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Title: New Theories in Astronomy
Author: Willam Stirling
Release Date: April 10, 2014 [EBook #45356]
Language: English
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NEW THEORIES IN ASTRONOMY
BY
WILLIAM STIRLING
CIVIL ENGINEER
[Illustration]
London:
E. & F. N. SPON, LIMITED, 57 HAYMARKET
New York:
SPON & CHAMBERLAIN, 123 LIBERTY STREET
1906
TO THE READER.
Mr. William Stirling, Civil Engineer, who devoted the last years of his
life to writing this work, was born in Kilmarnock, Scotland, his father
being the Rev. Robert Stirling, D.D., of that city, and his brothers,
the late Mr. Patrick Stirling and Mr. James Stirling, the well known
engineers and designers of Locomotive Engines for the Great Northern
and South Eastern Railways respectively.
After completing his studies in Scotland he settled in South America,
and was engaged as manager and constructing engineer in important
railway enterprises on the west coast, besides other concerns both in
Peru and Chile; his last work being the designing and construction
of the railway from the port of Tocopilla on the Pacific Ocean to
the Nitrate Fields of Toco in the interior, the property of the
Anglo-Chilian and Nitrate Railway Company.
He died in Lima, Peru, on the 7th October, 1900, much esteemed and
respected, leaving the MS. of the present work behind him, which is now
published as a tribute to his memory, and wish to put before those who
are interested in the Science of Astronomy his theories to which he
devoted so much thought.
CONTENTS.
PAGE
INTRODUCTION. 1
CHAPTER I.
The bases of modern astronomy. Their late formation 18
Instruments and measures used by ancient astronomers 19
Weights and measures sought out by modern astronomers 20
Means employed to discover the density of the earth.
Measuring by means of plummets not sufficiently exact 20
Measurements with torsion and chemical balances more accurate 21
Sir George B. Airy's theory,
and experiments at the Harton colliery 22
Results of experiments not reliable.
Theory contrary to the Law of Attraction 23
Proof by arithmetical calculation of its error 24
Difficulties in comparing beats of pendulums at top
and bottom of a mine 26
The theory upheld by text-books without proper examination 27
Of a particle of matter within the shell of a hollow sphere.
Not exempt from the law of Attraction 28
A particle so situated confronted with the law of the
inverse square ofdistance from an attracting body.
Remarks thereon 29
It is not true that the attraction of a spherical shell
is "zero" for a particle of matter within it 31
CHAPTER II.
The moon cannot have even an imaginary rotation on its axis,
but is generally believed to have.
Quotations to prove this 33
Proofs that there can be no rotation. The most confused
assertion that there is rotation shown to be without
foundations 35
A gin horse does not rotate on its axis in its revolution 37
A gin horse, or a substitute, driven instead of being a driver 38
Results of the wooden horse being driven by the mill 38
The same results produced by the revolution of the moon.
Centrifugal force sufficient to drive air and water
away from our side of the moon 39
That force not sufficient to drive them away from
its other side 40
No one seems ever to have thought of centrifugal force in
connection with air and water on the moon 41
Near approach made by Hansen to this notion 41
Far-fetched reasons given for the non-appearance
of air and water 42
The moon must have both on the far-off hemisphere 44
Proofs of this deduced from its appearance at change 44
Where the evidences of this may be seen if looked for
at the right place. The centrifugal force shown to
be insufficient to drive off even air, and less water,
altogether from the moon 45
The moon must have rotated on its axis at one period
of its existence 47
The want of polar compression no proof to the contrary 48
Want of proper study gives rise to extravagant conceptions,
jumping at conclusions, and formation of
"curious theories" 48
CHAPTER III.
Remarks on some of the principal cosmogonies. Ancient notions 49
The Nebular hypothesis of Laplace. Early opinions on it.
Received into favour. Again condemned as erroneous 50
Defects attributed to it as fatal. New cosmogonies advanced 51
Dr. Croll's collision, or impact, theory discussed 53
Dr. Braun's cosmogony examined 59
M. Faye's "Origine du Monde" defined 61
Shown to be without proper foundation, confused, and
in some parts contradictory 65
Reference to other hypotheses not noticed. All more or less
only variations on the nebular hypothesis 70
Necessity for more particular examination into it 71
CHAPTER IV.
Preliminaries to analysis of the Nebular hypothesis 72
Definition of the hypothesis 73
Elements of solar system. Tables of dimensions and masses 75
Explanation of tables and density of Saturn 78
Volume, density and mass of Saturn's rings, general remarks
about them, and satellites to be made from them 79
Future of Saturn's rings 79
Notions about Saturn's satellites and their masses 80
Nature of rings seemingly not well understood 81
Masses given to the satellites of Uranus and Neptune.
Explanations of 81
Volumes of the members of the solar system at density of water 82
CHAPTER V.
Analysis of the Nebular Hypothesis. Separation from the nebula
of the rings for the separate planets, etc. 83
Excessive heat attributed to the nebula erroneous
and impossible 84
Centigrade thermometer to be used for temperatures 85
Temperature of the nebula not far from absolute zero 86
Erroneous ideas about glowing gases produced by collisions
of their atoms, or particles of cosmic matter in the
form of vapours 86
Separation of ring for Neptune. It could not have been
thrown off in one mass, but in a sheet of cosmic matter 87
Thickness and dimensions of the ring 88
Uranian ring abandoned, and its dimensions 89
Saturnian ring do. do. 90
Jovian ring do. do. 91
Asteroidal ring do. do. 93
Martian ring do. do. 94
Earth ring do. do. 95
Venus ring do. do. 96
Mercurian ring do. do. 97
Residual mass. Condensation of Solar Nebula to various
diameters, and relative temperatures and densities 98
Unaccountable confusion in the mode of counting absolute
temperature examined and explained. Negative 274 degrees
of heat only equal 2 degrees of absolute temperature 100
The Centigrade thermometric scale no better than any other,
and cannot be made decimal 103
The sun's account current with the Nebula drawn up and
represented by Table III. 104
CHAPTER VI.
Analysis continued. Excessive heat of nebula involved
condensation only at the surface. Proof that this
was Laplace's idea 108
Noteworthy that some astronomers still believe in
excessive heat 109
Interdependence of temperature and pressure in gases
and vapours. Collisions of atoms the source of heat 110
Conditions on which a nebula can be incandescent.
Sir Robert Ball 110
No proper explanation yet given of incandescent
or glowing gas 112
How matter was thrown off, or abandoned by the Jovian nebula 115
Division into rings of matter thrown off determined
during contraction 116
How direct rotary motion was determined by friction and
collisions of particles 117
Saturn's rings going through the same process.
Left to show process 118
Form gradually assumed by nebulæ. Cause of Saturn's
square-shouldered appearance 120
A lens-shaped nebula could not be formed by
surface condensation 120
Retrograde rotary motion of Neptune and Uranus, and
revolution of their satellites recognised by
Laplace as possible 121
Satellites of Mars. Rapid revolution of inner one may
be accounted for 123
Laplace's proportion of 4000 millions not reduced but
enormously increased by discoveries of this century 124
CHAPTER VII.
Analysis continued. No contingent of heat could be imparted
to any planet by the parent nebula 126
Only one degree of heat added to the nebula from the
beginning till it had contracted to the density
of 1/274th of an atmosphere 127
Increase in temperature from 0° to possible average of 274°
when condensed to 4,150,000 miles in diameter 127
Time when the sun could begin to act as sustainer of life
and light anywhere. Temperature of space 128
The ether devised as carrier of light, heat, etc.
What effect it might have on the nebula 129
First measure of its density, as far as we know 130
The estimate _too_ high. May be many times less 133
Return to the solar nebula at 63,232,000 miles in diameter 134
Plausible reason for the position of Neptune not conforming
to Bode's Law. The ring being very wide had separated
into two rings 134
Bode's law reversed. Ideas suggested by it 135
Rates of acceleration of revolution from one
planet to another 137
Little possibility of there being a planet in
the position assigned to Vulcan 138
Densities of planets compared. Seem to point to differences
in the mass of matter abandoned by the nebula at
different periods 138
Giving rise to the continuous sheet of matter separating
into different masses. Probably the rings had to arrive
at a certain stage of density before contracting
circumferentially 139
Possible average temperature of the sun at the present day.
Central heat probably very much greater 140
Churning of matter going on in the interior of the sun,
caused by unequal rotation between the equator
and the poles 140
CHAPTER VIII.
Inquiry into the Interior Construction of the Earth.
What is really known of the exterior or surface 142
What is known of the interior 143
Little to be learned from Geology, which reaches
very few miles down 144
Various notions of the interior 145
What is learnt from earthquake and volcanoes.
Igno-aqueous fusion, liquid magma. 146
Generally believed that the earth consists of solid matter
to the centre. Mean density. Surface density 147
More detailed estimate of densities near the surface 148
Causes of increased surface density after the crust
was formed 148
Calculations of densities for 9 miles deep, and from
there to the centre forming Table IV. 150
Reflections on the results of the calculations 151
Notion that the centre is composed of the heaviest metals.
"Sorting-out" theory absurd 151
Considerations as to how solid matter got to the centre 152
Gravitation might carry it there, but attraction could not 153
How the earth could be made out of cosmic matter,
meteorites or meteors 154
CHAPTER IX.
Inquiry into the Interior Construction of
the Earth--_continued_ 165
The earth gasiform at one period. Density including the moon
may have been 1/10,000th that of air. Must have been a
hollow body. Proofs given 166
Division of the mass of the earth alone into two parts 169
Division of the two masses at 817 miles from surface 171
Reasons why the earth cannot be solid to the centre 172
Gasiform matter condensing in a cone leaves apex empty 172
Proportions of the matter in a cone 173
Calculations of the densities of the outer half of the hollow
shell of the earth. Remarks upon the condensation 174
Calculations of inner half of the hollow shell 175
Remarks upon position of inner surface of the shell 177
Calculations of the same 179
CHAPTER X.
Inquiry into the interior construction of
the Earth--_continued_ 184
Density of 8·8 times that of water still too high for the
possible compression of the component matter of the
earth as known to us 185
Reasons for this conclusion drawn from crushing strains
of materials 186
A limit to density shown thereby 187
The greatest density need not exceed 6·24 of water 188
Gases shut up in the hollow centre. Their weight must so
far diminish the conceded maximum of 6·24 189
Density of inner half of earth at 3000 miles diameter.
Greatest density may be less than 5·833 of water 190
Supposed pressure of inclosed gases very moderate 191
Meaning of heat limit to density. Temperature of interior
half of shell and inclosed gases must be equal 193
State of the hollow interior 194
Results of the whole inquiry 195
CHAPTER XI.
The Earth. The idea entertained by some celebrated men,
and others 197
Difficulties of forming a sphere out of a lens-shaped nebula 199
Various studies of the earth's interior made for special
purposes. Difficulty some people find in conceiving
how the average density of little over 5·66 can be
possible, the earth being a hollow sphere 200
What is gained by its being a hollow shell 201
Geological theories of the interior discussed. Volcanoes
and earthquakes in relation to the interior 202
Liquid matter on the interior surface of the shell, and
gases in the hollow, better means for eruptions than
magma layers 206
Focal depths of earthquakes within reach of water,
but not of lavas 207
Minute vesicles in granite filled with gases, oxygen and
hydrogen, but not water 209
The Moon. A small edition of the earth 211
Rotation stopped. Convulsions and cataclysms caused thereby.
Air, water, vapour driven off thereby to far-off
hemisphere. Liquid matter in hollow interior would
gravitate to the inside of the nearest hemisphere 212
Form and dimensions during rotation. Altered form after
it stopped 213
Agreeing very closely with Hansen's "curious theory" 214
CHAPTER XII.
Some of the results arising from the sun's being
a hollow sphere 215
Repetition of the effects of condensation on the
temperature of the nebula 216
Ideas called up by the apparently anomalous increase
of temperature 217
How heat is carried from the sun to the earth 218
The sun supposed to radiate heat only to bodies that can
receive and hold it, and not to all space. The heat
of the sun accumulated in a hot box to considerably
beyond the boiling point of water 219
The heat accumulated in this way supposed to be due to a
peculiar function of the ether, as it is a fact that
heat can be radiated from a cold to a hot body 220
The sun must be gaseous, or rather gasiform, throughout.
No matter in it solid or even liquid. Divisions and
densities of shell 221
The hollow centre filled with gases, whose mass naturally
diminishes the mean density of the whole body 222
The amount of this reduction so far defined. The presence
of gases or vapours in the hollow a natural result
of condensation 223
The hollow centre filled with gases not incompatible with
the sun's being a hollow sphere. The temperature at
the centre may be anything, not depending on any
law of gases 223
Further exposition of hollow-sphere theory put off till after
further development of the construction of the sun 224
CHAPTER XIII.
The ether. Its nature considered. Behaves like a gas 226
Can be pumped out of a receive 227
Light and heat do not pass through a tube _in vacuo_.
Laboratory experiments examined 228
Light and darkness in a partial vacuum, though high 229
Electricity not a carrying agent 230
Why there are light and dark strata in a high vacuum 232
The real carrying agent through a high vacuum is the residue
of ether left in it. Digression to consider the aurora 233
How air may be carried to extraordinary heights. Zones of
air carried up are made luminous by electricity 234
Comparison of this method with experiments quoted 236
Experiment suggested to prove whether light passes freely
through a vacuum tube 237
The ether does not pervade all bodies freely 238
It must be renounced altogether or acknowledged to be a
material body, subject to expansion, condensation,
heating or cooling 239
How light and heat pass through glass 239
Temperature of the ether variable. Zodiacal light, cause of 240
CHAPTER XIV.
The ether considered and its nature explained. Further proofs
given by Dr. Crookes's work, of its material substance 244
Highest vacuum yet produced. Absorbents cannot absorb
the ether 246
Dr. Crookes's definition of a gas. Not satisfactory. Why 247
A fluid required to pump matter out of a vessel 248
Gas as described by Dr. Crookes would not suit 249
The ether the only elastic fluid we have. The only real gas,
if it is a gas 250
A possible measure of the density of the ether 250
Causes of dark and light zones in high vacua 251
The real conductor of light in a high vacuum 252
How a vacuum tube glows, when electricity passes through it 254
Conclusions arrived at through foregoing discussions 255
Some exhibitions of light explained 256
Gases can be put in motion, but cannot move even themselves 257
The ether shown to be attraction. And primitive matter also 258
All chemical elements evolved from it. Its nature stated 259
Action at a distance explained by the ether and attraction
being one and the same 259
CHAPTER XV.
Construction of the solar system. Matter out of which
it was formed 261
Domains of the sun out of which the matter was collected 262
Stars nearest to the sun. Table VII. showing distances 263
Remarks on Binary Stars. Table VIII. showing spheres of
attraction between the sun and a very few 265
Sirius actually our nearest neighbour. Form of the sun's
domains of a very jagged nature 266
Creation of matter for the nebulæ, out of which the whole
universe was elaborated. Beginning of construction 267
The law of attraction begins to operate through the
agency of evolution 267
Form of the primitive solar nebula. The jagged peaks
probably soon left behind in contraction 268
How the nebula contracted. Two views of the form it might
take. Comparison of the two forms, solid or hollow 269
The hollow centre form adopted. The jagged peaks left behind 272
The nebula assuming a spherical form. Shreds, masses,
crescents separated from one side 273
Probable form of interior of nebula. Compared with envelopes
in heads of some comets 274
Reflections on the nebula being hollow.
Opinions of others quoted 275
The matter of a sphere solid to the centre must
be inert there 276
Further proofs of the nebula being hollow 277
How rotary motion was instituted 278
Such a nebula might take one of two forms 279
The form depending on the class of nebula. Planetary in the
case of the solar system. A similar conception of how
rotary motion could be instituted 280
CHAPTER XVI.
The sun's neighbours still exercise their attraction over him 282
Regions of greatest density in the 9 nebulæ dealt with;
compared with the orbits of the planets made from them 283
Results of comparison favourable to the theory 287
Differences of size in the planets have arisen from
variations in the quantity of matter accumulating
on the nebulæ 289
Causes of the retrograde motions in Neptune, Uranus,
and their satellites 290
Probable causes of the anomalous position of Neptune 292
Rises and falls in the densities and dimensions of
the planets explained 293
The form of the nebulæ must have resembled a dumb-bell 295
More about rises and falls in densities 296
Reason why the Asteroid nebula was the least dense
of the system 297
Not necessary to revise the dimensions given to the 9 nebulæ 298
Causes of the anomalies in the dimensions, densities, etc.,
of the Earth and Venus 299
The strictly spherical form of the sun accounted for.
But it may yet be varied 299
Repetition that a spherical body could not be made from a
lens-shaped nebula by attraction and condensation 300
CHAPTER XVII.
Former compromises taken up and begun to be fulfilled 301
Estimates of the heat-power of the sun made only from
gravitation hitherto 302
Contraction and condensation of a nebula solid to the
centre. Heat produced from attraction as well as
by gravitation 303
What quantity of heat is produced by a stone falling
upon the earth 304
Showing again that there is a difference between
attraction and gravitation 305
Contraction and condensation of a hollow-sphere nebula,
in the same manner as the solid one 305
Differences of rotation would be greater in a hollow nebula;
because a great deal of the matter would be almost
motionless in a solid sphere 306
In neither case could matter be brought to rest, but only
retarded in motion. Different periods of rotation
accounted for 307
Table of different rates explained 309
Heat produced by gravitation, attraction and churning,
not all constituents of the heat-power of the sun 310
There can be no matter in the sun so dense as water 311
The hollow part of the sun acting as a reservoir of
gases, heat and pressure 312
The behaviour of heat produced in the nebula, and its power 313
How sun-spots are produced 314
Cyclonic motions observed in sun-spots. Why not all in
certain directions, and why only observed in a very few 315
Cyclonic motions in prominences treated of 316
Many other things might be explained, on some of which we
do not dare to venture. Concluding observations 317
CHAPTER XVIII.
