in the lower part of Cassiopeia’s Chair. The transition to the fifth and
sixth magnitude took place between December, 1573, and February, 1574.
In the following month the new star disappeared, and, after having shone
seventeen months, was no longer discernible to the naked eye.” (The
telescope was not invented until thirty-seven years afterwards.)
Humboldt adds:—“At its first appearance, as long as it had the
brilliancy of Venus and Jupiter, it was for two months white, and then
passed through yellow into red. In the spring of 1573, Tycho Brahé
compared it to Mars; afterwards he thought it nearly resembled
Betelgeuse, the star in the right shoulder of Orion. The colour for the
most part was like the red tint of Aldebaran. In the spring of 1573, and
especially in May, its white colour returned (_albedinam quandam
sublividam induebat, qualis Saturni stellæ subesse videtur_). So it
remained in January, 1574; being, up to the time of its entire
disappearance in the month of March, 1574, of the fifth magnitude, and
white, but of a duller whiteness, and exhibiting a remarkably strong
scintillation in proportion to its faintness.”

[Illustration:

FIG. 8.—_The Temporary Star of 1572._

(From “Planetary and Stellar Studies.”)
]

According to a sketch of the position given in Tycho Brahé’s work,
referred to above, the star was situated a little to the north of Kappa
Cassiopeiæ, the faintest star in the Chair. This position is confirmed
by Argelander’s examination of Tycho Brahé’s observations: The spot is a
rather blank one to the naked eye, and even with an opera-glass, only a
few faint stars are visible. Quite close to the place fixed by
Argelander, d’Arrest observed in 1865 a star of the eleventh magnitude,
which seems to have escaped Argelander’s notice. Hind and Plummer
observed this small star in 1873, and thought they could detect
fluctuations in its light to the extent of about one magnitude. Espin
has also observed it, and the region has been photographed by Dr.
Roberts. Some have thought that Tycho Brahé’s star might possibly be
identical with the Star of Bethlehem, and this idea has been supported
by Cardanus, Chladni, and Klinkerfues, but Lynn and Sadler have shown
that the theory is quite untenable, and it has now been rejected by all
astronomers.

Ma-tuan-lin speaks of a star in 1578 “as large as the sun”(!) but does
not state its position.

The star known as P (34) Cygni is sometimes spoken of as a “Nova,” or
new star; but it is still visible to the naked eye as a star of the
fifth magnitude. It was observed of the third magnitude by Jansen in
1600 and by Kepler in 1602. After the year 1619, it appears to have
diminished in brightness, and is said to have vanished in 1621; but it
may merely have become too faint to be seen with the naked eye. It was
again observed of the third magnitude by Dominique Cassini in 1655, and
it afterwards disappeared. It was again seen by Hevelius in November,
1665. In 1667, 1682, and 1715, it is recorded as of the sixth magnitude,
and there is no further record of any marked increase in its light. A
period of about 18 years was assumed by Pigott; but this is now
disproved, and it seems probable that the star is a variable of
irregular period and fitful variability, and not, properly speaking, a
temporary star. Its present colour is yellow, and bright lines have been
seen in its spectrum.

Another remarkable object of the temporary class was observed by Kepler
in 1604 in Ophiuchus, and is described by him in his work, “De Stella
Nova in pede Serpentarii.” He and his assistants were observing the
planets Mars, Jupiter, and Saturn, which were then near each other in
this region of the heavens, a few degrees to the south-east of the star
Eta Ophiuchi, and on the evening of October 10, Brunowski, a pupil of
Kepler’s, noticed that a new and very brilliant star was added to the
group[122]. When first seen, it was white, and exceeded in brightness
Mars and Jupiter, but seems not to have quite equalled Venus in
brilliancy. It slowly diminished, and in January, 1605, it was brighter
than Antares but less than Arcturus. At the end of March, 1605, it had
faded to the third magnitude. Its proximity to the sun then prevented
further observations for several months. In March, 1605, it had
disappeared to the naked eye. It was also observed by Galileo and by
David Fabricius, whose observations place it about midway between the
fifth magnitude star Xi and 58 Ophiuchi. Its exact position, however,
does not seem to be known with such accuracy as that of Tycho Brahé’s
star, nor is there any known star very close to the spot indicated by
Schönfeld from an examination of Fabricius’ observations. It seems
possible that Kepler’s star may have been seen previously by Ptolemy,
for in his catalogue he gives a star of the fourth magnitude close to
the position of Kepler’s star; but there is some doubt about the exact
position indicated by Ptolemy. The Chinese annals mention a “ball-like”
star as having appeared near Pi Scorpii on September 30, 1604, and
remaining visible until March, 1606, which may possibly be identical
with Kepler’s star.

A new star of the third magnitude was observed near Beta Cygni by the
Carthusian monk Anthelmus in 1670. It remained visible for about two
years, and is said to have increased and diminished several times before
its final disappearance. Schönfeld computed its exact position from
observations made by Hevelius and Picard. Quite close to the spot
indicated, a star of the eleventh magnitude has been observed at the
Greenwich Observatory, and fluctuations of light were suspected in this
small star by Hind and others. Hind says that, to his eye, “there is a
hazy, ill-defined appearance about it which is not perceptible in other
stars in the same field of view. Mr. Talmage received the same
impression; and I may add that Mr. Baxendell, who has examined it with
Mr. Worthington’s reflector, observed that no adjustment of focus would
bring the star up to a sharp focus.” This hazy appearance is very
suggestive, as it indicates that the “Nova” may possibly have faded into
a small planetary nebula, as in the case of the new star in Cygnus,
observed by Schmidt in 1876, and the new star in Auriga, found by Dr.
Anderson in 1892. Near the position of Anthelm’s new star is a known
variable star, S Vulpeculæ, discovered by Hind in 1861, which might be
suspected to be identical with Anthelm’s star; but Hind has shown that
the variable has no proper motion which would account for the difference
of position since 1670, and he concludes that, “from the fixity of its
position during eight years, it may be inferred that the variable is
distinct from Anthelm’s.” It has been supposed that the star 11
Vulpeculæ in Flamsteed’s catalogue is identical with Anthelm’s star; but
Baily could not find any evidence to show that Flamsteed’s star ever
really existed, and he says: “Under the presumption, however, that it
may be a variable and not a _lost_ star, I have preserved its recorded
position with a view of inducing astronomers to look out for it from
time to time.”

On the evening of April 28, 1848, Hind, observing at Mr. Bishop’s
private observatory, in Regent’s Park, London, noticed a new star of
about the fifth magnitude, between Zeta and Eta Ophiuchi. Its colour was
reddish-yellow, and it seems to have subsequently increased in
brightness to nearly the fourth magnitude, but it soon faded to the
tenth or eleventh magnitude. This curious object has become very faint
in recent years. In 1866, it was of the twelfth magnitude, and in 1874
and 1875, not above the thirteenth.

On May 28, 1860, Pogson discovered a new star in the globular cluster,
80 Messier, which lies between Antares and Beta Scorpii. When first
noticed, it was about the seventh magnitude, and its brightness was
sufficient to obscure the cluster. In other words, the cluster was
apparently replaced by a star. On June 10, the star had nearly
disappeared, and the cluster again shone with great brilliancy, and with
a condensed centre. The observations of Auwers and Luther confirm those
of Pogson. Pogson states that he examined the cluster on May 9, but
noticed nothing peculiar; and, according to Schönfeld, the cluster
presented its usual appearance on May 18, when examined at the
Königsberg Observatory. The apparition of the temporary star was,
therefore, probably sudden, as in the case of other “new” stars. The
phenomenon was possibly caused by a collision between two of the stars
composing the cluster, which is, at least, apparently very condensed.

A very remarkable star, sometimes called the “Blaze Star,” suddenly
appeared in Corona Borealis, in May, 1866. It was first seen by the late
Mr. Birmingham, at Tuam, Ireland, about midnight, on the evening of May
12, when it was of the second magnitude, and equal to Alphecca, “the gem
of the coronet.” Its appearance must have been very sudden, for Schmidt,
the Director of the Athens Observatory, stated that he was observing the
constellation on the same evening, about 2½ hours previous to
Birmingham’s discovery, and observed nothing unusual. He was certain
that no star, of even the fifth magnitude, could possibly have escaped
his notice. On the following night it was seen by several observers in
different parts of the world. M. Faye, the French astronomer, in his
work—“L’Origine du Monde”—attributes the discovery to M. Courbebaisse, a
French engineer, and does not mention Mr. Birmingham! He says M.
Courbebaisse first saw it on the evening of May 13. This may be true; he
was not the only observer who saw it on that evening; but it was,
undoubtedly, _first_ seen by Mr. Birmingham on the _preceding_ night,
and to Mr. Birmingham alone is certainly due the credit of the
discovery. The star rapidly diminished in brightness, and on May 24 of
the same year, had faded to 8½ magnitude. It afterwards increased to
about 7·8 magnitude, but soon diminished again. Soon after its discovery
it was found that the star was not really a new one, as it had been
previously observed at Bonn by Schönfeld, in May, 1855, and March, 1856,
while making the observations for Argelander’s _Durchmusterung_, in
which it appears as No. 2765, in degree 26. On both occasions it was
rated as 9½ magnitude, and no suspicion of variable light seems to have
arisen. When viewed with the naked eye at the time of its greatest
brilliancy, it was remarked by some observers that it twinkled decidedly
more than other stars in the vicinity, and that this peculiarity made it
very difficult to form a correct estimation of its relative brilliancy
During the years 1866 to 1876, fluctuations in its light were observed
by Schmidt, and he deduced a probable period of about 94 days, with a
variation from the seventh to the ninth magnitude. This conclusion was
confirmed by Schönfeld, and the star would therefore seem to be an
irregular variable, and not a true temporary star.

A very remarkable and interesting variable star was discovered by
Schmidt at Athens, near Rho Cygni, on the evening of November 24, 1876,
when it was about the third magnitude, and somewhat brighter than Eta
Pegasi. Schmidt stated that he had observed the vicinity on several
occasions between November 1 and 20, and was certain that no star of
even the fifth magnitude could possibly have escaped his notice, so that
the star probably blazed out very suddenly, as most of these
extraordinary objects have done. Between November 20 and 24, the sky was
overcast, so the exact time of its appearance is unknown. The star would
seem to be quite new, as there is no star in any of the catalogues in
the position of the “Nova,” the nearest being one of the ninth
magnitude, which occurs in the Bonn observations. The new star rapidly
faded, and on November 30 had descended to the fifth magnitude. On the
night of its discovery it was remarked that its brightness was such as
to render its near neighbour, 75 Cygni (a sixth magnitude star),
invisible; while on December 14 and 15, 75 Cygni, in its turn, nearly
obliterated the light of the stranger. In the 48 hours following the
night of November 27, the star diminished in light to the extent of
nearly 1½ magnitude! It afterwards faded very regularly to August, 1877,
and showed no oscillations of brightness as have been observed in other
temporary stars. On the evening of its discovery, Schmidt considered the
star to be of a strong golden-yellow, and that it afterwards remained of
a deep golden-yellow, but at no time was it as ruddy as 75 Cygni. I
could see no trace of colour in the star with a 3-inch telescope in the
Punjab on January 12, 1877, but it had then faded to the eighth
magnitude. On February 7, 1877, I estimated it ninth magnitude. A few
days after its discovery, it was examined with the spectroscope, and its
spectrum showed bright lines similar to the “Blaze Star” in Corona,
which appeared in May, 1866. One of the bright lines was thought to be
identical with the line numbered 1474 by Kirchoff, visible in the
spectrum of the solar Corona during total eclipses of the sun. The other
bright lines were identified by M. Cornu of the Paris Observatory with
some of the lines of hydrogen, sodium, and magnesium. In September,
1877, the star was examined with a 15-inch refractor by Lord Lindsay
(now Lord Crawford), who found “the light coming from it almost entirely
monochromatic, that is, of only one colour, the star appearing exactly
the same as when looked at without the spectroscope, the direct prism
having no effect on it,” and he considers that “there is little doubt
that the star has changed into a planetary nebula of small angular
diameter!” On September 3, the star’s magnitude was 10½; “faint blue,
near another star of same size rather red.” Lord Crawford remarks that
no observer, discovering the object in its present state, would, after
viewing it through a prism, hesitate to pronounce as to its nebulous
character,[123] but no disc was detected with powers ranging up to 1000
diameters. Ward found the star only sixteenth magnitude in October,
1881, and it was estimated fifteenth magnitude at Mr. Wigglesworth’s
Observatory in September, 1885. At Lord Crawford’s Observatory the exact
position of the star, with reference to above fifty closely adjacent
stars, was carefully determined with the micrometer. The vicinity was
photographed by Dr. Roberts on September 27, 1891, with an exposure of
two hours, and “the _Nova_ appears as a star of about the thirteenth
magnitude.” Observations in 1894 and 1895, made its magnitude about
14·8, with an apparently continuous spectrum.[124]

In August, 1885, a star of about the seventh magnitude made its
appearance close to the nucleus of the Great Nebula in Andromeda
(Messier 31), a remarkable nebula, which will be described in the next
chapter. The new star was independently discovered by several observers
towards the end of August. It was not visible to Tempel at the Florence
Observatory on August 15 and 16, but is said to have been seen by M.
Ludovic Gully on August 17. It was, however, certainly seen by Mr. I. W.
Ward at Belfast on August 19, at 11 P.M., when he estimated it 9½
magnitude, and it was independently detected by the Baroness Podmaniczky
on August 22, by M. Lajoye on August 30, by Dr. Hartwig, at Dorpat, on
August 31, and by Mr. G. T. Davis, at Theale, near Reading, on September
1. On September 3, the star was estimated 7½ magnitude by Lord Crawford
and Dr. Copeland, and its spectrum was found to be “fairly continuous.”
On September 4, Mr. Maunder, at the Greenwich Observatory, found the
spectrum “of precisely the same character as that of the nebula, _i.e._,
it was perfectly continuous, no lines, either bright or dark, being
visible, and the red end was wanting.” Dr. Huggins, however, on
September 9, thought he could see a few bright lines in its spectrum, a
continuous spectrum being visible from the line D to F. The star
gradually faded away. On December 10, 1885, it was estimated of the
fourteenth magnitude at the Radcliffe Observatory, Oxford, and on
February 7, 1886, it was rated only sixteenth magnitude with the 26-inch
refractor of the Washington Observatory. A series of measures by
Professor Hall, from September 29, 1885, to February 9, 1886, showed “no
certain indications of any parallax,” so that the star and the nebula,
in which it probably lies, are evidently situated at a vast distance
from the earth. Seeliger has investigated the decrease in the light of
the star on the hypothesis that it was a cooling body, which had been
suddenly raised to an intense heat by the shock of a collision, and
finds a fair agreement between theory and observation. Auwers points out
the similarity between this outburst and the new star of 1860, in the
cluster 80 Messier (already described), and thinks it probable that both
phenomena were caused by physical changes in the nebulæ in which they
occurred. Proctor considered that the evidence of the spectroscope shows
that the new star was situated _in_ the nebula, and in this opinion I
fully concur.

Several temporary stars have been detected in recent years by Mrs.
Fleming, from an examination of photographs of stellar spectra, taken at
the Harvard Observatory, for the Draper Memorial. Plates of the
constellation Perseus show the existence of a star in 1887, the spectrum
of which shows the bright lines of hydrogen, and it was on this account
assumed to be a long period variable. During the following eight years,
however, 81 photographs of the same region show no trace of the star,
and it has been frequently looked for with a telescope, but without
success. It would, therefore, seem probable that the star was a
temporary one. Its magnitude was about the ninth.

A remarkable and very interesting temporary star was discovered in 1892
in the constellation Auriga. On February 1, of that year, an anonymous
post-card was received by Dr. Copeland at the Royal Observatory,
Edinburgh, with the following announcement:

“Nova in Auriga. In Milky Way, about two degrees south of χ Aurigæ,
preceding 26 Aurigæ. Fifth magnitude, slightly brighter than χ.”

Such an announcement evidently required immediate attention, and on that
evening, Dr. Copeland and his assistants looked for the new star, and
easily found it with an opera-glass at 6 hours 8 minutes. They estimated
it of the sixth magnitude, and equal to 26 Aurigæ. It was of a yellow
colour. When examined with a prism placed before the eye-piece of a
24-inch reflector, its spectrum was seen to resemble the “Blaze Star” of
1866 in Corona. “The C line was intensely bright, a yellow line about D
fairly visible; four bright lines, or bands, were conspicuous in the
green; and, lastly, a bright line in the violet (probably Hγ) was easily
seen.” Notice of the discovery was at once telegraphed to Greenwich and
Keil Observatories, and the star was photographed at Greenwich on the
same night. It is not in the Bonn star charts, which show stars to
nearly the tenth magnitude. In _Nature_ of February 18, 1892, a letter
appeared, signed Thomas D. Anderson, in which the writer stated that the
post-card was sent by him, and he gives the following details respecting
the discovery:

“Prof. Copeland has suggested to me that as I am the writer of the
anonymous post-card mentioned by you a fortnight ago (p. 325), I should
tell your readers what I know about the Nova.

“It was visible as a star of the fifth magnitude certainly for two or
three days, very probably even for a week, before Prof. Copeland
received my post-card. I am almost certain that at two o’clock on the
morning of Sunday, the 24th ult., I saw a fifth magnitude star making a
very large obtuse angle with β Tauri and χ Aurigæ, and I am positive
that I saw it, at least, twice subsequently during that week.
Unfortunately, I mistook it on each occasion for 26 Aurigæ, merely
remarking to myself that 26 was a much brighter star than I used to
think it. It was only on the morning of Sunday, the 31st ult., that I
satisfied myself that it was a strange body. On each occasion of my
seeing it, it was slightly brighter than χ. How long before the 24th
ult. it was visible to the naked eye I cannot tell, as it was many
months since I had looked minutely at that region of the heavens.

“You might also allow me to state, for the benefit of your readers, that
my case is one that can afford encouragement to even the humblest of
amateurs. My knowledge of the technicalities of astronomy is,
unfortunately, of the most meagre description; and all the means at my
disposal on the morning of the 31st ult., when I made sure that a
strange body was present in the sky, were Klein’s ‘Star Atlas’ and a
small pocket-telescope, which magnifies ten times.”

Soon after the discovery of the new star, an examination was made by
Professor Pickering of photographs taken of the region at Harvard
Observatory, previous to Dr. Anderson’s discovery. It was found that on
eighteen photographs taken between the dates November 3, 1885, and
November 2, 1891, there is no trace of the new star; but in those taken
from December 16, 1891, to January 31, 1892, a star of the fifth
magnitude is shown in the position of the new star. “In another series
of plates taken with the transit photometer, no record of the new star
up to December 1, 1891, was obtained, although χ Aurigæ (magnitude 5·0)
was always visible, but the plates taken on the nights of December 10,
1891, and ending January 20, 1892, indicated clearly the position of the
new star.” Professor Pickering says: “It appears that the star was
fainter than the eleventh magnitude on November 2, 1891, than the sixth
magnitude on December 1, and that it was increasing rapidly on December
10. A graphical construction indicates that it had probably attained the
seventh magnitude within a day or two of December 2, and the sixth
magnitude on December 7. The brightness increased rapidly until December
18, attaining its maximum about December 20, when its magnitude was 4·4.
It then began to decrease slowly, with slight fluctuations, until
January 20, when it was slightly below the fifth magnitude. All these
changes took place before its discovery, so that it escaped observation
nearly two months. During half of this time it was probably brighter
than the fifth magnitude.”

It would seem from the above remarks that the star did not—like some
other temporary stars—attain its full brilliancy at once, but increased
gradually in brightness. After the decrease of light in January, 1892,
it seems to have again risen to another maximum, for photographs taken
at the Greenwich Observatory after its discovery show that the star rose
to a magnitude of 3·5 (photographic) on February 3, and then began to
fade again slowly during February, but rapidly during the month of
March. Owing to cloudy weather in the west of Ireland, I could not
observe the new star until February 14. The following are my
observations, made with a binocular field-glass, the comparison stars
being Chi Aurigæ, 26 Aurigæ, and D M + 30°, 898:—February 14, 4·55
magnitude; February 15, 5·56; February 16, 5·84; February 18, 5·51;
February 21, 5·56; February 24, 5·66; February 28, 5·44; March 1, 5·68;
March 5, 5·66; March 10, 7·3; March 11, 7¾; March 16, 8½, or fainter;
March 18, 9 magnitude, or less, “only _very_ faint stars seem near the
place of the Nova; clear sky, no moon.” The general accuracy of the
above observations were confirmed by the photographic estimates of the
star’s light made at Greenwich,[125] and also by Schaeberle’s
observations of its brightness.

After March 18, the light of the star steadily and rapidly decreased,
and on April 1, it had faded to nearly the fifteenth magnitude, and
afterwards to about the sixteenth. In August, 1892, it brightened again,
as it was found by Corder of about the ninth magnitude on August 21. Dr.
J. Holetschek of the Vienna Observatory observed it from August 24 to
September 2, 1892, and estimated it about 9½ magnitude. In October,
1892, most observers rated it between 10 and 10½ magnitude. Observations
by Mr. C. E. Peck, “from October 3, 1893, to May 4, 1894, only vary from
10·1 to 11·0 magnitude, and observations up to the end of 1894 give the
same results.”[126] In 1895 Professor Barnard found that it “is still
visible as a small star, and has not changed in physical appearance
since the autumn of 1892. It remains perfectly fixed with reference to
the comparison stars.”[127]

Examined with the spectroscope soon after its discovery, many bright
lines were seen in its spectrum, and it was found that “the bright lines
in the spectrum of the new star were accompanied by dark ones on their
more refrangible sides,” that is, the dark lines were on the blue side
of the bright ones. This suggested the idea that the outburst was
probably due to a collision between two bodies, one of which, having a
spectrum of dark lines, was rushing towards the earth, and the other,
with a bright-line spectrum, was receding. Lockyer supposed the outburst
to be due to a collision between two swarms of meteorites. Dr. Huggins
advanced the view that the phenomenon was due to the near approach of
two gaseous bodies. “But,” he says, “a casual near approach of two
bodies of great size would be a greatly less improbable event than an
actual collision. The phenomena of the new star scarcely permits us to
suppose even a partial collision, though, if the bodies were diffused
enough, or the approach close enough, there may have been, possibly,
some interpenetration and mingling, of the rare gases near the
boundaries.” But Maunder and Seeliger consider this hypothesis to be
untenable. Mr. Monck suggested that a star or swarm of meteorites
rushing through a gaseous nebula might explain the phenomena. Seeliger
advocates a similar theory. Maunder also favours a collision theory.

A photograph of the spectrum taken by Maunder on February 22, 1892 (when
the photographic magnitude was 4·78, and visual magnitude about 5·7),
showed a displacement of the dark lines, which implied a relative motion
of the two supposed colliding bodies of about 820 miles a second! Vogel
found that the bright lines showed a double maxima, and he thought that
these were due to “two different bodies moving with different
velocities, so that the spectrum of the Nova consists of, at least,
three spectra superposed. The measurement of the photograph gives the
body showing the dark line spectrum as approaching the earth with a
speed of nearly 420 miles per second, one of the two bright line bodies
as approaching with a speed of 22 miles, whilst the other is receding
with a speed of 300 miles a second.”[128]

At the time of its increase of brightness, in August, 1892, Professor
Barnard, observing it with the great 36-inch Lick telescope, says, the
“Nova appeared as a small, bright nebula, with a star-like nucleus of
the tenth magnitude. The nebulosity was pretty bright and dense, and was
3″ in diameter. Surrounding this was a fainter glow, perhaps half a
minute in diameter.” At this time, Professor Campbell of the Lick
Observatory found that its spectrum showed the characteristic nebular
lines. This observation was confirmed by Dr. Copeland on August 25 and
26, and by Herr Gothard, who photographed the spectra of a number of
nebulæ, and compared them with his photograph of the spectrum of the new
star. He says, “Each new photograph increased the probability, which may
be considered as a proved fact, that the _spectrum not only resembles,
but that the aspect and position of the lines show it to be identical
with the spectra of the planetary nebula_. In other words, the new star
has changed into a planetary nebula.”

A nebulous spectrum was also found by Espin. From observations of the
spectrum in November, 1894, Professor Campbell finds that “the spectrum
is not only nebular, but it is approaching the average type of nebular
spectrum,” and he adds, “We may say that only five ‘new stars’ have been
discovered since the application of the spectroscope to astronomical
investigations, and that three of these had substantially identical
spectroscopic histories.” Espin found the star distinctly nebulous on
December 9, 1895, and its magnitude about 10½.

Another new star was discovered by Mrs. Fleming by the photographic
method in the southern constellation, Norma, in the year 1893. When at
its brightest, it seems to have been about the seventh magnitude. It was
situated in the Milky Way, a little to the east of the pair of stars
known as Gamma one and Gamma two Normæ. Its spectrum was similar to that
of the new star in Auriga, when it first appeared, and, like that
object, the spectrum has now, according to Professor Campbell, “become
distinctly nebular.”

Another temporary star of about the eighth magnitude was also discovered
by Mrs. Fleming in 1895, in that portion of the southern constellation
Argo, known as Carina. It was in or close to the Milky Way—like so many
of these new stars—between the variable star Eta Argûs and the star
Lambda Centauri, near the Southern Cross, and close to a star of
magnitude 5½. The photographic plates on which the discovery was made
were taken at the Arequipa Station, in Peru. An examination of 62
photographs of the region showed no trace of the star on May 17, 1889,
and March 5, 1895, although stars so faint as the fourteenth magnitude
are visible on some of the plates. On nine plates, however, taken
between April 8, 1895, and July 1, 1895, the star is visible, and during
this interval the brightness diminished from the eighth to the eleventh
magnitude. The spectrum showed the bright lines of hydrogen “accompanied
by dark lines of slightly shorter wave-length,” and in all its
“essential features” was “apparently identical” with the spectra of the
temporary stars in Auriga and Norma.

With reference to this outburst, and the similarity of the star’s
spectrum to that of the new star in Auriga, Professor William H.
Pickering points out “the improbability of two successive collisions
between stars, occurring nearly in the line of sight, in both cases a
bright and a dark line star being involved, and in each case the
bright-line star being the one to recede from us. The same remark
applies to the theory of a collision of a star and a nebula. As a
substitute I offered an explosion hypothesis, in which a dark sun
suddenly gave out in all directions large quantities of hydrogen in an
incandescent state. This would, of course, merely produce a spectrum
with bright lines. But if the expulsion of hydrogen continued, the outer
layers of gas would cool, producing absorption lines in the spectrum of
the approaching hydrogen, but still leaving the spectrum lines of the
receding hydrogen bright. Finally, when the expulsion ceased, we should
find a heated spherical mass of gas, similar to a planetary nebula. It
was shown that the velocities which were observed in the cases of these
two _novæ_ were less than fifty per cent. greater than had been observed
in our own sun. The discovery of this third _nova_, with a spectrum
identical with that of the two others, increases many times the
improbability of the collision theories, and thereby strengthens the
explosion hypothesis. If this latter is correct, we must look upon the
phenomena presented by a _nova_ not as indicating the birth of a new
star, but rather as a cataclysm testifying to the death and final
disrupture of an old one.”[129]

Another apparently new star was detected by Mrs. Fleming in 1895, in the
constellation Centaurus. It was situated about three degrees north-west
of the double star 3 Centauri, and when at its brightest, seems to have
been about the seventh magnitude. Mrs. Fleming’s attention was first
directed to it by its peculiar spectrum, as shown on a photographic
plate taken at Arequipa in July, 1895. No trace of the star is visible
on 55 plates taken from May 21, 1889, to June 14, 1895, but on plates
taken on July 8 and 10, 1895, it appears of about the seventh magnitude.
A photograph taken on December 16, 1895, shows it as a star of about the
eleventh magnitude. On that date, and on December 19, it was seen about
the same magnitude by Mr. O. C. Wendell, with a 15-inch telescope. The
spectrum at first resembled that of the nebula 30 Doradus, and was
unlike the spectra of the temporary stars in Auriga, Norma, and Carina.
When it had faded to the eleventh magnitude, its spectrum seemed to be
monochromatic, and very similar to that of a neighbouring nebula, N G C
5253, so that, like the new stars in Cygnus, Auriga, and Norma, “it
appears to have changed into a gaseous nebula.”

It is a remarkable fact that the great majority of the temporary stars
appeared in or near the Milky Way. The chief exceptions to this rule
are:—the star of 76 B. C., in the Plough, the star recorded by
Hepidannus in Aries, 1012, A.D., and the “Blaze Star” of 1866 in Corona
Borealis.

CHAPTER VI.
CLUSTERS AND NEBULÆ.

Clusters of stars and nebulæ are frequently classed together in one
group. But this is incorrect. The term nebulæ should be restricted to
those objects which the spectroscope shows to consist of gaseous matter,
while the term cluster should be applied to those groups of stars in
which the components are individually visible as distinct star-like
points. There may be, of course, intermediate forms, like the Great
Nebula in Andromeda, which, although not resolvable into stars with
powerful telescopes, the spectroscope shows to be not gaseous. We will
begin with clusters of stars, many of which can be seen with telescopes
of moderate power, and some, like the Pleiades, even with the naked eye.

The Pleiades form perhaps the most remarkable group of stars in the
heavens, and are probably familiar to most people, even to those whose
knowledge of the constellations is limited to a few of the brighter
stars. The cluster is a very remarkable and brilliant one, and forms a
striking object in a clear sky. There is no other group visible to the
naked eye in either hemisphere similar to it in the brightness and
closeness of the component stars. It seems to have attracted the
attention of observers since the earliest ages. Job says: “Can’st thou
bind the sweet influences of Pleiades, or loose the bands of Orion?”

Hesiod, writing nearly 1,000 years B.C., speaks of the Pleiades in words
thus translated by Cooke:—

“There is a time when forty days they lie,
And forty nights conceal’d from human eye;
But in the course of the revolving year,
When the swain sharps the scythe, again appear.”

This passage refers to the disappearance of the group in the sun’s rays
in summer, and their reappearance in the evening sky in the east at
harvest time. Hesiod also speaks of them as the seven sisters, and in
Cicero’s “Aratus,” they are represented as female heads, bearing the
names Merope, Alcyone, Celæno, Electra, Taygeta, Asterope, and Maia,
names by which they are still known to astronomers. The origin of the
name Pleiades is somewhat doubtful. Some think that it is derived from
the Greek word _pleia_, to sail. Others from the words _pleios_, full, a
name perhaps suggested by the appearance of the cluster. Although seven
stars are mentioned by Hipparchus and Aratus, Homer only speaks of six,
and this is the number now visible to average eyesight. A larger number
has, however, been seen with the naked eye by those gifted with
exceptionally keen eyesight. Möstlin, Kepler’s tutor, is said to have
seen fourteen, and he actually measured and recorded the position of
eleven, with wonderful accuracy, without the aid of a telescope! In
recent years, Miss Airy, daughter of the late astronomer-royal, has seen
twelve, and Carrington and Denning fourteen. But to most eyes probably
six only are visible with any certainty. There is a tradition that,
although seven stars were originally visible, one disappeared at the
taking of Troy. Professor Pickering has recently discovered that the
spectrum of Pleione, which forms a wide pair with Atlas, bears a
striking resemblance to that of P Cygni, the so-called “temporary star”
of 1600. This similarity of spectra suggests the idea that Pleione may
possibly—like the star in Cygnus—be subject to occasional fluctuations
of light, which might perhaps account for its visibility to the naked
eye in ancient times.

The grouping of even six stars visible to the naked eye in so small a
space is very remarkable. Considering the total number of stars visible
without optical aid, Mitchell—writing in 1767—calculated by the
mathematical theory of probability that the chances are 500,000 to one
against the close arrangement of six stars in the Pleiades being merely
the result of accident. He therefore concludes “that this distribution
was the result of design, or that there is reason or cause for such an
assemblage.”

Although to a casual observer the component stars may appear of merely
equal magnitude, there is considerable difference in their relative
brilliancy. Measures with a photometer show that Alcyone—the brightest
of the group—is of the third magnitude, Maia, Electra, and Atlas of the
fourth, Merope about 4⅓, Taygeta 4½, Celæno about 5⅓, and Asterope about
the sixth. Pleione is about 5½, according to the photometric measures
made at Oxford, but it lies so close to Atlas that to most eyes the two
will probably appear as one star. About thirty more range from the sixth
to the ninth magnitude, and this is about the number visible with an
opera-glass. Galileo counted thirty-six stars with his small telescopes,
but with modern instruments the number is largely increased. Some years
since, M. Wolf, the distinguished French astronomer, published a chart
of the Pleiades, showing about 500 stars made from his own observations.
Photography has further added to the number of stars visible in this
interesting group. On a photograph taken at the Paris Observatory in
1887, with an exposure of three hours, no less than 2,326 stars can be
distinctly counted on a space of about three square degrees. The fainter
stars on this photograph are supposed to be of the seventeenth
magnitude. Now, as Alcyone, the brightest star of the group, is of the
third magnitude, we have a difference of fourteen magnitudes between the
brightest and the faintest. This implies that Alcyone is 398,100 times
brighter than the faintest stars visible on the photographic plate. If
we could conclude that the fainter stars really belonged to the cluster,
they would be at practically the same distance from the earth, and the
great difference of brightness would be very remarkable, and would
suggest that Alcyone is a vastly larger body than the smallest stars of
the group. The difference of brilliancy given above would indicate that
the diameter of Alcyone is 631 times greater than that of the faintest
stars revealed by photography. This is of course on the assumption that
all the stars of the cluster are, surface for surface, of the same
intrinsic brilliancy, and that this apparent brightness to the eye
depends simply on their diameter. As spheres vary in volume as the cubes
of their diameters, we have the volume of Alcyone equal to the cube of
631, or over 250 million times the volume of the faintest stars of the
group. This startling result was very difficult to explain, for either
we must assume that Alcyone is an enormously vast body, or else that the
faint stars of the group are exceedingly small. If we take the diameter
of Alcyone as 1,400,000 miles, then the diameter of the faintest stars
in the group would be only 2,200 miles, or about the size of our moon,
and it seems highly improbable, if not impossible, that such small
bodies should shine with inherent light of their own. They would indeed
be “miniature suns.” On the other hand, if we assume that the faintest
stars are of about the same size as the planet Jupiter, or about 87,000
miles, the diameter of Alcyone would be nearly 55 millions of miles, a
result which is also highly improbable. The difficulty has, I think,
been satisfactorily cleared up by some photographs recently taken by
Professor Barnard at the Lick Observatory. A photograph taken with a
lens of six inches aperture, and 31 inches focal length, and an exposure
of 10 hours 15 minutes, shows that the sky surrounding the Pleiades is,
on all sides, as thickly studded with small stars as the cluster itself.
It seems clear, therefore, that the faint stars in the Pleiades are
merely some of the “hosts of heaven” which happen to lie in that
direction, and have probably no connexion with the cluster, which is
merely projected on a starry background of faint and distant stars.

The brilliancy of the Pleiades cluster would naturally suggest a
comparative proximity to the earth. Attempts to determine their distance
have, however, hitherto proved unsuccessful. This would indicate that
the distance is very great, and would, of course, lead to the conclusion
that the group is of vast dimensions. An effort has been made to
determine the distance indirectly by a consideration of the “proper
motion” of the principal stars. Professor Newcomb finds a proper motion
for Alcyone of about 5·8 seconds of arc per century. This motion is in a
direction nearly opposite to that of the sun’s motion in space, and may
possibly be due to that cause. If we assume that this apparent motion of
Alcyone is wholly due to the effect of the sun’s real motion at the rate
of, say, fourteen miles a second, the distance of Alcyone would
correspond to a “light journey” of about 267 years! Our sun, placed at
this vast distance, would, I find, be reduced in brilliancy to a star of
about the ninth magnitude, or six magnitudes fainter than Alcyone. This
would imply that Alcyone is about 250 times brighter than the sun! As,
however, the spectrum of Alcyone is of the first or Sirian type, it
cannot properly be compared with the sun.

There are six other small stars in the Pleiades having proper motions
similar in amount and direction to that of Alcyone. As the other bright
stars of the group have much smaller motions, it has been suggested that
the seven stars with comparatively large, proper motions do not really
belong to the group, but are only optically associated with it. This
would imply that the real cluster lies much farther from us than
Alcyone, and the comparative brilliancy of some of its component stars
would still denote enormous size.

In the year 1859, the well-known astronomer, Tempel, announced his
discovery of a faint nebulosity extending in a southerly direction from
Merope, the nearest bright star to Alcyone. This interesting discovery
was practically confirmed by other astronomers; but from its visibility
to some observers with small telescopes, and the failure of others to
detect it with much larger instruments, the variability of its light was
strongly suspected. The question remained in doubt for many years, but
has now been finally set at rest by photography, which shows not only a
mass of nebulous light surrounding Merope, but other nebulous spots
involving Alcyone, Maia, and Electra. Indeed, a photograph taken by Dr.
Roberts in 1889 shows that all the brighter stars of the group are more
or less surrounded by nebulosity. The nebula surrounding Maia is of a
somewhat spiral form, and its existence was not even suspected until it
was revealed by photography. It was afterwards seen with the great
30-inch refractor of the Pulkowa Observatory. Had, however, its
existence been unknown, it would probably have escaped detection, even
with this large telescope, as it is one thing to see a faint object
known to exist and another to discover it independently. Maia is
surrounded by several faint stars of the twelfth to the fourteenth
magnitude; and the Russian observers believe that one of these is
variable in light, as it was seen distinctly on February 5, 1886, when
its magnitude was carefully determined with reference to the
neighbouring stars; but on February 24 of the same year, it could not be
seen with a telescope of 15 inches aperture. Some of the other stars in
the group seem to be connected by nebulous rays with the principal
nebulous centres, and in looking at this wonderful Paris chart it seems
impossible to avoid the conclusion that the stars and nebulous masses
are actually mixed up together, and not merely placed accidentally in
the same direction. Indeed, Professor Barnard’s photograph referred to
above shows the whole group involved in dense nebulosity.

Other well-known clusters or groups of stars are the Hyades, marked by
the bright, reddish star, Aldebaran, the Præsepe, or Beehive, in Cancer,
and Comæ Berenices, but these are larger and more scattered.

[Illustration:

FIG. 9.—_The Double Star Cluster in Perseus._

(From “Scenery of the Heavens.”)
]

Of other irregular clusters, somewhat similar to the Pleiades, but not
so bright, may be mentioned the double cluster in Perseus, which is
visible to the naked eye on a clear night as a hazy spot of light in the
midst of the Milky Way. Admiral Smyth says they form “one of the most
brilliant telescopic objects in the heavens.” They may be seen with a
binocular field-glass, but, of course, a good telescope is necessary to
see them well. They have been beautifully photographed at the Paris
Observatory, the photograph showing no trace of nebulosity. They have
also been photographed by Dr. Roberts, who says, “The photograph
presents to the eye the stars in the two clusters, and in the
surrounding parts of the sky, with a completeness and accuracy of detail
never before seen. The stars are shown in their true relative positions
and magnitudes to about the sixteenth, and among them are many apparent
double, triple, and multiple stars. They also appear to be arranged in
clusters, curves, festoons, and patterns that are suggestive of some
physical connexion existing between the groups; but it is premature to
assert that these appearances are not due to perspective effect by the
eye arranging numerous close points of light into various patterns.
Similar photographs to this, taken at intervals of several years between
them, will determine the reality, or otherwise, of these remarkable
groupings of the stars.”

[Illustration:

FIG. 10.—_Star Cluster in Gemini._

(From “Scenery of the Heavens.”)
]

A little north of the star Eta Geminorum is a pretty cluster of small
stars known as 35 Messier, which is just visible to the naked eye. The
component stars may be well seen with a telescope of moderate power.
This cluster has been also photographed at the Paris Observatory, and
shows a well-marked clustering tendency in the component stars. Admiral
Smyth says: “It presents a gorgeous field of stars from the ninth to the
sixteenth magnitude, but with the centre of the mass less rich than the
rest. From the small stars being inclined to form curves of three or
four, and often with a large one at the root of the curve, it somewhat
reminds one of the bursting of a sky rocket.”

[Illustration:

FIG. 11.—_37 Messier._

(From “Worlds of Space.”)
]

About ten degrees to the north of the cluster just described is another
fine cluster known as 37 Messier. The accompanying photograph will show
its telescopic appearance.

In the Southern Hemisphere there is a magnificent cluster of small stars
surrounding the star Kappa Crucis, a reddish star of the seventh
magnitude. It was thus described by Sir John Herschel: “A most vivid and
beautiful cluster of 50 to 100 stars. Among the larger there are one or
two evidently greenish. South of the red star is one, 13 minutes, also
red, and near it one, 12 minutes, bluish ... though neither a large nor
a rich one, is yet an extremely brilliant and beautiful object when
viewed through an instrument of sufficient aperture to show distinctly
the very different colours of its constituent stars, which gives it the
effect of a superb piece of fancy jewellery.” He gives the positions of
110 stars, from the seventh to the sixteenth magnitude. It lies near the
northern edge of the well-known “coal sack,” and Dr. Gould says of it:
“The exquisitely beautiful cluster, κ _Crucis_, contains a large number
of stars of various tints and hues, contrasting wonderfully with each
other, when viewed with a telescope of large aperture.” Mr. Russell’s
drawing of this cluster, made at Sydney (N.S.W.) in 1872, shows several
changes in the relative positions of the stars as laid down by Sir John
Herschel, probably the result of proper motion.

About 2½° north of the star M Velorum, Sir John Herschel describes “an
enormous cluster, of a degree and a half in diameter, very rich in stars
of all magnitudes, from 8 minutes downwards, a sort of telescopic
Præsepe.”

Another fine cluster is that known as 11 Messier. It lies a little to
the west of the star Lambda Aquilæ, and is just visible to the naked eye
on a clear night. It consists of stars of about the eleventh magnitude,
and Admiral Smyth compared it to a “flight of wild ducks.” It has been
beautifully photographed by Dr. Roberts, who says: “The negative shows
the stars individually, though the print, owing to their closeness, does
not separate them.... It is entirely free from nebulosity.”

There are many other similar objects in both hemispheres too numerous to
mention here, but those described are interesting objects of their
class.

[Illustration:

FIG. 12.—_Star Cluster in Hercules._

(From “Scenery of the Heavens.”)
]

We now come to the “globular clusters.” This term has been applied to
those clusters of stars which evidently occupy a space of more or less
spherical form. Some of these “balls of stars,” as they have been
called, are truly wonderful, and are among the most interesting objects
visible in the sidereal heavens. Good specimens of the class are,
however, rather rare objects, and there are not many in the Northern
Hemisphere. The most remarkable, perhaps, is that called “the Hercules
cluster,” but known to astronomers as 13 Messier, it being No. 13 in the
first catalogue of remarkable “nebulæ” formed by Messier, the famous
discoverer of comets. It was discovered by Halley in 1714. This
wonderful object lies between the stars Zeta and Eta in Hercules, nearer
to the latter star. It may be seen with a binocular or good opera-glass
as a hazy star of the sixth magnitude. Messier was certain that it
contained no stars; but when examined with a good telescope it is at
once resolved into a multitude of small stars, which can be individually
seen, and even counted, with large telescopes. According to Admiral
Smyth, “No plate can give a fitting representation of this magnificent
cluster. It is indeed truly glorious, and enlarges on the eye by
studious gazing.” And Dr. Nichol says: “Perhaps no one ever saw it for
the first time through a telescope without uttering a shout of wonder.”
The number of stars included in the cluster was estimated by Sir William
Herschel at 14,000; but the real number is probably much smaller. Were
the number so great as Herschel supposed, I find that the cluster would
form a much brighter object than it does. Assuming the average magnitude
of the component stars at 12½, I find that an aggregation of 14,000
stars would shine as a star of about the second magnitude. But the
cluster is only as bright as a star of about the sixth magnitude, and,
with this magnitude, I find that the total number would be about 400.
Examining it with his giant telescope, Lord Rosse observed three dark
rifts radiating from the centre. These were afterwards seen by Buffham
with a 9-inch reflector, and also by Webb. They were also observed at
Ann Arbor Observatory (U.S.A.), in April, 1887, by Professor Harrington
and Mr. Schaeberle, using telescopes of six and twelve inches aperture.
It has been well photographed at the Paris Observatory, and also by Dr.
Roberts and Mr. Wilson. In some of these photographs the dark rifts are
perceptible to some extent, but owing to the over exposure of the
central portion of the cluster, they are not so distinct as in drawings
made at the telescope. Dr. Huggins, examining it with the spectroscope,
finds that the spectrum is not gaseous; but spectroscopic evidence is
not necessary to prove that the cluster consists of small stars, as
these are distinctly seen as points of light with telescopes of moderate
power, and with the great Lick telescope the component stars are visible
even in the central portion of the cluster. Its globular shape is
evident at a glance, and we cannot doubt that the stars composing it
form a gigantic system, probably isolated in space. Many people might
think that this cluster was a mass of double and multiple stars; but
this is not so. The components, close as they are, are too far apart to
constitute true double stars. Mr. Burnham, the famous double star
observer, finds _one_ close double star near the centre, and notes the
remarkable absence of close double stars in bright and apparently
compressed clusters.

In the same constellation, Hercules, between the stars Eta and Iota, but
nearer the latter, will be found another object of the globular class,
but not so bright or so easily resolvable into stars as the cluster
described above. It is known as 92 Messier. Buffham, with a 9-inch
mirror, thought the component stars brighter and more compressed than in
13 Messier. Sir William Herschel found it seven or eight minutes of arc
in diameter. The brighter components are easily visible in telescopes of
moderate power, but even Lord Rosse’s giant telescope failed to resolve
the central blaze. This object was photographed by Dr. Roberts in May,
1891, with a 20-inch reflecting telescope, and an exposure of one hour.
He says: “The photograph shows the cluster to be involved in dense
nebulosity, which, on the negative, almost prevents the stars being seen
through it, and on the print quite obscures the stars. The stars in
this, as in all other globular clusters, are arranged in various
patterns, and many of them appear to be nebulous.”

About three degrees north preceding the star 9 Boötis, is another fine
globular cluster, known as 3 Messier. Smyth describes it as “a brilliant
and beautiful globular congregation of not less than 1,000 stars,
between the southern Hound and the knee of Boötis; it blazes splendidly
towards the centre, and has outliers.... This mass is one of those balls
of compact and wedged stars, whose laws of aggregation it is so
impossible to assign.” The idea of the component stars being “compact
and wedged” is, however, a mistake, as I have shown elsewhere.[130] Sir
John Herschel described it as a remarkable object, exceedingly bright
and very large, with stars of the eleventh magnitude. Buffham found it
resolved even in the centre with a 9-inch mirror. It was photographed by
Dr. Roberts in May, 1891, with an exposure of two hours, and the
photograph confirms the general descriptions given of the cluster,
though “the print fails to show the stars that on the negative crowd the
space covered by the dense nebulosity.” Dr. Roberts remarks that
“nebulosity seems invariably to be present in globular clusters.” From
photographs of this cluster, taken at Arequipa in Peru, Professor Bailey
finds 87 stars of the cluster to be variable in light, the variability
amounting in some cases to two magnitudes, with usually short periods.