Return to the peaks abandoned by the original nebula.
An idea of their number 319
Example of their dimensions. What was made out of them 320
What could be made from one of them 321
How it could be divided into comets and meteor swarms 322
An example given. How a comet may rotate on its axis.
And what might be explained thereby. Orbits and
periods of revolution 323
Not ejected from planets. Their true origin 324
Study of the velocities in orbit of comets, and
results thereof 326
How far comets may wander from the sun and return again 327
No reason why comets should wander from one sun to another.
Confirmatory of the description, in Chapter XV. of the
sun's domains 328
Of the eternal evolution and involution of matter.
The atmosphere and corona of the sun 329
Partial analogy between it and the earth's atmosphere 331
The density of it near the sun's surface cannot be normally
less than 28 atmospheres, but might be so partially
and accidentally 332
Probable causes of the enormous height of its atmosphere 332
The mass taken into account, but cannot be valued 334
Most probably no matter in the sun exceeds half the density
of water. The unknown line in the spectrum of the
corona belongs to the ether 335
NEW THEORIES IN ASTRONOMY.
INTRODUCTION.
That a little knowledge is a dangerous thing to the possessor, has
been pointed out often enough, probably with the idea of keeping him
quiet, but it is very certain that the warning has not always had the
desired effect; and in some respects it is perhaps much better that it
has not, for it is sometimes the case that a little knowledge exhibited
on an inappropriate occasion, or even wrongly applied, throws light
upon some subject that was previously not very well understood. It
sometimes happens that unconscious error leads to the discovery of what
is right. The fact is, all knowledge is at first little, so that if
the first possessor of it is kept quiet there is little chance of its
ever increasing. On the other hand, much knowledge seems to be quite
as ready to become dangerous on occasion, for it has sometimes led its
possessor to fall into errors that can be easily pointed out, even by
the possessor of little, if it is combined with ordinary intelligence.
The possessor of much knowledge is apt to forget, in his keen desire
to acquire more, that he has not examined with sufficient care all the
steps by which he has attained to what he has got, and that by placing
reliance on one false step he has erected for himself a structure that
cannot stand; or, what is worse perhaps, has prevented those who have
followed him in implicit dependence on his attainments and fame from
finding out the truth. If, then, both of these classes are liable to
fall into error, there appears to be no good reason why one belonging
to the first mentioned of them should absolutely refrain from making
his ideas known, especially as he may thus induce someone of the
second to re-examine the foundations on which he has built up his
knowledge.
These reflections are in greater or lesser degree applicable to all
knowledge and science of all kinds, even theological, in all their
individual branches, and can be very easily shown to be both reasonable
and true. And it may be added, or rather it is necessary to add, that
every one of all the branches of all of them has a very manifest
tendency towards despotism; to impose its sway and way of thinking upon
the whole world.
At various intervals during the present century speculation has been
indulged in, and more or less lively discussion has taken place about
the great benefit it would confer on universal humanity, were all the
weights and measures of the whole earth arranged on the same standard.
The universal standard proposed has been, of course, the metrical
system, which had been elaborated by French _savants_ who most probably
thought they had arrived at such a state of knowledge that they were
able to establish the foundations of all science of all kinds and
for all time, upon the most sure and most durable principles. These
periods of metrical fever, so to speak, seem to come on without any
apparent immediately exciting cause, and some people succumb to the
disease, others do not, just the same as in the cases of cholera,
influenza, plague, etc. Whether some species of inoculation for it may
be discovered, or whether it will be found that an unlimited attack is
really perfect health, will most probably be found out in the course of
time, although it may be some centuries hence. What is of interest to
understand at the present time is, what are the benefits to be derived
from the proposed universal standard of weights and measures, and how
they are to be attained.
The principal and most imposing reason for its adoption is that it
would be of immense service to scientific men all over the world,
who would thus be able to understand the discourses, writings,
discoveries, etc. of each other without the necessity of having to
enter into calculations of any kind in order to be able to comprehend
the arithmetical part of what they have listened to or read. Another
argument brought forward in favour is, that it would greatly facilitate
commercial transactions with foreign countries; and it has been lately
advanced that great loss is suffered by one country selling its goods,
manufactured according to its own measures, in countries where the
metrical system has been adopted. Yet another advantage held out is
the convenience it would be to travellers in money matters; but as
this argument cannot be admitted without taking into consideration
the necessity for one universal language all over the world, it has
practically no place in any discussion on the subject, until the evil
caused by the building of the Tower of Babel has been remedied.
Not long after one of the periodical attacks of metric fever we came
upon an essay written by J. J. Jeans on "England's Supremacy," and
published in New York by Harper and Brothers, in 1886, in which we
found the following:--
Numerical relation of occupations in England and Wales in 1881:
Professional 2·5 per cent.
Domestic 7·0 "
Agricultural 5·3 "
Commercial 3·7 "
Industrial 24·5 "
In all 43·0 "
This statement shows that 43 per cent. of the whole population are
occupied in some business or work of some kind, and leads us reasonably
to suppose that the remaining 57 per cent. consist of women, children,
and people who--to put it short--are non-producers; the whole of whom
can hardly be considered as much interested in the making of any
alterations in the weights and measures of their country, rather the
contrary, for they cannot expect to be much benefited by any change.
The professional class naturally comprehends Theology, Law, Medicine,
and Science generally, so that the 2·5 per cent. ascribed to it would
be seriously reduced, if the advantage derived from the desired change
were reckoned by the number really benefited by it. A similar reduction
would have to be made on the 3·7 per cent. stated to be occupied in
Commerce, as it is not to be supposed that the whole of the number
are engaged in foreign trade. Thus the number of people in these two
classes who might really reap some advantage from the change, may
be reduced by at least one half; and if we consider that one person
in ten of those occupied in the Agricultural and Industrial classes
is a scientist--we may pardon the Domestic class--a very liberal
allowance indeed, we arrive at the conclusion that 6 per cent. of the
whole population might find, some more, some less, interest in the
introduction into our country of the French metric system.
The above statement refers only to England and Wales, but if Scotland
and Ireland are added to them, the 6 per cent. proportion could not
be very greatly altered: perhaps it would be less favourable to the
change. Thus 94 per cent., or something like 37 millions, of the whole
population of the United Kingdom would be called upon to change their
whole system of weights and measures, in order that 6 per cent.,
or somewhere between 2 and 2-1/2 millions, should find some little
alleviation in a part of their labours; and surely 2 to 2-1/2 millions
of scientists and merchants engaged in foreign trade is a very liberal
allowance for the population of our country. If this does not show a
tendency towards despotism, it would be hard to tell what it does show.
Of course, it would not be fair to assume that the whole of the 6 per
cent. would desire to see the proposed change carried into effect. In
all likelihood, a very considerable portion of the number would be
disposed to count the cost of erecting such a structure before actually
laying its foundations, and would refrain from beginning the work on
considering by what means it was to be brought to a conclusion; even
without going so far as to find out that 94 per cent. of it at least
would have to be done by forced labour. They might even go the length
of speculating on how long it would take to coerce the 94 per cent.
into furnishing the forced labour, and on the hopelessness of the task.
On the other hand, they might think it more natural to lay hold of the
alternative of adopting a special system of weights and measures for
the use of Science and Foreign Commerce alone, and leave the 94 per
cent. to follow their own national and natural customs, which they
would be very likely to do whatever might be determined, if we may
judge by the progress made in France a century after the system was
thought to be established. Very little opposition could be made to
such a course, and if the best possible system were not adopted, the
scientists would be the only parties put to inconvenience. They could
improve and reform it, should they find it not to be perfect, without
the necessity of coercing the 94 per cent. into furnishing another
contingent of forced labour. But little is to be gained by saying any
more about it. Should the metrical system be adopted some day by Act
of Parliament, Science will have obtained what it has so long coveted,
will be quite satisfied, and will trouble itself very little about how
it affects the rest of the population. It will perhaps never even think
of how India will be brought to buy and sell through the medium of the
French Metrical System.
And now we have only one step to take on this subject. We may say
that the project of establishing one standard of weights and measures
for the whole world has a most unpleasant resemblance to the object
proposed by the builders of the Tower of Babel; the only thing that
can be said in its favour being that it points towards an endeavour to
do away with the bad results produced by that enterprise and to bring
matters back to the state the world was in before the foundations of
that celebrated edifice were laid.
The foregoing is only one instance of the many that could be cited
where science has schemed projects for universal progress without due
thought, and has come to the conclusion that they could be easily
carried out. There are as many examples of this jumping at conclusions
as would fill many books, which of course it is not our purpose to
do; but there is one that it is necessary to have brought forward for
examination, because of its having, through a most incomprehensible
want of thought, a tendency to establish Natural Religion on the very
bases upon which the Christian Religion is established.
The one referred to is that by which some of the most eminent
scientists of the present century, following up what was done in former
times, have been able by deep study and experiment, unfortunately
coupled with unaccountable blindness or preconceived erroneous ideas,
to formulate processes by which the whole universe may have elaborated
itself from protyle and protoplasm, or some such substances which,
without any foundation to build upon, they suppose to have existed
from all eternity. This advance in science has been called the Theory
of Evolution, and has been very generally considered to be new, or of
comparatively very recent conception; but it is only a piece of the
evidence of a very general propensity in those who come to acquire a
little more knowledge, to flatter themselves that they have power to
seize hold of the Unknown.
The theory may be _new_, but evolution most assuredly is not, as any
one may convince himself who will take the trouble to read the first
chapter of the Book of Genesis _and to think_. There he will find it
stated that the earth and all things in it and on it were created and
made in six days, or periods of time, showing him distinctly, if he
does not shut his eyes wilfully, that two operations were employed in
the process, one of creation and the other of making, which last can
mean nothing but _evolution_. It does not matter a straw whether the
latter operation was carried on personally by the Creator and Maker,
or under the power of laws ordained by Him for the purpose; it was
evolution all the same, and just the kind of evolution the scientists
above alluded to would have us believe to be new, not far from 3500
years after the account of the creation and making of the world was
written by Moses.
It will do no harm to take special notice of the work that was done
in each of the six periods, as it will help to fix attention on the
subject during examination and judgment; and may even tend to open the
eyes of any one who had made up his mind to keep them shut.
In the first period the heavens and the earth were created, but the
earth was without form and void, _inanis et vacuus_, according to _The
Vulgate_--(does that mean empty and hollow?)--and darkness was upon the
face of the deep; but light was _let_ shine upon the earth to alternate
with darkness, and between the two to establish day and night. It
is therefore evident that after the earth was created it had to be
reduced to something like its present form, a globe of some kind, and
to rotate on an axis, otherwise there could have been no alternations
of light and darkness, of day and night. Where did the light come from?
Some people seem to think that Moses should have included a treatise
on the creation and evolution of the universe, in his account of the
work done in the first period of creation. For all that can be truly
said to the contrary, he seems to have been quite as able to do so
as any scientist of the present day; but it is evident he thought it
best to limit himself to writing only of the earth, as being of most
interest to its inhabitants, and enough for them as a first lesson.
The literature of science, however, of the present day, will tell them
that long ages after the earth was _evolved_ into a globe, it must have
been in a molten, liquid state, surrounded by an atmosphere of vapours
of some of the chemical elements so dense that no light from without
could shine through it, and could only be penetrated by light after
the cooling of the earth had dispelled a sufficient portion of that
dense atmosphere. With this explanation, which they had at hand for the
looking for, they might have been so far satisfied, and have left Moses
to tell his story in his own way.
In passing, it may not be out of place to say that, after the cooling
of the earth had proceeded so far that the vapours of matter had
been condensed and precipitated on its surface, all boiling of water
whether in the seas or on its surface must soon have ceased, so that
no inconceivably enormous volumes of steam could be thrown upwards
to maintain an atmosphere impenetrable to light; and that when dense
volumes of steam ceased to be thrown up, the condensation of what was
already in the atmosphere would be so rapid, and its density so soon
reduced sufficiently to admit of the passage of light through it, that
one can almost fancy himself present on the occasion and appreciate the
sublimity of the language. "And God said, Let there be light, and there
was light"; more especially if he had ever stood by the side of the
cylinder of a large steam engine, and understood what he heard when the
steam rushed from it into the condenser, and noted how instantaneous it
seemed to be. Any one who has watched a pot of water boiling on the
fire and emitting clouds of steam, will have noticed how immediately
the boiling ceased whenever the pot was removed from the fire; but
he will also have noticed that the water still continued to emit a
considerable quantity of vapour, and will be able to understand how it
was that the cloudy atmosphere of the earth, at the time we are dealing
with, could allow light to pass through it but still keep the source of
light from being visible. He experiences daily how thin a cloud will
hide the sun from his sight. But there is more to be said about this
when the time comes for taking note of the actual appearance on the
scene of the sun, moon, and stars.
To obtain some rude idea of the time to be disposed of for evolution
during the first period, let it be supposed that the whole of the time
consumed in the creation and development of the earth was 300 million
years, as demanded by some geologists, the first period of the six
would naturally be somewhere about 50 millions of years, a period which
would allow, probably, very liberal time for evolution, but could never
have been consumed in creation, seeing that creation has always been
looked upon as an almost instantaneous act. And if anyone is still
capable of exacting that the period was a day of twenty-four hours, he
has to acknowledge that at least twenty-three of them were dedicated to
the work of evolution.
The second period was evidently one solely of evolution, as all that
was done during it was confined to _making_ the firmament which
divides the waters from the waters; an operation which could never be
confounded with creation, being probably brought about solely by the
cooling of the earth, which was the only means by which a separation
between the waters covering the earth, and those held in suspension
above it by the atmosphere, could be brought about, and must have been
purely the work of evolution.
The third period was begun by collecting the waters under the firmament
into one place and letting the dry land appear; which, it may be well
to note, gives it to be understood that the surface of the solid
part of the earth had come to be uneven either by the elevation or
depression, perhaps both, of some parts of it, and next the earth was
_let_ bring forth grass and trees, and in general vegetation of all
kinds. These cannot be considered otherwise than as operations of
evolution: there was no creation going on beyond what may have been
necessary to help evolution, and of that not a word is said. Here it is
well to notice that until the waters were gathered together into one
place and the dry land appeared there could be no alluvial deposits
made in the sea, and that till well on into this third period, that is
well on for 150 million years from the beginning, there could be no
geological strata deposited in it containing vegetable matter, for the
very good reason that although rains and rivers may have swept earthy
matter into the sea, the rivers could not carry along in their flow any
vegetable matter until it had time to grow.
Should evolutionists think they have discovered something new in
spontaneous generation, we refer them to the 11th verse of the chapter,
where they will see--"And God said, Let the earth bring forth grass,
the herb yielding seed, and the fruit-tree yielding fruit after his
kind, whose seed is in itself, upon the earth." The conclusion of this
passage asserts plainly that the seed was already in the earth, somehow
or other, ready to germinate and sprout when the necessary accompanying
conditions were prepared. The words are very few, and they can have no
other meaning.
In the first period "God made two great lights: the greater light to
rule the day and the lesser light to rule the night; he made the stars
also." This passage has been "a stumbling block and rock of offence"
to some people possessed of much knowledge and to some possessed of
little; the one party professing to disbelieve all because the sun was
_made_ four days after there was light, and the other party, supposing
that there might have been light proceeding from some other source
during the first four days. Both parties seem to have forgotten that
the earth was created without form and void, and that being so the same
would naturally be the case with the sun and the moon; all of them had
to be made into form after their creation. By what means? By evolution,
of course, or whatever else anyone chooses to call it; that will make
no difference.
As far as it can penetrate into the mysteries of creation, Physical
Astronomy has endeavoured to show how the solar system may have been
formed out of a mass of nebulous matter. Furthermore, as has already
been adduced in evidence, that at one time the earth must have been
a molten, liquid globe surrounded by vapours of metals, metalloids,
gases, and finally by water; and even goes the length of supposing
that the planets were evolved to something approaching their present
state, long before the sun attained its present form. Following up this
hypothesis, it is more than probable that the sun had not attained that
form when this fourth period began, and, although capable of emitting
light early in the first period, still required a vast amount of
evolution to reduce it to the brilliant globe now seen in the heavens.
Everybody knows that plants grow without sunshine, and it is generally
believed that the primary forests of the earth grew most rapidly in
a moist, stifling atmosphere, which neither admitted of animal life,
nor could be penetrated by sunshine. Thus Physical Astronomy cannot
say that the sun could not have been made into its present state until
near the end of this fourth period. It _may_ have been as bright as it
is now, though very probably not, as we shall see in due time; but it
could not _shine_ upon the earth, neither could the earth, nor anything
thereon, see it. It is not necessary to say anything about the moon, as
it only reflects sunlight, and the reflection could not reach the earth
if the light could not.
In the fifth period the waters were _let_ "bring forth the moving
creature that hath life, and fowl that may fly above the earth in the
open firmament of heaven." Here again spontaneous generation may have
been provided for beforehand, the same as in the case of vegetation.
Also it is said "God created great whales," and it is to be observed
that this is only the second time that creation has been mentioned in
the book, and would seem to teach that _making_, or evolution, was the
most active agent at work in the construction of the earth--and, we may
add, of the universe.
The sixth period was one almost exclusively of evolution, unless it
should be considered that spontaneous generation is a different, and
newly discovered process. In it God _made_ the beast of the earth,
cattle, and everything that creepeth upon the earth, after his kind.
Last of all: "God said, let us make man in our image, after our
likeness." Thus it appears that the only work of creation done in this
period was that of creating man, and even that _after_ some length of
time and work had been expended in _making_ or _evolution_, which may
have extended over a very considerable portion of the fifty millions of
years corresponding to it.
We have supposed the work of creation to have extended over three
hundred million years to satisfy some geologists, but our arguments
would not be affected in any way by the time being reduced to the limit
given by Lord Kelvin to the heat-giving power of the sun in the past,
which he has made out to be between fifteen and twenty million years.