Another fine globular cluster is that known as 5 Messier. It lies
closely north of the fifth magnitude star, 5 Serpentis. It was
discovered by Kirch in 1702, and was observed in 1764 by Messier, who
found he could see it with a telescope of one foot in length, but could
not resolve it into stars. Smyth says: “This superb object is a noble
mass, refreshing to the senses after searching for faint objects, with
outliers in all directions, and a bright central blaze, which even
exceeds 3 Messier in concentration.” Sir William Herschel, with his
40-foot telescope, could count about 200 stars, but could not
distinguish the stars near the central blaze. Sir John Herschel
describes it as an excessively compressed cluster of a globular form,
with stars from the eleventh to the fifteenth magnitude, condensed into
a blaze at the centre. Lord Rosse found it more than seven or eight
minutes of arc in diameter, with a nebulous appearance in the centre.
This cluster was photographed by Dr. Roberts in April, 1892. “The
photograph shows the stars to about the fifteenth magnitude, and the
cluster is involved in dense nebulosity about the centre. The nebulosity
hides the stars even on the negative.” With reference to this latter
remark, however, Dr. Common says[131] that, in photographs of this
cluster taken with a larger instrument, “the stars are quite distinct,
though the exposure was much longer, a result that might fairly be
expected.” From photographs of this cluster taken at Arequipa, Peru, by
Professor Bailey, he finds that the cluster contains about 750 stars, of
which 46 are variable in light, or about 6 per cent. of the whole. This
is remarkable, for, of the stars visible to the naked eye, less than 1
per cent. are variable, so far as is at present known. A further
examination of the photographs made by Miss Leland shows that the
periods of these variables are in general very short, not exceeding a
few hours.[132] One star, situated about eight minutes of arc from the
centre of the cluster, has a probable period of 11 hours, 7 minutes, 52
seconds, and varies from about magnitudes 13·50 to 14·73. The star
remains at the minimum light for about half the period, and the maximum
brightness is of comparatively short duration. The rate of increase is
more rapid than the decrease—as in most short period variables—but in
other respects the character of the light fluctuations does not seem to
be similar to that of any other known variable star.

Another fine object of this class is that known as 15 Messier in
Pegasus, discovered by Maraldi in 1745. Sir John Herschel describes it
as a remarkable globular cluster, very bright and large, and blazing in
the centre. Webb found it a glorious object with a nine and one-third
inch mirror. It was photographed by Dr. Roberts in November, 1890, with
an exposure of two hours. He says: “The photograph confirms the general
descriptions, and the negative shows, separately, the stars of which the
cluster is composed distinctly through the nebulosity in the centre.
Many of the stars have a nebulous appearance, and they are arranged in
curves, lines, and patterns of various forms, with lanes or spaces
between them.”

We may also mention the globular cluster known as 2 Messier, which is
situated about five degrees north of the star Beta Aquarii. It was
discovered by Maraldi in 1746 while looking for Cheseaux’s comet. Sir
William Herschel, with his forty-foot telescope, could “actually see and
distinguish the stars even in the central blaze.” Sir John Herschel
compared it to a mass of luminous sand, and estimated the stars to be of
the fifteenth magnitude. It is about five or six minutes of arc in
diameter, and Smyth says: “This magnificent ball of stars condenses to
the centre, and presents so fine a spherical figure that imagination
cannot but figure the inconceivable brilliancy of the visible heavens to
its animated myriads.” Taking Sir John Herschel’s estimate of the
component stars at fifteenth magnitude, and the total light of the
cluster at sixth magnitude, I find that the total number of stars it
contains would be about 4,000.

[Illustration:

FIG. 13.—_The Star Cluster, Omega Centauri._

(From “Worlds of Space.”)
]

In the Southern Hemisphere there are some magnificent examples of
globular clusters, and indeed, this hemisphere seems to be richer in
these objects than the northern sky. Among these southern clusters is
the truly marvellous object known as Omega Centauri. Its apparent size
is very large—about two-thirds of the moon’s diameter—and it is
distinctly visible to the naked eye as a hazy star of the fourth
magnitude, and I have often so seen it in the Punjab sky. Sir John
Herschel, observing it with a large telescope at the Cape of Good Hope,
describes it as “beyond all comparison, the richest and largest object
of its kind in the heavens. The stars are literally innumerable.... All
clearly resolved into stars of two sizes, _viz._, 13 and 15; the larger
lying in lines and ridges over the smaller.... The larger form rings
like lace-work on it. One of these rings, 1½″ diameter, is so marked as
to give the appearance of comparative darkness, like a hole in the
centre.... On further attention, the hole is double, or an oval space
crossed by a bridge of stars.... Altogether, this object is truly
astonishing.” This wonderful object has recently been photographed by
Dr. Gill, at the Royal Observatory, Cape of Good Hope, and also at
Arequipa, Peru, with a telescope of thirteen inches aperture. On the
latter photograph, the individual stars can be distinctly seen and
counted. The enumeration has been made by Professor and Mrs. Bailey, and
a mean of their counts gives 6,389 for the number of stars in the
cluster, but they consider that the real number is considerably greater.

Another wonderful object is that known as 41 Toucani, which lies near
the smaller “Magellanic Cloud” in the Southern Hemisphere. Humboldt
found it very visible to the naked eye in Peru, and mistook it for a
comet.[133] Sir John Herschel describes it as “a most magnificent
globular cluster. It fills the field with its outskirts; but within its
more compressed part I can insulate a tolerably defined circular space
of 90″ diameter, wherein the compression is much more decided, and the
stars seem to run together, and this part has, I think, a pale pinkish
or rose colour, ... which contrasts evidently with the white light of
the rest.... The stars are equal, fourteen magnitude, immensely
numerous, and compressed.... It is _completely insulated_. After it has
passed, the ground of the sky is perfectly black throughout the whole
breadth of the sweep. There is a double star of eleventh magnitude
preceding the centre, ... condensation in three distinct stages.... A
stupendous object.” Dr. Gould calls it one of the most impressive, and
perhaps the grandest, of its kind in either hemisphere, and he estimated
its apparent magnitude at 4½, as seen with the naked eye.

Another remarkable globular cluster is that known as 22 Messier, which
lies about midway between Mu and Sigma Sagittarii. Sir John Herschel
says: “The stars are of two sizes, _viz._, 15 ... 16 and 12m; and, what
is very remarkable, the largest of these latter are visibly reddish, one
in particular, the largest of all (12–11m) south following the middle,
is decidedly a ruddy star, and so, I think, are all the other larger
ones ... very rich, very much compressed, gradually much brighter in the
middle, but not to a nucleus ... consists of stars of two sizes ... with
none intermediate, as if consisting of two layers, or one shell over
another. A noble object” I saw the larger stars well with a 3-inch
refractor in the Punjab.

Sir John Herschel remarks “the frequent association of nebulæ in pairs
forming double nebulæ,” and in his “Cape Observations” he figures
several examples of this class. One of these is evidently a globular
cluster, with two centres of condensation, one nucleus being much
brighter than the other. Two others, much smaller, show two distinct
nuclei. Another drawing shows apparently two globular clusters in
contact. There are other examples in the Northern Hemisphere. Dr. See
considers that some of these double nebulæ represent an early stage in
the evolution of binary or revolving double stars, and certainly some of
the drawings of these nebulæ are very remarkable and suggestive.

The actual dimensions of the globular clusters is an interesting
question. Are they composed of stars comparable in size and mass with
our sun? or are the component stars really small and comparatively close
together? This is a difficult question to answer satisfactorily, as the
distance of these objects from the earth has not yet been determined.
They may, on the one hand, be collections of suns similar to ours in
size and brightness, and situated at vast distances from the earth; or,
on the other hand, the stars composing them may be comparatively small
objects, lying at a distance from the earth not exceeding that of some
stars visible to the naked eye. Perhaps the latter hypothesis may be
considered the more probable of the two. But there is really no reason
to suppose that these collections of suns are comparatively near our
system. The probability seems to be in favour of their great distance
from the earth. The question of the absolute size of the component stars
is one which, I think, has not been hitherto sufficiently considered.
Let us examine both alternatives, and let us take the cluster Omega
Centauri as one in which the number of the component stars has been
_actually counted_. Assuming that the real number of stars in this
cluster is 10,000, and that they are individually equal, on an average,
to our sun in mass and volume, we may estimate the probable distance and
dimensions of the cluster. Taking the stellar magnitude of Omega
Centauri as four (as estimated at the Cordoba Observatory), I find that,
with the number 10,000, the average magnitude of the component stars
would be fourteen. This agrees with Sir John Herschel’s estimate of
thirteenth to fifteenth magnitude. Now, to reduce the sun to a star of
the fourteenth magnitude, I find that, assuming the sun to be 28
magnitudes brighter than an average star of the first magnitude, it
would be necessary to remove it to a distance of about 158,500,000 times
the sun’s distance from the earth—a distance so great that light would
take no less than 2,500 years to reach us from the cluster! Taking the
apparent diameter of the cluster at twenty minutes of arc, I find that
its real diameter would be 922,000 times the sun’s distance from the
earth—a distance so great that light would take over 14 years to pass
across the cluster. These results are certainly very startling, and
might lead us to suspect that these globular clusters are external
universes. Judging, however, from the average distance recently found
for stars of the first and second magnitude (see p. 423), the distance
of ordinary stars of the first magnitude—on the supposition that they
are of the same size and brightness as the sun, and that their light is
simply reduced by distance—would be about five times greater than that
found above for Omega Centauri. If, then, we increase the distance of
the cluster five times, it would be necessary to increase the diameters
of the component stars to five times that of the sun. This would give
them a volume 125 times that of our sun—a result which seems improbable.
If, on the other hand, we do not like to admit that each of the faint
points of light composing the cluster is equal in volume to our sun, let
us diminish the distance ten times. If we do so, we must also diminish
the diameter of the component stars ten times. This would make them
about the size of the planet Jupiter, and it seems improbable that such
comparatively small bodies could retain their solar heat for any great
length of time. They would probably have cooled down, as Jupiter has
done—at least to a great extent—ages ago, and would not now be visible
as a cluster of stars. Even this reduction of the distance to one-tenth
of the value first found would still leave the cluster at an immense
distance from the earth, a distance represented by 250 years of light
travel! A reduction of the distance to one-tenth of this again, or 25
years of light travel, would make the components about the size of the
earth, and that bodies of this small size could shine with stellar light
seems to be an untenable hypothesis. We seem, therefore, forced to
conclude that these globular star clusters lie at an immense distance
from the earth.

There is, however, another point to be considered with reference to the
size of the bodies composing a globular cluster. This is the character
of their light. I am not aware that the spectrum of a globular cluster
has yet been thoroughly examined, but if that of Omega Centauri is of
the first or Sirian type, it would modify the above conclusions to some
extent. It now seems probable that stars having a spectrum of the Sirian
type are intrinsically brighter than our sun, and I have shown already
that Sirius is considerably brighter than the sun would be if placed at
the same distance, although the mass of Sirius is but little more than
twice the sun’s mass. The components of a star cluster, therefore—if of
the Sirian type of stars—might be as bright as the sun, and at the same
time have a smaller mass and volume. This, however, would not make a
very great difference in the computed vast distance of the cluster, and
the calculations given above seem to point to the conclusion that these
globular clusters are probably composed of stars of average size and
mass, and that the faintness of the component stars is simply due to
their immense distance from the earth.

We will now consider the nebulæ, properly so-called, that is to say,
objects which the spectroscope shows to consist of glowing gas. These
are sometimes large and irregular in form, like the great nebula in the
“Sword” of Orion, sometimes with spiral convolutions, and sometimes of a
definite shape, like the planetary and annular nebulæ.

Of the large and irregular nebulæ, one of the most remarkable is that
known as “the great nebula in Orion.” It surrounds the multiple star,
Theta Orionis, which has been already referred to in a preceding
chapter. It is a curious fact that it escaped the searching eye of
Galileo, although he gave special attention to the constellation of
Orion, for even with a good opera-glass a nebulous gleam is distinctly
visible round the central star of the “Sword.” The nebula seems to have
been discovered by Cysat, a Swiss astronomer, in the year 1618, and it
was sketched by Huygens in 1656. Huygens says: “While I was observing
with a refractor of twenty-five feet focal length, the variable belts of
Jupiter, a dark central belt in Mars, and some phases of this planet, my
attention was attracted by an appearance among the fixed stars, which,
as far as I know, has not been observed by anyone else, and which,
indeed, could not be recognised, except by such powerful instruments as
I employ. Astronomers enumerate three stars in the Sword of Orion, lying
very near one another. On one occasion when, in 1656, I was accidentally
observing the middle one of these stars through my telescope, I saw
twelve stars instead of a single one, which, indeed, not unfrequently
happens in using the telescope. Three of this number were almost in
contact with one another, and _four_ of them shone as if through a mist,
so that the space around them, having the form drawn in the appended
figure, appeared much brighter than the rest of the sky, which was
perfectly clear, and looked almost black. This appearance looked,
therefore, almost as if there were a _hiatus_ or interruption. I have
frequently observed this phenomenon, and up to the present time, as
always unchanged in form; whence it would appear that this marvellous
object, be its nature what it may be, is very probably permanently
situated at this spot. I never observed anything similar to this
appearance in the other fixed stars.”[134] It has been called the
“fish-mouth” nebula, from the fancied resemblance of the centre portion
to the mouth of a fish. A number of small stars are visible over the
surface of the nebula, and at one time, Lord Rosse thought it showed
indications of resolution into stars when examined with his giant
telescope; but this is now known to have been a mistake, for Dr. Huggins
finds, with the spectroscope, that it consists of nothing but glowing
gas, of which hydrogen is certainly one constituent, and he has
succeeded in photographing the complete series of lines of this gas in
the spectrum of the nebula.

Referring to his earlier observations, Dr. Huggins says:—“The light from
the brightest parts of the nebula near the trapezium was resolved by the
prisms into three bright lines, in all respects similar to those of the
gaseous nebulæ. The whole of this great nebula, as far as lies within
the power of my instrument, emits light which is identical in character.
The light from one part differs from the light of another in intensity
alone.” The brightest line in the nebular spectrum—the “chief nebular
line,” as it is called—has not yet been identified with that of any
terrestrial substance. It was at first supposed to be identical with a
line of nitrogen, but this was afterwards disproved. It was then
incorrectly identified with a line of lead, and more recently by Lockyer
with the edge of a “fluting” in the magnesium spectrum. Dr. Huggins and
Professor Keeler, however, have shown conclusively that the nebular line
does not coincide with the magnesium fluting, although very close to it.
Observations by Dr. Copeland in 1886 showed the existence of the yellow
line, know as D_{3}, which is visible in the solar spectrum during total
eclipses of the sun, and indicates the existence of a gas in the sun’s
surroundings, to which the name “helium” has been given. Dr. Copeland
says:—“The recurrence of this line in the spectrum of a nebula is of
great interest, as affording another connecting link between gaseous
nebula and the sun and stars with bright line spectra, especially with
that remarkable class of stars of which the finest examples were
detected by M. M. Wolf and Rayet in the constellation of Cygnus.”[135]
As has been already mentioned in the chapter on variable and new stars,
the bright lines of hydrogen and helium have also been observed in the
spectra of these remarkable objects. The gas, giving the line D_{3} in
its spectrum, has quite recently been discovered by Professor Ramsay in
gases obtained by heating certain terrestrial minerals, so that the
objective existence of the gaseous element “helium”—previously only
suspected—is now definitely established. From recent spectroscopic
observations of the Orion nebula, Dr. Huggins thinks that “the stars of
the ‘trapezium’ are not merely optically connected with the nebula, but
are physically bound up with it, and are very probably condensed out of
the gaseous matter of the nebula.” With reference to this point,
Professor Keeler, who has carefully examined the spectra of the nebula
and the associated stars, says:—“The trapezium stars have spectra marked
by strong absorption bands; they have not the direct connexion with the
nebula that would be indicated by a bright line spectrum, but are, in
fact, on precisely the same footing (spectroscopically) as other stars
in the constellation of Orion. While their relation to the nebula is
more certain than ever, they can no longer be regarded as necessarily
situated _in_ the nebula, but within indefinite limits they may be
placed anywhere in the line of sight.” These results were confirmed by
Professor Campbell. He finds, “that of the twenty-five bright lines
known to exist in the spectrum of the Orion nebula, at least nineteen
are definitely matched by dark lines in the Orion stars, and at least
fifteen by dark lines in the six faint stars situated in the dense parts
of the nebula.”

Numerous drawings of this wonderful nebula have been made. Of these, the
best are those by Sir John Herschel, made at the Cape of Good Hope in
the years 1834–38, by Bond in America, and by Lassell at Malta. The
difficulty of accurately delineating so difficult and delicate an object
has given rise to discrepancies in the drawings, which have led to the
idea that changes of form have occurred, but this seems improbable. The
nebula has been very successfully photographed by Dr. Common and Dr.
Roberts, and these photographs confirm the general accuracy of the later
drawings.

From a consideration of the apparent size of the Orion nebula and its
probable mass and distance from the earth, the late Mr. Ranyard came to
the conclusion that its average density “cannot exceed one ten thousand
millionth of the density of atmospheric air at the sea-level.”[136]

Mr. W. H. Pickering and Dr. Max Wolf have photographed another nebula
surrounding the star Zeta Orionis—the southern star of the “Belt,” which
seems to be connected with the nebula in the “Sword”; and, Prof.
Barnard, using the “lens of a cheap oil lantern” of 1½ inch aperture,
and 3½ inches focal length, has photographed “an enormous curved
nebulosity” stretching over nearly the whole of the constellation of
Orion, and involving the “great nebula.”

[Illustration:

FIG. 14.—_The Orion Nebulæ._

(From “Worlds of Space.”)
]

Prof. Keeler has recently found, with the spectroscope, that the Orion
nebula is apparently receding from the earth at the rate of nearly
eleven miles a second, but this motion may be, in part at least, due to
the sun’s motion in space in the opposite direction. Prof. Pickering
considers that the parallax of the nebula is probably not more than
0·″003, which corresponds to a thousand years’ journey for light!

In the southern constellation, Argo is a magnificent nebula, somewhat
similar in appearance to the great nebula in Orion. It surrounds the
famous variable star Eta Argûs, whose remarkable fluctuations in light
have been already described in the chapter on variable stars. It is
sometimes spoken of as the “key-hole” nebula, owing to a curious opening
of that shape near its centre. It was carefully drawn by Sir John
Herschel at the Cape of Good Hope in the years 1834–38. It lies in a
very brilliant portion of the Milky Way, and Sir John Herschel thus
describes it: “It is not easy for language to convey a full impression
of the beauty and sublimity of the spectacle which the nebula offers as
it enters the field of view of a telescope, fixed in right ascension, by
the diurnal motion, ushered in as it is by so glorious and innumerable a
procession of stars, to which it forms a sort of climax, and in a part
of the heavens otherwise full of interest,” and he adds: “In no part of
its extent does this nebula show any appearance of resolvability into
stars, being, in this respect, analogous to the nebula of Orion. It has,
therefore, nothing in common with the Milky Way, on the ground of which
we see it projected, and may therefore be, and not improbably is, placed
at an immeasurable distance behind that stratum.” Sir John Herschel’s
conclusion as to its physical constitution has been fully confirmed by
the spectroscope, which shows it to consist of luminous gas. As in the
Orion nebula, there are numerous stars scattered over it. Some of these
may possibly have a physical connexion with the nebula, while others may
belong to the Milky Way. The nebula is of great extent, covering an
apparent space about five times the area of the full moon, and its real
dimensions must be enormous. It was photographed by Mr. Russell,
director of the Sydney Observatory, in July, 1890, and the photograph
shows that “one of the brightest and most conspicuous parts of the
nebula”—the swan-shaped form near the centre of Herschel’s drawing—has
“wholly disappeared,” and its place is now occupied by “a great, dark
oval.” Mr. Russell first missed the vanished portion of the nebula in
the year 1871, while examining it with a telescope of 11½ inches
aperture, and the photograph now confirms the disappearance, which is
very remarkable, and shows that changes are actually in progress in
these wonderful nebulæ, changes which may be detected after a
comparatively short interval of time.

[Illustration:

FIG. 15.—_Sir John Herschel’s drawing of the Nebula round Eta Argus._

(From Flammarion’s “Popular Astronomy.”)
]

Smaller than the nebula in Argo, but somewhat similar in general
appearance, is that known as 30 Doradus, which forms one of the numerous
and diverse objects which together constitute the greater Magellanic
Cloud. Sir John Herschel drew it carefully at the Cape of Good Hope, and
describes it as “one of the most singular and extraordinary objects
which the heavens present,” and he says “it is unique even in the system
to which it belongs, there being no other object in either nubecula to
which it bears the least resemblance.” It is sometimes called the
“looped nebula,” from the curious openings it contains. One of these is
somewhat similar to the “key-hole” opening in the Argo nebula. Near its
centre is a small cluster of stars, and scattered over the nebula are
many faint stars, of which Sir John Herschel gives a catalogue of 105
ranging from the ninth to the seventeenth magnitude. I do not know
whether this nebula has been examined with the spectroscope, but its
appearance would suggest that it is gaseous. It is remarkable as being
the only object of its class which is found outside the zone of the
Milky Way.

Among the nebula of irregular shape, although its spectrum is said to be
not gaseous, may be mentioned that known as the “trifid nebula,” or 20
Messier. It lies closely north of the star 4 Sagittarii in a magnificent
region of the heavens. As will be seen in the drawing made by Sir John
Herschel at the Cape of Good Hope, the principal portion consists of
three masses of nebulous matter separated by dark “lanes” or “rifts.”
Near the junction of the three “rifts” is a triple star. A beautiful
drawing of this nebula has also been made by Trouvelot. It agrees fairly
well with that of Sir John Herschel, but shows more detail.

[Illustration:

FIG. 16.—_The Trifid Nebula, Sagittarius._

(From “Scenery of the Heavens.”)
]

Among other gaseous nebula may be mentioned that called by Sir John
Herschel the “dumb-bell” nebula. It lies a little south of the sixth
magnitude star 14 Vulpeculæ, and was discovered by Messier in 1779,
while observing Bode’s comet of that year. In small telescopes it has
the appearance of a dumb-bell, or hour-glass, but in larger telescopes
the outline is filled in with fainter nebulous light, giving to the
whole an elliptical form. Several faint stars have been seen in it, but
these probably belong to the Milky Way, as Dr. Huggins finds the
spectrum gaseous. Dr. Roberts has photographed it, and he thinks that
“the nebula is probably a globular mass of nebular matter, which is
undergoing the process of condensation into stars, and the faint
protrusions of nebulosity in the _south following_ and _north preceding_
ends are the projections of a broad ring of nebulosity which surrounds
the globular mass. This ring, not being sufficiently dense to obscure
the light of the central region of the globular mass, is dense enough to
obscure those parts of it that are hidden by the increased thickness of
the nebulosity, thus producing the ‘dumb-bell’ appearance. If these
inferences are true, we may proceed yet a step, or a series of steps,
farther, and predict that the consummation of the life-history of this
nebula will be its reduction to a globular cluster of stars.”

Among the gaseous nebula may also be included those known as “annular
nebulæ.” These are very rare objects, only a few being known in the
whole heavens. The most remarkable is that known as 57 Messier, which
lies between the stars Beta and Gamma Lyræ, south of the bright star
Vega. It was discovered by Darquier, at Toulouse, in 1779, while
following Bode’s comet of that year. Lord Rosse thought it resolvable
into stars, and so did Chacornac and Secchi, but no stars are
perceptible with the great American telescopes, and Dr. Huggins finds it
to be gaseous. The central portion is not absolutely dark, but contains
some faint nebulous light. Examined with the great telescope of the Lick
Observatory, Professor Barnard finds that the opening of the ring is
filled in with fainter light “about midway in brightness between the
brightness of the ring and the darkness of the adjacent sky.”[137] “The
aperture was more nearly circular than the outer boundary of the nebula,
so that the ends of the ring were thicker than the sides.” The entire
nebula was of a milky colour. A central star, noticed by some observers,
was usually seen by Professor Barnard, but was never a conspicuous
object. He found the extreme dimensions of the nebula about 81″ in
length by about 59″ in width, or more than double the apparent area of
Jupiter’s disc. It has been beautifully photographed by Dr. Roberts, and
he says “the photograph shows the nebula and the interior of the ring
more elliptical than the drawings and descriptions indicate; and the
star of the _following_ side is nearer to the ring than the distance
given. The nebulosity on the _preceding_ and _following_ ends of the
ring protrudes a little, and is less dense than on the _north_ and
_south_ sides. This probably suggested the filamentous appearance which
Lord Rosse shows. Some photographs of the nebula have been taken between
1887 and 1891, and the central star is strongly shown on some of them,
but on others it is scarcely visible, which points to the star being
variable.” On a photograph taken by MM. Androyer and Montaugerand of the
Toulouse Observatory, with an exposure of nine hours (in multiple
exposures), about 4,800 stars are visible on and near the nebula in an
area of three square degrees.