That would only limit our periods of evolution to two and a half or
three million years each; each of them quite long enough to be totally
inconsistent with our ideas of creation, which conceive of this as an
instantaneous act. But although Lord Kelvin has in rather strong terms
placed this limit, he at the same time says that it could by no means
exceed four hundred million years, which is one-third more than we have
calculated upon. Neither can our arguments be affected in any serious
way by our dividing the periods into fifty million years each; these
may have varied much in length, but whatever was taken from one would
have to be added to the others.
Furthermore, we may be allowed to say that fifteen to twenty millions
of years of the sun's heat at the rate it is now being expended, can be
no reliable measure of the time required for the operations of geology,
for the reason that its heat must have been emitted in proportion to
the quantity it possessed at any time. When it was created without form
and void as no doubt it was, the same as the earth, it would have no
heat to emit, but that does not mean that it possessed no heat until
it was formed into the brilliant globe that we cannot now bear to turn
our eyes upon. Even when it became hot enough to show light sufficient
to penetrate the "darkness that was upon the face of the deep," it
may still have been an almost shapeless mass, and have continued more
or less so until it was formed into the body of the fourth period,
which may even then have been very different from what it is now. Thus
geology would have not far from one hundred and fifty million years
in which a very small fractional part of the sun's emission of heat
would suffice for its operations. But we shall have more to say on this
subject when the time comes.
It being, therefore, a matter beyond all question--to people possessed
of the faculty of thinking, and of candour to confess that they
cannot help seeing what has been set plainly before their sight and
understanding--that the opening chapter of the book of Genesis plainly
teaches that making--evolution--had a very large and active part to
perform in the creation of the universe and--much more within our
grasp--of the earth; we can come to the conclusion that the theory
of evolution, instead of being new and wonderful, comes to be almost
infinitely older than the everlasting hills, without losing any of its
power of inspiring inexpressible wonder.
Looking back over the examination into the first chapter of the book of
Genesis we have just concluded, we cannot conceive how it could ever
have entered into the thoughts of man, that the state of vegetable and
animal life on the earth, at the present day, must have been brought
about by continual and unceasing acts of creation, when creation
has been mentioned only on three occasions during the whole process
described in the chapter we have analysed, that is, 3 out of 31 verses;
and while the other processes which we have brought forward--making and
spontaneous generation--have never been alluded to, perhaps not even
thought of.
We have no desire, neither are we qualified, to follow up this subject
any further, but we have still one or two things to bring into
remembrance.
One of the most illustrious of the founders of the Theory of Evolution
has based his dissertations on the Descent of Man, on the Variation
of Animals and Plants under Domestication, and on their _wonderful
plasticity under the care of man_. Here there is an explicit
acknowledgment of the necessity for the direction of an intelligent
guiding power to produce such variations; these never having any useful
or progressive results except under such care. If, then, there is a
necessity of such directing and guiding power in the case of variations
of such inferior importance, the superintendence of some similar power
must have assuredly been much more necessary for the creation and
evolution of matter, of life, and of man himself. This is what, one
would think, common sense and reason would point, and what the Theory
of Evolution seems to think--evidently without studying the subject
far enough; but all that it has been able to do has been to substitute
Nature for the Creator to whom Moses has ascribed not only _Creation_
but the _Making--Evolution_--of the universe.
This naturally leads us to speculate on what Evolutionists consider
Nature to be, and as none of them--nor anyone else--as far as we know,
has ever thought it necessary to define Nature, we have to endeavour
to draw from their writings what, in some measure and some way, they
would like us to believe it to be. We find, then, that the base of
their operations seems to be Natural Selection, which can hardly be
interpreted in any other way than by calling it the Selection of
Nature. Thus, then, they apparently want us to look upon Nature as
the _First Cause_. But, if Nature can select, it must be a being, an
entity, a something, that can distinguish one particle of matter from
another, and be able to choose such pieces of it, be they protyle or
protoplasm, and to make them unite, so as to form some special body,
organic or inorganic. It is plain, also, that Selection can only be
performed by such a being, or something, such as just so far described,
that can distinguish, choose, and arrange the particles of matter
destined to form the very smallest body or the universe. Thus we see
that in whatever way the basis of the Theory of Evolution is looked
upon--_even for its own evolution_--there is required a being of some
kind that has knowledge and power to evolve or make all things that
are "in heaven above, or in the earth beneath, or in the waters under
the earth." So we see that, if the theory of evolution dethrones the
Creator and Evolver of the first chapter of Genesis, it has to enthrone
another god which it calls Nature; and has to get rid of that god, and
any number of others, before it can be what it pretends to be.
We are all very voluble in talking of Nature, and enthusiastic in
admiring its beauties, wonders, and wisdom, but it seldom occurs to
us that we are really doing so without thinking of whence come the
beauty, wonders, and wisdom. We must, therefore, not be too hard on
evolutionists, as they have only done what we all do every day of
our lives; but if the theory of evolution is to be looked upon as a
branch of science, we would recommend its students to open their eyes
and think of it as a process which has been in existence from the
beginning of things at least, and not as one of their invention or
discovery. They may be able some day, through more accurate study and
more convincing argumentation than they generally use, to lay claim to
having discovered, as far as it is possible for man to do, the _modus
operandi_ of evolution, but that is all, and we would also warn some
of them to think that, when we see them in their highest flights of
science, genius, and self-sufficiency, we can
"Conceive the bard the hero of the story."
We have read a good deal of what has been called the War of Science,
without having been able to see that there ever was any cause for such
a war, with the exception of ignorance.
If Theology had been able, or rather had taken the trouble, to study
thoroughly the first chapter of Genesis, and thus to comprehend that,
if the earth was created without form and void, a great deal of
work had to be done, after creation, in forming it into its present
condition, there was no call upon it to find fault with Copernicus or
persecute Galileus, because they said the earth revolved round the
sun; more especially as they do not appear to have ever said anything
against religion or revelation. Neither was there any necessity for
opposing the so-called new science of evolution, because it (Theology)
ought to have seen that the work expended in reducing the earth into
form could hardly be conceived of otherwise than as a process of
evolution; and would thus have been in a position to tell the authors
of the _new_ science that they had only discovered what had existed
before the beginning of time.
On the other hand, there was no occasion for Science to take up the
war. If it, in its turn, had taken the trouble to study and understand
the first chapter of Genesis, it could have shown Theology that _it_
did not comprehend, and could not give a true account of what religion
and revelation are; whereas it (Science) seems to have had a strong
tendency to demonstrate that religion and revelation are altogether
false, and that the great work it has to perform is to dethrone
Theology, and set itself up it in its stead.
It is not worth while even to think of who or which was the aggressor,
seeing that the war originated from ignorance caused by want of thought
and study on both sides. All that has to be said on the subject reduces
itself to the fact that both Religion and Science have been coming,
and are at present going, through the process of evolution. Can anyone
say that Science has been truly scientific, without ever incurring in
error, from the beginning of history up to the present day? Will any
one venture to maintain that there has been no evolution, no progress,
no softening of the spirit of Religion, from the institution of
Christianity up to the end of the nineteenth century? If such there be,
let the one look back to the time of Aristotle, and the other to the
establishment of the Church under Constantine.
There has been for long an opinion, which goes on increasing in
strength, that Science will ultimately reform Theology and put Religion
in its right place; but if such is to be the case, Science has to
begin by reforming itself and putting an end to error it has been, in
many cases, teaching for generations; and by ceasing to formulate new
theories, or bases of progress, which can be in many cases exploded
by suppressing some of the error just alluded to. Little advance is
made in science by forming hypotheses and theories, however brilliant
they may appear, unless they are carefully studied and thought out to
the very uttermost; because, if published abroad on the authority of
some celebrated or even well-known name, they have a tendency to stop
further investigation, and prevent students from exercising their own
judgment and perhaps discovering what they might possibly find out
were they to study them to the very end for their own satisfaction.
This is in some measure the case even with respect to the solar
system. We believe it can be shown that a more complete knowledge and
comprehension of it, and even of the universe, has been kept back by
the unquestioning acceptation by successive astronomers of the ideas
and conceptions of their predecessors.
We have to acknowledge, at the same time, that Astronomy could not
start into perfection at once, any more than any other science, and it
is not to be wondered at that in times past ideas relating to it should
have been formed without being properly thought out; even ideas that
could not be properly thought out to the end for want of the requisite
knowledge. But it is much to be regretted that such ideas should
continue to be published at the present day as trustworthy instruction
for readers who may look upon it as strictly correct. Among those who
read text-books even on Astronomy, there must be a very considerable
number who are rather surprised when they see statements made which do
not agree with what they were taught at school, or with what they have
practised in other sciences in their own professions or trades. It may
be said that any person of ordinary intelligence will easily be able to
correct such errors, but the evil does not stop here. If he can really
correct them he will most probably find as well, that his instructors
have been led into more serious errors, perhaps in more important
matters, founded on the ideas which they had not fully studied out
before giving them a place in their books. He may also find sometimes,
in his reading, such ideas brought forward to substantiate some theory,
just as far as they are required and then dropped, while a step or two
further forward in the examination of these same ideas, would have
exploded the theory altogether; because, although founded to a certain
extent on one law of nature, they are in contradiction with what is
laid down in some other law.
The above will be looked upon as an unwarrantably bold assertion; but a
careful study of, or attention to, what is taught in the most advanced
works on the solar system, even in science generally, will show it to
be perfectly true. It is not only true, but the consequences of its
being true have been much more serious than will be readily believed.
In our own endeavours to understand what we had been reading, we have
seen that some of the notions presented to us were only half formed,
and that they have led to theories being founded which could never
have been entertained at all had they been thoroughly studied out.
More than that, they have prevented the truth from being arrived at in
the fundamental conceptions of the construction of the earth, and, as
a natural consequence, of the whole solar system, perhaps even of the
whole universe.
There are probably many, even a great many, people who have arrived
at the same conclusions as we have, but as far as it has been in our
power to search into the matter, we have met with no attempt from any
quarter to put an end to this defect in the literature of science;
perhaps because the work has the appearance of being too great to be
readily undertaken, and also because it may be thought that there is
little to be gained by it--as all is sure to be set right through time.
But, as we believe that it will be beneficial immediately, in the case
of the earth and solar system at least, we shall first attempt to show
what are some of the defects alluded to, and then what knowledge may be
acquired through their removal.
CHAPTER I.
PAGE
18 The bases of modern astronomy. Their late formation
19 Instruments and measures used by ancient astronomers
20 Weights and measures sought out by modern astronomers
20 Means employed to discover the density of the earth.
Measuring by means of plummets not sufficiently exact
21 Measurements with torsion and chemical balances more accurate
22 Sir George B. Airy's theory,
and experiments at the Harton colliery
23 Results of experiments not reliable.
Theory contrary to the Law of Attraction
24 Proof by arithmetical calculation of its error
26 Difficulties in comparing beats of pendulums at top
and bottom of a mine
27 The theory upheld by text-books without proper examination
28 Of a particle of matter within the shell of a hollow sphere.
Not exempt from the law of Attraction
29 A particle so situated confronted with the law of the
inverse square ofdistance from an attracting body.
Remarks thereon
31 It is not true that the attraction of a spherical shell
is "zero" for a particle of matter within it
Before astronomers could begin to determine the relative distances
from each other, and the relative dimensions and masses of the
various members of the solar system, they had to establish scales of
measurements appropriate to their undertaking. This entailed upon
them, of course, the necessity of determining the form, the different
circumferences and diameters, and the weight of the whole earth, as any
other scales derived from the only available source, the earth, would
have been too small to give even an approximate value of the measures
and masses to be sought for.
History tells us that at least one attempt had been made, over two
thousand years ago, to find the circumference and necessarily the
diameter of the earth, but it says nothing of any to ascertain its
weight. There may have been many to determine both diameter and mass,
but we know nothing of them; and when we think seriously about this,
we cannot help feeling somewhat surprised that no attempt had been
made to find out the density and mass till more than a century after
Sir Isaac Newton's discovery of the law of Attraction, or Gravitation,
as it is more usually called. But perhaps this is an idea that could
only occur to one who has been _spoilt_ by witnessing, in great
measure, the immense strides in advance that have been made during the
nineteenth century in science of all kinds, and does not duly take
into account the immense labour, and the incessant meeting with almost
insurmountable difficulties, that astronomers have had to encounter
and overcome between the birth of modern astronomy and the end of the
eighteenth century. Indeed, the difficulties can hardly be looked upon
as altogether overcome even yet, as efforts are still being made to
find out the exact distance of the sun, and it is not impossible that
some small difference may be found, plus or minus, in the density at
present adopted for the earth of 5·66 times the weight of water.
The geometer who, more than two thousand years ago, set himself the
task of measuring the circumference of the earth, is supposed to have
made use of very much the same kind of implements as those employed
by modern astronomers. He must have had a very fair instrument for
measuring angles, and have known very well how to use it, seeing he
was able to determine a value for the obliquity of the ecliptic which
agrees so well with that established by modern science, its variations
being, for what we know, taken into account; and for length or distance
he would doubtless have some implement analogous to the metre, chain,
foot-rule, or something called by other name that would, in those days,
present facilities for selling a yard of calico. His operations would
probably be as plain and simple as those applied to the measuring of a
village green--for we are not told that he had any idea of there being
any difference between the length of a degree of the meridian at the
equator and one nearer either of the poles--and involved no hypotheses
or theories, any more than modern operations have done.
When the time came for making efforts to ascertain the density of the
earth, science seems to have employed the very simplest means it had
at its disposal for attaining its object, and to have gone on refining
its implements and operations in conformity with the lessons it went
on learning while pursuing its self-imposed task. Every one who, even
for recreation, has read a fair amount of the multitude of works and
writings that have been published on Popular Astronomy--not to speak of
text-books--knows that the first attempts were made by measuring the
attraction of steep, or precipitous, mountains for plummets suspended
in appropriate positions in their neighbourhood; then--evidently from
knowledge acquired during these operations--by the attraction for each
other of large and small leaden balls suspended on frames and torsion
balances, which go under the name of the Cavendish Experiment; and
afterwards by a refinement on this in using the Chemical Balance,
where only one large and one small ball of metal are required. All
these operations and their results are to be found described in works
of various kinds, and are generally reduced to something like the
following tubular form, which we reproduce in order to make more
intelligible what we have just said, and that we may make a few remarks
upon them.
There is no hypothesis, no theory, connected with any of the
operations, unless it was the supposition that a plummet--which was
naturally believed to point to the centre of the earth--should be
pulled to one side by the attraction for it of a mountain in its
neighbourhood, and that was found to be a fact.
METHODS EMPLOYED FOR FINDING THE DENSITY OF THE EARTH,
AND THEIR RESULTS.
(1) _Deviation of Plummet by the Attraction of Mountains_:--
Experiments made. By whom, and Date. Mean Density found.
At Schiehallien Maskelyne 1772 4·713
At Arthur's Seat Sir H. James 1855 5·316
(2) _Torsion Balance Experiments_:--
Cavendish 1798 5·448
At Freyberg, Saxony Reich 1837 5·438
At Manchester Francis Baily 1838-1842 5·675
(3) _Chemical Balance Experiments_:--
J. H. Pointing 1878 5·690
In the case of the plummet deviating from its absolutely straight
direction towards the centre of the earth, caused by their attraction,
not only the mountains themselves had to be measured and virtually
weighed as far as they were measurable, but the weight of the wedge or
pyramid between that measurable point, in each case, and the centre
of the earth had to be estimated in some way; then the centre of
gravity of the whole of this mass had to be ascertained, as well as
the respective distances from the centre of the earth of this centre
of gravity and that of the plummet, and only after all this and a deep
study of the mutual attractions of this mass and the plummet could
an estimate be formed of the mass of the earth. It will thus be seen
that such measurements and estimates could never be looked upon as
very exact and reliable; and nevertheless they have come very near the
density of 5·66 finally adopted for the earth.
In the case of the Torsion Balance experiments a very considerable
advance was made in consequence, most undoubtedly, of the knowledge
acquired from what had been done by Maskelyne. When it was found that
the attraction of Schiehallien for the plummets was such a measurable
quantity, Cavendish evidently saw that the attraction of manageable
leaden balls for each other would be measurable also, and that as no
calculations of any kind whatever were necessary to find the masses
of the balls, the mutual attraction of large and small balls would
furnish a more exact means of measuring the density of the earth, than
the roundabout way of having to calculate the weight of a mountain as
a beginning; and with the requisite ingenuity, invention, and labour,
he found the means of applying the torsion balance, to make the
experiments.
After these experiments were revised by Reich and Baily--and the
density of 5·66 adopted, we believe--still another set were undertaken
by J. H. Pointing, with the Chemical Balance, in which only two metal
balls, one large and one small were required, which gave a density of
5·690 as shown opposite, and from its extreme simplicity may perhaps
have been the most exact of all.
We have said, we think with truth, that there is no hypothesis or
theory involved in any of these experiments, but only the simplest
form of--we might almost say--arithmetical calculation. But there is
a theory built up on hypothesis which has no foundation whatever, and
about which most people, who take the trouble to study it out to the
very end, will come to the conclusion that "the less said the better."
This, at all events, is our opinion, and we would not have taken any
notice whatever of it had it not been that up to the present day, it
is published in many works on Popular Astronomy, and even in some
text-books, and is looked upon in them, apparently, as an example of
the transcendent height to which human science can reach.
We allude, of course, to the theory that the deeper we go down into the
earth--at least to an undefined and undefinable depth--the greater is
its attraction for the bob of a pendulum at that depth, and the greater
the number of vibrations the pendulum is caused to make in a given
time. The explanation of the theory is, that were the earth homogeneous
throughout its whole volume, the pendulum ought to make the fewer
vibrations, the deeper down in the earth it is placed; but as the earth
is not homogeneous, it actually makes a greater number of vibrations in
a given time, because the attractive force of the earth increases--up
to the undefined and undefinable depth--on account of the denser matter
beneath the pendulum bob more than overbalancing the loss of attraction
from the lighter matter left above it. The author of the theory was the
late Astronomer Royal, Sir George B. Airy, who from it endeavoured to
calculate the mean density of the earth, and with that view made two
experiments which are thus described by Professor C. Piazzi Smythe in
his work on the Great Pyramid:--
"Another species of experiment... was tried in 1826 by Mr. (now Sir)
George B. Airy, Astronomer Royal, Dr. Whewell, and the Rev. Richard
Sheepshanks, by means of pendulum observations at the top and bottom
of a deep mine in Cornwall; but the proceedings at that time failed.