Another object of the annular class will be found a little to the
south-west of the star Lambda Scorpii. It is thus described by Sir John
Herschel: “A delicate, extremely faint, but perfectly well defined,
annulus. The field crowded with stars, two of which are on the nebula. A
beautiful, delicate ring, of a faint, ghost-like appearance, about 40″
in diameter in a field of about 150 stars, eleven and twelve magnitude
and under.”

Near the stars 44 and 51 Ophiuchi is another object of the annular
class, which Sir John Herschel describes as “exactly round, pretty
faint, 12″ diameter, well terminated, but a little cottony at the edge,
and with a decided darkness in the middle, equal to a tenth magnitude
star at the most. Few stars in the field, a beautiful specimen of the
planetary annular class of nebula.”

The Planetary Nebulæ form an interesting class. They were so named by
Sir William Herschel from their resemblance to the discs of the planets,
but, of course, much fainter. They are generally of uniform brightness,
without any nucleus or brighter part in the centre. There are numerous
examples of this class, one of the most remarkable being that known as
97 Messier, which is situated about two degrees south-east of Beta Ursæ
Majoris—the southern of the two “pointers” in the Plough. It is of
considerable apparent size, and even supposing its distance to be not
greater than that of 61 Cygni, its real dimensions must be enormous.
Lord Rosse observed two openings in the centre with a star in each
opening, and from this appearance he called it the “owl nebula.” One of
the stars seems to have disappeared since 1850, and a photograph
recently taken by Dr. Roberts confirms the disappearance.

Another fine object of the planetary class is one which lies close to
the pole of the ecliptic. Webb saw it “like a considerable star out of
focus.” Smyth found it pale blue in colour. Dr. Huggins finds a gaseous
spectrum, the first discovery of the kind made. Professor Holden,
observing it with the great Lick telescope, finds its structure
extraordinary. He says it “is apparently composed of rings overlying
each other, and it is difficult to resist the conviction that these are
arranged in space in the form of a true helix,” and he ranks it in a new
class which he calls “helical nebulæ.”

A somewhat similar nebula lies a little to the west of the star Nu
Aquarii. Secchi believed it to be in reality a cluster of small stars,
but Dr. Huggins finds its spectrum gaseous. A small nebula on each side
gives it an appearance somewhat similar to the planet Saturn, with the
rings seen edgeways. The great Lick telescope shows it as a wonderful
object—“a central ring lies upon an oval of much fainter nebulosity.”
Professor Holden says “the colour is a pale blue,” and he compares the
appearance of the central ring “to that of a footprint left in the wet
sand on a sea beach.”

About two degrees south of the star Mu Hydræ is another planetary
nebula, which Smyth describes as resembling the planet Jupiter in “size,
equable light and colour.” Webb saw it of “a steady, pale blue light,”
and Sir John Herschel, at the Cape of Good Hope, speaks of its colour as
“a decided blue—at all events, a good sky-blue,” a colour which seems
characteristic of these curious objects. Although Sir William Herschel,
with his large telescopes, failed to resolve it into stars, Secchi
thought he saw it breaking up into stars with a “sparkling ring.” Dr.
Huggins, however, finds the spectrum to be gaseous, so that the luminous
points seen by Secchi could not have been stellar.

Sir John Herschel, in his “Cape Observations,” describes a planetary
nebula which lies between the stars Pi Centauri and Delta Crucis. He
says it is “perfectly round, very planetary, colour fine blue ... very
like Uranus, only about half as large again, and blue.... It is of the
most decided independent blue colour when in the field by itself, and
with no lamplight and no bright star. About 10′ north of it is an
orange-coloured star, eighth magnitude. When this is brought into view,
the blue colour of the nebula becomes intense ... colour, a beautiful
rich blue, between Prussian blue and verditer green.”

There are some rare objects called “nebulous stars.” The star Epsilon
Orionis—the centre star of Orion’s Belt—is involved in a great nebulous
atmosphere. The triple star Iota Orionis is surrounded by a nebulous
haze. The star Beta in Canes Venatici is a 4½ magnitude star surrounded
by a nebulous atmosphere.

The term elliptical nebulæ has been applied to those of an elliptical or
elongated shape. This form is probably due in many cases to the effect
of perspective, their real shape being circular, or nearly so. Perhaps
the most remarkable object of this class is the well-known “nebula in
Andromeda,” known to astronomers as 31 Messier. It can be just seen with
the naked eye, on a clear moonless night, as a hazy spot of light near
the star Nu Andromedæ, and it is curious that it is not mentioned by the
ancients, although it must have been very visible to their keen eyesight
in the clear Eastern skies. It was, however, certainly seen so far back
as 905 A.D., and it Is referred to as a familiar object by the Persian
astronomer, Al-Sûfi, who wrote a description of the heavens about the
middle of the tenth century. Tycho Brahé and Bayer failed to notice it,
but Simon Marius saw it in December, 1612, and described it “as a light
seen from a great distance through half-transparent horn plates.” It was
also observed by Bullialdus, in 1664, while following the comet of that
year. It has frequently been mistaken for a comet by amateur observers
in recent years. Closely north-west of the great nebula is a smaller one
discovered by Le Gentil in 1749, and another to the south, detected by
Miss Caroline Herschel in 1783. The great nebula is of an elliptical
shape and considerable apparent size. The American astronomer, Bond,
using a telescope of 15 inches aperture, traced it to a length of about
four degrees, and a width of two and a half degrees. A beautiful
photograph taken by Dr. Roberts in December, 1888 (see p. 398), shows an
extension of nearly two degrees in length, and about half a degree in
width, or considerably larger than the apparent size of the full moon.
Bond could not see any symptom of resolution into stars, but noticed two
dark rifts or channels running nearly parallel to the length of the
nebula. In Dr. Roberts’ photograph these rifts are seen to be really
dark intervals between consecutive nebulous rings into which the nebula
is divided. Dr. Roberts says: “A photograph which I took with the
20-inch reflector on October 10, 1887, revealed for the first time the
true character of the great nebula, and one of the features exhibited
was that the dark bands, referred to by Bond, formed parts of divisions
between symmetrical rings of nebulous matter surrounding the large
diffuse centre of the nebula. Other photographs were taken in 1887,
November 15; 1888, October 1; 1888, October 2; 1888, December 29;
besides several others taken since, upon all of which the rings of
nebulosity are identically shown, and thus the photographs confirm the
accuracy of each other, and the objective reality of the details shown
of the structure of the nebula.” Dr. Roberts adds: “These photographs
throw a strong light on the probable truth of the _Nebular Hypothesis_,
for they show what appears to be the progressive evolution of a gigantic
stellar system.”

The largest telescopes have hitherto completely failed to resolve this
wonderful object into stars. Dr. Huggins, however, finds that the
spectrum is _not_ gaseous, so that if the nebula really consists of
stellar points, they must be of very small dimensions. Assuming a
parallax of one-fiftieth of a second of arc—corresponding to 163 years
of “light travel”—I find that our sun, placed at this distance, would be
reduced in brightness to a star of about the eighth magnitude. If we
assume the components to have only one-hundredth of the sun’s diameter,
they would shine as stars of only the eighteenth magnitude, which no
telescope yet constructed would show as separate points of light. A more
probable explanation, however, seems to be that the nebula may consist
of masses of nebulous matter partially condensed into the solid form,
but not yet arrived at the stage in which our sun is at present. In
other words, the whole nebulous mass may be in a fluid or viscous state,
which might perhaps account for the continuous spectrum found by Dr.
Huggins.

The question may be asked, What is the probable size and distance of
this wonderful nebula? and could it be an external universe? Possibly
its distance from the earth may be even greater than that indicated by
the small parallax I have assumed above, but taking this parallax and
the apparent dimensions of the nebula as shown by Dr. Huggins’
photograph, I find that its real distance would be no less than 330,000
times the sun’s diameter from the earth, a diameter so great that light
would take over five years to pass from one side of the nebula to the
other! This result might lead us to imagine that the nebula may be
really an external universe. But let us consider the matter a little
further. The diameter found above is not very much greater than the
distance of the _nearest_ fixed star, Alpha Centauri, from the earth,
and the limits of _our_ universe are certainly far beyond Alpha
Centauri. If we diminish the parallax to, say ¹⁄₂₀₀th of a second, or a
“light journey” of 652 years, the diameter of the nebula would be
increased to 1,320,000 times the sun’s distance from the earth, or about
five times the distance of Alpha Centauri, and there are probably many
faint stars belonging to our system much farther from the earth than
this.

The temporary star which appeared near the nucleus of the nebula in
August, 1885—already referred to in the chapter on variable stars—was of
the seventh magnitude. I find that our sun, if placed at the distance
indicated by a parallax of ¹⁄₂₀₀th of a second, would be reduced to a
star of about the eleventh magnitude, or four magnitudes fainter than
the temporary star appeared to us. That is to say, the star would have
been—with the assumed distance—about forty times brighter than the sun.
With any greater distance, the star would have been proportionately
brighter, compared with the sun. This seems improbable, and tends to the
conclusion that the nebula is _not_ an external galaxy, but a member of
our own sidereal system, a system which probably includes all the stars
and nebulæ visible in our largest telescopes. Dr. Common, indeed,
suggests that it may be comparatively near our system. He says: “It is
difficult to imagine that such an enormous object, as the Andromeda
nebula must be, is not very near to us; perhaps it may be found to be
the nearest celestial object of all beyond the solar system. It is one
that offers the best chance of the detection of parallax, as it seems to
be projected on a crowd of stars, and there are well defined points that
might be taken as fiducial points for measurement,” and he adds: “Apart
from the great promise this nebula seems to give of determining
parallax, there is a fair presumption that in the course of time, the
rotation of the outer portion may perhaps be detected by observation of
the positions of the two outer detached portions in relation to the
neighbouring stars.”[138] Prof. Hall’s failure to detect any parallax in
the temporary star, as mentioned in the last chapter, is, of course,
against Dr. Common’s idea of its proximity to the earth. Referring to
the latter portion of Dr. Common’s remarks, Mr. C. Easton points
out[139] that a comparison of a drawing by Trouvelot, in 1874, with Dr.
Roberts’ photograph, suggests that the small elongated nebula—_h_
44—which lies to the north of the great nebula, “has turned about 15°
from left to right. The globular nebula (M 32), to the other side of M
31, seems to have slightly shifted its position.”

[Illustration:

FIG. 17.—_Spiral Nebula, 51 Messier._

(From “The Visible Universe.”)
]

The spiral nebulæ are wonderful objects, and were discovered by the late
Lord Rosse, with his great six-foot telescope. Their character has been
fully confirmed by photographs taken by Dr. Roberts. One of the most
remarkable of these extraordinary objects is that known as 51 Messier.
It lies about three degrees south-west of the bright star Eta Ursæ
Majoris—the star at the end of the Great Bear’s tail. It was discovered
by Messier while comet-hunting on October 13, 1773. Telescopes of
moderate power merely show two nebulæ nearly in contact, but Lord Rosse
saw it as a wonderful spiral, and his drawing agrees fairly well with a
photograph taken by Dr. Roberts in April, 1889. The nebula has also been
photographed by Dr. Common. Dr. Roberts says: “The photograph shows both
nuclei of the nebula to be stellar, surrounded by dense nebulosity, and
the convolutions of the spiral in this as in other spiral nebulæ are
broken up into star-like condensations with nebulosity around them.
Those stars that do not conform to the trends of the spiral have
nebulous trails attached to them, and seem as if they had broken away
from the spirals.” A tendency to a spiral structure in the smaller
nebula is also visible on the original negative. Dr. Huggins finds that
the spectrum is _not_ gaseous.

The nebulæ known as 99 Messier is of the spiral form. It lies on the
borders of Virgo and Coma Berenices, near the star 6 Comæ. In large
telescopes it somewhat resembles a “Catherine wheel.” D’Arrest and Key
thought it resolvable into stars. It has been photographed by M. Von
Gothard.

Among the clusters and nebulæ, we may class the Magellanic Clouds, or
Nubeculæ in the Southern Hemisphere, as they consist of stars, clusters,
and nebulæ. These very remarkable objects form two bright spots of milky
light, which, at first sight, look like luminous patches of the Milky
Way, but are in no way connected with the Galaxy. Sir John Herschel,
speaking of the larger cloud, says: “The immediate neighbourhood of the
Nubecula Major is somewhat less barren of stars than that of the Minor,
but it is by no means rich, nor does any branch of the Milky Way
whatever form any certain or conspicuous junction with, or include, it,”
and again he says, with reference to the smaller cloud: “Neither with
the naked eye, nor with a telescope, is any connexion to be traced
either with the greater Nubecula, or with the Milky Way.” The Nubeculæ
are roughly circular in form, and, viewed with the naked eye, they very
much resemble irresolvable nebulæ as seen in a telescope. The larger
cloud, or Nubecula Major, as it is called, is of considerable extent,
and covers about 42 square degrees, or over two hundred times the
apparent size of the full moon. It was called by the Arabs _el-baker_,
or “the White Ox,” and is referred to by Al-Sûfi in his “Description of
the Heavens,” written in the tenth century. When examined with a good
telescope, it is found to consist of about six hundred stars of the
sixth to the tenth magnitude, with many fainter ones, and about three
hundred clusters and nebulæ. Sir John Herschel, in his “Cape
Observations,” says: “The Nubeculæ Major, like the Minor, consists
partly of large tracts and ill-defined patches of irresolvable nebula,
and of nebulosity in every stage of resolution, up to perfectly resolved
stars like the Milky Way, as also of regular and irregular nebulæ
properly so-called, of globular clusters in every stage of
resolvability, and of clustering groups sufficiently insulated and
condensed to come under the designation of ‘clusters of stars.’... It is
evident, from the intermixture of stars and unresolved nebulosity, which
probably might be resolved with a higher optical power, that the
nubeculæ are to be regarded as systems _sui generis_, and which have no
analogues in our hemisphere.”

The smaller Magellanic Cloud, or Nubecula Minor, is fainter to the eye,
and not so rich in the telescope. It covers about 10 square degrees, or
about fifty times the area of the full moon. Sir John Herschel, in his
“Cape Observations,” describes it as “a fine large cluster of very small
stars, 12 ... 18 magnitude, which fills more than many fields, and is
broken into many knots, groups, and straggling branches, but _the whole_
(_i.e._, the whole of the clustering part) is clearly resolved.” It is
surrounded by a barren region remarkably devoid of stars. Sir John
Herschel says: “The access to the Nubecula Minor is on all sides through
a desert.”... “It is preceded at a few minutes in R. A. by the
magnificent globular cluster, 47 Toucani (Bode), but is completely cut
off from all connexion with it; and with this exception, its situation
is in one of the most barren regions in the heavens.” Herschel found the
middle of the cloud clearly resolved into stars, while its edges
remained irresolvable with his large reflector. He says: “The edge of
the smaller _cloud_ comes on as a mere nebula.... We are now _in the
cloud_. The field begins to be full of a faint light perfectly
irresolvable.... I should consider about this place to be the body of
the cloud which is here fairly resolved into excessively minute
stars.... It is not like the stippled ground of the sky. The borders
fade away, quite insensibly, and are less or not at all resolved.”
Herschel gives a catalogue of 244 objects in the Nubecula Minor. Of
these about 200 are stars, and the remainder nebula and clusters. From
this it appears that the smaller nubecula contains a much larger
proportion of stars than the larger cloud.

Judging from their roughly globular form, the dimensions of the
Magellanic Clouds are probably small compared with their distance from
the earth, so that in these remarkable objects—particularly in the
larger cloud—we see stars of the seventh, eighth, ninth, and tenth
magnitude, apparently mixed up with fainter stars, and “clusters of all
degrees of resolvability,” and Sir John Herschel says: “It must
therefore be taken as a demonstrated fact, that stars of the seventh or
eighth magnitude, and irresolvable nebulæ, may co-exist within limits of
distance not differing in proportion more than as 9 to 10.”[140] It
should be remembered, however, that possibly some of the fainter stars
may—as in the Pleiades—lie far out in space beyond the greater
Magellanic Cloud.

The Magellanic Clouds have recently been photographed by Mr. Russell at
the Sydney Observatory. He finds the larger cloud—the Nubecula Major—to
be of a most complex form, with evidence of a spiral structure, a
feature also traceable, but not so clearly, in a photograph of the
Nubecula Minor, or smaller cloud.

Dr. Dreyer’s new index catalogue of recent discoveries of nebulæ,
together with the general catalogue previously published, gives the
position of 9,369 nebulæ.[141] A very small proportion of the new
discoveries have been made by photography, and more than half of them
were found by M. Javelle with the great refractor of the Nice
Observatory. Most of the new objects are very small and faint, and form
probably “only a small portion of the number visible in large
telescopes.”

[Illustration:

FIG. 18.—_Magellanic Clouds._

(From “Worlds of Space.”)
]

Several nebulæ have been suspected of variation in light. One discovered
by Dr. Hind in 1852 near the variable star T Tauri was found to be an
easy object with the great Lick telescope in February, 1895, but in
September of the same year it had “entirely vanished.” In the same
instrument, “T Tauri was involved in a small hazy nebulosity, but the
definite nebula in which it shone in 1890 did not exist in September,
1895.”[142]

CHAPTER VII.
THE CONSTRUCTION OF THE HEAVENS.

The construction of the visible universe is one of great interest, but
of considerable difficulty. If we reflect that in viewing the starry
heavens we are placed at the centre of a hollow sphere of indefinite
extent, and that the distance of only a few of the stars from the earth
has hitherto been ascertained with any approach to accuracy, the great
difficulty of framing a satisfactory theory of the construction of the
heavens will be easily understood.

In considering the subject, let us first inquire as to the probable
number of stars visible in our largest telescopes. Are the visible stars
infinite or limited in number? The reply to this question is easy. As
the number of stars visible to the naked eye is limited, so the number
of stars visible in the largest telescopes is limited also. Those who do
not give the subject sufficient consideration seem to think that the
number of the stars is practically infinite, or at least that the number
is so great that it cannot be estimated. But this idea is totally
incorrect, and due to complete ignorance of telescopic revelations. It
is certainly true that, to a certain extent, the larger the telescope
used in the examination of the heavens, the more the number of the stars
seems to increase; but we now know that there is a limit to this
increase of telescopic vision. And the evidence clearly shows that we
are rapidly approaching this limit. Although the number of stars visible
in the Pleiades rapidly increases at first with increase in the size of
the telescope used, and although photography has still further increased
the number of stars in this remarkable cluster, it has recently been
found that an increased length of exposure—beyond three hours—adds very
few stars to the number visible on the photograph taken at the Paris
Observatory in 1885, on which over 2,000 stars can be counted. Even with
this great number on so small an area of the heavens, comparatively
large vacant spaces are visible between the stars, and a glance at the
original photograph is sufficient to show that there would be ample room
for many times the number actually visible. I find that, if the whole
heavens were as rich in stars as the Pleiades, there would be only 33
millions in both hemispheres.

On a photograph of the region surrounding Gamma Cassiopeiæ, taken by Dr.
Roberts in December, 1895, with a reflecting telescope of 20 inches
aperture, and an exposure of two hours and twelve minutes, he finds
17,100 stars on an area of four square degrees. This would give for the
whole area of the heavens—if equally rich in stars—a total of about 176
millions; but Gamma Cassiopeiæ lies in a rich region of the Milky Way,
and probably the great majority of the stars shown on Dr. Roberts’
photograph belong to the Galaxy, which we know to be especially rich in
stars. One thing is certain, that the heavens as a whole are not nearly
so rich as this particular spot. There may, perhaps, be richer spots
elsewhere in the Milky Way, but in other parts of the sky there are many
regions considerably poorer.

Let us consider a still more extreme case of stellar richness. On a
photograph of the great globular cluster, Omega Centauri, recently taken
in Peru, a count of the stars has been carefully made by Professor and
Mrs. Bailey, and, as stated in the last chapter, the number of stars
contained in the cluster may be taken as 10,000. Now, if the whole sky
were as thickly studded with stars as in this cluster, the total number
visible in the whole heavens would be 1,650 millions, a very large
number, of course, but not much in excess of the present population of
the earth, and I am not aware that the number of the earth’s inhabitants
has ever been described as “infinite.”

Clusters, such as the Pleiades and Omega Centauri, are, of course,
remarkable, and rare exceptions to the general rule of stellar
distribution, and the heavens in general are not—even in the richest
portions of the Milky Way—nearly so rich in stars as the globular
clusters. The fact of these clusters being remarkable objects, proves
that they are unusually rich in stars, and there is strong
evidence—evidence amounting to absolute proof in the case of the
globular clusters—that these collections of stars are really, and not
apparently, close, and that they are actually systems of suns, and
occupy a comparatively limited volume in space. We cannot, then,
estimate the probable number of the visible stars by counting those
visible in one of the globular clusters.

That the number of the visible stars will not probably be largely
increased by any increase in telescopic power, is indicated by the fact
that Celoria, using a small telescope, of power barely sufficient to
show stars to the eleventh magnitude, found that he could see almost
exactly the same number of stars near the north pole of the Milky Way as
were visible in Sir William Herschel’s great telescope! thus indicating
that, here at least, no increase of optical power will materially
increase the number of stars visible in that direction; for Herschel’s
large telescope certainly showed far fainter stars than those of the
eleventh magnitude in other portions of the heavens. It should therefore
have shown fainter stars at the pole of the Milky Way also, if such
stars existed in that region of space. Their absence, therefore, seems
certain proof that very faint stars do _not_ exist in that direction,
and that, here at least, our sidereal universe is limited in extent A
photograph, taken by Dr. Roberts not very far from the spot in question,
shows only 178 stars to the square degree. This rate of distribution
would give a total of only 7,343,000 stars for both hemispheres!

An examination by Miss Clerke of Professor Pickering’s catalogue of
stars surrounding the north pole of the heavens shows that “the small
stars are overwhelmingly too few for the space they must occupy, if of
average brightness; and they are too few in a constantly increasing
ratio.”[143] Here again, a “thinning out” of the stellar hosts seems
clearly indicated, and suggests that a limit will soon be reached,
beyond which our most powerful telescopes and photographic plates will
fail to reveal any further stars.

Let us now consider the number of stars actually visible. Maps of the
northern portion of the heavens have been published by Argelander and
Heis, and charts of the southern sky by Behrmann and Gould. Heis shows
stars to about magnitude 6⅓, and Behrmann to about the same brightness.
I find that the total number shown by both observers, as visible to the
naked eye, is 7,249. The total number, to the sixth magnitude inclusive,
shown by both observers, is 4,181. Argelander gives 5,000 stars to the
sixth magnitude inclusive, and for stars to the ninth magnitude, the
following numbers in each magnitude:—First magnitude, 20; second
magnitude, 65; third magnitude, 190; fourth magnitude, 425; fifth
magnitude, 1,100; sixth magnitude, 3,200; seventh magnitude, 13,000;
eighth magnitude, 40,000; and ninth magnitude, 142,000, or a total of
“200,000 for the entire number of stars from the first to the ninth
magnitude inclusive.”[144] This result agrees closely with an estimate
previously made by Struve. From a formula given by Dr. Gould, deduced
from observations in the Southern Hemisphere, I find the number of stars
to the ninth magnitude inclusive would be 215,674, so that Argelanders
estimate of 200,000 stars to the ninth magnitude inclusive cannot be far
from the truth. It will be seen from Argelanders figures that the number
of stars in each class of magnitude is roughly three times that in the
class one magnitude brighter. Supposing this progressive increase
continued to the seventeenth magnitude—the faintest visible in the great
Lick telescope—I find that the total number of stars would be nearly
1,400 millions, or less than the number found from a consideration of
the cluster Omega Centauri. But it is evident from Celoria’s
observation, referred to above, and from Professor Pickering’s
photographs of stars near the North Pole, that the fainter stars do
_not_ increase in the ratio assumed above. We must therefore conclude
that there is a “thinning out” of the fainter stars at some point below
the ninth magnitude. Taking into consideration the rich regions of the
Milky Way, and the comparatively poor portions of the sky, it is now
generally admitted by astronomers, who have studied this particular
question, that the probable number of stars visible in our largest
telescopes does not exceed 100 millions, a number which, large as it
absolutely is, may be considered as relatively very small, and even
utterly insignificant, when compared with an “infinite number.”