Subsequently, in 1855, the case was taken up again by Sir George B.
Airy and his Greenwich assistants, in a mine near Newcastle. They were
reinforced by the new invention of sympathetic electric control between
clocks at the top and bottom of a mine, and had much better, though
still unexpectedly large results--the mean density of the earth coming
out, for them, 6·565."
From other sources we have also found that the pit, or mine, was at the
Harton Colliery and 1260 feet deep, that the pendulum at the bottom of
it gained 2-1/4 seconds on the similar one at the top, in 24 hours; and
that the surrounding country had to be extensively surveyed, the strata
had to be studied, and their specific gravities ascertained.
A little unbiassed thought bestowed on this theory will at once show
that it begins by violating the law of attraction discovered by Newton,
when he showed _that the mutually attractive forces of several bodies
are the same as if they were resident in the centres of gravity of
the bodies_. In the case in point this means, that the attraction of
the earth for the bob of the pendulum at the top of the mine was the
same as if all its force was collected at its (the earth's) centre.
In that position the force of the earth's attraction comprehended,
most undeniably, the whole of its attractive power, including whatever
might be imagined to be derived from the non-homogeneity of the earth,
due to its density increasing towards the centre; and we are called
upon to believe that when, virtually, the same pendulum was removed to
the bottom of the mine, and a segment 1260 feet thick, at the centre
as good as cut off from the earth and--as far as the pendulum was
concerned--hung up on a peg in a laboratory, the diminished quantity
of its matter had a greater attractive force, a very little beyond the
centre--non-homogeneity again included--than the whole when the sphere
was intact. This we cannot do, because all that we can see in the
placing of the pendulum at the bottom of the mine, is that the position
of the bob has divided the earth into two sections, one of which has a
tendency to pull it up towards the surface, and the other to pull it
down towards its centre of gravity; and because the mass of the smaller
segment is so insignificant that its entire removal to the laboratory
peg, not only could not produce the reverse action, on which the theory
is based, but could not be measured by any stretch of human invention
or ingenuity; it is far beyond the reach of mathematics and human
comprehension of quantity.
The difficulty of belief is increased when we reflect that, were
the pendulum taken down towards the centre of the earth, the number
of its vibrations in a given time ought gradually to decrease as it
approached the centre, and would cease altogether when that point was
reached. And we feel confident that no mathematician could calculate
where the theoretical acceleration of the vibrations would cease, and
the inevitable retardation commence; where the theory would come to
an end and the law of attraction begin to assert its rights, simply
because he does not know how the non-homogeneity is distributed in the
earth. No man can tell, even yet, how the mean density of 5·66 is made
up throughout the earth, and without that any theory founded on its
non-homogeneity is out of place.
But to follow up our assertion of non-commensurability. Taking the
diameter of the earth at 8000 miles, and its mean specific gravity at
5·66, its mass would be represented by 1,517,391,000,000 cubic miles
of water. On the other hand, supposing the earth to be a true sphere,
the volume of a segment of it cut off from one side, at one quarter
of a mile deep--not 1260, but 1320 feet--would be 785·35 cubic miles
in volume, and if we suppose its specific gravity to be 2·5--greater
most probably than the average of all the strata in the neighbourhood
of the Harton Colliery--its mass would be represented by 1963·38 cubic
miles of water. Then, if we divide the mass of the section below the
pendulum, that is, 1,517,391,000,000 minus the mass of the one above
it, 1963·38, viz. 1,517,390,998,036·62 by the mass of 1963·38 just
mentioned, we find that the proportion they bear to each other is as 1
to 772,846,315. This being so, we are asked to believe that by removing
1/772,846,315th part of the mass of the earth from one side of it,
its force of attraction at the centre will not only not be decreased,
but will be so increased that it will cause a pendulum, suspended at
the centre of the flat left by the removal of the segment, to vibrate
86,402·25 times in twenty-four hours instead of 86,400 times as it did
when suspended at the surface before the segment was removed; that is,
that the vibrations will be increased by 1/38,400th part. Again we
cannot do so. Had we been asked to believe that the removal of so small
a fraction as 1/772,846,315th had decreased the earth's attraction at
its centre, so much as to produce a diminution of 1/38,400th part in
the number of vibrations of the pendulum, we could not have done so;
how much less then can we believe that the central attractive force had
increased so much as to produce an augmentation of the vibrations in
the same proportions? But more in this strain presently.
We have no doubt whatever that Sir George B. Airy and his assistants
satisfied themselves that the pendulum at the bottom of the mine gained
2-1/4 seconds in twenty-four hours over the one at the top, but they
may have been deceived by their over-enthusiastic adoption of what
seemed to be a very grandly scientific theory, or by some unperceived
changes in the temperature in the pendulums, caused by varying
ventilation in the mine or the varying weather outside of it, or by the
insidious manifestations of the "sympathetic electric control between
clocks at the top and bottom of a mine," called in to assist at the
experiments. An error of 1/38,400th part of the time the sympathetic
electricity would take to travel from the top to the bottom of the
shaft would be sufficient to make the experiments of no value whatever;
not to speak of the small errors that may have been made in surveying
the surrounding country, calculating the specific gravities of the
strata--for we are told that all this had to be done-and applying the
elements thus obtained to the solution of the problem they had in hand.
We have read of the difficulties met with by Mr. Francis Baily when he
began to revise the Cavendish Experiment--some twelve or fifteen years
before the final Harton Colliery experiments were made, and suppose it
possible that they met with similar difficulties without being aware
of it. And 1/38,400th part is such a very small fractional difference
in the vibrations in twenty-four hours, of the pendulums of the two
separate clocks, that--taking into consideration the circumstances
under which it was found--it would hardly be looked upon as reliable
at the present day, when the clocks of astronomical observatories are
placed in the deepest cellars or even caves available, so as to free
them as much as possible from variations of temperature.
Having referred to the difficulties met with by Mr. Baily, we believe
it worth while to transcribe Professor C. Piazzi Smythe's account of
them, given in his work already referred to at page 22; because it not
only has a very direct bearing on what we have been saying of changes
of temperature, but is exceedingly interesting, and probably very
rarely to be met with in other works. It is as follows:--
"Nearly forty years after Cavendish's great work, his experiment was
repeated by Professor Reich of Freyberg, in Saxony, with a result of
5·44; and then came the grander repetition of the late Mr. Francis
Baily, representing therein the Royal Astronomical Society, and, in
fact, the British Government and the British Nation.
"With exquisite care did that well-versed and methodical observer
proceed to his task, and yet his observations did not prosper.
"Week after week, and month after month, unceasing measures were
recorded; but only to show that some disturbing element was at work,
overpowering the attraction of the larger on the smaller balls.
"What could it be?
"Professor Reich was applied to, and requested to state how he had
continued to get the much greater degree of accordance with each other,
that his published observations showed.
"'Ah!' he explained, 'he had to reject all his earlier observations
until he had guarded against variations of _temperature_ by putting the
whole apparatus into a cellar, and only looking at it with a telescope
through a small hole in the door.'
"Then it was remembered that a very similar plan had been adopted
by Cavendish, who had furthermore left this note behind him for his
successor's attention--'that even still or after all the precautions
which he did take, minute variations and small changes of _temperature_
between the large and small balls were the chief obstacles to full
accuracy.'
"Mr. Baily therefore adopted yet further, and very peculiar, means to
prevent sudden changes of temperature in his observing room, and then
only did the anomalies vanish and the real observations begin.
"The full history of them, and all the particulars of every numerical
entry, and the whole of the steps of calculation, are to be found in
the Memoirs of the Royal Astronomical Society, and constitute one of
the most interesting volumes (the Fourteenth) of that important series;
and its final result for the earth's mean density was announced as
5·675, probable error ± 0·0038."
After reading this story of Baily's experiments with care, one cannot
help feeling something stronger than want of confidence in those made
at the Harton Colliery, especially after what has been shown of the
smallness of the fraction of the earth that was dealt with, and due
consideration is given to the insignificant difference of effect that
the non-homogeneity of the earth could produce on the remainder after
the supposed removal of such a small fraction; and here we might let
the theory drop. Perhaps it may be thought that now there is nothing
to be gained by spending time and work in showing it to be more truly
erroneous than we have yet made it out to be; but if there is error,
it cannot be too clearly exposed, and the sooner it is put an end to,
the better; more especially as it has been accepted as true by some
authors of text-books, and by some competent astronomers who, in trying
to explain the anomaly of the increase instead of decrease in the force
of attraction at the bottom of a mine compared with the top, have used
arguments which are not consistent with the law of gravitation, or
rather attraction.
Messrs. Newcomb and Holden in their work, entitled "Astronomy for High
Schools and Colleges," sixth edition, 1889, apparently accept the
theory, and proceed to explain and support it by showing what would be
the action of a hollow spherical shell of any substance on a particle
of it, say the bob of a pendulum, placed on the outside and also on the
inside of the shell; and give us two theorems which are supposed to
comprehend both cases. These are:--
(1) "If the particle be outside of the shell, it will be attracted as
if the whole mass of the shell were concentrated at its centre."
(2) "If it be inside the shell, the opposite attractions in every
direction will neutralise each other, no matter whereabouts in the
interior the particles may be, and the resultant attraction of the
shell will therefore be zero."
To the first theorem no objection can be made: The particle on the
outside of the shell will undoubtedly be attracted by every particle in
the shell, with the same force as if the attractive power of all the
particles composing it were concentrated in the centre. Not so with
the second theorem: for it can be objected that it altogether ignores
the Law of Attraction laid down by Sir Isaac Newton, where it asserts
that the resultant attraction of the shell for the particle will be
zero, when it is placed anywhere on the inside. In fact the theorem
supposes a case impossible for the Harton Colliery experiments, in
order to demonstrate their accuracy; for it makes use of the bob of
the pendulum--a particle of matter--as if it were transferable to any
part of the interior of the earth instead of being confined within
the bounds of its swing. That the attraction of the shell--1260 feet
thick all round the earth--on the pendulum bob inside of it continues
in all its force, and is only divided into two opposing parts, is made
plain by Fig. 1. Supposing O to represent the bob of the pendulum at
the bottom of the mine, and the space between the two circles the
shell of the earth. Then the line B C will show where the attraction
of the shell for the bob is divided into two parts acting in opposite
directions. Supposing these two parts to be separated from each other,
only far enough to admit the bob--a particle to all intents and
purposes--between them; the part B A C will attract the bob as if its
whole attractive force were collected at its centre of gravity, and
the part B D C as if the whole of its attractive force were collected,
not at the centre B of the shell, but at its centre of gravity, a
very little distance from B in the direction towards D. This is an
incontrovertible fact, because it is in strict accordance with Newton's
Law of Attraction, which is: _Every particle of matter in the universe
attracts every other particle with a force directly as their masses,
and inversely as the square of the distance which separates them._
[Illustration: FIG. 1.]
If we now suppose the interior of the shell to be filled up solid,
that will make no difference, because the mass of the part B D C will
only be increased vastly thereby, while the mass of A B C will remain
the same; the two parts only increasing their proportion to each
other, and thus coming to be for the earth--in the Harton Colliery
experiments--what we represented them to be at page 24; and we can now
proceed to find the attractive force of each of the two masses for the
bob of the pendulum which is as the inverse square of their distances
from it. These distances may be taken, without any very great stretch
of conscience, as one-tenth of a mile and 3999·75 miles; because the
centre of gravity of the segment A B C will be about that distance from
O, and that of B D C cannot be adequately represented by a greater
sum than 3999·75, always supposing the diameter of the earth to be
8000 miles. Thus the squares of these two distances will be 0·01 and
15,898,000 miles respectively, and the relative force of attraction
for the pendulum of the two segments A B C and B D C will be as 1 ×
0·01 and 772,846,315, and 772,846,315 × 15,898,000; that is as 1 is
to 1,228,671,000,000,000,000. Here then we get confirmed the unbelief
in the theory we expressed at pages 23 and 24. Surely no one will be
bold enough to assert that by decreasing the total attractive force
of the earth by a little less than a 1-1/4 trillionth part cut off
from one side of it, the want of homogeneity in what remains will not
only not decrease its attractive force at the centre, but increase it
so as to make a pendulum be lessened by 1/38,400th part of its time
in beating one second. This fraction of time is quite small enough to
inspire doubt of any theory founded upon it; and if there ever is a
quantity in mathematics that can be called negligible, the fraction of
attractive force found above ought to be included in the same category.
We may therefore assert that no human measurements could find a true
difference between the beats of a seconds pendulum at the top and
bottom of the pit at the Harton Colliery. If all the people who have
puzzled themselves with this theory had spent an hour or two in making
the above calculations before they began them, there would have been
no experiments made, and the theory would have died almost ere it was
born. Those who believed in it may have looked upon a particle as a
negligible quantity, but as the whole earth is made up of particles a
little thought would have put an end to such a notion. What puzzles
us is how such a theory could be formed by people who knew nothing
whatever of the nature of the interior of the earth at a depth of even
one mile, and how they could speculate on its want of homogeneity
without knowing anything of how the density of 5·66 is made up in it?
To suppose that the earth is made up of strata of different densities,
and that each is in some degree elliptical--the ellipticity of one
stratum being different from another, as the French mathematician
Clairaut did--is all very allowable; but to build up any theory on any
such suppositions is to build upon shifting sands without examining the
foundations. For anything that is known up to the present time, the
density of the earth may go on increasing gradually from the surface to
the centre, or it may attain nearly its greatest density at a few miles
from the surface, and continue homogeneous or nearly so from there to
the centre.
To go further now: it is not true that the attraction of a hollow
shell of a sphere for any particle within it, is the same "no matter
whereabouts in the interior the particle may be." The only place where
the attraction will be the same is when the particle is at the centre.
In that position a particle would be in a state of very unstable
equilibrium, and a little greater thickness of the shell on one side
than the others, would pull it a little, perhaps a great, distance from
the centre towards that side; and if we extend our ideas to a plurality
of particles within the shell of a sphere, we are led to speculate on
how they would be distributed, and to see the possibility of there not
being any at all at the centre. This is a point which has never been
mooted, as far as we have been able to learn, and we shall have to
return to it when the proper time comes.
It is difficult to understand how any man could conceive the notion
that a shell of a sphere, such as that shown at Fig. 1, could have no
attraction for each separate one of all the particles which make up the
mass of the whole solid sphere within it; for that is the truth of the
matter if properly looked into, when it is asserted, as has been done
by Messrs. Newcomb and Holden, that "the resultant attraction of the
shell will therefore be zero." If such a notion could be carried out in
a supposed formation of the earth, an infinity of particles would carry
off the whole of the interior, and leave the earth as only a shell of
1260 feet thick, as per the Hartley Colliery experiment; only we are
told, or left to understand, that that process could not go on for
ever, but would have to come to an end somehow and somewhere; and then
we are left to speculate on how the unattracted particles could come
back to take part in the composition of the earth. Left to ourselves
we can only liken the process to that followed by a man who peels off
the outer layer of an onion, eats the interior part, and when he is
satisfied throws down the outer layer and thinks no more of it; not
even that he might be asked what had become of the interior part.
Curiously enough, there is a way of explaining how, or rather why, the
notion was formed--not unlike the one just given--to be found in the
third of Sir George B. Airy's lectures on Popular Astronomy, delivered
at Ipswich several years before the final experiments were made at
the Harton Colliery. In that lecture, while describing how the Greek
Astronomers accounted for the motions of the sun and planets round the
stationary earth, he says, "It does appear strange that any reasonable
man could entertain such a theory as this. It is, however, certain that
they did entertain such a notion; and there is one thing which seems to
me to give something of a clue to it. In speaking to-day and yesterday
of the faults of education, I said that we take things for granted
without evidence; mankind in general adopts things instilled into them
in early youth as truths, without sufficient examination; and I now
add that philosophers are much influenced by the common belief of the
common people."
We can agree with Sir George B. Airy in his ideas about education, and
now conclude by saying that he has given us a very clear and notable
example of a theory being accepted very generally, without being
thoroughly examined to the very end, and of how easy it is for such
theories to be handed down to future generations for their admiration.
CHAPTER II.
PAGE
33 The moon cannot have even an imaginary rotation on its axis, but
is generally believed to have. Quotations to prove this.
35 Proofs that there can be no rotation. The most confused assertion
that there is rotation shown to be without foundations.
37 A gin horse does not rotate on its axis in its revolution.
38 A gin horse, or a substitute, driven instead of being a driver.
38 Results of the wooden horse being driven by the mill.
39 The same results produced by the revolution of the moon.
Centrifugal force sufficient to drive air and water away
from our side of the moon.
40 That force not sufficient to drive them away from its other side.
41 No one seems ever to have thought of centrifugal force in
connection with air and water on the moon.
41 Near approach made by Hansen to this notion.
42 Far-fetched reasons given for the non-appearance of air and water.
44 The moon must have both on the far-off hemisphere.
44 Proofs of this deduced from its appearance at change.
45 Where the evidences of this may be seen if looked for at the right
place. The centrifugal force shown to be insufficient to drive
off even air, and less water, altogether from the moon.
47 The moon must have rotated on its axis at one period of
its existence.
48 The want of polar compression no proof to the contrary.
48 Want of proper study gives rise to extravagant conceptions,
jumping at conclusions, and formation of "curious theories."