Let us see what richness of stellar distribution is implied by this
number of 100 millions of visible stars. It may be easily shown that the
area of the whole sky, in both hemispheres, is 41,253 square degrees, or
about 200,000 times the area of the full moon. This gives 2,424 stars to
the square degree. The moon’s apparent diameter being slightly over half
a degree (31′ 5″), the area of its disc is about one-fifth of a square
degree. Hence, for 100 millions of stars in the whole star sphere, we
have 485 stars to each space of sky, equal in area to the full moon.
This seems a large number, but stars scattered even as thickly as this
would appear at a considerable distance apart when viewed with a large
telescope and a high power. As the area of the moon’s disc contains
about 760 square minutes of arc, there would not be an average of even
one star to each square minute. A pair of stars half a minute, or 30
seconds, apart, would form a very wide double star, and with stars
placed at even this distance, the moon’s disc would cover about 3,000,
or over six times the actual number visible in the largest telescopes.
In Dr. Roberts’ photograph of the region surrounding Gamma Cassiopeiæ,
which shows over 17,000 stars, on four square degrees, or over 4,000
stars to the square degree, the stars do not seem very crowded, and
there is a good deal of black sky visible between them.

But, in addition to the conclusive evidence as to the limited number of
the visible stars derived from actual observation and the results of
photography, we have indisputable evidence from mathematical
considerations that the number of the visible stars _must necessarily_
be limited. For were the stars infinite in number, and scattered through
infinite space with any approach to uniformity, it may be proved that
the whole heavens would shine with the brightness of the sun. As the
surface of a sphere varies as the square of its radius, and light
inversely as the square of the distance (or radius of the star sphere at
any point), we have the diminished light of the stars exactly
counterbalanced by the increased number at any given distance. For a
distance of say ten times the distance of the nearest fixed star, the
light of each star would be diminished by the square of 10 or 100 times,
but the total number of stars would be 100 times greater, so that the
total star light would be the same. This would be true for _all_
distances. The total light would therefore—by addition—be proportional
to the distance, and hence, for an infinite distance we should have an
infinite amount of light For an infinite number of stars, therefore, we
should have a continuous blaze of light over the whole surface of the
visible heavens. Far from this being the case, the amount of light
afforded by the stars on the clearest nights is, on the contrary,
comparatively small, and the blackness of the background, “the darkness
behind the stars,” is very obvious. According to Miss Clerke (“System of
the Stars,” p. 7), the total light of all the stars, to magnitude 9½, is
about one-eightieth of full moonlight. M. G. l’Hermite found for the
total amount of starlight one-tenth of moonlight; but this estimate is
evidently too high. Assuming the sun’s brightness as 28 magnitudes
brighter than a star of the first magnitude,[145] and Zöllner’s estimate
that sunlight is 618,000 times that of moonlight, I find that the total
light of the stars to magnitude 9½, as stated by Miss Clerke, would be
equivalent to the combined light of about 320,000 stars of the sixth
magnitude, or 3,200 stars of the first magnitude. Even taking M.
l’Hermite’s high estimate of one-tenth of moonlight, the total starlight
would be represented by 25,600 stars of the first magnitude.

To explain the limited number of the visible stars, several hypothesis
have been advanced. If space be really infinite, as we seem compelled to
suppose, it would be reasonable to expect that the number of the stars
would be practically infinite also. But, as I have shown above, the
number of the _visible_ stars is certainly finite, and the number
visible and invisible must be finite also, for otherwise the amount of
starlight would be much greater than it is. To account for the limited
number of visible stars, it has been suggested that beyond a certain
distance in space, there may be an “extinction of light,” caused by
absorption in the luminiferous ether. In a recent paper on this subject,
Schiaparelli, the famous Italian astronomer, suggests that if any
extinction of light really takes place, it may probably be due, not to
absorption in the ether, but to fine particles of matter scattered
through interstellar space. In support of this hypothesis, he refers to
the supposed constitution of comets’ tails, of falling stars, and
meteorites, and he shows that the quantity of matter necessary to
produce the required extinction would be very small—so small, indeed,
that a quantity of this matter scattered through a volume equal to that
of the earth, if collected into one mass, would only form a ball of less
than one inch in diameter. We can readily admit the existence of such a
minute quantity of matter in a fine state of subdivision scattered
through space, but it seems to me much more probable that the limited
number of the visible stars is due, not to any extinction of their light
by absorption in the ether, or by fine particles scattered through
space, but to a real thinning out of the stars as we approach the limits
of our sidereal universe. Celoria’s observation, mentioned above, seems
to prove that near the pole of the Milky Way very few stars fainter than
the eleventh magnitude are visible, even in a large telescope, and Dr.
Roberts’ photographs, taken in the vicinity of the celestial pole,
confirm this conclusion. Now, this paucity of stars of the fainter
magnitudes cannot be due to any absorption of light in the ether, for
numerous stars of the sixteenth magnitude, or perhaps fainter, are
visible in other parts of the heavens, and if in one place, why not in
another? Sir John Herschel’s observations of the Milky Way in the
Southern Hemisphere appear to render the hypothesis of any extinction of
light very improbable. He says that the hypothesis, “if applicable to
any, is equally so to every part of the Galaxy. We are not at liberty to
argue that at one part of its circumference our view is limited by this
sort of cosmical veil, which extinguishes the smaller magnitudes, cuts
off the nebulous light of distant masses, and closes our view in
impenetrable darkness; while at another we are compelled, by the
clearest evidence telescopes can afford, to believe that star-strewn
vistas _lie open_, exhausting their powers, and stretching out beyond
their utmost reach, as is proved by that very phænomenon which the
existence of such a veil would render impossible, _viz._, infinite
increase of number and diminution of magnitude, terminating in complete
irresolvable nebulosity.”

How then are we to explain the limited number of the visible stars? If
space be infinite, as we seem compelled to suppose, the number of the
stars would probably be infinite also, or at least vastly greater than
the number actually visible. It has been suggested that, owing to the
progressive motion of light, the light of very distant stars may
probably not yet have reached the earth, although travelling through
space for thousands of years. But considering the vast periods of time
during which the stellar universe has probably been in existence, this
hypothesis seems very unsatisfactory. The most probable hypothesis seems
to be that all the stars, clusters and nebulæ, visible in our largest
telescopes, form together one vast system, which constitutes our visible
universe, and that this system is isolated by a starless void from other
similar systems which probably exist in infinite space. The distance
between these separate systems—or “island universes,” as they have been
called—may be very great, compared with the diameter of each system, in
the same way that the diameter of our visible universe is very great
compared with the diameter of the solar system. As the sun is a star,
and the stars are suns, and as our sun is separated from his neighbour
suns in space by a sunless void, so may our universe be separated from
other universes by a vast and starless abyss. On this hypothesis, the
supposed extinction of light—which may have little or no perceptible
effect within the limits of our visible universe—may possibly come into
play across the vast and immeasurable distances which probably separate
the different universes from each other, and may perhaps extinguish
their light altogether.

Another hypothesis which also seems possible is that the luminiferous
ether which extends throughout our visible universe may perhaps be
confined to this universe itself, and that beyond its confines, the
ether may thin out, as our atmosphere does at a certain distance from
the earth, and finally cease to exist altogether, ending in an
_absolute_ vacuum, which would, of course, arrest the passage of all
light from outer space, and thus produce “the darkness behind the
stars.”

Let us now consider the apparent distribution of the stars and nebulæ on
the celestial vault, and their probable relation to each other in space.
As already stated, Argelander considered the number of stars of the
first magnitude to be about twenty, but modern photometric measures have
reduced this number to thirteen or fourteen. According to the Harvard
measures, the fourteen brightest stars in the heavens, in order of
magnitude, are: Sirius, Canopus, Arcturus, Capella, Vega, Alpha
Centauri, Rigel, Procyon, Achernar, Beta Centauri, Betelgeuse, Altair,
Aldebaran and Alpha Crucis. Seven of these are in the Northern
Hemisphere, namely: Arcturus, Capella, Vega, Procyon, Betelgeuse,
Altair, and Aldebaran; and seven in the Southern Hemisphere: Sirius,
Canopus, Alpha Centauri, Rigel, Achernar, Beta Centauri, and Alpha
Crucis, so that the brightest stars are pretty evenly distributed
between the two hemispheres. Of these bright stars, no less than twelve
lie in or near the Milky Way, Arcturus and Achernar being the only two
at any considerable distance from the Galaxy. This is very remarkable
and suggestive, as the area covered by the Milky Way is probably not
more than one-fourth of the whole star sphere.

Of the stars fainter than the first magnitude, but brighter than
magnitude 2·0, there are about 10 in the Northern Hemisphere, of which 4
lie in or near the Milky Way, and about 19 in the Southern Hemisphere,
of which no less than 14 are situated in or near the Galaxy.

Of those brighter than magnitude 3·0, I find 33 stars in or near the
Milky Way out of a total of about 95 in both hemispheres. To extend this
investigation to all stars visible to the naked eye, I made, some years
since, an examination of all the stars in Heis’ atlas that lie in the
Milky Way, and found that number to be 1,186 out of a total of 5,356, or
a percentage of about 22. At my request, Col. Markwick, F.R.A.S., made a
similar count for the stars in Dr. Gould’s charts of the Southern
Hemisphere (_Uranometria Argentina_), and found that, down to the fourth
magnitude, there are 121 stars on the Milky Way out of 228, or a
percentage of 53, and for all stars to the seventh magnitude inclusive,
there are 3,072 on the Milky Way out of a total of 6,694, or a
percentage of nearly 46. Col. Markwick finds that the Milky Way in the
Southern Hemisphere, as shown on Gould’s charts, covers about one-third
of the whole hemisphere. As will be seen by the above figures, the
percentage of stars, even to the fourth magnitude, lying on the Milky
Way is considerably greater than this proportion.

The above results show that the brighter stars which are apparently
projected on the Milky Way probably belong to that zone, and are not
merely fortuitously scattered over the surface of the heavens.

To extend the investigation still further, and include stars to the
eighth magnitude, I made an examination of the stars shown on Harding’s
charts to that magnitude, in a zone of 30° in width—15° degrees on each
side of the Equator—and found a marked increase in the number of stars
where the zone crossed the Milky Way. The numbers per hour of Right
Ascension varied from a minimum of 275 (hours I. and II.) to maxima of
601 in the Milky Way in Monoceros, and 611 in the Galaxy in Serpens and
Aquila. A valuable investigation by the late Mr. Proctor went further
still. He plotted all the stars shown in the charts of Argelander’s
_Durchmusterung_, which contains stars to 9½ or 10th magnitude. In this
remarkable chart the course of the Milky Way is clearly defined by a
marked increase of stellar density. Proctor says: “In the very regions
where the Herschelian gauges showed the minutest telescopic stars to be
most crowded, my chart of 324,198 stars shows the stars of the higher
orders (down to the eleventh magnitude) to be so crowded that, by their
mere aggregation within the mass, they show the Milky Way with all its
streams and clusterings. This evidence, I venture to affirm, is
altogether decisive as to the main question, whether large and small
stars are really intermixed in many regions of space, or whether the
small stars are excessively remote. It is utterly impossible that
excessively remote stars could seem to be clustered exactly where
relatively near stars are richly spread. This might happen, no doubt, in
a single instance; but that it could be repeated over and over again, so
as to account for all the complicated features seen in my chart of
324,198 stars, I maintain to be utterly incredible.”[146]

From a careful examination of the Milky Way in Aquila and Cygnus, Mr.
Easton finds that “(1) In the zones considered, the distribution of
stars down to 9·5 magnitude corresponds to the greater or less intensity
of galactic light. (2) There is a real correspondence of the general
outlines of the galactic forms with the distribution of 11 magnitude
stars, and with those of stars between 10 and 15 magnitude. (3) Thus, in
general, for the zones considered, the faint stars which form the Milky
Way are thickly or sparsely scattered in respectively the same regions
as the stars in Argelander’s last class; it follows, therefore, with a
great degree of probability, that there is a real connexion between the
distribution of 9 and 10 magnitude stars and that of the very faint
stars of the Milky Way. Consequently, the very faint stars are at a
distance which does not greatly exceed that of 9–10 magnitude stars. If
stars of 13–15 magnitude were at their theoretical distance, there would
be no reason why they should have the same apparent distribution in
galactic latitude and longitude as 9–10 magnitude stars separated from
them by enormous intervals.”[147]

There are some regions in both hemispheres especially rich in naked eye
stars. Of these the following may be mentioned in the Northern
Hemisphere:—the region including the Pleiades, and Hyades in Taurus, the
Northern portion of Orion, and the adjoining part of Gemini, the
constellation Lyra, the northern portion of Cygnus, Cassiopeia’s Chair,
and Coma Berenices. In the Southern Hemisphere there are several rich
spots. A rich region extends from Canis Major to the Southern Cross, and
nearly coincides with the course of the Milky Way. The richest spot of
all, and perhaps the richest in the whole heavens in naked eye
stars—with exception of the Pleiades—is that including the Southern
Cross. This spot has an average of three stars to five square degrees,
and if the whole heavens were as richly studded with stars there would
be about 24,000 visible to the naked eye! The poverty of the adjoining
“coal sack” is very remarkable. Another rich spot surrounds the variable
star Eta Argûs, and the great nebula in Argo. There is another rich spot
in the constellation Hydrus, not far from the greater Magellanic Cloud,
and another will be found in Centaurus and Lupus, with its centre about
Alpha of the latter constellation. According to Gould’s maps of the
Southern Hemisphere, the richest region in stars down to the seventh
magnitude is the southern portion of that part of the constellation
Argo, known as Puppis.

In contrast to these rich regions, and in many cases closely adjoining
them, are some barren regions, very poor in naked eye stars. For
example, closely following the rich spot in Cassiopeia and between Iota
Cassiopeiæ and Eta Persei is a remarkably poor spot, where a space of
some sixty square degrees does not contain a single star brighter than
the sixth magnitude! There is another poor region south of Alpha Hydræ,
and another in the southern portion of the constellation Cetus.

A region of considerable extent, remarkably deficient in bright stars,
will be noticed in the Northern Hemisphere. This comparatively barren
region, which contains no star brighter than the fourth magnitude, is
bounded by Cepheus, Cassiopeia, Perseus, Auriga, Gemini, Ursa Major,
Draco, and Ursa Minor, and forms a conspicuous feature in the
north-eastern portion of the sky in the early winter evenings. It will
be noticed that the surrounding constellations all contain bright stars.

Whether the apparent crowding of stars in certain regions of the heavens
is caused by a real proximity in space, or whether it is merely due to
their being placed accidentally in the line of sight, is a question
difficult to determine. In the case of star clusters, and especially the
globular clusters, there is a high mathematical probability, amounting
almost to absolute certainty, that they are comparatively close
together, but in groups scattered over a considerable area, like those
referred to above, the probability in favour of proximity is not so
great. As we know the distance of so few stars from the earth, it is
impossible to say whether the crowding is real or only apparent, but the
probability seems to be that it is to some extent real.

A tendency to an arrangement of stars in streams was pointed out by
Proctor in his “Universe and the Coming Transits.” This tendency to
stream formation may be noticed on a large scale among the naked eye
stars, for example, in Pisces, Scorpio, the River Eridanus, Aquarius,
and the festoon of stars in Perseus. In some of these cases, of course,
the stars are so far apart that the formation may be more apparent than
real, but the tendency can also be clearly recognised among the fainter
stars, and even among those only visible in telescopes and stellar
photographs. This tendency to run in streams is well marked on the
photographs taken at the Paris Observatory, and on those taken by
Professor Barnard, Dr. Max Wolf, and others. It is a suggestive fact
that these star streams are also very noticeable in star clusters, where
there can be little or no doubt of a physical connexion between the
component stars. With reference to a photograph of the southern portion
of Aquila taken by Dr. Max Wolf in July, 1892, the late Mr. Ranyard,
remarked: “Some of the streams of fainter stars in this region are very
striking, and must convince the most sceptical of their reality. It is
possible to draw an arc of a circle through any three stars, and a conic
section through any five; but where we find ten or twenty stars falling
into line, not once, but in many cases, and that there is a curious
similarity between the strange curves and branching streams which these
phalanges of stars mark out on the heavens, there is no room left for
doubt that the mind is not being led away by a tendency of the
imagination similar to that which finds faces in the fire, or sees a man
carrying sticks on the face of the moon. If it is proved that a group of
stars is arranged in line or marshalled in any order, it would follow
that the individuals of the group must be actually as well as apparently
close to one another, and that they form some kind of system, having all
of them had a common origin, or been subject to some common
influence.”[148]

The great majority of the star clusters are found along the course of
the Milky Way, while the irresolvable nebulæ seem to congregate towards
the poles of the galactic zone.

Dr. Gould is of opinion that “a belt or stream of bright stars appears
to girdle the heavens very nearly in a great circle, which intersects
the Milky Way at about the points of its highest declination, and forms
with it an angle not far from 20°; the southern node being near the
margin of the Cross, and the northern in Cassiopeia.” According to
Gould, this belt covers Orion, Canis Major, Columba, Puppis, Carina, the
Southern Cross, Centaurus, Lupus, and the head of Scorpion in the
Southern Hemisphere, its northern course being indicated by the
brightest stars in Taurus, Perseus, Cassiopeia, Cepheus, Cygnus, and
Lyra. Dr. Gould considers that our sun may possibly be a member of this
belt of stars, which perhaps numbers less than 500, and which constitute
“a small cluster, distinct from the vast organisation of that which
forms the Milky Way, and of a flattened and somewhat bifid form. The
southern portion of this supposed stream of bright stars had been
previously recognised by Sir John Herschel, who says in his ‘Cape
Observations,’ (p. 385), ‘It is about this region, or, perhaps, somewhat
earlier, in the interval between η Argus and α Crucis, that the galactic
circle, or medial line of the Milky Way may be considered as crossed by
that zone of large stars, which is marked out by the brilliant
constellation of _Orion_, the bright stars of Canis Major, and almost
all the more conspicuous stars of _Argo_, the Cross, the Centaur, Lupus,
and _Scorpion_. A great circle passing through ε Orionis and α Crucis
will mark out the axis of the zone in question, whose inclination to the
galactic circle is, therefore, about 20°, and whose appearance would
lead us to suspect that our nearest neighbours in the sidereal system
(if really such) form part of a subordinate sheet or stratum deviating
to that extent from parallelism to the general mass which, seen
projected on the heavens, forms the Milky Way.’”

These conclusions might seem probable enough when we compare the
supposed zone of bright stars with the very diagrammatic drawings of the
Milky Way as shown in many star maps; but when we consider the stars
referred to with reference to the more artistic and accurate
delineations of the Milky Way as drawn by Boeddicker, and even by Gould
himself, we see that most of them are involved in the milky light of the
Galaxy, and their connexion with the Milky Way itself seems quite as
probable as that they form a belt distinct from the galactic zone. The
apparent connexion of the stars in question with the Milky Way does not,
however, disprove the existence of Dr. Gould’s belt or zone of bright
stars. If the plane of the supposed belt nearly coincided with that of
the Milky Way, the apparent connexion might not be real.

Mr. J. R. Sutton advances the theory[149] that the Milky Way consists of
“a great ring of large stars”—Dr. Gould’s solar cluster above referred
to—“intersecting an equal ring of small ones (the Milky Way) at the
extremities of a common diameter.” He considers that “the great star
belt is a genuine girdle of stars in space, in which also the
foundations of the sidereal system are laid, the Milky Way being an
appendant to it of lesser rank.”

That the Milky Way really forms a ring of stars in space there is strong
evidence to show. Sir William Herschel’s original theory that the
galactic gleam is due to our sun being situated near the centre of an
indefinite stratum of stars—the “disc theory,” as it is termed—was
abandoned by its illustrious author in his later writings, and is now
considered to be wholly untenable by nearly all astronomers who have
studied the subject. Sir John Herschel remarks that the general aspect
of the galaxy near the Southern Cross indicates “that the Milky Way, in
this neighbourhood, at any rate, is really what it appears to be, a belt
or zone of stars separated from us by a starless interval.” It certainly
seems utterly improbable that the nearly circular blank space near the
Southern Cross, known as “the coal sack,” should represent a tunnel
through a disc, of which the thickness is comparatively small, while its
diameter, on the “disc theory,” stretches out almost to infinity. A
straight, tunnel-shaped opening of great length, pointing directly
towards the earth, would form an extraordinary phenomenon even in a
solitary instance; yet there are several somewhat similar openings to be
found in the Milky Way, as viewed both with the naked eye and with a
telescope. That _all_ these openings should represent tunnels radiating
from a common centre is quite beyond the bounds of probability, and,
indeed, such an hypothesis does not deserve serious consideration. With
reference to a photograph of the Milky Way in the constellation Cepheus,
Professor Barnard says, “the sky (or Milky Way) is broken up into
numerous black cracks or crevices. Looking at these peculiar features, I
cannot well see how one can avoid the conclusion that they are
necessarily real vacancies in the Milky Way, through which we look out
into the blackness of space.”[150] Using a telescope with a low power,
Mr. S. M. Baird Gemmill says, “December 1, 1886. In sweeping over the
constellation of Monoceros, I was much struck with the reticulated
character of the arrangement of the brighter stars upon the glimmering
background, and the way in which this background seemed to follow the
reticulation. By ‘brighter stars’ are meant stars of from 8 to 10
magnitude, for it was among these that I noticed this peculiarity of
arrangement. It put me in mind of M. M. Henry’s photographs of Cygnus.
The region seemed, in fact, a vast network of stars, the reticulations
of which were separated by desert, or comparatively desert spaces.”[151]
I have noticed the same thing myself while examining the Milky Way with
a binocular field-glass. On October 26, 1889, I noted as follows: “North
of Alpha Cygni, and near Xi and Nu Cygni, the nebulous light of the
Milky Way seems to cling round and follow streams of small stars in a
very remarkable way; numerous small ‘coal sacks’ and rifts are visible,
in which comparatively few stars are to be seen with the binocular.”
This observation has been fully confirmed by photographs of this region,
taken by Dr. Max Wolf in 1891.

[Illustration:

FIG. 19.—_Photograph of Milky Way, Sagittarius._

(From “Visible Universe.”)
]

That the Milky Way is not indefinitely extended in the line of sight
seems clearly shown by Sir John Herschel’s observations in the Southern
Hemisphere. In his “Outlines of Astronomy” (p. 578), he says: “When
examined with powerful telescopes, the constitution of this wonderful
zone is found to be no less various than its aspect to the eye is
irregular. In some regions, the stars of which it is wholly composed are
scattered with remarkable uniformity over immense tracts, while in
others the irregularity of their distribution is quite as striking,
exhibiting a rapid succession of closely clustering rich patches,
separated by comparatively poor intervals, and indeed, in some
instances, by spaces absolutely dark _and completely void of any
star_,[152] even of the smallest telescopic magnitude.... In some, for
instance, extremely minute stars, though never altogether wanting, occur
in numbers so moderate, as to lead us irresistibly to the conclusion
that, in those regions, we see _fairly through_ the starry stratum,
since it is impossible otherwise (supposing their light not
intercepted), that the members of the smaller magnitude should not go on
increasing _ad infinitum_. In such cases, moreover, the ground of the
heavens, as seen between the stars, is for the most part perfectly dark,
which again would not be the case if innumerable multitudes of stars,
too minute to be individually discernible, existed beyond. In other
regions we are presented with the phænomenon of an almost uniform degree
of brightness of the individual stars, accompanied with a very even
distribution of them over the ground of the heavens, both the larger and
smaller magnitudes being strikingly deficient. In such cases it is
equally impossible not to perceive that we are looking _through_ a sheet
of stars nearly of a size and of no great thickness compared with the
distance which separates them from us. Were it otherwise, we should be
driven to suppose the more distant stars uniformly the larger, so as to
compensate by their greater intrinsic brightness for their greater
distance, a supposition contrary to all probability. In others again,
and that not unfrequently, we are presented with a double phænomenon of
the same kind, _viz._, a tissue, as it were, of large stars spread over
another of very small ones, the intermediate magnitude being wanting.
The conclusion here seems equally evident that in such cases we look
through two sidereal sheets separated by a starless interval.”

An examination of the evidence at present available, with reference to
the distribution of the visible stars in space, has recently been
undertaken by Professor Kapteyn of Groningen, and an account of the
conclusions he has arrived at may prove of interest to the reader.

[Illustration:

FIG. 20.—_The Milky Way._

(From _Knowledge_, Nov., 1894.)
]

We must first explain that in order to obtain a clear view of the
construction of the visible universe, it would be necessary to know the
relative distances of a large number of stars; but as the distances of
only a few stars from the earth have yet been determined by actual
measurement, and the results hitherto obtained are open to much
uncertainty, we must have recourse to some other method of estimating
the distances. While travelling in a railway carriage, if we fix our
attention on trees, buildings, and other objects we pass on our journey,
it will be noticed that all objects apparently move past us in the
opposite direction to that in which we are travelling, and that the
nearer the object is the faster it seems to move with reference to
distant objects near the horizon. So it is with the stars. As we showed
in Chapter III., the sun is moving through space, carrying along with
the earth all the planets, satellites, and comets, forming the solar
system. The effect of this motion is to cause an apparent small motion
of the stars in the opposite direction, and the nearer the star is to
the earth, the greater will this apparent motion seem to be as in the
case of the railway train. In addition to this apparent motion, the
stars are themselves—like the sun—moving through space, and this _real_
motion is also visible. If this real motion takes place in the
_opposite_ direction to that in which the sun and earth are moving, it
will add to the apparent motion, and will increase the star’s “proper
motion,” as it is termed. If, on the other hand, the real motion is in
the _same_ direction as the earth’s motion, the proper motion will be
diminished. In either case, the nearer the star is to the earth, the
greater will be its apparent annual displacement on the background of
the heavens. The amount of the “proper motion” is, therefore, considered
by astronomers to form a reliable criterion of the star’s distance from
the earth, and the actual measures of distance which have been made show
that this assumption is approximately true. Of fourteen stars which have
proper motion of over three seconds of arc per annum, eleven have
yielded a measurable parallax, or displacement, due to the earth’s
annual motion round the sun; that is to say, eleven out of fourteen
fast-moving stars are within a measurable distance of the earth, and
are, therefore, near us, when compared with the great majority of stars
which are not within measurable distance, or, at least, are beyond the
reach of our present methods of measurement.

In the case of small groups of stars, we may assume that the real
motions of the individual stars take place indifferently in all
directions, and that consequently, taking an average of all the motions
of the stars composing the group, the effects due to the real motions
will destroy each other, and there will remain, as the most reliable
criterion, the effect due to the sun’s motion in space. If, however, we
compare the proper motions of groups situated in _different parts_ of
the sky, there is a consideration which, to a great extent, vitiates
this conclusion. For, near the point of the heavens, towards which the
sun and earth are moving, known as the “apex of the solar way,” and
probably situated not far from the bright star Vega, as indicated by
recent researches, and near the point away _from_ which the sun is
moving known as the _ant-apex_, about 15° south of Sirius, there will be
no apparent displacement due to the solar motion through space, as this
motion takes place in the line of sight with reference to these points
of the sky. The observed proper motion at these points will, therefore,
be solely due to the real motions of the stars themselves in those
regions. In other parts of the heavens, however, the total proper motion
will be a combination of the apparent and real motions of the stars, and
for stars in different parts of the sky, it will not follow that stars
having equal proper motions are necessarily at the same distance from
the earth. To make this point clearer, let us suppose that there are two
stars at absolutely the same distance from the earth, one situated at or
near the solar “apex,” and the other at a point 90° from the apex, and
let us suppose that both stars are moving through space with exactly the
same velocity and in the same direction, say at right angles to the
direction of the solar motion. Then in the case of the star near the
apex, the observed “proper motion” will be solely due to the star’s real
motion, and in the star 90° distant from the apex, the proper motion
will be solely due to the solar motion, as the star’s _real motion_,
being in the line of sight, will not be visible. Now, unless the stellar
motion and the solar motion happen to be equal, the observed “proper
motions” will not be equal, although both stars are at the same distance
from the earth. If both the stars are really at rest, the star at the
apex will have no proper motion, while the star 90° distant will have an
apparent proper motion due to the sun’s motion. To overcome this source
of error in estimating the distance of a star from its proper motion,
Professor Kapteyn made use of another measure, which is independent of
the solar motion. This is the component of the proper motion measured at
right angles to a great circle of the sphere passing through a star and
the solar apex. The amount of motion in this direction will evidently
not be affected by the sun’s motion, and from a discussion of the stars,
contained in the Draper “Catalogue of Stellar Spectra,” which were
observed by Bradley (and of which the proper motions are now known with
accuracy), Professor Kapteyn finds that this motion is “nearly inversely
proportional to the distance,” that is, the greater the motion, the less
the distance of the stars, and the smaller the motion, the greater the
distance. Excluding stars with proper motions greater than half a second
of arc per annum, Professor Kapteyn found that for stars at various
distances from the Milky Way this component of the “proper motion” forms
a good measure of distance.

As the result of his investigations on the subject, Professor Kapteyn
arrives at the following conclusions. Neglecting stars with small or
imperceptible proper motions, we have a group of stars which no longer
show any condensation in a plane. Stars with very small or no proper
motions show a condensation towards the plane of the Milky Way. This
applies to stars of the second or solar type, as well as to those of the
first or Sirian type of spectrum, and evidently indicates that the stars
composing the Milky Way lie at a great distance from the earth. The
extreme faintness of the majority of the stars composing the Galaxy
seems in favour of this conclusion. The condensation of stars of the
first type is more marked than those of the second, and this agrees with
the fact which has been noticed by Professor Pickering, that the
majority of the brighter stars of the Milky Way have spectra of the
Sirian type.

Professor Kapteyn finds that this condensation of stars with small
proper motions is very perceptible even for stars visible to the naked
eye, and is as well marked in those stars which have spectra of the
second type as for all the stars of the ninth magnitude; but for stars
of the first type the condensation is still more marked. He considers
that this condensation is either partly real, or that there is a real
thinning out of stars near the pole of the Milky Way. As already
mentioned (in the beginning of this chapter), Celoria’s observations
with a small telescope, compared with Sir William Herschel’s
observations with a large telescope, indicate clearly that there _is a
real thinning out_ of stars near the poles of the Galaxy.

Professor Kapteyn concludes that the arrangement of the stars suggested
by Struve—a modification of the “disc theory”—has no real
existence.[153] He attributes the fallacy in Struve’s hypothesis to the
fact that the mean distance of stars of a given magnitude in the Milky
Way, and outside it, is not the same.

Professor Kapteyn finds that the vicinity of the sun is almost
exclusively occupied by stars of the second or solar type, a conclusion
which evidently tends to strengthen Dr. Gould’s theory of a “solar
cluster.” He finds that the number of Sirian type stars increases
gradually with the distance, and that beyond a distance corresponding to
a proper motion of about ¹⁄₁₄th of a second of arc per annum, the Sirian
stars largely predominate. In the group of stars known as the Hyades,
however, the components of which have a common proper motion both in
amount and direction, stars of the first and second types appear to be
mixed, and Professor Kapteyn assumes that the two types represent
different phases of evolution, and that as the brightest stars of the
group are chiefly of the solar type, these stars must be the largest of
the group. From this fact he concludes the solar type stars are in a
less advanced stage of evolution than those of the Sirian type. This
does not agree with the generally accepted view. Professor Vogel
considers the Sirian stars to represent an earlier stage of stellar
evolution. Mr. Proctor held the same opinion, and in Professor Lockyer’s
hypothesis of increasing and decreasing temperatures in stars of various
types, he places the Sirian stars at the summit of the evolution curve,
and the sun and solar stars just below them on the descending branch of
the curve.[154] These hypotheses are in conformity also with the current
opinion that the sun is a cooling body. The discrepancy may perhaps be
explained by supposing that the _brighter_ stars of the Hyades form a
connected group, and that some, at least, of the fainter stars do not
belong to the group, but lie at a great distance behind it. In the case
of the Pleiades, which form a more evident cluster, I find from the
Draper “Catalogue of Stellar Spectra” that the great majority of the
brighter stars have spectra of the Sirian type. Most of the stars in the
Pleiades have a very similar proper motion, both in amount and in
direction, and there can be no doubt that most of the brighter stars, at
least, form a connected system. As already stated, it seems highly
probable that the fainter stars in the Pleiades lie far beyond the
brighter components, and have merely an optical connexion with them, and
the same may be the case in the Hyades. The superior brilliancy of the
stars composing the Hyades would suggest that they are nearer to the
earth than the Pleiades group, and they may possibly form members of
Gould’s “solar cluster.”

Assuming that the distances are inversely proportional to the proper
motions, Professor Kapteyn computes the relative volumes of the
spherical shells which contain the stars with different proper motions
(from one-tenth of a second to one second of arc and more). Comparing
these volumes with the corresponding number of stars, we arrive at an
estimate of the density of star distribution at various distances. The
result of this calculation shows that the distribution of stars of the
Sirian type approaches uniformity when a large number of the faint stars
(ninth magnitude) are considered. With reference to the stars of the
second type, however, the larger the proper motion the greater the
number of the stars; or, in other words, the second type, or solar
stars, are crowded together in the sun’s vicinity. Evidence in favour of
this conclusion is afforded by the fact that, of eight stars having the
largest measured parallax (and whose spectrum has been determined), I
find that seven have spectra of the solar type. The exception is Sirius,
which is evidently an exceptional star with reference to its brightness
and comparative proximity to the earth, no other star of the first
magnitude having nearly so large a parallax. Indeed, the average
distance of all the first magnitude stars is about forty times the
distance of Sirius.

Professor Kapteyn finds that the centre of greatest condensation of the
solar type stars lies near a point situated about ten degrees to the
west of the great nebula in Andromeda, and that this centre nearly
coincides with the point which, according to Struve and Herschel,
represents the apparent centre of the Milky Way considered as a ring.
This would indicate that the sun and solar system lie a little to the
north of the Milky Way, and towards a point situated in the northern
portion of the constellation of the Centaur. The fact is worth noting,
that the nearest fixed star to the earth, Alpha Centauri, lies not very
far from this point. Possibly there may be other stars in this direction
having a measured parallax, as the southern portion of the heavens has
not yet been thoroughly explored.

Professor Kapteyn finds that for stars of equal brightness, those of the
Sirian type are, on an average, about two and three-quarter times
farther from the earth than those of the solar type. Now, as light
varies inversely as the square of the distance, this would imply that
the Sirian stars are intrinsically brighter than those of the solar
type. This conclusion is confirmed by the great brilliancy of Sirius and
other stars of the same type in proportion to their mass. I have shown
in Chapter IV. that Sirius is about ten times brighter than the sun
would be if placed at the same distance, although its mass is only twice
the sun’s mass, as computed from the orbit of its satellite.

The general conclusions to be derived from the above results seems to be
that the sun is a member of a cluster of stars, possibly distributed in
the form of a ring, and that outside this ring, at a much greater
distance from us than the stars of the solar cluster, lies a
considerably richer ring-shaped cluster, the light of which, reduced to
nebulosity by immensity of distance, produces the Milky Way gleam of our
midnight skies.

INDEX

Aberration of light, discovered, 18;
a proof of the earth’s revolution, 57;
of meteor-radiants, 396

Aboul Wefa, the moon’s variation, 5

Acceleration, 152

Achromatic lens, 177

Adams, 449;
discovery of Neptune, 32, 349;
orbit of November meteors, 393

Aerolites. _See_ Meteorites

Airy, reduction of Greenwich observations, 19;
search for Neptune, 32

Albategnius, movement of the sun’s apogee, 5

Albedo of Mercury, 274;
of Venus, 278;
of the earth, 289;
of the moon, 290;
of Mars, 298, 334;
of asteroids, 312;
of Jupiter, 320;
of Jupiter’s satellites, 330, 332;
of Saturn, 334;
of rings, 338;
of Titan, 342;
of Uranus, 345;
of Neptune, 349

Alcor, 402

Alcyone, 499–502

Aldebaran, 403, 404, 407, 415, 421, 423, 427

Algol, 407, 415, 453, 457, 469–474

Almagest, 4, 6

Al-Mamûm’s school of astronomy at Baghdad, 5

Alphard, 409, 415

Alphonsine tables, 6

Al-Sûfi, description of the stars, 5;
Alphard, red, 415;
Algol, red, 472

Altair, 404, 427

Altazimuth, 184, 202

Altitude, 65

Amplitude, 66

Anderson, Dr., discovery of new star, 489

Andromeda nebula, 409, 529–532

Andromedæ, Gamma, 412, 417

— Nova, 489, 491

Andromede meteor-showers, 393, 394

Angelot, lunar volcanic action, 293

Annular eclipse, 113

— nebulæ, 526, 527

Antares, 404, 415

Anthelmus, new star, 484

Antlia, 468

Aphelion, 75

Apogee, 89

Apse Line, 75

Aquilæ, Eta, 467

Arago, nature of meteorites, 392;
parallax of 61 Cygni, 422

Arc of meridian, 130

Arcturus, 403, 405, 406, 415, 423, 427

Argelander, solar translation, 28;
survey of the heavens, 38;
comet of 1811, 357;
estimate of stars of ninth magnitude, 541

Argo Nebula, 522, 523, 549

— Eta, 462–464

Argon, not a solar element, 250;
peculiar qualities, 255;
found in meteorites, 389

Aries, first point of, 67

Aristarchus, heliocentric system, 4

Aristotle, description of a comet, 358

Asteroids, position in solar system, 229, 230, 310;
discoveries, 311, 314;
diameters, 312, 315;
computation of orbits, 314;
numbers and joint mass, 315;
distribution, 316;
groups, 317;
origin, 318

Asterope, 498, 499

Astronomy, Greek, 3, 4;
Arab, 4–6;
Tartar, 5;
of the Invisible, 31;
gravitational, 11, 33;
spectroscopic, 33–36;
photographic, 36–38

Astrophysics, foundation of, 36

Atmosphere, of the sun, 240, 271;
of Mercury, 277;
of Venus, 278, 279;
of the earth, 286, 313;
of the moon, 294, 313;
of Mars, 299, 307;
of Vesta, 312–313;
presence dependant upon mass, 313;
of Jupiter, 326;
of Uranus, 345

Atmospheric refraction, 52

Augmentation of moon’s diameter, 144

Aurigæ Beta, 404, 454, 456, 457

— New Star, 489

Auroræ, magnetic relations, 17, 288

Auwers’ reduction of Bradley’s observations, 19;
proper motion of Sirius, 437

Azimuth, 65

Babinet, rarity of cometary matter, 366

Baden-Powell, Sir George, eclipse-expedition, 259;
coronal photographs, 271

Bailey, Prof., 441, 464, 511, 513, 539

Ball, Sir Robert, 422, 433

Barnard, Prof., photograph of corona of January 1, 1889, 268–9;
effect of totality, 270;
zodiacal counterglow, 272;
photograph of eclipsed moon, 296;
drawing of Mars, 302;
seas of Mars, 306;
measurements of asteroids, 312;
markings on Jupiter’s satellites, 330;
discovery of fifth satellite, 331;
measures of Saturn, 335;
of ring-system, 330;
disappearance of rings, 337;
eclipse of Japetus, 338;
compression of Uranus, 343, 344;
Encke’s comet, 366;
comet-photographs, 378–381;
Swift’s comet, 383;
Nova in Auriga, 494;
Alcyone, 500;
curved nebulosity stretching over constellation of Orion, 520;
annular nebulæ, 526;
stars in streams, 551;
vacancies in the Milky Way, 554

Base line, 131

Baxendell, 484

Bayer, 404, 529

Behrmann, 400, 433, 541

Bellatrix, 408

Bélopolsky, spectrographic determination of Jupiter’s rotation, 325;
absolute velocity of 61 Cygni, 427;
spectroscopic examination of Castor, 451;
observation of Delta Cephei, 456;
Beta Lyræ, 466–467

Berberich, variability of Encke’s comet, 360

Berson, aeronautic ascent, 286

Bessel, _Fundamenta Astronomiæ_, 19;
astronomy of the invisible, 31, 32;
measurement of the Pleiades, 37;
Halley’s comet, 355;
comet of 1807, 362;
Epsilon Lyræ, 411

Betelgeuse, 404, 408, 415, 427

Bianchi, 459

Bianchini, rotation of Venus, 280

Biela, discovery of a comet, 365

Bigelow, theory of Zodiacal Light, 272

Binary stars, 431

Biot, meteoric fall, 387

Bird, quadrants, 19, 20

“Bird, Red,” 415

Birmingham, 417, 485, 486

“Blaze Star,” 485, 487

Bliss, astronomer-royal, 19

Bode’s law, 145, 232, 311, 317, 349

Boeddicker, Dr., heat-phases of eclipsed moon, 295

Bolometer, 226, 239

Bompas, 430

Bond, W. C., discoveries of Hyperion and of Saturn’s dusky ring, 25,
336, 341;
celestial photography, 36, 37;
the great nebula, 530

Bradley, discoveries of aberration and nutation, 18, 20;
reduction of his observations, 19;
Saturn’s rings, 337;
the distance of stars, 419–420;
Gamma Virginis, 445–446

Brahé, Tycho, the moon’s variation, 5;
career, 8;
scheme of the celestial movements, 9

Bredichin, theory of comets’ tails, 369, 370.
(_See also_ Tycho.)

Brenner, ashen light of Venus, 279;
rotation of Venus, 280

Brightest stars, 403, 404, 546

Brinkley, 422

British catalogue, 15, 16

Brooks’ cometary discoveries, 365, 371, 380

Bunsen, foundation of spectrum analysis, 33

Burnham, 433, 437, 441, 448, 509

Calcium, represented in Fraunhofer spectrum, 230;
in chromospheric and prominence-spectra, 258, 261, 262

Calendar, 86

Callandreau, capture of comets, 372

Campbell, Prof., spectrum of Mars, 306;
mountains on, 307

Canals of Mars, 301–305

Cancri, S., 474

— Zeta, 439, 440

Canis Majoris, R, 473

Canopus, 403

Capella, 403, 406, 415, 427

Capricornus, 411

Capture-theory of comets, 372

Carbon in sun, 242, 250;
in comets, 368;
in meteorites, 389

Cardinal points, 51

Carrington, sun-spot zones, 247;
sun’s rotation, 248, 249

Casey, 433

Cassegrain telescope, 180

Cassini, rotation of Venus, 280;
red spot on Jupiter, 323;
division of Saturn’s rings, 336;
discoveries of Saturnian satellites, 341

Cassiopeia, Chair of, 405, 481, 549

Cassiopeiæ, Eta, 413, 450

Castor, 404, 406, 413, 450, 451

Catalogues of stars, 70

Celoria, 433, 442, 540

Centauri, Alpha, 410, 413, 422, 440, 441

— Omega, 512, 513, 516, 539

— R, 478

Cephii Delta, 417, 456, 466

— U, 474

Ceraski, luminous night-clouds, 286;
discovery of U Cephei, 474

Ceres, discovery, 311;
diameter, 312

Cerulli, rotation of Venus, 280

Ceti, Mira, 458

Challis, search for Neptune, 32

Chandler, 462, 472, 476

Charlois, asteroidal discoveries, 314

Chemistry, universal, 35, 36;
solar, 250, 255;
of prominences, 256;
of chromosphere, 258;
of comets, 368, 370, 384;
of meteorites, 389

Chromosphere, 253, 258

Chronograph, 175

Chronometer, 175

Circle, meridian, 198;
transit, 198;
position, 208

Circumpolar stars, 46

Clairaut, verification of Newton’s law, 11;
calculation of Halley’s comet, 16

Clark, Alvan, great refractors, 26

— — G., detection of the companion of Sirius, 26, 437

Clarke, dimensions of earth, 134

Clausen, groups of comets, 361

Clerke, Agnes, appearance of R Sculptoris, 416;
examination of Pickering’s catalogue of stars, 541;
estimate of total light of stars to magnitude 9½, 543

Clock, astronomical, 174;
driving, 186;
sidereal, 68

Clock stars, 82

Clusters, globular, 507–517;
irregular, 497–507

“Coal sacks” in Milky Way, 554

Coelostat, 194

Collimation of transit instrument, 200

Collimator of spectroscope, 215

Colours of double stars, 417

Comæ Berenices, 434, 502, 549

Comet, Aristotle’s, 352, 353;
of 1743, 354;
Newton’s, 355;
of 1843, 358, 359;
Tebbutt’s, 362, 368;
Donati’s, 362, 369;
Lexell’s, 365, 370, 371;
Brooks’, of 1889, 365;
of 1893, 380;
Winnecke’s, 368, 371, 372;
Brorsen’s, 370;
Tuttle’s, 372, 393;
Wolf’s, 377;
Rordame’s, 383;
Gale’s, 383;
Leonid, 393, 395

— Halley’s, return in 1759, 16, 17;
status in solar system, 230, 232;
return in 1835, 335, 336;
type of tail, 369;
a client of Neptune, 371, 372

— Encke’s, disturbed by Mercury, 273;
rarefaction, 366;
acceleration, 307;
exempt from Jupiter’s influence, 371

— of 1811, structure, 356, 357;
type of tail, 369;
bulk, 383

— of 1843, surprising appearance, 358;
conditions of movement, 359

— of 1882, photographs, 38, 361;
transit, 359, 361;
period, 300;
spectrum, 369

Comet, Biela’s, discovery, 365;
duplication, 366;
related meteor-swarm, 393, 394

— Wells, spectrum, 368

— photographically detected, 377

Comets, orbits of, 108;
periodic, 109;
domiciled in solar system, 230, 371, 372;
granular nuclei, 353, 379, 384;
tenuity, 354, 384;
classification by Olbers, 358, 383;
groups, 359, 361, 362;
disruption, 360, 366, 379;
photographs, 361, 377, 380;
chemistry, 368, 370, 385;
luminous by electricity, 309, 384;
lost, 370;
short-period, 370, 371;
capture by planets, 371, 372, 384;
share sun’s translation, 372;
meteoric relationships, 384, 393, 394

— tails, multiple, 354, 355, 361, 377;
electrical theory, 357, 369, 383;
passage of the earth through, 302, 365;
three types, 369;
structure shown in photographs, 377, 383

Common, Dr., 25, 510, 520, 532, 534

Conjunctions, 99, 103

Constant of aberration, 59

Constellations, 45

Contacts in eclipse, 114

Copeland, Dr., cometary spectra, 368;
Nova in Auriga, 490;
helium, 519

Copernicus, residence in Italy, 7;
theory of planetary revolutions, 8, 9, 418

Cornelius, Gamma, 479

Corona Borealis, Eta, 437

— — Gamma, 442

— solar, 253;
compound nature of light, 202;
daylight photography, 267;
periodicity of type, 208, 270, 272;
photographs, 268–271;
rarefaction, 271, 361;
connexion with Zodiacal Light, 272, 273

Coronium, 238, 262

Co-tidal lines, 165

Coudé telescope, 27, 296

Crateris, R, 478

Craters, lunar, 292, 307

Crema meteorite, 386

Cross, Southern, 410, 416, 549

Crosswires, 195, 199, 206

Crucis, Kappa, 506

Cygni Beta, 417

— Chi, 460

— (_34_), 482

— (_61_), 422, 427

— Rho, new star near, 486

— Y, 474

Cygnus, 407

D’Alembert, verification of Newton’s Law, 11

D’Arrest, asteroidal orbits, 316;
comet, 371, 372

Darwin, G. H., tidal friction, 236;
origin of the moon, 236, 237;
density of Saturn, 333

Day and night, 52

— apparent solar, 79;
mean solar, 79

Declination, 66

De la Rue, celestial photography, 36, 295

Delphini, Beta, 435

— Gamma, 412

Deneb, 407

Denning, rotation of Saturn, 334;
discovery of a comet, 370;
August meteors, 391;
meteor-radiants, 395, 396