A good deal of theorising has been expended in accounting for the
absence of all but traces of an atmosphere and water on the moon, which
might have been avoided had astronomers not caught up the notion, and
stuck to it, that it rotates on its axis once for every revolution
that it makes round the earth. It might be difficult to find out with
whom the notion originated; but perhaps it was first conceived to
be the case by some celebrated astronomer, and has been accepted by
almost all his successors without being properly looked into. Any one
who chose to take the trouble to study the matter thoroughly, would
have easily discovered that the moon can have no rotation of any kind
on its axis, and immediately afterwards have found out the reason why
nothing beyond traces of air and water were to be seen on the side
of it constantly turned towards the earth. This is another example
we can give of erroneous ideas leading to erroneous and impossible
conclusions, and preventing the truth from being discovered. That the
rotation of the moon on its axis is stated to be a fact, by recognised
and celebrated astronomers, will be seen from the following quotations.
(1) Sir John Herschel, in his "Treatise on Astronomy," new edition of
1835, says at page 230: "The lunar summer and winter arise, in fact,
from the rotation of the moon on its own axis, the period of which
rotation is exactly equal to its sidereal revolution about the earth,
and is performed in a plane 1° 31´ 11´´ inclined to the ecliptic, and
therefore nearly coincident with her own orbit. This is the cause why
we always see the same face of the moon, and have no knowledge of the
other side."
(2) In his "Poetry of Astronomy," page 187, Mr. Proctor says: "For
my own part, though I cannot doubt that the substance of the moon
once formed a ring around the earth, I think there is good reason for
believing that when the earth's vaporous mass, receding, left the
moon's mass behind, this mass must have been already gathered up into
a single vaporous globe. My chief reason for thinking this is, that I
cannot on any other supposition find a sufficient explanation of one
of the most singular characteristics of our satellite--her revolution
on her axis in the same mean time, exactly, as she circuits around the
earth."
(3) Professor Newcomb, in his "Popular Astronomy," 5th edition, 1884,
at page 313, has what follows: "The most remarkable feature in the
motion of the moon is, that she makes one revolution on her axis
in the same time that she revolves around the earth, and so always
presents the same face to us. In consequence, the other side of the
moon must remain for ever invisible to human eyes. The reason for this
peculiarity is to be found in the ellipticity of her globe." Then he
enlarges upon and confirms the fact of her rotation.
(4) Mr. George F. Chambers, in his "Handbook of Astronomy," 4th
edition, 1889, says at page 119, Vol. I.: "In order that the same
hemisphere should be continually turned towards us, it would be
necessary not only that the time of the moon's rotation on its axis
should be precisely equal to the time of the revolution in its orbit,
but that the angular velocity in its orbit should, in every part of its
course, exactly equal its angular velocity on its axis."
It may be necessary, to avoid misconception, to note that angular
velocity on its axis confirms rotation; and what is more extraordinary,
that Chambers must have thought that its angular velocity on its axis
must have increased and diminished in order to agree with its increased
and diminished velocities in its elliptic orbit at its perigee, apogee,
and quadratures. A rather strange notion in mechanics where there is no
provision made for acceleration or retardation of rotation.
(5) Dr. Samuel Kinns, in "Moses and Geology," twelfth thousand, 1889,
says at page 208, "the same side of its (the moon's) sphere is always
towards us. This could only happen by its having an axial rotation
equal in period to its orbital revolution, which is 27d. 7h. 43m. 11s."
(6) In the "Story of the Heavens," Sir Robert S. Ball informs us, in
the fifteenth thousand, 1890, page 530, "That the moon should bend
the same face to the earth depends immediately on the condition that
the moon should rotate on its axis in precisely the same period as
that which it requires to revolve around the earth. The tides are a
regulating power of the most unremitting efficiency to ensure that this
condition should be observed."
(7) And finally we have what follows from Messrs. Newcomb and Holden,
at page 164 of their work already referred to at page 27, "The moon
rotates on her axis in the same time and in the same direction in
which she moves around the earth. In consequence, she always presents
very nearly the same face to the earth." And in a footnote to this
consequence, add: "This conclusion is often a _pons asinorum_ to some
who conceive that, if the same face of the moon is always presented
to the earth, she cannot rotate at all. The difficulty arises from a
misunderstanding of the difference between a relative and an absolute
rotation. It is true that she does not rotate relatively to a line
drawn from the earth to her centre, but she must rotate relative to a
fixed line, or a line drawn to a fixed star."
In six of the above cases it is distinctly maintained that the moon
rotates once on its axis in the same time that it makes one revolution
round the earth, and that it is in consequence of this rotation that
it always presents the same side to the earth. Thus we feel authorised
to conclude that their authors did either believe that it does so
rotate, or that they entertained some confused idea on the subject,
which they did not take the trouble to examine properly, but accepted
as a dogma, because some predecessor, with a great name, had stated
that such rotation was necessary in order that its same side should
be always turned towards the earth. In the seventh case the authors,
while actually making the same assertion, try to persuade those who
they acknowledge can see that the moon does not rotate on its axis in
any sense, that their difficulty in comprehending what is meant by
rotation, arises from the misunderstanding of the difference between
an absolute rotation and one relative to a line drawn to a fixed star.
But they do not attempt to show how this relative rotation has anything
to do with or has any effect in causing the moon to present always the
same side to the earth; and leave the story in the same confused state,
out of which nobody can draw any satisfactory conclusion. Also, though
they distinctly recognise that it does not rotate relatively to a line
drawn from the surface of the earth to its centre, they do not include
in their general description of the moon anything in any way connected
with what would be the consequences of its not really rotating on its
axis relatively to the earth. So they leave us the problem in much the
same state as they found it, and it is still necessary to show that
there can be no actual rotation of any kind on its axis; and the worst
of it is that it is a thing that will have to be done in such very
plain language that it will compel people to think of the absurdity of
the idea so generally accepted.
To begin, it is very difficult to comprehend what the authors, above
alluded to, meant by saying that the moon "must rotate relative to a
fixed line, or a line drawn to a fixed star." It may mean relative to
the line itself or to the star to which it is drawn. If it is to the
line itself we cannot form any notion of what direction the rotation
will have, direct, retrograde, or otherwise; and if it is relative
to the star itself, then we can see that the relative rotation must
depend on what is the position of the star. Should it be placed in the
"milky way," we can understand how the moon could show every side it
has--almost, not quite--to the star during every revolution it makes
round the earth, and how they may look upon it as a relative rotation.
But if we draw the line to the pole star we cannot see how the moon
can show every side it has to it in every revolution round the earth,
so there can be no relative rotation in that case--and the "almost,
not quite," applies to every star between the pole and the ecliptic.
The moon shows only the northern hemisphere, or a little more due to
libration of its own kind, to that star, and would have to remove
its poles to the equator, and make a new departure, in order to show
the whole of its surface to that star in every revolution round the
earth. Thus it is clear that the explanation given us of the relative
rotation, is evidently one of the kind not properly thought out to the
end.
No one has ever said, or perhaps even thought, that a gin-horse makes
one rotation on his vertical axis, in the same time as he makes a
circuit round his ring, but, all the same, he keeps his same side
always towards the gin, or mill, he is giving motion to. The proof
that he does not make any such rotation is easy--no proof is really
required. But, suppose he is giving motion to a whim for raising ores
from a mine, and that his motion is what is called direct. When the
cage containing the ore is brought to bank, is emptied, and has to be
lowered into the mine again, the horse has then to reverse his motion
to retrograde, in doing which he has to make a half rotation on his
vertical axis, and turn his other side to the whim. When again the
cage has to be raised to bank, he has to resume his direct motion, for
which he has to make another half rotation on his vertical axis, but
it is this time in the opposite direction. Thus it is shown that he
can only make half rotations, under any circumstances, on his axis,
and these in opposite directions, when he changes his motion from
direct to retrograde, or _vice versâ_; and that, when he moves in only
one direction he cannot make even one rotation on his vertical axis,
however long he may travel round the mill. In the same manner the
moon which never turns back in its orbit can never make even one half
rotation on its axis, which is all that we have had to prove. It is
hardly necessary to observe that its axis is nearly parallel to the
earth's, just the same as the horse's is to that of the whim. Neither
could any one say that the relative rotation of the horse to a star, or
tower, or, say, a bridge, outside of his ring, could have any effect on
his revolution round the mill, or his always keeping his same side to
it, there being no mechanical connection between them, nor any law of
attraction; and the same is the case between the moon and a fixed star.
Now, we may begin to consider what effects must be produced by the moon
not rotating on its axis, and we can do so most easily by continuing to
work with our gin horse, or some equivalent substitute. It would not
cost a great deal of ingenuity to plant a steam engine in the centre of
the mill he is supposed to be driving, and to drive with it not only
the mill but the horse also at the end of his lever. There might be
some dissipation--Professor Tate would call it degradation--of energy
in such an experiment, but we could get over that by making _divina
Palladis arte_ a wooden horse. We might arrange the steam-engine so as
to cause the mill to make 27-1/3 revolutions for one made by our wooden
horse, and so have a sort of a model of the earth and moon performing
their most important relative motions. Then, having got our model ready
for action, instead of filling it _armato milite_ we might fill it half
full of water. We fill it only half full, because the armed soldiers
could not lie on the top of each other in the _other_ horse, and there
would be a vacant space above them for air, thus making the resemblance
between the two the more similar; and also because it suits our purpose
better, as will soon be seen. We have still to propose that a lot of
holes should be supposed to be made in the sides of _our_ horse all
round, just a little higher than between wind and water. _Pallas_
did not order any holes to be made in _hers_ as far as we know, even
for ventilation, though we think it would have been an advantage; but
that will not spoil the experiment we are now prepared for. Let the
steam-engine be started now and we shall soon see what will happen to
the water. As the speed increases it will not be long till it begins to
be thrown out, not from the side turned towards the mill but from the
one furthest from it; and if it is increased sufficiently the whole of
it will be very soon thrown out. If we could now close up the holes on
the side of the horse turned towards the mill, it would so happen that
a good deal of the air would be expelled also; and if the speed of the
horse were brought up so as to equal that of the moon in its orbit,
there would be nothing more, at the most, than traces of air left even
in it. The expelling agent in this experiment would, of course, be
centrifugal force, and we do not need to exercise our mental faculties
very greatly, to comprehend that it is the same force that has driven
both air and water away from the side of the moon always turned towards
the earth. All the difficulty we have to contend with will be to make
sure that the orbital velocity of the moon is sufficient to produce
the force required. That the force is exceedingly greater than what is
required is proved by the fact, that the velocity with which the moon
travels in its orbit is a little more than 38 miles per minute, whereas
the velocity of the circumference of a centrifugal machine, used for
clarifying sugar, drying clothes, or any other similar industrial
purpose, does not require a greater velocity than about _one_ mile per
minute, in order to throw everything in the form of water out of the
material to be dried, and out of the centrifugal machine itself; and
we know that air would be expelled more easily than water, were none
re-admitted to supply the place of what was expelled.
Here the idea very naturally occurs to any one, that so great a
velocity would drive both air and water away, even from the far off
side of the moon, into space, but in order to do so the velocity would
have to be 120, not 38, miles per minute. Our authority for this
statement will be found in "The Nineteenth Century," for August 1896,
in an article written by Prince Kropotkin, in which he says: "But
it appears from Dr. Johnstone Stoney's investigations that even if
the moon was surrounded at some time of its existence with a gaseous
envelope consisting of oxygen, nitrogen and water vapour, it would not
have retained much of it. The gases, as is known, consist of molecules
rushing in all directions at immense speeds; and the moment that
the speed of a molecule which moves near the outer boundary of the
atmosphere exceeds a certain limit (which would be about 10,600 feet
in a second for the moon) it can escape from the sphere of attraction
of the planet. Molecule by molecule the gas must wander off into
interplanetary space; and the smaller the mass of the molecule of a
given gas, the feebler the planet's attraction, and this is why no free
hydrogen could be retained in the earth's atmosphere, and why the moon
could retain no air or water vapour."
A velocity of 10,600 feet per second is as near 120 miles per minute as
there is any use for, which is more than three times as great as the
velocity of the moon in its orbit, so there is no possibility whatever
of air and water having been swept away from the far off side of it
by centrifugal force; more especially as it ought to be well known
that that force is always counteracted by the attractive force of the
satellite for these or any other elements.
We do not want to discuss the point of whether the mutual collisions
of the molecules of a gas could get up such a velocity as would enable
them to free themselves from the attraction of the moon, for it looks
to us too much like one of those notions that are got up to account for
something that does not exist; but we do want to state our dissent to
the conclusion--evidently jumped at--that because there are hardly any
signs of there being air or water on our side of the moon, there can
be none on the other. No astronomer, physicist, scientist of any kind,
can prove that there is none, simply because he has never been round
there to see or make experiments to prove it; and if there is any one
bold enough to make such an assertion, it is only an example of how
stupendous a jump to a conclusion can be made.
When we first read, many years ago, some of the reasons given for there
being no water visible on the side of the moon constantly turned to
the earth, one of which was that if there ever had been any it must
have been absorbed into its body during the process of cooling and
consolidation; and when we had convinced ourselves, by placing two
oranges on two ends of a wire and revolving the one round the other,
that the moon did not rotate on its axis in any sense whatever, we
came to the conclusion that both water and air could be removed to the
far off hemisphere by centrifugal force. We thought this so simple,
so self-evident, and so indisputable an explanation, that every one
who had read what we had read must have come to the same conclusion;
so that we were not a little surprised when we saw it stated by "The
Times" of September 15, 1893, in its first report of the meeting of the
British Association for that year, that Sir Robert Ball had suggested,
some time previously, that the "absence of any atmosphere investing the
moon is a simple and necessary consequence of the kinetic theory of
gases." This at once made us suspect that the theory--our theory--must
have been new, but we could not altogether believe it. It seemed to us
passing strange that it should not have occurred to astronomers, from
the moment they discovered that they could not find any, or hardly any,
traces of air or water on the only hemisphere they could examine; but
it would appear from Sir Robert Ball's suggestion, being even discussed
at that meeting, that the notion of their having been removed simply by
centrifugal force to the unseen hemisphere, had never been entertained
by, to say the least, any one who was present at that discussion.
Not satisfied with this conclusion, we proceeded to examine all the
books, journals, magazines, and _papers_ we could get hold of, to
see whether we could find any indication of such a conception having
been published previously, and the nearest approach to anything of
the kind having been conceived of by anyone, we found in Chambers's
work--already referred to--at page 134, Vol. I., where we read,
"Professor Hansen has recently started a curious theory from which
he concludes that the hemisphere of the moon which is turned away
from the earth may possess an atmosphere. Having discovered certain
irregularities in the moon's motion, which he was unable to reconcile
with theory, he was led to suspect that they might arise from the
centre of gravity of the moon not coinciding with the centre of
figure. Pursuing this idea, he found upon actual investigation that
the irregularities could be almost wholly accounted for by supposing
the centre of gravity to be at a distance of 33-1/2 miles _beyond_
the centre of figure. Assuming this hypothesis to be well founded,
Professor Hansen remarks that the hemisphere of the moon, which is
turned towards the earth, is in the condition of a high mountain, and
that consequently we need not be surprised that (little or) no trace of
an atmosphere exists; but that on the opposite hemisphere, the surface
of which is situated _beneath_ the mean level, we have no reason
to suppose that there may not exist an atmosphere and consequently
both animal and vegetable life. Professor Newcomb has disputed these
conclusions of Hansen, which it is obvious must be very difficult of
either proof or disproof."
What Professor Newcomb's objections to the conclusions of Hansen were
we do not know, but we do know that Mr. Proctor also objected to the
"curious theory," as it is called by Mr. Chambers. In his "Poetry on
Astronomy," he discusses pretty fully the withdrawal of water from the
surface of the moon during the process of cooling and condensation,
ascribing the conception of it to four independent authors, namely,
Seeman, a German geologist, Frankland in England, Stanislas Mennier in
France, and Sterry Hunt in America; and in a footnote, at page 163,
says of Hansen's theory: "The idea was that the moon, though nearly
spherical, is sometimes egg-shaped, the smaller end of the egg-shaped
figure being directed towards the earth. Now, while it is perfectly
clear that on this supposition the greater part of the moon's visible
half would be of the nature of a gigantic elevation above the mean
level, and would, therefore, be denuded (or might be denuded) of its
seas and denser parts of the air covering it, yet it is equally clear
that all around the base of this monstrous lunar elevation, the seas
would be gathered together, and the air would be at its densest. But
it is precisely round the base of this part of the moon or, in other
words, round the border of the lunar hemisphere, that we should have
the best chance of perceiving the effects of air and seas, if any
really existed; and it is because of the absolute absence of all
evidence of the kind, that astronomers regard the moon as having no
seas and very little air."
Had the idea of centrifugal force ever occurred to Mr. Proctor, he
could not have written this last sentence; for he could not have
failed to see that "the border of the visible lunar hemisphere" would
be the very place, from which it could most easily remove air and
water, after they had got so far down the monstrous elevation; because
there it--the centrifugal force--would be acting at right angles to
the moon's attraction, instead of having to contend against it, as it
would have to do in a constantly increasing degree until it arrived at
its maximum, just in proportion to the distance the air and water got
down to the similar monstrous _depression_ on the other hemisphere,
down which the gradient would start off under the most favourable
circumstances possible.
From what has been said, it is very evident that neither Hansen,
Chambers, Proctor, nor any of those whose names have been mentioned
by the last, in connexion with the withdrawal of water into the body
of the moon by absorption, while cooling and condensing, had ever
thought of the possibility of air and water having been removed by
centrifugal force from the side of the moon turned towards the earth.
That it should not have occurred to Hansen seems passing strange,
seeing that he had conceived the idea of their possible existence on
the hemisphere turned away from the earth, which could hardly fail to
make him think of how they got there, and could exist only there; and
the only explanation of his not having perceived the true cause seems
to be, that his thoughts were hampered by a sort of confused notion
that the moon actually rotates on its axis once for every revolution
it makes around the earth, that being, as it were, one of the dogmas
of astronomic belief, handed down from some great authority of times
past, and never properly inquired into.