Density of earth, 160

Deslandres, prominence-photography, 261;
photographs of the sun as a bright-line star, 262;
daylight coronal photography, 267;
eclipse of 1893, 270;
rotation of Jupiter, 325

Dewar, atmospheric resistance to meteorites, 388

Dhurmsala meteorite, 389

Diameters, determination of, 141

Diamonds in meteorites, 390

Diffraction grating, 216

Direct movement, 89

— vision spectroscope, 216

Distance of the stars, 417

Doberck, Dr., 441, 442, 447, 450, 451

Dollond, invention of achromatic lenses, 21

Donati, discovery of a comet, 362;
cometary spectrum, 368

Double-slit method of photography, 261

Draconis, Gamma, 419, 420

Draper, Henry, photograph of the moon, 36

Dubjago, 435

Dunér, spectroscopic measurement of the sun’s rotation, 249;
R Hydræ, 462;
Y Cygni, 474;
Z Herculis, 475

Earth, shape of, 41, 134;
size of, 42, 134;
rotation of, 47, 48, 283, 284;
revolution of, 57;
orbit of, 59, 72;
varying speed of, 75;
real path of, 77;
shadow of, 110;
mass of, 159;
internal heat, 284, 285;
age, 285;
atmosphere, 286, 289;
magnetic relations, 287, 288

Easton, 532, 548

Eccentricity of ellipse, 74

Eclipse, solar, of 1842, 253;
of 1860, 254;
of 1868, 254;
of 1870, 258;
of 1896, 259, 271;
of 1882, 260, 268;
of 1878, 268;
of 1889, 268, 270;
of 1893, 270

Eclipses, lunar, 111;
partial, 111, 114;
annular, 113;
magnitude of, 113;
total of sun, 113;
duration of solar, 115;
number of in a year, 118;
recurrence of, 119;
of satellites, 121;
varieties of lunar, 295;
of Jupiter’s satellites, 329;
of Saturn’s, 342

Ecliptic, 56

— obliquity of, 61

Electrical theory of photospheric radiance, 242;
of corona, 271, 272;
of comets’ tails, 357, 358, 383;
of cometary luminosity, 369, 384

Electra, 498, 499

Elements of an orbit, 106

Elevating floor, 193

Elger, lunar _maria_, 290

Elkin, Dr., transit of great comet, 359;
meteorograph, 396;
measurements, 421–423, 425, 433, 438

Ellipse, properties of, 73;
eccentricity of, 74;
foci of, 74;
to draw an, 74

Elliptical nebulæ, 529–533

Elongations, 99

Encke, discovery of a comet, 366;
resisting medium, 367

Enoch, Book of, 404

Equation of time, 79

Equator, terrestrial, 50;
celestial, 66

Equatorial coudé, 193

Equatorial telescope, 185

Equinoxes, 55;
precession of, 69, 167, 170

Equulei, Delta, 433

Eridani, (_40_), 444

Espin, 460, 482, 494

Establishment of a port, 165

Ether of space, 546

Euler, lunar theory, 11

Evening star, 100

Evolution, of solar system, 235, 310;
of terrestrial, 236, 237, 283

Eye-pieces, 182

Fabricius, 458, 483

Fabry, cometary orbits, 372

Faculæ, associated with sun-spots, 244;
rotation, 249;
photographed, 262

Faye, planetary origin, 235, 350;
water on Mars, 299

Fényi, solar eruptions, 259, 260

Finder of telescope, 187

First Point of Aries, 67

Fixed stars, 45, 423

Flammarion, rotation of Venus, 280;
canals of Mars, 304;
condition of Mars, 309

Flamsteed, first astronomer-royal, 15;
stellar parallax, 18;
Flamsteed’s star, 461

Fleming, Mrs., 460, 465, 489, 494–496

Fletcher, 447

Fomalhaut, 404

Fontana, pseudo-satellite of Venus, 282

Forbes, ultra-Neptunian planets, 231

Foucault’s pendulum, 48–50

Fraunhofer, improvement of telescopes, 21;
solar spectrum mapped by, 34

Fraunhofer lines, 34, 249, 259, 271;
interpreted, 35, 250;
reflected in spectrum of Uranus, 346;
in spectra of comets, 368

Fritsche, 433

Frost, spectrograph of Uranus, 346

Froley, 434

Galaxy. _See_ Milky Way

Galileo, telescopic observations, 9;
double-star method of parallaxes, 28, 418

Gaseous nebula, 517

Gemini, star cluster in, 504

Geminorum, Zeta, 468

Gemma, Cornelius, 479

Gemmill, 554

Geocentric positions, 70

Geodesy, 129

Gill, Dr., photographs of comet of 1882, 38, 361;
parallax of Sirius, 421;
parallax and velocity, Lacaille, 424;
Omega Centauri, 513

Glasenapp, 433–434

Gledhill, red spot on Jupiter, 323

Globular clusters, 507

Gnomon, 125

Goodricke, 465, 466, 470

Gould, Dr., photographic measurement of the Pleiades, 37;
planetary photography, 327;
Pi Gruis and R Sculptoris, 416;
Kappa Crucis, 506;
stars in Southern Hemisphere, 541;
belt of stars intersecting the Milky Way, 551

Graduated circles, 171

Grating spectroscope, 216

Gravity, surface, on Mercury, 274;
on Venus, 278;
on the moon, 293;
on Mars, 298;
on Saturn, 335;
on Uranus, 345;
on Neptune, 349

Gravitation, laws of, 153;
universal, 156

Greenwich observations, 15, 19, 20

Groombridge, 424

Grosch, corona of 1867, 268

Grubb, Sir Howard, great refractors, 26

— Thomas, Melbourne reflecting telescope, 24

Guinand, optical glass, 21

Gully, Ludovic, 488

Gylden, 423

Gyroscope, 50

Hadley, improvement of reflecting telescopes, 21

Hale, spectrographs of prominences, 261;
calcium light pictures of sun and surroundings, 262;
double-slit method of coronal photography, 267

Hall, Prof. Asaph, discovery of the moons of Mars, 26, 309;
rotation of Saturn, 334

— Chester More, invention of achromatic lenses, 20

— Maxwell, 472

Halley, law of gravitation, 10;
acceleration of the moon, 12;
astronomer-royal, 16;
comet calculated by, 16;
transits of Venus, 17;
discovery of proper motion in stars, 423;
discovery of the star cluster in Hercules, 507

Harding, 548

Hartwig, 488

Harvest moon, 95

Heavens, diurnal motion of, 45

Heis, 400, 401, 541

Heliocentric positions, 70

Heliometer, 209

Helium, a chromospheric element, 255, 258;
extracted from clevite, 255

Helmholtz, maintenance of sun’s heat, 234;
past duration of sunlight, 285

Hencke, asteroidal discoveries, 314

Henderson, 422, 447

Henry’s belts of Uranus, 343

Hepidannus, 479

Herculis, Alpha, 413, 416

— Zeta, 435

— Z, 475

Herschel, Sir John, mathematical analysis at Cambridge, 15;
observations of nebulæ, 23, 31;
Magellanic clouds, 30, 31;
survey of the heavens, 31;
photography of sun-spots, 36;
telescope, 180;
great spot-group in 1837, 244;
cyclonic theory of sun-spots, 252;
Halley’s comet, 355;
comet of 1843, 358;
Biela’s comet, 365;
red stars, 416;
orbit of Gamma Virginis, 446;
Kappa Crucis, 506;
2 Messier, 511–512;
22 Messier, 514;
nebula round Eta Argus, 522–523;
30 Doradus, 524;
the trifid nebula, Sagittarius, 525;
planetary nebula, 528–529;
the Nubecula Major, 534–536;
Milky Way, crossed by zone of large stars, 552;
observations in the Southern Hemisphere, 554

— Sir William, the sun’s translation, 19, 28;
reflecting telescopes, 21–23;
discovery of Uranus, 21, 22;
of binary stars, 28;
comprehensive designs, 27, 29;
nebular theory, 30, 35;
rotation of Jupiter’s satellites, 331;
variability of Japetus, 341;
discovery of Uranian moons, 347;
binary stars, 419, 431;
motion real and apparent, 428;
Zeta Herculis, 435;
Xi Ursæ Majoris, 440;
70 Ophiuchi, 441;
5 Messier, 510

Hevelius, 459, 462, 484

Hind, 433, 474, 482, 484

Hipparchus, construction of a star catalogue, 3;
mathematical standpoint, 4

Holden, Prof., solar rotation, 249;
names of asteroids, 315;
helical nebulæ, 528

Holmes, discovery of a comet, 379

Holwarda, Phocylides, 458

Hooke, law of gravitation, 10;
observations of Greek letter Draconis, 18;
Gamma Arietis, 412;
parallax of Gamma Draconis, 419–420

Horizon, visible, 41;
sensible, 44;
celestial, 44;
rational, 44

Horrebow, satellite of Venus, 282

Hour circle, 186

Howlett, depression of sun-spot umbræ, 251

Huggins, Dr., stellar and nebular spectra, 35;
photographed, 37;
observations of prominences, 255;
daylight coronal photography, 267;
prismatic occultation of a star, 294;
spectrum of Mars, 306;
of Jupiter, 326;
of Uranus, 345;
of Winnecke’s comet, 368;
spectrograph of Tebbutt’s comet, 368;
measurement of motion in the line of sight, 426;
spectroscopic examination of new star, 493;
spectroscopic examination of the “fish-mouth” nebula, 518;
discovery of gaseous spectrum, 528

Humboldt, meteoric shower of 1799, 392;
temporary star of 1572, 479–481

Hussey, cometary forms, 380;
photograph of Rordame’s comet, 383

Huygens, 417, 517

Hyades, 407, 549

Hydræ, R, 462

Hydrogen, ultra-violet spectrum in stars, 37;
a gaseous metal, 250;
a constituent of prominences and chromosphere, 255, 258;
velocity of molecules, 313;
free in atmospheres of Uranus and Neptune, 346, 349;
assumed constituent of comets’ tails, 369, 370

Hypothesis of external galaxies, 546

Infinity of Space, 546

Jacob, 433, 447

Jacoby, measures of photographs, 37

Janssen, photograph of the sun, 243;
spectroscopic method of prominence-observation, 254;
double-slit method, 261

Japetus, remarkable eclipse, 338;
variability, 341;
plane of orbit, 342

Jesse, luminous night-clouds, 286

Job, Book of, 404

Johnson, 450

Juno, discovery, 311;
diameter and albedo, 312, 316;
a twin of Clotho, 317

Jupiter, long inequality, 12, 17;
disturbance of Halley’s comet, 16;
influence upon asteroidal distribution, 316–318;
mass and figure, 318;
rotation, 318, 325, 326;
density, 319, 326;
reflective power, 320;
belts and streamers, 321, 322, 326;
spots, 323, 325;
photographs, 327;
disturbance of comets, 371

Jupiter’s satellites, Galilean quartette, 9, 327, 328;
transits, 329;
constitution, 330;
fifth satellite, 331, 332

Kapteyn, 422, 556, 561–563

Keeler, drawings of Jupiter, 321;
description of markings, 322;
spectroscopic test of the meteoric constitution of Saturn’s rings,
339;
measuring velocities of nebula in line of sight, 428;
spectra of the Orion nebula, 519–520

Kelvin, Lord, subterranean temperature, 285

Kepler’s Laws, 10, 155, 339, 417

Kirch, 460, 470, 510

Kirchhoff, spectrum analysis, 33;
Fraunhofer’s lines, 34

Kirkwood, distribution of asteroids, 316, 317;
divisions in Saturn’s rings, 338

Kleiber, number of shooting stars, 390

Koch, 461

Kreutz, relations of great southern comets, 360

Krüger, 442

Lacaille, southern nebulæ, 30

Lagrange, verified principle of gravitation, 11;
stability of solar system, 13

Lajoye, 488

Lamp, fate of Brorsen’s comet, 370

Lane’s law, 242

Langley, solar radiation, 238, 239;
spectroscopic effects of sun’s rotation, 249;
temperature of the moon, 294;
fireball, 386

Laplace, verified Newton’s law, 11;
lunar acceleration, 12;
_Mécanique Céleste_, 13, 14;
nebular hypothesis, 235

Lassell, large reflectors, 24;
discoveries of Hyperion, Ariel, and Umbriel, 24, 341, 347;
Saturn’s dark ring, 336

Latitude, terrestrial, 50, 125;
celestial, 68;
of sun, 77;
geocentric, 135;
geographical, 135;
astronomical, 136;
variation of, 136

Leland, Miss, 511

Leonid meteors, 391–395

Leonis, Gamma, 413

— R, 461

Lepaute, Madame, computation of Halley’s comet, 16

Leverrier, discovery of Neptune, 32;
intra-Mercurian planet, 232;
mass of asteroids, 315;
orbit of November meteors, 395

Lewis, 426

Libræ, Delta, 473

Librations, of Mercury, 277;
of Venus, 281;
of the moon, 93, 289

Lick observatory, 25, 26

Light-equation, 329

“Light journey,” 420

Limited number of visible stars, 538, 545

Limiting apertures, 212

Lippershey, inventor of the telescope, 9

Lockyer, spectroscopic observations at the sun’s limb, 254;
classification of prominences, 250;
solar tornadoes, 259

Loewy, Coudé telescope, 27;
lunar photography, 296

Longitude, terrestrial, 50, 125;
celestial, 68

Lowell, rotation of Mercury, 277;
observations of Venus, 279, 281;
lakes of Mars, 301, 302;
relation to canals, 302–304

Luminous night-clouds, 286

Lunar distances, 129

— ecliptic limit, 112

Lyncis (_12_), 450

Lyra, annular nebula in, 526

Lyræ, Beta, 465

Lyraid meteors, 393, 395

Maclear, 464

Mädler, search for Martian moons, 309;
compression of Uranus, 343

Madrid meteorite, 385

Magellanic clouds, 30, 534–537

Magnetism, terrestrial, 287, 288

Magnitude, of eclipses, 113;
of stars, 212

Magnitudes, star, 403, 404

Mann, 433

Maps, 133

Maraldi, 462, 470, 511

Marchand, observations of the Zodiacal Light, 273

Markwick, Col., 547

Mars, phases of, 104;
parallax of, 147;
a superior planet, 297;
seasons, 298, 301, 302;
snow-caps, 299, 303, 306;
land and water, 299–301, 305, 306;
continents, 300, 301;
canals, 301, 304;
duplication, 301, 305;
spectrum, 306;
atmosphere, 307, 313;
mountains, 307;
climate, 308;
moons, 309, 310

Marth, Neptune’s satellite, 350

Mascari, rotation of Venus, 280

Maskelyne, astronomer-royal, 19;
founded _Nautical Almanac_, 20;
star-motions, 28

Mass, defined, 151;
sun, 156;
planets, 157;
moon, 158;
of asteroids, 158;
earth, 159;
satellites, 159

Maunder, 460, 488, 493

Maxwell, Clerk, constitution of Saturn’s rings, 337, 340

Mayer, Tobias, lunar tables, 11;
star-motions, 28

Mazapil meteorite, 396

Measurement, of earth, 42, 129;
of sun’s distance, 146;
of binary stars, 208;
of planets, 208

_Mécanique Céleste_, character, 13, 14

Megrez, 402

Mercury, Copernican theory of movements, 8;
transit of, 101;
phases of, 101;
orbit, 273, 274;
atmosphere, 274, 275;
rotation, 275–277;
as an abode of life, 277;
capture of Encke’s comet, 372

Meridian, 50;
line, 51;
arc of, 130;
circle, 198;
photometer, 214

Merope, 498, 499

Messier (_3_), 509

— (_5_), 510

— (_11_), 506

— (_22_), 514

— (_37_), 505

— (_51_), 533

— (_57_), 526

— (_80_), new star in, 485

— (_92_), 509

— (_99_), 534

— discoveries of nebulæ, 30

Metonic cycle, 92

Meteoric systems, 231, 390, 391;
radiants, 392, 395, 396

Meteorites, falls, 385–387;
legal status, 387;
velocities, 387, 388, 390;
thumb-marks, 388;
chemical composition, 389;
enclosed diamonds, 390

Meteors, Perseid, 391, 393;
Leonid, 391–393;
Andromede, 393–394, 396;
relations to comets, 393, 395

Micrometer, wire, or pillar, 205;
evolution of, 207

Michell, prevision of binary stars, 28

Midnight sun, 63

Milky Way, 402, 430, 555, 557

— — star streams, 9;
disc theory, 29

Minimum deviation, 215

Mira Ceti, 458, 459

Mitchell, 421, 431

Mizar, 402, 411, 455, 457

Molyneux, 419, 420

Montanari, 471

Month, 91

Moon, acceleration, 12;
_contumax sidus_, 16;
observations, 19;
apparent motion of, 87;
orbit of, 88, 94;
phases of, 89;
sidereal period of, 89;
synodic period of, 91;
rotation of, 92;
librations of, 93;
harvest, 95;
high and low, 97;
shadow of, 115;
distance of, 143;
size of, 144;
mass of, 158;
possible disintegration, 233;
origin, 236, 237;
rotation, 289;
cones and craters, 290, 292, 293;
rays and rills, 293;
absence of air and water, 294, 313;
temperature, 294, 295;
eclipses, 295;
photography, 295–297

Morning star, 100

Müller, surface of Mercury, 275;
photometry of asteroids, 312;
albedo of Jupiter, 320;
of Saturn, 334;
of Neptune, 349

Muscæ, R, 468

Nadir, 45

Nasir Eddin, planetary tables, 5

Nasmyth, conjunction of Mercury and Venus, 278

Nearest fixed stars, 417

Nebula, Orion, 23, 25, 30

Nebulæ, structure, 23;
spiral, 24;
photographs, 23, 25;
first discoveries, 29, 30;
status, 30, 31;
gaseous nature, 30, 35;
annular, 526, 527;
elliptical, 529, 533;
gaseous, 517–524;
planetary, 527–529;
spiral, 533, 534

Nebular hypothesis, 30, 35, 235, 530

Nebulous stars, 529

Neptune, discovery, 32, 229;
distance from the sun, 232;
dimensions, 349;
compression, 351;
retrograde rotation, 351;
planets as viewed from, 351, 352;
family of comets, 371, 372

Neptune’s satellite, discovery, 24;
plane of revolution, 350;
precessional disturbance, 351

Newall, 25-inch refractor, 26

Newcomb, Prof., past duration of sunlight, 285;
light changes of Ariel, 347;
satellite of Neptune, 351;
the runaway star, 424;
proper motion of Alcyone, 501

New stars, 477–497

Newton, H. A., capture of comets, 372;
meteoric cult, 387;
daily number of shooting stars, 390

— Sir Isaac, law of gravitation, 10, 11;
invention of reflecting telescope, 21;
comet of 1680, 355;
decay of comets, 366

Newtonian telescope, 179

Nichol, Dr., 508

Niesten, rotation of Venus, 280;
mass of asteroids, 315

Nodes, 94

North polar distance, 66

Nova Andromedæ, 488

— Aurigæ, 489

— Cassiopeiæ, 479

— Cygni, 486

— Ophiuchi, 484

— Serpentarii, 483

— Vulpeculæ, 484

Nubecula Major, 534

— Minor, 535

Number of visible stars, 538–544

Nutation, 169

Oases of Mars, 302–305

Object-glass, achromatic, 177;
photographic, 195;
photo-telescope, 196

Objective prism, 223

Obliquity of ecliptic, 61

Observatories, 191

— Lick, 189, 190, 202

— Nice, 192

— Yerkes, 189

Occultations, 121

— of stars, by the moon, 294;
by comets, 366

Olbers, discovery of Pallas and Vesta, 311;
origin of asteroids, 311, 316;
electrical theory of comets, 357;
classification, 358, 383;
comet discovered by, 371

Ophiuchi, Nova, 483–485

— (_70_), 441

— U, 473, 476

Opposition, 103, 105

Orbit, of earth, 72, 76;
of moon, 88;
elements of a planetary orbit, 106;
of binary stars, 432

Orion, 406, 408, 417

— great nebula in, 517–521

Orionis, Alpha (Betelgeuse), 404, 408, 415, 427

— Iota, 414

— Sigma, 414

— Theta, 414

“Owl,” nebula, 528

P (_34_) Cygni, 482

Palisa, discoveries of asteroids, 314

Palitzsch, 470

Pallas, discovery, 311;
diameter, 312

Parallax of stars, 419, 420

— diurnal, 140;
equatorial horizontal, 140;
horizontal, 140;
of sun, 146;
of Mars, 147

Parmentier, distribution of asteroids, 316

Pegasus, Square of, 409

Pegasi, Kappa, 433

— (_85_), 434

— U, 469

Pendulum observations, 135;
compensated, 174

Penumbra, of earth’s shadow, 111

Percentage of stars in Milky Way, 547, 548

Perigee, 89

Perihelion, 75

Perrotin, rotation of Venus, 280;
of Uranus, 343;
markings on Uranus, 344

Persei, Beta (Algol). _See_ Algol

Perseid meteors, 391;
associated with Tuttle’s comet, 393

Perseus, 407

— star clusters in, 503

Perturbations, 158

Peters, 428

Phases of moon, 89;
of Venus, 101;
of Mars, 104

Phocylides Holwarda, 458

Photographic telescopes, 194

Photography of nebulæ, 23, 25, 38;
of sun-spots, 36, 243, 244;
of the moon, 36, 295–297;
of stellar spectra, 37;
of comets, 38, 354, 377–383;
celestial, 194;
of spectra, 219, 223;
of the eclipsed sun, 254;
of the reversing layer, 259;
of prominence-spectra, 260;
of prominences and faculæ, 261, 262;
of the corona, 267, 269–271;
planetary, 327; meteoric, 396

Photoheliograph, 197

Photometers, wedge, 213;
meridian, 214

Photosphere, visible structure, 242

Piazzi, five-foot circle, 20;
discovery of Ceres, 311

Pickering, Prof. E. C., photometric measures of asteroids, 312;
photograph of Jupiter, 327;
the spectrum of Alpha Centauri, 441;
the spectrum of Pleione, 498

Pickering, W. H., lunar photographs, 296;
mounting of telescopes, 297;
lakes and canals of Mars, 301, 304;
water area on Mars, 305;
star collisions, 495;
nebula surrounding Zeta Orionis, 520

Pigott, 467

“Pilgrim star,” 479–482

Planetary nebulæ, 527–529

Planets, apparent movements of, 98;
interior and exterior, 98;
conjunctions of, 99, 103;
phases of, 101, 104;
oppositions of, 103;
synodic periods of, 107;
times of revolution, 107;
relative distances of, 144;
distances of, 150;
terrestrial, 229;
giant, 229, 319, 343;
trans-Neptunian, 231;
intra-Mercurian, 232;
decay, 233;
comets captured by, 371, 372

— minor. _See_ Asteroids

Pleiades, 404, 407, 497–502, 539, 549

Pleione, 498

“Plough,” 400–402, 405

Plummer, short-period comets, 371;
Encke’s, 372

Podmaniczky, Baroness, 488

Pogson, 485

Polar axis, 185

Polaris. _See_ Pole Star

Pole, celestial, 46; terrestrial, 50;
movements of, 138

Pole Star, 46, 405, 412, 421, 427

Pollux, 404, 406, 415, 427

Pond, defects of Greenwich quadrant, 19;
astronomer-royal, 20

Position, angle, 208;
circle, 208

Poynting’s experiment, 160

Præsepe, 502

Precession, of equinoxes, 69;
effects of, 170;
luni-solar, 169

Prime vertical, 210

Principia, publication, 10, 13;
character, 14

Prism, action of, 215;
objective, 223

Prismatic camera, 223

— spectroscope, 215

Pritchard, Prof., 422, 424

Proctor, Saturn’s rings, 341;
distance of Uranus, 344;
Proctor’s chart, 548;
stars in streams, 550

Procyon, supposed satellite, 31, 32;
order of magnitude, 404;
parallax of Procyon, 421;
Procyon approaching the Earth, 427

Prominences, solar appendages, 253, 254;
spectrum, 254, 256, 258, 260;
daylight observations, 254, 255;
quiescent and eruptive, 256;
periodicity, 257;
rapid development, 259;
spectral photography, 260, 261