We do not want to question the suggestion, that the absence of any
atmosphere investing the moon is a simple and necessary consequence of
the kinetic theory of gases--though we see that a good deal could be
argued against it--as we do not consider it to be necessary--neither
the questioning nor the theory. We have demonstrated clearly, how both
air and water could be removed from the side of the moon constantly
shown to us, and that is sufficient for our purpose both now and later
on; besides it would appear that the moon really has some sort of an
atmosphere somewhere.
Following up the quotation, made at page 39, from Prince Kropotkin's
article in the "Nineteenth Century" as being the latest information we
have on the subject, we are told that "a feeble twilight is seen on our
satellite, and twilight is due, as is known, to the reflection of light
within the gaseous envelope; besides it has been remarked long since
at Greenwich that the stars which are covered by the moon during its
movements in its orbit remain visible for a couple of seconds longer
than they ought to be visible if their rays were not slightly broken as
they pass near the moon's surface. Consequently it was concluded that
the moon must have an atmosphere" ... and:
"The observations made at Lick, Paris, and Arequipa, fully confirm
this view. A twilight is decidedly visible at the cusps of the
crescent-moon, especially near the first and last quarters. It prolongs
the cusps as a faint glow over the dark shadowed part, for a distance
of about 70 miles (60"), and this indicates the existence of an
atmosphere having on the surface of the moon the same density as our
atmosphere has at a height of about forty miles."
What is of interest for us to know is where that "feeble twilight," or,
"reflection of light within the gaseous envelope," is seen. Whether
it is at what Mr. Proctor calls "the border of the visible lunar
hemisphere," on this side of it, or beyond it. It cannot be a difficult
matter to decide. It must be beyond it, for the following reasons: If
the atmosphere has been driven away to the far-off hemisphere of the
moon by centrifugal force, its natural tendency would be to spread
out immediately after it had passed the visible border where we have
said the centrifugal force would be acting most effectively. Also, if
all the air at one time belonging to our side of the moon has been
driven away to the other, that side must have a double allowance of
atmosphere, which, though it does not increase its density at the
surface, on account of the centrifugal force, will double its volume,
and enable it to extend to a greater proportionate distance in all
directions from the border and from the far-off hemisphere. In this
way there must be a considerable wedge of atmosphere illuminated by
the sun, and visible past the edge of the moon's disc, to reflect a
feeble twilight--perhaps something stronger--towards the earth, and to
intercept the light of a star before its edge and that of the moon come
into actual apparent contact. But before the wedge becomes thick enough
to reflect that light, the reflecting part must be far beyond the edge
of the moon's disc. Perhaps the feeble light might be seen more clearly
when looked for in the proper place; quite possibly hundreds of miles
beyond the disc.
In order to make more clear the truth of what we have said about water
and air--and more especially the latter--being thrown away to the
far-off side of the moon by centrifugal force, we may add the following
details: If the force of gravity at its surface is one-sixth part of
what it is at the surface of the earth, the pressure of an atmosphere
there would be 2·5 lb. per square inch, if it rotated on its axis;
but as it does not so rotate and is subjected to centrifugal force,
the pressure of an atmosphere will vary according to the part of it
over which it exists. On the nearest part of the side turned towards
the earth, gravity, which we have just seen must be equal to 2·5 lb.,
would be acting in the same direction as centrifugal force, which in
its turn is equal to 0·7 lb. or thereby, and the whole would be 3·2
lb. per square inch tending to drive off air and water to the far-off
hemisphere. But from that place, gravity would gradually diminish its
aid till it came to be nil at the disc separating the two hemispheres,
where it would have no effect whatever as it would be acting at right
angles to centrifugal force, and this would be reduced to 0·7 lb. per
square inch. Then, from the edges of the disc forward, on the far-off
hemisphere, gravity would begin to act against centrifugal force, or
rather _vice versâ_, until it, gravity, got reduced to 1·8 lb. per
square inch. Also, as that hemisphere must have a double portion of
air or atmosphere on it, and as its pressure on any part of it cannot
be greater than the 1·8 lb. just mentioned, we can imagine that the
double quantity will hang closer to the surface than if there was
only one portion. Such being the case the atmosphere would spread out
much more rapidly than would be represented by the extension of a
triangle starting from the earth and reaching beyond the moon's disc
to the farthest limit of the atmosphere; and thus the wedge, which we
have supposed to be visible beyond the edges of the disc may come to
have a very considerable thickness. What that thickness may be, and
up to what distance beyond the disc the density of the wedge would be
sufficient to reflect the light of the sun, it would be very difficult
to calculate, but we think it might possibly extend even as far as
one-fourth of the radius of the moon--because at that point the force
of gravity pulling it towards the centre, or the axis, would be very
small, and its distance from the axis would be little less than the
radius, not over 33 miles--and cause it to project over the edges as
far, to appearance, as the 70 miles (60") that have been observed at
Greenwich. This reflected light must be all round the moon--not at the
cusps only of the crescent-moon--and it has occurred to us that it may,
most probably does, account for the appearance of what we call "the old
moon in the young moon's arms." We know what effect the "earth-shine"
has upon the moon at its change, and the brighter _ring-shine_ just
outside of it, may very well be caused by the sunlight reflected from
the atmosphere far beyond the visible limit of the hemisphere turned to
us.
In support of this suggestion we may refer to Professor C. A. Young's
description, in his "Sun," p. 213, of one particular feature observed
at the time of a total eclipse of the sun. He says:--"On such an
occasion, if the sky is clear, the moon appears of almost inky
darkness, with just a sufficient illumination at the edge of the disc
to bring out its rotundity in a striking manner. It looks not like a
flat screen, but like a huge black ball, as it really is. From behind
it stream out on all sides radiant filaments, beams, and sheets of
pearly light, which reach to a distance sometimes of several degrees
from the solar surface, forming an irregular stellate halo, with the
black globe of the moon in its apparent centre."
There can be little doubt, we think, from what is said here, that
Professor Young looks upon this "illumination of the edge of the
disc" as pertaining to the moon, and upon the "radiant filaments,
beams," etc. behind it as belonging to the sun. And in that case the
illumination can only be caused by the light of the sun, refracted by
the atmosphere belonging to the hemisphere of the moon that is never
seen from the earth.
We have taken it for granted in what we have been doing, that the
moon has really rotated on its axis, and to some purpose, at some
former period of its existence. Some people think otherwise, or that
there is at least a doubt about it; we cannot see even the shadow of
a doubt. All that we need to say in support of our opinion is, that
there is no other conceivable way of accounting for its perfectly
circular form. All the planets are circular, or spheroidal--to speak
more correctly--in form, admittedly in consequence of rotation on their
axes; and if one or two of Jupiter's satellites are not completely
circular or spheroidal, it does not stretch our conscience very much
to suppose that it is because they have not yet been rotated into
form. Saturn apparently has satellites still in the form of rings, and
there can be nothing out of the way in supposing that all of Jupiter's
are not yet licked into shape. The fact that there is no appearance
of compression on the moon makes us think of why there is none, and
the only explanation that occurs to us is, that, as its rotation
must have come to an end gradually, the compression it must have had
when rotating must have disappeared gradually also, by reason of the
differences of force in the equatorial and polar attractions, drawing
in the bulged out, and thus forcing out the compressed parts. This is
a notion that will be scoffed at by those who have always thought,
and maintained, that the earth acquired its present form when in a
liquid state; but they have not thought this supposition--for it is
nothing else--out to the very end. Several reasons could easily be
given against their opinion, among others the variations in rate of
rotation we so frequently see used in favour of other notions; but we
shall content ourselves with the best one of all, which is this: The
pressures in the interior of the earth must be so enormous that they
are quite sufficient to compress steel, or adamant if that is supposed
to be more resistant, into any shape whatever, almost as if it were
dough, and there can be no doubt--mathematics notwithstanding--that
the earth has the form, to-day, due to its present rate of rotation.
We shall have to return to this subject some time hence, if we live to
complete what we have taken in hand.
How many things there are, in what is considered to be astronomical
science, that have not been properly thought out to the end, and to
what strange notions they have given rise! This one of the rotation of
the moon which we have been discussing, has evidently given occasion
for the conception of the theory that the absence of atmosphere and
seas from the moon is the natural consequence of the kinetic theory of
gases; and the author of the theory, and its supporters, have never,
apparently, taken the trouble to think whether their absence from the
near hemisphere is a satisfactory and convincing proof of there not
being any air or water on the far-off one. In what we have proposed to
write many similar examples of want of study will be met with, but we
do not intend to call special attention to them, unless it be in cases
where we consider it to be of some importance to do so. In fact we have
already been working on that plan.
CHAPTER III.
PAGE
49 Remarks on some of the principal cosmogonies. Ancient notions.
50 The Nebular hypothesis of Laplace. Early opinions on it. Received
into favour. Again condemned as erroneous.
51 Defects attributed to it as fatal. New cosmogonies advanced.
53 Dr. Croll's collision, or impact, theory discussed.
59 Dr. Braun's cosmogony examined.
61 M. Faye's "Origine du Monde" defined.
65 Shown to be without proper foundation, confused, and in some parts
contradictory.
70 Reference to other hypotheses not noticed. All more or less only
variations on the nebular hypothesis.
71 Necessity for more particular examination into it.
We have thought it worth while to dedicate this chapter to some remarks
on cosmogonies in general, and examination into a very few conceived by
eminent men; these forming in our opinion the most attractive matter
for those readers who do not pretend to make a study of astronomy,
but are very desirous to have some knowledge of the most plausible
ideas which have been conceived by astronomers, of how the universe,
and more particularly the solar system, were brought into existence;
while, at the same time, they are the subjects on which more crude
conceptions, more limited study, and more fanciful unexamined thought
have been expended, than any others we have met with. Some readers
will, no doubt, be able to reject what is erroneous, to speak mildly,
but there will be, equally surely, some who cannot do so; and it
must be confessed there are a good many to whom the most complicated
conceptions, and the most difficult of comprehension, are the most
attractive.
A great many centuries ago, astronomers and philosophers had already
conceived the idea that the sun and stars had been formed into
spherical bodies by the condensation of celestial vapours; but when
the telescope was invented, and the nature of nebulæ in some measure
understood, it was not long till it came to be thought that the matter,
out of which the sun and stars were formed, must have been much more
substantial in its nature than celestial vapours. Being visible,
they were naturally considered to be self-luminous, and consequently
endowed with great heat, because the self-luminous sun was felt to
be so endowed, though perhaps not with the same degree. Accordingly,
astronomers began to form theories, or hypotheses, on the construction
of the solar system out of a nebula, which, like everything else,
went on each one improving on its predecessor as, through continued
observation and study, more knowledge was acquired of the nature of
nebulæ. The most notable of these cosmogonists were Descartes, Newton,
Kant, and Laplace, each of whom contributed valuable contingents to the
general work; which may be said to have culminated about a century ago
in the Nebular Hypothesis of the last-named; for the many attempts that
have been made to improve upon it, or to supplant it altogether, have
been very far from successful.
The hypothesis is about a century old, as we have said, and there may
still be many people who can remember having heard it denounced as a
profane, impious, atheistic speculation, for it is not over half a
century since the ban begun to be taken off it. Sir David Brewster,
in his "Life of Newton," said of it, "That the nebular hypothesis,
that dull and dangerous heresy of the age, is incompatible with the
established laws of the material universe, and that an omnipotent arm
was required to give the planets their positions and motions in space,
and a presiding intelligence to assign to them the different functions
they had to perform." With others, its chief defect was that the time
required to form even the earth in the manner prescribed by it, must
have been infinitely greater than six days of twenty-four hours each.
In the meantime, geologists had also discovered that, for the formation
of the strata of the earth, which they had been examining and studying,
the time required for their being deposited must have been, not days
of twenty-four hours, but periods of many millions of years each; and
the evidence adduced by them that such must have been the case was so
overwhelming, that Theology had to acknowledge its force, and gradually
to recognise that the days must have been periods of undefinable
length. Thus relieved from the charge of heresy, the hypothesis rose
rapidly into favour, and came to be generally accepted by the most
eminent astronomers, subject always to certain modifications, which
modifications have never been clearly defined, if at all. It was not,
however, allowed to enjoy long the exalted station to which it had
attained.
Astronomers had begun to consider from whence the sun had acquired the
enormous quantity of heat it had been expending ever since the world
began, and, after long discussion, had come to the conclusion that
by far the greatest source must have been the condensation from the
nebulous state of the matter of which it is composed. Having settled
this point, it was calculated that the amount of heat derived from that
and all other sources could not have kept up its expenditure, at the
present rate of consumption, for more than twenty million years, and
could not maintain it for more than from six to eight million years in
the time to come. Owing in good part to this great difference between
the calculations of astronomers and geologists about the age of the
earth, the hypothesis began again to suffer in repute, and then all its
faults and shortcomings were sought out and arrayed against it.
The chief defects attributed to it were: The retrograde motion of
rotation of Uranus and Neptune and revolution of their satellites--that
fault in the former having been noted by Sir John Herschel, in his
Treatise on Astronomy already cited; the discovery of the satellites
of Mars which exposed the facts, that the inner one revolves round
the planet in less than one-third of the time that it ought to, and
that the outer one is too small to have been thrown off by Mars,
in accordance with the terms of the hypothesis; the exclusion from
it of comets, some of which at least have been proved, in the most
irrefutable manner, to form part of the solar system; and what can only
be called _speculations_, on the formation of a lens-shaped nebula
brought about by the acceleration of rotation--caused by condensation
according to the areolar theory--which it is supposed would be
enormously in excess of the actual revolution of the inner planets, and
of the rotation of the sun. Here we must protest against retrograde
motion of rotation in any of the members of the solar system being
considered as militating against the theory, because Laplace states
distinctly, while explaining his hypothesis, that the rotation of the
earth might just as well have been retrograde as direct: a fact that
some eminent astronomers have not noticed, simply because they have
not paid proper attention to what they were reading. We shall have to
return to this statement again, and to present the proof of its being
true.
An idea of how far the hypothesis had fallen into disrepute may be
formed from the following extract, from "Nature" of August 4, 1887, of
a Review of a "New Cosmogony," by A. M. Clerke, in which it is said:
"But now the reiterated blows of objectors may fairly be said to have
shattered the symmetrical mould in which Laplace cast his ideas. What
remains of it is summed up in the statement that the solar system did
originate somehow, by the condensation of a primitive nebula. The rest
is irrecoverably gone, and the field is open for ingenious theorising.
It has not been wanting.... The newer cosmogonists are divided into
two schools by the more or less radical tendencies of the reforms
they propose. Some seek wholly to abolish, others merely to renovate
the Kant Laplace scheme. The first class is best represented by M.
Faye, the second by Mr. Wolfe and Dr. Braun"--the author of the "New
Cosmogony."
We cannot pass this quotation without remarking "How glibly some people
can write!" More we do not want to say about it, except that it gave us
the notion to examine closely some of the new cosmogonies, _which have
not been wanting_, to see whether they are better than Laplace's.
We have not had the opportunity of knowing what are Mr. Wolfe's
amendments, but the Review, just cited, gives us a pretty good notion
of those of Dr. Braun, and we have been able to study carefully M.
Faye's "Origine du Monde," in which he considers the solar system to
have been evolved from cosmic matter partially endowed with motion
in the form of eddies, whirlwinds, vortices, or _tourbillons_, which
last may comprehend all of them, and even more. We have also studied,
with some surprise, in "Climate and Cosmology" Dr. Croll's Impact, or
Collision, Theory, and will confine our examination to the three of
which we know something, beginning with Dr. Croll's, which we believe
to be the oldest of the three.
We understand that Dr. Croll accepts the nebular hypothesis in all its
main features, including the intense heat in which the original nebula
is supposed to have existed from the beginning; and has only invented
the collision theory in order to increase its quantity, to suit the
demands of geologists for unlimited time, by showing how an unlimited
supply of both heat and time may be obtained. But he has incurred
an oversight in not taking into consideration the kind of matter in
which that unlimited supply of heat was to be stored up--whether it
would hold it. He wrote in times when something was really known about
heat, and we cannot suppose him to have believed that heat could exist
independent of matter, or that a gas or vapour could be heated to
a high temperature except under corresponding pressure; but he has
evidently overlooked this point, his thoughts recurring to old notions;
and he has fallen, probably for the same reason, into other oversights
equally as grave.
When showing how a supply of fifty millions of years of sun-heat
could be produced from the collision of two half-suns colliding with
velocities of 476 miles per second, Dr. Croll says in his "Discussions
on Climate and Cosmology," of 1885, at page 301: "The whole mass would
be converted into an incandescent gas" (the handmaid of the period),
"with a temperature of which we can have no adequate conception. If we
assume the specific heat of the gaseous mass to be equal to that of air
(viz. 0·2374), the mass would have a temperature of about 300,000,000°
C., or more than 140,000 times that of the voltaic arc."
Now, let us suppose the whole mass of the whole solar system to be
converted into a gas, or vapour, at the pressure of our atmosphere,
and temperature of 0° C., its volume would be equal to that of a sphere
of not quite 9,000,000 miles in diameter. Suppose, then, this volume to
be heated to 300,000,000° C. in a close vessel, as would necessarily
have to be the case, the pressure corresponding to that temperature
would be 1,094,480 atmospheres, according to the theory on which the
absolute zero of temperature is founded. Without stopping to consider
whether air or any gas could be heated to the temperature mentioned;
or the strength of the vessel 9,000,000 miles in diameter required
to retain it at the equivalent pressure; if we increase the diameter
of the containing sphere to a little more than that of the orbit of
Neptune, or, say 6,000,000,000 miles, and allow the air or gas or
vapour to expand into it; then, as the volume of the new sphere will
be greater than the former one in the proportion of 9,000,000 cubed to
6,000,000,000 cubed, or as 1 is to 296,296,296, the pressure of the gas
will be reduced to 296,296,296 divided by 1,094,980, that is just over
the 270th part of an atmosphere; which, in its turn would correspond to
a temperature of a very little more than -273°, or what is considered
to be[A] 273° C. above absolute zero of temperature; or, at all events,
to the temperature of space, whatever that may be.
[A] This temperature is altogether erroneous, as we shall show in
due time; at present our proof would not be accepted without a
demonstration, for which we have not sufficient data.
Dr. Croll goes on to say at page 302: "It may be objected that enormous
as would be such a temperature, it would nevertheless be insufficient
to expand the mass against gravity so as to occupy the entire space
included within the orbit of Neptune. To this objection it might be
replied, that if the temperature in question were not sufficient to
produce the required expansion, it might readily have been so if the
two bodies before encounter be assumed to possess a higher velocity,
which of course might have been the case. But without making any such
assumption, the necessary expansion of the mass can be accounted for on
very simple principles. It follows in fact from the theory, that the
expansion of the gaseous mass must have been far greater than could
have resulted simply from the temperature produced by the concussion.
This will be obvious by considering what must take place immediately
after the encounter of the two bodies, and before the mass has had
sufficient time to pass completely into the gaseous condition. The
two bodies coming into collision with such enormous velocities would
not rebound like two elastic balls, neither would they instantly be
converted into vapour by the encounter. The first effect of the blow
would be to shiver them into fragments, small indeed as compared with
the size of the bodies themselves, but still into what might be called
in ordinary language immense blocks. Before the motion of the two
bodies could be stopped, they would undoubtedly interpenetrate each
other; and this of course would break them up into fragments. But this
would only be the work of a few minutes. Here then we should have all
the energy of the lost motion existing in the blocks as heat (molecular
motion), while they were still in the solid state; for as yet they
would not have had time to assume the gaseous condition. It is obvious,
however, that the greater part of the heat would exist on the surface
of the blocks (the place receiving the greatest concussion), and would
continue there while the blocks retained their solid condition. It
is difficult in imagination to realize what the temperature of the
surfaces would be at this moment. For supposing the heat were uniformly
distributed through the entire mass, each pound, as we have already
seen, would possess 100,000,000,000 foot-pounds of heat. But, as the
greater part of the heat would at this instant be concentrated on the
outer layers of the blocks, these layers would be at once transformed
into the gaseous condition, thus enveloping the blocks and filling up
the interstices. The temperature of the incandescent gas, owing to this
enormous concentration of heat, would be excessive, and its expansive
force inconceivably great. As a consequence the blocks would be
separated from each other, and driven in all directions with a velocity
far more than sufficient to carry them to an infinite distance against
the force of gravity were no opposing obstacle in the way. The blocks,
by their mutual impact, would be shivered into small fragments, each
of which would consequently become enveloped in incandescent gas. These
smaller fragments would in a similar manner break up into smaller
pieces, and so on until the whole came to assume the gaseous state. The
general effect of the explosion would be to disperse the blocks in all
directions, radiating from the centre of the mass. Those towards the
circumference of the mass, meeting with little or no obstruction to
their outward progress, would pass outwards into space to indefinite
distances, leaving in this manner a free path for the layers of blocks
behind them to follow in their track. Thus eventually a space, perhaps
twice or even thrice that included within the orbit of Neptune, might
be filled with fragments by the time the whole had assumed the gaseous
condition.
"It would be the suddenness and almost instantaneity with which the
mass would receive the entire store of energy before it had time even
to assume the molten, far less the gaseous condition, which would lead
to such fearful explosions and dispersion of the materials. If the
heat had been gradually applied, no explosions, and consequently no
dispersion of the materials would have taken place. There would first
have been a gradual melting; and then the mass would pass by slow
degrees in vapour, after which the vapour would rise in temperature as
the heat continued, until it became possessed of the entire amount.
But the space thus occupied by the gaseous mass would necessarily be
very much smaller than in the case we have been considering, where the
shattered materials were first dispersed in space before the gaseous
condition could be assumed."
We have made this very long quotation; first, because we have not
been able to condense it without running the risk of not placing
sufficiently clearly the whole of the argumentations employed in it;
secondly, because the purport of the whole explanation set forth is
evidently to demonstrate that, by means of the explosions of gases
produced by the collision, the matter of the whole mass would be more
extensively distributed into space--bearing heat along with it--than
were it gradually melted and converted into vapour; and thirdly,
because every argument advanced in favour of the theory of explosions,
if carefully looked into, brings along with it its testimony that it
has not been studied thoroughly out to the end. Thus the quotation in a
great measure saves us that labour.
Dr. Croll seems sometimes to demand more from the laws of nature than
they can give. He says, at p. 42 of the work cited, that the expansion
of the gaseous mass, produced by the collision of the two bodies,
must have been far greater than could have resulted simply from the
temperature produced by the concussion; and goes on to show how it--the
expansion--might be caused by explosions of gases blowing out blocks
of matter in all directions to indefinite distances. But he forgets
that these explosions of gases would consume a great part of the heat
they contained, that is, turn it into motion of the blocks, and so
diminish the quantity produced by the collision, just in proportion
to the velocities given to the masses of all the blocks blown out; so
that what was gained in expansion would be lost in heat, and the object
aimed at--of producing heat for the expenditure of the sun--so far
lost. Also, that, were the thing feasible, the blocks could not carry
with them any of the heat of the exploded gases that might not be used
up, and that the heat contained in them derived from the concussion
would have time in their flight--about two hours at 476 miles per
second--to melt the matter composing them and turn it into vapour, long
before even the orbit of Neptune was reached. The heat produced by the
explosion of powder in a cannon gives the projectile all the impulse it
can, and disappears; it is converted into motion. It does not cluster
round the projectile, nor follow it up in its flight, nor push it
through an armour plate when it pierces one. We cannot admit--for this
reason--the possibility of a block of matter flying off into space,
with a mass of heat clustering round it, like bees when swarming round
a branch of a tree. Thermodynamics does not teach us anything about a
mass of heat sticking to the surface of a block of matter of any kind.
If the heat were, at a given moment--that is, when motion was
stopped--brought into existence uniformly throughout the entire mass,
which, according to the law of conversion of motion into heat and _vice
versâ_, would most assuredly be the case, and each pound of the mass
possessed 100,000,000,000 foot-pounds of heat, it could not be heaped
up on the outer layers of the blocks--it matters not whether this means
the layers of the outside of the whole mass, or at the outsides of
the blocks--for the energy of lost motion, converted into heat, must
have existed at the centres of the blocks or masses just in as great
force as it did at the surfaces when motion was stopped. If each pound
of matter carried along with it 100,000,000,000 foot-pounds of heat,
that given out by one pound at the centre of a block would be as great
as that given out by one pound at its surface; and the pounds at the
surface could not acquire any greater heat from a neighbouring pound,
because its neighbour could have no greater quantity to give it. Pounds
of matter would be melted and vaporized, or converted into gas, just
as readily at the centre of the mass or block as at its surface; and
storing up of heat in the interstices of the blocks is rather a strange
notion, because we are not at liberty to stow away heat in a vacuum.
Besides, it is impossible to conceive how anything in the shape of
a block could exist in any part of the whole mass, long enough for
it to be blown out into space as a block. But supposing that a block
could exist, it would most notoriously be in a state of _unstable
equilibrium_; and were it then to receive from an explosion of gas, an
impulse sufficient to drive it off to the verge of the sun's power of
attraction--or rather to a distance equal to what that is--which would
imply a velocity of not less than 360 miles per second, the shock would
be quite sufficient to blow it into its constituent atoms. Moreover, as
already stated, the heat of the explosion of the gas required to give
the impulse would be immediately converted into motion, and disappear;
so that out of the heat produced by the stoppage of a motion of 476
miles per second, that required to produce a motion of 360 miles per
second, in each one of the blocks blown out to the distance above
mentioned, would be entirely lost to the stock of heat schemed for so
boldly. Of course, the less the distance from the centre the blocks
were blown the less would be the loss, but the fact remains that there
would be a loss instead of a gain of heat, in dispersing the matter
of two half suns into space by explosions of gas. In fine, a given
amount of heat will raise the temperature of a given amount of matter
to an easily calculable degree, and no more; and if part of that is
expended in expanding the volume of the matter, the whole stock of
heat will be diminished by exactly the quantity required to produce
the expansions. So that we come back to what we have said at page 54,
viz., that when the matter and the heat of the collision of the two
half suns were dispersed, under the most favourable circumstances, into
a sphere of 6,000,000,000 miles in diameter, the mean density of the
matter would be equal to about 1/270th part of an atmosphere, and its
temperature--what is called--273° C. of absolute temperature, always
considering the quantity of the heat to have been 300,000,000° C.
Dr. Croll says that if a velocity of 476 miles per second were not
sufficient to produce the quantity of heat required, any other
necessary velocity might be supposed, but when we consider that his
supply of 300,000,000° C. would have to be increased to 82,000,000,000°
C., in order to add 1° C. of heat to the matter dispersed through a
sphere of 6,000,000,000 miles in diameter, it seems unnecessary to
pursue the subject any farther.
We may now take a look at Dr. Braun's Impact Cosmogony, of which we
know nothing beyond what is set forth in the Review in "Nature" already
alluded to, but that is enough for our purpose. We understand that he
extends his operations to the whole universe, which he conceives to
have been formed out of almost unlimited, and almost imponderable,
nebulous matter, not homogeneous, but with local irregularities in it,
which "would lead to the breaking up of the nebula into a vast number
of separate fragments." Out of one of these fragments he supposes the
solar system to have been formed. This fragment would contain local
irregularities also, which through condensation would lead to the
formation of separate bodies, and these bodies are supposed to have
been driven into their present forms, and gyrating movements of all
kinds, by centric and eccentric collisions among themselves, caused by
their mutual attractions. Of course anything can be supposed, but in a
construction of this kind the idea is forced upon us of the necessity
of the active superintendence of the Creator, to create in the proper
places and bring in the matter at the exact moment required, and to
see that the collisions were directed with the proper degree of energy
and eccentricity, to construct the kind of machine that was proposed.
To this idea we have no objections whatever, but we would like to see
the necessity for it acknowledged. Perhaps Dr. Braun does acknowledge
it, but the cosmogony is given to us, it would seem, to show what most
probably was the original scheme of construction, and implying that no
continual supervision and direction were required during the process.
If Dr. Braun could show us some method of attraction, and suspension
and variation of attraction, by which some of the separate bodies could
be drawn towards each other so as to form a central mass, nebula, or
sun, and to give it, by their impacts of collision, a rotary motion;
and how others of the separate bodies could be formed and held in
appropriate places, so as to be set in motion at the right moment; and
how they were to be so set in motion without the direct action of the
constructor, to revolve as planets around the central mass, we might
be able to recognise that a mechanism such as that of the solar system
might be brought into existence; but when we are left to discover all
these requisites, and their _modus operandi_, we find that we might be
as well employed in designing a cosmogony of our own.
Dr. Braun indulges in somewhat startling numbers in temperature and
pressure. He considers that the temperature of the sun, at the surface,
may be from 40,000° to 100,000° C., and that it may reach to from ten
to thirty million degrees at the centre. In this he may be right for
anything we know to the contrary. When riding over a sandy desert,
under an unclouded vertical sun, we could easily have believed
anything of the central heat of such a fire, especially when we
considered that it was at a distance of ninety-three millions of miles
from us. But when he tells us that in the depths of the sun's interior
the pressure reaches a maximum of two thousand millions of atmospheres,
we "pull in resolution and begin to doubt." Air at that pressure would
have a density 2,585,984 times that of water, or 456,887 times the mean
density of the earth, and we should have a species of matter to ponder
over, of which no physicist has ever as yet dreamt.
We have been able to study M. Faye's cosmogony in his work on
"L'Origine du Monde," second edition of 1885, and can give a better
account of it than of Dr. Braun's.
(1) He repudiates almost all existence of heat in the cosmic matter he
is about to deal with, recognising that its temperature must have been
very near the point of absolute zero, and also that its tenuity must
have been almost inconceivable; so tenuous that a cubic miriamètre of
it would not contain more perhaps than 5·217 grammes in weight. And
very properly, we think, he looks upon the solar systems as having,
at one time, formed a part of the whole universe, all of which was
brought into existence, created, more or less, about the same time. In
this universe, he considers that the stars have been formed, as well
as the sun, by the progressive concentration of primitive materials
disseminated in space, which conception gives rise to a totally new
notion of the most positive character: viz. that each star owes to its
mode of formation a provision of heat essentially limited; that it is
not permissible, as Laplace thought he could do, to endow a sun with an
indefinite amount of heat; and that what it has expended and what it
still possesses, depend upon its volume and actual mass. And also that
the primitive materials of the solar system were, at the beginning,
part of a universal chaos from which they were afterwards separated, in
virtue of movements previously impressed on the whole of the matter;
and sums up his first ideas in the following manner or theorem:
_"At the beginning the universe consisted of a general chaos, of
extreme tenuity, formed of all the elements of Chemistry more or less
mixed and confounded together. These materials under the force of their
mutual attractions were, from the beginning, endowed with diverse
movements which brought about their separation into masses or clouds.
These still retained their movements of rapid translation, and very
gentle interior gyrations. These myriads of chaotic fragments have
given birth, by means of progressive condensations, to the diverse
worlds of the universe."_
(2) So much for the formation of the universe, including, of course,
the solar system, for which he acknowledges the necessity for the
intervention of a creating power, because it is impossible to account
for it simply by the laws of nature; and adds: It is unnecessary to
say that the universe is an indefinite series of transformations, that
what we see results logically from a previous condition, and thus
necessary in the past as in the future; we cannot see how a previous
condition could tend towards the immense diffusion of matter, to the
chaos out of which the actual condition has arisen; and that it is,
therefore, necessary to begin with a hypothesis, and postulate of God,
as Descartes did, the disseminated matter and the forces which govern
it.
(3) From dealing with the universe, M. Faye comes to the formation
of an isolated star, and begins with an entirely ideal case, that of
a spherical homogeneous mass, without interior movement of any kind,
and concludes that the molecules would fall in straight lines towards
the centre; that the mass would condense regularly without losing
its homogeneity, and would end in producing an incandescent sphere
perfectly immovable; and that that would be a star, but a star without
satellites, without rotation, without proper movement. This not being
what was wanted, he goes on to show how, previous to its separation and
complete isolation from the universal chaos, such a mass would possess,
and carry with it when separated, a considerable velocity of rotation,
and would still retain the internal movements it had acquired from the
attraction of the other masses with which it had been previously in
contact; and how the molecules, drawn towards the centre in obedience
to gravitation, would not fall in straight lines but in concentric
ellipses.
(4) From this state of affairs, two very different results might arise.
One, that the molecules might resolve themselves into a multitude of
small masses without the centre acquiring a preponderating increase.
The other, that the central condensation might greatly exceed the
others, and there would be formed a central star accompanied by a crowd
of small dark bodies. M. Faye accepts the second result, in which case
the ellipses described by the small bodies, now become satellites,
would, as the central mass increased in preponderance, have one of
their centres at the centre of the preponderating mass, and their times
of revolution would vary from one to another in conformity to the third
law of Kepler.
(5) For the formation of the solar system M. Faye finds that it is of
little importance whether the movements of bodies around the sun be
very eccentric or almost circular; the first cause is always the same.
They arise from the eddies, _tourbillonnements_, they have brought
with them from their rectilinear movements in the primitive chaos. But
the circle is such a particular case of the ellipse, that we ought not
to expect to see it realized in any system. It is therefore necessary
that, among the initial conditions of the chaotic mass, one should be
found which would prevent the gyrations, eddies, from degenerating into
elliptical movements, and which has at first made right, and afterwards
firmly preserved, the form, more or less circular, in all its changes.
(6) For the formation of circular rings he gives us the following
conceptions: In order that a star should have companions, great or
small, circulating round the centre of gravity of the system, it is
necessary that the partial chaos from whence it proceeded should have
possessed, from the beginning, a gentle eddying movement affecting a
part of its materials. Besides, if the partial chaos has been really
round and homogeneous, we shall see that these gyrations must have
taken up, and to some extent preserved, the circular form. He then
requests the reader not to lose sight of the feeble density of the
medium, in which a succession of mechanical changes are to be brought
about; and not to conclude that that density was such that a cubic
miriamètre of the space occupied by it might not contain 3250 grammes
of matter, as he stated in the preceding chapter (we think he said
5217 grammes), but that it might contain only 3 grammes or even less.
And adds that in such a medium, the small agglomerations of matter
which would be formed all through it, would move as if they were in an
absolute vacuum, and any changes in them would be produced extremely
slowly.
(7) Then he goes on to say that the gyrating movements belonging to
the chaotic mass, would have very little difficulty in transforming a
part of a motion of that kind into a veritable rotation, if this last
were compatible with the law of the internal gravitation; that it is
the nature of that kind of masses to only permit, to the bodies moving
in them, revolutions, elliptic or circular, concentric and of the
same duration; that therefore notable portions of the gyrating matter
could take the form and movements of a flat ring, turning around the
centre with the same angular velocity, exactly as if this nebulous
ring were a solid body; that all the particles which have the proper
velocity in the plane of the gyrations, will arrange themselves under
the influence of gravitation in a flat ring with a veritable rotation
around the centre; that any other parts having velocities too great or
too small, will move in the same plane, describing ellipses concentric
to the ring; that if the ellipses are very elongated the materials
composing them will approach the centre, where they will produce a
progressive condensation, communicating to the central globe formed
there a rotation in the same plane with the primitive gyrations; and
finishes off the whole scheme by specifying the first results to
be: (1) The formation of concentric rings turning in one piece, in
the manner of a solid body, around a centre almost empty (_d'abord
vide_); and (2) A rotation in the same direction, communicated to
the condensation which would be produced, little by little, by means
of matter coming in, partly, from regions affected by the internal
eddyings (_tourbillonnements_).