“Proper motions” of stars, 423–431

Ptolemaic system, 3, 4, 6

Quadrature, 105

Rambaud, absorption in solar atmosphere, 240;
fireball, 380

Ramsay, terrestrial discovery of helium, 255

Ramsden, astronomical circles, 20

Raynard, the sun a nebulous body, 253;
future of Saturn’s ring-system, 340;
outflows from comets, 380;
star streams, 551

Ravené, gravitational disturbance by asteroids, 315

R Centauri, 478

Reading microscope, 172

Recurrence of eclipses, 119

“Red Bird,” 415

Red spot on Jupiter, 323, 324

Red stars, 416

Reduction of observations, 18, 19

Refracting telescope, 176

Refraction, 52

— in Venus, 278

Reflecting telescope, 178

Regression of moon’s nodes, 94

Regulus, 406, 410, 427

Retrogradation, 89, 103

Reversing layer, 249, 258, 271;
photographed, 259

Rich and poor regions, 549

Richaud, 440

Rigel, 404, 414, 427

Right ascension, 66

Roberts, Dr., 23, 107, 502, 503, 508, 511, 520, 525–528, 530, 533, 534,
539, 540

Roberts, A. W., 440, 441, 469

Roche, minimum distance of satellites, 340

Römer, velocity of light, 329

Rosse, Earl of, giant reflector, 24

Roszl, mass of 311 asteroids, 315

Rotation of earth, 47, 48;
of moon, 92

Rowland grating, 217

— solar elements, 250

Russell, photograph of Swift’s comet, 377;
Kappa Crucis, 506;
the “key-hole” nebula, 522;
the Magellanic clouds, 536

Rutherfurd, photographs of the moon, 295

Sacrobosco, treatise on the sphere, 6

Sagittarii, Zeta, 434

Saros, 120

Satellites, movements of Satellites, 108;
masses of Satellites, 159

— discoveries, 9, 23, 25, 26, 309, 347;
apportionment, 230;
formation checked by tidal friction, 277, 282;
planes of revolution, 328, 347, 348, 350;
transits, 329, 330, 342;
eclipses, 329, 342;
variability, 330, 341, 347;
rotation, 331, 341, 342, 347

Saturn, density, 333;
spectrum, 334;
rotation, 334, 339;
dimensions, 535

Saturn’s ring-system, dusky member, 25, 336, 338;
dimensions, 336;
constitution, 337, 339, 340;
albedo, 338

Sawyer, U Ophiuchi discovered, 473;
variability of R Canis Majoris detected, 473

Schaeberle, photographs of corona of 1893, 270;
land and water on Mars, 306

Scheiner, spectra of sun-spots, 251

Schiaparelli, rotation of Mercury, 275;
map of Mercury, 277;
rotation of Venus, 280, 281;
canals of Mars, 301;
duplication, 305;
climate of Mars, 308;
compression of Uranus, 343;
comets and meteors, 393;
theory of extinction of light, 544

Schiehallion experiment, 161

Schmidt, map of the moon, 290

Schönfeld, 461, 464, 466, 467, 473, 483

Schorr, 442

Schur, 433, 442

Schuster, photograph of eclipsed sun, 268

Schwabe, discovery of sun-spot periodicity, 245

Seasons, 61

Secchi, observations of prominences, 256;
spectrum of Uranus, 345

See, Dr., 413, 433–435, 440, 442, 447, 448

Seeliger, photometric measures of Saturn’s rings, 339

Serpentarii, Nova, 483

Sextant, 211

Shackleton, photograph of the reversing layer, 259

Ship, position of, 128

“Sickle” in Leo, 406

Siderostat, 194

Sidgreaves, elevations of chromosphere, 258

Sirius, proper motion, 17, 31;
companion, 32;
spectrum, 37;
size, 403;
position, 409;
colour, 414;
distance, 418, 421;
discovery of proper motion, 423;
a binary star, 437;
comparative magnitude, 438

Smyth, 447, 448, 502, 505, 508

Solar, constant, 239

— diagonal, 183

— eclipses, 113

— ecliptic limit, 118

— System, dominated by gravity, 29;
constitution, 229, 232;
dimensions, 231;
stability, 232;
origin, 235, 236

Southern Cross, 410, 416, 549

Shouting, 68, 198

Spectroheliograph, 225

Spectroscope, prismatic, 215;
direct vision, 216;
grating, 216;
Lick star-, 219;
Rowland, 217;
tele-, 219

Spectroscopic measurements of rotation;
the sun, 248;
Venus, 281;
Saturn, 339

Spectrum, solar, 34, 250;
of stars and nebulæ, 35, 37;
measurement of, 218;
sun-spot, 250, 251;
prominence, 254, 256, 261;
chromospheric, 258;
of Mercury, 275;
of Venus, 279;
auroral, 288;
of Jupiter, 326;
of Saturn’s rings, 338;
of Uranus, 345, 346;
of Neptune, 351;
of comets, 368

Spherical excess, 133

Spica, 404, 410

Spiral nebulæ, 533, 534

Spoerer, solar rotation, 249

Star of Bethlehem, 101

Star-charting, photographic, 38

— cluster, 17

— spectroscope, 219

— time, 68

Stars, temporary, 3, 8, 477;
proper motions of, 17, 19, 28, 425, 427;
fixed, 45;
circumpolar, 46;
diurnal motion of, 46;
aberration of, 58;
catalogues of, 71;
clock, 82;
morning and evening, 100;
magnitudes, 403, 404;
Pole, 405, 412;
double, 410;
coloured, 416;
red, 416;
nearest, 417;
binary, 431;
variable, 458

Stationary points, 103

Stone, mass of Titan, 342

Stoney, G. Johnstone, atmospheres of planets, 313

Stratonoff, sun’s rotation from faculæ, 249

Suess, theory of lunar formations, 292

Sun, translation, 28, 229;
apparent movements of, 55, 77;
midnight, 63;
apparent diameter of, 72;
mean, 79;
eclipses of, 113;
distance of, 146;
mass of, 156;
maintenance of heat, 234;
radiative power, 237–239, 241, 242;
temperature, 239, 240;
magnitude, 240, 241;
luminous surface, 242;
spots, 243–249, 251, 252;
periodicity, 246;
rotation, 247–249;
chemistry, 250;
theories, 252

Sun-dial, 78

Sun’s motion in space, 428

Sun-spots, observed by Galileo, 9;
construction, 243, 251;
zones, 245, 247;
periodicity, 245, 247;
irregular movements, 247–249;
spectra, 250–252

Sutton, 553

Swift, Lewis, comet discovered by, 377, 378, 383

Sykora, elevation of spotted areas on the sun, 252

Synodic period, of moon, 91;
of planets, 107

Tacchini, spectrum of Venus, 279;
rotation, 280

Talcott’s latitude method, 124

Tauri, Alpha. _See_ Aldebaran

— Lambda, 473

Tebbutt’s comet, 362, 368

Telescope, invention of, 9;
achromatic, 20, 21;
reflecting, 21, 24, 25, 178;
refracting, 20, 25–27, 176;
future improvement, 26, 27, 297;
Newtonian, 179;
Cassegrain, 180, 181;
Herschellian, 180;
Skew Cassegrain, 181;
magnifying power of, 184;
illuminating power of, 184;
altazimuth, 184;
equatorial, 185;
Rosse, 187;
Common, 5-foot, 188;
Lick, 190;
fixed, 194;
photographic, 194

Telespectroscope, 219

Tempel, 501

“Temporary stars,” 477–497

Theodolite, 205

Thiele, 435, 447, 451

Thome, comet of 1887, 360

Tidal evolution, 167

Tidal friction, 166;
in earth-moon system, 236, 283, 284;
on Mercury, 277;
effect on satellite-formation, 278, 282;
on Venus, 282;
on Phobos, 310;
on Saturnian satellites, 342

Tides, 162;
spring and neap, 164;
priming and lagging, 164

Time, apparent, 78;
equation of, 79;
mean solar, 79;
determination of, 82;
at different places, 83;
Greenwich mean, 83;
local, 83;
telegraphy, 84;
zone, 84;
balls, 85

Tisserand, revolutions of Jupiter’s fifth satellite, 331;
disturbance of Neptune’s satellite, 351;
capture of comets, 372

Todd, Miss M. L., drawing of corona, 268

— Prof., trans-Neptunian planet, 231

Toucani (_41_), 513

Transit circle, 198–202

— instrument, 202

— of Venus, 101, 148

Triangulation, 53

Troughton, instrumental improvements, 19, 20

Trouvelot, mountains of Venus, 279;
rotation, 280

Twilight, 53

Tycho Brahé, 5, 8, 9, 405, 418, 479, 481, 529

Ulugh Beigh, observations at Samarcand, 5

Umbra of earth’s shadow, 111

Uranus, discovery, 22, 229;
perturbations, 32, 231;
dimensions and markings, 343–345;
analogy with Neptune, 343, 351;
rotation, 344, 348;
spectrum, 345, 346;
satellites, 347, 348;
comets captured by, 371, 395

Ursa Major, stars in, 400, 401

Ursæ Majoris, Xi, 440

Variation of latitude, 136

Variable stars, 458

Vega, 403, 406, 414, 422, 427

Venus, phases observed by Galileo, 9;
transits, 17;
phases of, 101;
transit of, 101, 148;
atmosphere, 278, 281, 282;
ashen light, 279;
spectrum, 279;
rotation, 280, 281;
imaginary satellite, 282

Vernier, 172

Very, distribution of lunar heat, 295

Vesta, discovery, 311;
diameter and brightness, 312;
mass, 313

Villarceau, 433

Virginis, Alpha (Spica), 404, 410

— Gamma, 413, 444–450

— Tau, 456

— W, 469

Visible stars, number of, 538–546

Vogel, spectrum of Jupiter, 326;
of Uranus, 345;
binary or multiple system of Beta Lyræ, 466;
diameter of Algol, 472

Volcanic action, terrestrial, 284;
lunar, 290, 292

Von Gothard, 465

Vulpeculæ, Nova, 484

— S, 484

Ward, 488

Way, Milky, 402, 430, 549, 557

Webb, 528

Wedge, photometer, 213

Weight, defined, 151;
of the earth, 160

Wells’ comet, 368

Williams, A. Stanley, rotation of Venus, 280;
of Jupiter, 325;
photographs of Jupiter, 327;
spots on Saturn, 334

Wilson, Alexander, depression of sun-spots, 251

— W. E., temperature of the sun, 240

Winnecke, 422

Winnecke’s comet, 368, 371, 372

Wire micrometer, 205

Wolf, Max, photographic discovery of asteroids, 314;
comet discovered by, 377;
chart of the Pleiades, 499

Wrublewsky, 434

Year, 85;
sidereal, 85;
tropical, 85;
leap, 86

Yendell, 474

Yerkes, 40-inch refractor, 26, 27

Young, solar eruption, 256;
spectrum of chromosphere, 258;
reversing layer, 258;
spectrum of Venus, 279;
brightness of Phobos, 309;
belts of Uranus, 343;
size of Uranus, 345;
the sun and planets, seen from Neptune, 349, 352;
Andromede meteors, 394

Zenith, 45

— telescope, 210

Zodiac, 60

Zodiacal Light, 272, 273

Zöllner, albedo of Mars, 298, 334;
of Jupiter, 320;
of Neptune, 349;
estimate of sunlight, 543

Zone time, 84

THE END.

-----

Footnote 1:

There is a very complete paper on “How to find Easter,” by Dr.
Downing, in the _Journal_ of the British Astronomical Association,
vol. ii., p. 264.

Footnote 2:

The application of Kepler’s third law gives us P = _a_^{³⁄₂} years,
but as this is not strictly true, both P and _a_ must be given where
the greatest possible accuracy is desired.

Footnote 3:

The diagram is based upon one given by Prof. Albrech in the
_Astronomische Nachrichten_, No. 3333. The dotted part of the curve
could not be directly derived on account of insufficient observations.

Footnote 4:

The focal length of a lens is the distance from its centre at which an
image of a very distant object, such as the sun, is formed.

Footnote 5:

In a British inch there are 25·4 millimetres.

Footnote 6:

Proctor: “Old and New Astronomy,” p. 327.

Footnote 7:

Langley: “The New Astronomy,” p. 108.

Footnote 8:

The “bolometer,” invented by Langley, measures heat with exquisite
refinement by means of its electrical effects.

Footnote 9:

W. E. Wilson: _Monthly Notices_, vol. lv., p. 457.

Footnote 10:

_Observatory_, vol. xviii., p. 344.

Footnote 11:

Frost-Scheiner: “Astronomical Spectroscopy,” p. 177.

Footnote 12:

_Astronomische Nachrichten_, No. 3330.

Footnote 13:

_Knowledge_, vol. vi., p. 13.

Footnote 14:

“The Sun,” p. 206, first edition.

Footnote 15:

“Memoirs of the Royal Astronomical Society,” vol. xli., p. 435.

Footnote 16:

_Astronomy and Astro-Physics_, vol. xiii., p. 122.

Footnote 17:

_Comptes Rendus_, December 26, 1893.

Footnote 18:

_Knowledge_, vol. iv., p. 105.

Footnote 19:

“Rapport de la Mission envoyée an Sénégal,” p. 31.

Footnote 20:

“Harvard Annals,” vol. xix., part ii.; 1893.

Footnote 21:

“The Solar Corona discussed by Spherical Harmonics;” Washington, 1889.

Footnote 22:

_Bulletin Astronomique_, April, 1896.

Footnote 23:

According to G. Müller, _Potsdam Publicationen_, No. 30, p. 369,
Zöllner fixed the albedo of Mercury at 0·13.

Footnote 24:

_Astr. Nach._, No. 3171.

Footnote 25:

_Astr. Nach._, No. 3406.

Footnote 26:

_Ibid._, No. 2944.

Footnote 27:

_Astr. Nach._, No. 3332.

Footnote 28:

This was in principle suggested by Proctor in “The Old and New
Astronomy.”

Footnote 29:

_Nature_, vol. li., p. 227.

Footnote 30:

Kelvin, _Nature_, p. 440; Clarence King, _American Journal of
Science_, January, 1893.

Footnote 31:

_Ciel et Terre_, 16th March, 1895.

Footnote 32:

_Himmel und Erde_, Feb., 1889; _Astr. Nach._, No. 3347; A. Battandier,
_L’Astronomie_, 1894.

Footnote 33:

Balfour Stewart: “Ency. Brit.,” vol. xvi. pp. 164, 165.

Footnote 34:

A. Paulsen: _Ciel et Terre_, 1 Juillet, 1895, p. 202.

Footnote 35:

Elger: “The Moon,” p. 73.

Footnote 36:

“Publications, Astronomical Society of the Pacific,” vol. vii., p.
144.

Footnote 37:

“Harvard Annals,” vol. xxxii., part i., p. 109.

Footnote 38:

_Astronomy and Astro-Physics_, Nov., 1894, p. 718.

Footnote 39:

“Popular Astronomy,” 1895, p. 347.

Footnote 40:

_Astr. Nach._, No. 3271 (Schiaparelli).

Footnote 41:

“Popular Astronomy,” vol. i., p. 348.

Footnote 42:

_Scientific American_, Feb. 29, 1896.

Footnote 43:

Schiaparelli: _Astronomy and Astro-Physics_, Nov., 1894, p. 720.

Footnote 44:

_Astronomy and Astro-Physics_, August, 1894, p. 554.

Footnote 45:

“Publ. Astro. Soc. of the Pacific,” vol. iv., p. 196.

Footnote 46:

_Monthly Notices_, vol. lvi., p. 166.

Footnote 47:

Campbell: “Publ. A. S. P.,” vol. vi., p. 273.

Footnote 48:

_Ibid._, vol. ii., p. 248.

Footnote 49:

_Ibid._, vol. vi., p. 110.

Footnote 50:

_Astronomy and Astro-Physics_, October, 1894, p. 640.

Footnote 51:

_Potsdam Publicationen_, No. 30, 1893.

Footnote 52:

Barnard: _Monthly Notices_, vol. lvi., p. 55.

Footnote 53:

John Hopkins’ _University Circular_, Jan., 1895.

Footnote 54:

_Astr. Nach._, No. 3359.

Footnote 55:

_Monthly Notices_, vol. lvi., p. 250.

Footnote 56:

Barnard: _Astr. Journal_, No. 325, 1894.

Footnote 57:

“Publ. A. S. P.,” vol. ii., p. 286.

Footnote 58:

Maunder: _Knowledge_, vol. xix., p. 5.

Footnote 59:

_Monthly Notices_, vol. lvi., p. 143.

Footnote 60:

“Scientific Proceedings, R. Dublin Society,” vol. viii., p. 398.

Footnote 61:

_Astro.-Phys. Journal_, May, 1896, p. 394; “Rapport de l’Observatoire
de Paris,” 1895, p. 22.

Footnote 62:

Proctor: “Old and New Astronomy,” p. 584.

Footnote 63:

“The subject of slant-markings,” Mr. Stanley Williams remarks (_loc.
cit._), “has only just begun to be investigated.”

Footnote 64:

“Jupiter and his System,” by Ellen M. Clerke, p. 43.

Footnote 65:

_Comptes Rendus_, t. cxix., p. 581.

Footnote 66:

G. H. Darwin: _Harper’s Magazine_, June, 1889.

Footnote 67:

Barnard, _Monthly Notices_, vol. lvi., p. 163.

Footnote 68:

Lewis: _Observatory_, vol. xviii., p. 379.

Footnote 69:

_Monthly Notices_, vol. lii., p. 419.

Footnote 70:

“Abhandlungen Akad. der Wissensch.” München, Bl. xvi., p. 403.

Footnote 71:

_Astro-Physical Journal_, May, June, 1895.

Footnote 72:

“Old and New Astronomy,” p. 640.

Footnote 73:

“Phil. Trans.,” vol. lxxxii., p. 17.

Footnote 74:

“Publications Astr. Soc. of the Pacific,” vol. iii., p. 284.

Footnote 75:

_Astr. Journal_, No. 370.

Footnote 76:

Perrotin: “Vierteljahrsschrift Astr. Ges.,” Jahrg. xxiv., p. 267.

Footnote 77:

“Annales de l’Observatoire de Nice,” t. ii., 1887.

Footnote 78:

Keeler: _Astr. Nach._, No. 2927.

Footnote 79:

Gregory: _Nature_, vol. xl., p. 236.

Footnote 80:

“General Astronomy,” p. 372.

Footnote 81:

_Astronomical Journal_, No. 342.

Footnote 82:

Tisserand: _Astronomy and Astro-Physics_, vol. xiii., p. 291 (1894).

Footnote 83:

_Comptes Rendus_, t. cvii., p. 804.

Footnote 84:

_Astronomical Journal_, No. 186.

Footnote 85:

“General Astronomy,” p. 372.

Footnote 86:

“Observations at the Cape of Good Hope,” p. 396.

Footnote 87:

“Monat. Correspondenz,” Bd. xxv., pp. 3–22, 1812.

Footnote 88:

Fessenden: _Astro-Physical Journal_, vol. iii., p. 40.

Footnote 89:

_Astr. Nach._, No. 2837.

Footnote 90:

Guillemin: “The World of Comets,” p. 282.

Footnote 91:

_Astr. Nach._, No. 2437.

Footnote 92:

_Knowledge_, Feb., 1896, p. 41.

Footnote 93:

For an account of its spectral changes, see Campbell in _Astr. and
Astr.-Physics_, vol. xi., p. 698.

Footnote 94:

Barnard, _Knowledge_, vol. viii., p. 229.

Footnote 95:

Denning: _Astronomy and Astro-Physics_, vol. xii., p. 371.

Footnote 96:

_Astroph. Journal_, Jan., 1896, p. 42.

Footnote 97:

Ranyard: _Knowledge_, vol. ix., p. 159.

Footnote 98:

“Publications Astr. Pac. Society,” vol. vii., p. 166.

Footnote 99:

Hussey: _loc. cit._, p. 171.

Footnote 100:

Holden: “Publ. Astr. Pac. Society,” vol. ii., p. 19. H. A. Newton:
_Ibid._, vol. iii., p. 91.

Footnote 101:

“Report Bri. Ass.,” 1891, p. 805.

Footnote 102:

S. Meunier: “Encycl. Chimique,” t. ii., p. 461.

Footnote 103:

Young: “Gen. Astr.,” p. 435.

Footnote 104:

Cornish: _Knowledge_, vol. vi., p. 163.

Footnote 105:

_Journal Brit. Astr. Ass._, vol. vi., p. 432.

Footnote 106:

H. A. Newton: “Proc. Amer. Phil. Society,” vol. xxxii.

Footnote 107:

Quoted by Sir F. Palgrave: “Phil. Trans.,” vol. cxxx., p. 175.

Footnote 108:

_Observatory_, April, 1895.

Footnote 109:

_Observatory_, Jan., 1896.

Footnote 110:

It has been recently seen again in America.

Footnote 111:

_Journal of the British Astronomical Association_, March, 1891.

Footnote 112:

_Nature_, Feb. 13, 1896.

Footnote 113:

“Planetary and Stellar Studies,” p. 257.

Footnote 114:

See Chapter V.

Footnote 115:

_Comptes Rendus_, March 30, 1896.

Footnote 116:

_Nature_, April 30, 1896.

Footnote 117:

“Cape Observations,” p. 34.

Footnote 118:

_Journal of the British Astronomical Association_, vol. iv., No. 11,
p. 21.

Footnote 119:

_Journal of the British Astronomical Association_, vol. vi., No. 6, p.
312.

Footnote 120:

Recent observations show that the total variation is 2·71
magnitudes—the largest variation known for an Algol star.

Footnote 121:

“Cosmos,” Bohn’s edition, vol. iii., p. 205.

Footnote 122:

It was, however, asserted by Herlicius that he had seen it on Sept.
27.

Footnote 123:

The spectrum, however, seems to have since become continuous.

Footnote 124:

_Astronomical Journal_, No. 100.

Footnote 125:

_Journal of the British Astronomical Association_, March, 1892.

Footnote 126:

_Journal of the British Astronomical Association_, February, 1895,
vol. v. No. 4.

Footnote 127:

_Ibid._, April, 1895, p. 328.

Footnote 128:

_Journal of the British Astronomical Association_, February, 1892.

Footnote 129:

_The Observatory_, December, 1895.

Footnote 130:

“Planetary and Stellar Studies,” p. 188.

Footnote 131:

_Nature_, September 6, 1894.

Footnote 132:

_Nature_, June 4, 1896.

Footnote 133:

“Cosmos,” vol. iii., Bohn’s edition, p. 192.

Footnote 134:

Humboldt’s “Cosmos,” Bohn’s edition, vol. iv., pp. 327, 328.

Footnote 135:

_Monthly Notices_, Royal Astronomical Society, June, 1888.

Footnote 136:

“Old and New Astronomy,” p. 794.

Footnote 137:

_Nature_, June 4, 1896.

Footnote 138:

_Nature_, September, 1894.

Footnote 139:

_Ibid._, October 4, 1894.

Footnote 140:

“Outlines of Astronomy,” tenth edition, p. 657.

Footnote 141:

_Nature_, November, 21, 1895.

Footnote 142:

_Nature_, January 16, 1896.

Footnote 143:

_Nature_, August 9, 1888.

Footnote 144:

Humboldt’s “Cosmos,” Bohn’s edition, vol, iii., p. 143.

Footnote 145:

See _Knowledge_, June, 1895.

Footnote 146:

“The Universe and the Coming Transits,” p. 200.

Footnote 147:

_Journal of the British Astronomical Association_, May, 1895, p. 383.

Footnote 148:

_Knowledge_, May, 1896.

Footnote 149:

_Knowledge_, July, 1891.

Footnote 150:

_Knowledge_, January, 1894, p. 17.

Footnote 151:

_Journal of the British Astronomical Association_, April, 1895, p.
304.

Footnote 152:

The Italics are Herschel’s.

Footnote 153:

A full discussion of Struve’s views will be found in Chapter XVI. of
“The Visible Universe,” by the present writer.

Footnote 154:

“The Meteoritic Theory,” pp. 380, 381.

------------------------------------------------------------------------

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