(8) It is unnecessary to go any farther, and take note of his method
of the formation of planets and satellites from rings, as it is much
the same as what we have seen described by others who have written on
the same subject; only interpreted by him in a way to suit his own
purposes, and in which interpretation he does not do full justice
to Laplace, through not having paid sufficient attention to his
explanation of how planets could be formed out of rings. Except in so
far as to note that all along he has considered that rings were formed,
and even those nearest to the centre condensed into globes, long before
the central condensation had attained any magnitude of importance, or
assumed any distinctive shape, and that afterwards all the disposable
matter of the rings and also all the exterior matter that had not
formed part of what was separated from the original universal chaos,
had fallen in towards the small central mass, and so completed the
formation of the sun last of all.
We shall now proceed to make a few remarks with respect to this
condensation of M. Faye's cosmogony, which we think we have made
without adding to or omitting anything of importance that we have met
with in his work, for which purpose we have numbered the paragraphs
containing it, in the last six pages, in order to do away with the
necessity of repeating the parts to which we refer.
No. 1. All those who believe that "the solar system did originate
somehow, by the condensation of a primitive nebula," agree with M.
Faye in considering that the density of the nebulous matter must have
been extremely low, and some of them seem almost to vie with each
other in showing how great must have been the degree of its tenuity;
but M. Faye is one of the few who, paying due respect to the law of
the interdependence of temperature and pressure in a gas or vapour,
maintain that it must have been almost devoid of temperature, and we
have to acknowledge that he is in the right. Then we believe that his
assumption, that the whole universe of stars, including the sun, was
created, humanly speaking, about the same time, is shared by the great
majority of those who have thought at all seriously on the subject.
Also, we agree with him firmly in his statement that each star--and we
add planet, satellite, etc.--was originally supplied with an extremely
limited quantity of heat, and that what it has expended and what it
still retains has been derived entirely from the condensation of the
original cosmic matter out of which it was made.
With regard to his theorem: we cannot follow him in his statement
that the diverse movements caused by the mutual attractions of parts
of the original universal mass of cosmic matter, have brought about
its separation into myriads of fragments; nor how these fragments
could carry with them a rapid movement of translation, unless the
whole universal mass was endowed with a rapid movement of translation
through space, in which case we think that such a motion would have
had no greater particular effect in producing new forms of motion in
the fragments, than if the whole had been created in a state of rest.
Stray movements of translation might give rise to collisions among
the multitude of fragments, and perhaps that was one of the modes of
formation into suns through which they had to pass; but we cannot
follow it out. Neither can we see clearly how translation could be
effected of one mass into the space occupied by another mass--unless
empty spaces were reserved for that purpose from the beginning. Without
that, translation could not exist: it would be collision.
No. 2. We have nothing to object to what is said in this paragraph;
except that a rotating sphere might have been postulated at once,
in imitation of Laplace, instead of trying like Descartes to join
fragments together, endowed with movements so adjusted that, among the
whole of them, they would produce in the whole mass, when united, the
kind of movement that was wanted.
No. 3. To the ideal case of the formation of an isolated sun from a
homogeneous mass without interior movement of any kind, we cannot
agree in any way. The molecules of matter would not, could not, fall
in towards the centre in straight lines. Their mutual collisions would
drive them generally in curved lines in all directions as they fell in,
which would create new internal movements; and these movements would
prevent the possibility of the formation of an immovable incandescent
sphere such as is described. There could be no immobility in the
interior of a sun, as long as its temperature was sufficient to keep
the surface incandescent. But we cannot give our reasons here for this
assertion--to most people they will, we think, occur at once--because
we have a long road to travel before we can do so.
When M. Faye abandons the isolated case, he leaves us without giving
us any help, to conceive for ourselves how the mass would possess and
carry with it a considerable velocity of rotation, and still retain the
internal movements it had acquired from the attraction of the other
masses--of the universal chaos--with which it had been in contact;
and also how the molecules drawn towards the centre would not fall in
straight lines but in concentric ellipses. And this last we have to
do without his giving us any reason why the molecules should fall in
towards the centre at all; or rather in spite of the fact that one of
his principal ideas would lead us to expect exactly the contrary, as we
shall see presently.
No. 4. Here he places before us again, two cases in one of which the
molecules might resolve themselves into a multitude of small masses,
without the centre acquiring any preponderating increase; and the other
where the central condensation might greatly exceed the others, and
there would be formed a central star accompanied by a crowd of small
dark bodies, now become satellites, describing ellipses around the
central preponderating mass. This second case he seems, for the time
being, to accept as the most probable; but it is strangely at variance
with what he sets forth afterwards. He does not give us the least
hint as to why or how the satellites acquired their various times of
revolution, but only assumes that they did so; and we are very sure
that it was not the third law of Kepler that was the agent in the case,
however much it might suit his purpose.
No. 5. Although this part of his exposition is dedicated to the
formation of the solar system, all that M. Faye says is that it is
of little importance whether the movements of bodies around the sun
be very eccentric or almost circular; and that among the initial
conditions of the chaotic mass, all that we require is that one should
be found which would prevent the gyrations from degenerating into
elliptic movements, and which had first put right and afterwards firmly
preserved the form, more or less circular, in all its changes. But
he does not make any attempt to show what that one condition is, and
allows us to find it out for ourselves.
No. 6. What M. Faye says about the formation of circular rings is more
or less a repetition of what he has adduced, to explain all the other
movements which he has derived from the universal chaos; and which he
seems to think sufficient to account for such movements being nearly
circular. For our part we do not think they are sufficient, and he does
not show us how they influence each other to bring about the final
movements he wants to present to us.
We duly take note of the tenuity of the cosmic matter on which he
operates, which at 3 grammes in weight to 1 cubic miriamètre would
correspond to one grain in weight to 771,947,719,300 cubic feet of
space, or 1 grain to a cube of 9173 feet--more than 3000 yards--to
the side. We do this in order to remind him of what he says at page
151 of his work, when dealing with the rotation of the Kant-Laplace
nebula--namely, that it is impossible to comprehend how an immense
chaos, of almost inconceivable tenuity, could possess such a rotation
from the beginning, and that for want of that inadmissible supposition
nothing remains to fall back upon but the _mouvements tourbillonnaires_
of Descartes. Thus he wants us to believe that his _tourbillons_ could
move in straight or curved lines, have motions of translation, could
attract, restrain, and drive each other into all sorts of movements
with the tenuity he has indicated; but that Laplace's nebula, with a
density of 1 grain to a cube of 90 feet--or at most 150 feet--to the
side, could not be conceived to have the single movement of rotation.
And lastly, we repeat that if the centre of the chaos was almost
empty, we do not see what induced the cosmic matter to fall into it in
elliptic orbits.
Nos. 7 and 8. In these paragraphs, the main features are repetitions of
the simple assertions made in all the others, that certain movements
possessed by matter in one state would produce other movements in
another state, without attempting to show how they all came to so
far coincide with each other and form one harmonious whole, with
movements in almost one single direction. It is clear that one side
of the separated chaos might have acquired motion in one direction
from the universal chaos with which it had been in contact, and that
the opposite side might have acquired motion in exactly the opposite
direction from the original chaos with which it had been in contact;
and we are left to find out how these came to agree with each other
in the end. And, going back to the beginning, we are left to find out
where the mass, out of which he constructs his solar system, was stowed
away, after it was separated from the original universal chaos. We
can conceive of its being separated by condensation, in obedience to
the law of attraction, from the surrounding chaos, in which case it
might fall towards a centre, or that some parts of it might come to
revolve round each other, and that finally the whole of these parts
might come to rotate about a common centre; but that is evidently very
different from the mode of formation of the solar system which M. Faye
has advocated. It comes to be by far too like the nebula which Laplace
supposed to be endowed with rotary motion from the beginning, probably
because he did not see, or did not take the trouble to see, how such
a motion could be produced. In any case, Laplace did not consider
that the primary motion of rotation was the most important part of
his hypothesis; neither was it, as it seems to have been in the case
we have been considering. And he did not go much further than M. Faye
in postulating primary motion, only he did it in a more effectual and
business-like manner. He drew on the bank at once for all the funds he
required, instead of having to draw afresh every time he found himself
in difficulties, as has been the lot of his critic and successor.
Finally, M. Faye tries to show that after all his rings, flat or
otherwise, converted or not converted into globes, had been formed
according to his ideas, the greater mass by far of the chaos had fallen
into the centre, and had formed the sun there last of all. Now, if the
preponderating mass of the chaos had been outside of the field of his
operations, up to the period when all his planets, satellites, etc.
were formed, or at least laid out, it is more natural to suppose that
the matter inside of his structure, if there was any, would be drawn
outwards by the attraction of the greatly preponderating mass outside,
than that any portion of it should have fallen in, in elongated
ellipses, towards the insignificant mass that he supposes to have
been inside his structure. This, of course, would be nearly exactly
the reverse of the mode of formation he was trying to demonstrate,
and clearly shows that he was working on unsound principles from the
beginning to the end of his cosmogony. It had never occurred to him
that matter could be attracted outwards as well as inwards, most
probably because it would seem to him ridiculous to imagine that
anything in the universe could _gravitate_ upwards.
There are other theories of the formation of the solar system from
meteorites and meteors, giving us the idea of its being made out of
manufactured articles instead of originally created raw material,
which does not in any way simplify the process. In some of them, the
inrush of meteor swarms is invoked as the cause of gyratory motion,
which places them in much the same category as impact theories. We know
that broadcloth is made out of woollen yarn, but we also know how the
yarn is made out of wool, and how it is woven into the cloth, whereas
we are not told by what process, or even out of what the meteors and
meteorites are made, although some of them are said to have thumb-marks
upon them.
All these theories and cosmogonies may be very appropriately classified
as variations of the nebula hypothesis, and like variations in another
science, may be very brilliant, scientific, imaginative, grand, but
after all the flights of fancy exhibited by them are set before us,
we feel in a measure relieved when a return is made to the original
air. They all assume original motion, varied, accidental, opportune,
more dependent upon the will of the cosmogonist than on the laws of
nature, which tend to confound rather than enlighten any one who
tries to understand and bring them, mentally, into actual operation.
Laplace assumed rotary motion for the whole of his nebula, and was
thus able to account at once for the relation which exists among the
planets in respect of distance from, and period of revolution around
the sun--arising from the original rotation of the whole mass in one
piece--a result which, in any impact theory, has to be accounted for
separately, and, in plain truth, empirically in each case, and at each
step.
Seeing, then, that we have not been able to find any cosmogony, or
speculation, that gives us a more plausible idea of how the solar
system has been formed, we shall try whether from the original nebula
as imagined by Laplace, it is possible to separate the various
members, and form the system in the manner described in his celebrated
hypothesis. In other words, we shall endeavour to analyse the
hypothesis.
CHAPTER IV.
PAGE
72 Preliminaries to analysis of the Nebular hypothesis.
73 Definition of the hypothesis.
75 Elements of solar system. Tables of dimensions and masses.
78 Explanation of tables and density of Saturn.
79 Volume, density and mass of Saturn's rings, general remarks about
them, and satellites to be made from them.
79 Future of Saturn's rings.
80 Notions about Saturn's satellites and their masses.
81 Nature of rings seemingly not well understood.
81 Masses given to the satellites of Uranus and Neptune,
Explanations of.
82 Volumes of the members of the solar system at density of water.
PRELIMINARIES TO ANALYSIS OF THE NEBULAR HYPOTHESIS.
It may be thought that there is little benefit to be derived from
analysing an hypothesis which has been declared, by very eminent
authorities in the matter treated of, to be erroneous in some points of
very serious importance; but hypotheses are somewhat of the nature of
inventions, and we know that it has often happened that many parties,
aiming at the same invention, have altogether failed, while some other
person using almost exactly the same means as his predecessors, has
been entirely successful in his pursuit. How many times has it been
pointed out to us, that if such a person had only gone one step further
in the process he was following, or had only studied more deeply the
matter he had in hand, he would have anticipated by many years one of
the greatest discoveries of the age! In some cases the failure to take
that one step was occasioned through want of knowledge acquired long
years afterwards; whereas we think that in the case we have in hand, it
can be shown that the want of knowledge acquired many years after he
had formulated his hypothesis, or if otherwise, the want of faith in
what he knew, enabled Laplace to construct an edifice which otherwise
he could hardly have convinced himself could be built up in a practical
form. We think also that if he had made the proper use of the knowledge
he must have had of the law of attraction, he would have seen that no
nebula could ever have existed such as the one he assumed, extending
far beyond the orbit of the remotest planet. Furthermore, we think it
can be shown that if he had thoroughly considered what must have been
the interior construction of his nebula, he would have found one that
would have suited his hypothesis in the main point, viz. condensation
at the surface, at least equally as well as endowing it with excessive
heat. But to be able to show these things our first step must be to
analyse the hypothesis, to examine into it as minutely and deeply as
lies in our power.
For this purpose it will be necessary to define what the hypothesis is.
Many definitions have been given, more or less clear, and it would be
only a waste of time to try to set forth Laplace's own exposition of
it, with all its details, which he had no doubt studied very carefully.
But in those definitions that have come under our observation,
several of the conditions he has specified are wanting, or not made
sufficiently prominent; so instead of adopting any one of them we
will make a sort of condensation of the whole, adding the conditions
that have been left out; because the want of them, has been the cause
of mistaken conceptions of the evolution of the system having been
formed by very eminent astronomers. Our definition will therefore be as
follows:--
I. It is supposed that before the solar system was formed the portion
of space in which its planets and other bodies now perform their
revolutions and other movements, was occupied by an immense nebula
of cosmic matter in its most simple condition--of molecules or
atoms--somewhat of a spherical form, extending far beyond its present
utmost limits, and that it was endowed with excessive heat and a slow
rotary motion round its centre; which means that while it made one
revolution at the circumference it also made one at the centre. The
excessive heat, by counteracting in a certain measure the force of
gravitation, kept the molecules of matter apart from each other; but
as the heat was gradually radiated into space, gravitation became more
effective, and then began to condense and contract more rapidly, by
which process its rotary motion was, in accordance with the areolar
law, gradually increased at the surface, _in the atmosphere of the
sun_, where the cooling took place, and condensation was most active;
and the increase of rotation was propagated from there towards the
centre.
(2) As the contraction and rotation increased a time or times arrived,
when the centrifugal force produced by the rotation came to balance the
force of gravitation, and a series of zones or rings were separated
from the nebula, each one of them continuing to rotate--revolve
now--around the central mass, with the same velocities they had at
the times of their separation; until at last the nebula became so
contracted that it could not abandon any more rings, and what of it
remained condensed and contracted into a central mass which ultimately
assumed the form of the actual sun.
(3) In the meantime, or following afterwards, each one of the rings
which were abandoned by the nebula, acquired, through the friction
of its molecules with each other, an equal movement of revolution
throughout its entire mass, so that the real velocities of the
molecules furthest removed from the centre of the nebula were greater
than those of the molecules nearest to its centre, and the ring
revolved as if it were in one solid piece. Arrived at this stage the
rings broke up and formed themselves into smaller nebulæ, each of which
condensed into a globe or planet, and continued to revolve around the
central mass in the same time as its mass had done when in the form of
a ring. And some of these sub-nebulæ, imitating the example of their
common parent more perfectly than others, abandoned in space in their
turn smaller rings which in the same manner condensed, broke up, and
formed themselves into smaller globes or satellites; all, as far as we
know, except the rings of Saturn, which have not as yet been converted
into satellites.
TABLE I.
ELEMENTS AND OTHER DATA OF THE SOLAR SYSTEM EMPLOYED
IN THIS ANALYSIS.
PART I.--SUN AND PLANETS.
--------+-------------+----------+-----------------------+-----------+
|Mean Distance|Equatorial|Volume in Cubic Miles. | Density. |
Name. | from Sun |Diameter | |(Water = 1)|
| in Miles. |in Miles. | | |
--------+-------------+----------+-----------------------+-----------+
Sun | -- | 867,000 |341,237,637,800,000,000| 1·413 |
Mercury | 35,987,000| 2,957 | 13,537,968,847| 6·850 |
Venus | 67,245,000| 7,660 | 235,334,728,260| 4·810 |
Earth | 92,965,000| 7,918 | 259,923,832,335| 5·660 |
Mars | 141,650,000| 4,185 | 38,378,333,333| 4·188 |
Supposed| | | | |
planet| 260,300,000| -- | -- | -- |
Jupiter | 483,678,000| 87,680 | 352,940,162,601,626| 1·358 |
Saturn | 886,779,000| 73,713 | 209,716,183,575,000| 0·736 |
Uranus |1,783,383,000| 33,563 | 19,796,209,090,910| 1·302 |
Neptune |2,794,000,000| 36,620 | 25,713,106,508,876| 1·132 |
--------+-------------+----------+-----------------------+-----------+
| Volume at Density of | Time of Revolution |
Name. | Water in Cubic Miles. | round Sun in Days. |
| | |
--------+------------------------+-----------------------+
Sun | 482,169,000,000,000,000| -- |
Mercury | 92,735,000,000| 87·9692 |
Venus | 1,131,960,000,000| 224·7007 |
Earth | 1,471,169,000,000| 365·2563 |
Mars | 160,728,460,000| 686·9796 |
Supposed| | |
planet| 367,792,000,000| 1,714·1876 |
Jupiter | 479,292,741,000,000| 4,332·2548 |
Saturn | 154,351,000,000,000| 10,759·2198 |
Uranus | 25,874,664,000,000| 30,688·5076 |
Neptune | 29,107,237,000,000| 60,186·6385 |
--------+------------------------+-----------------------+
PART II.--SATELLITES OF PLANETS.
----------+--------------+-------------+-----------------+
| Mean Distance| Equatorial | Volume |
Names. | from Primary | Diameter | in Cubic Miles. |
| in Miles. | in Miles. | |
----------+--------------+-------------+-----------------+
| _Of the Earth._ |
Moon | 238,833 2160 5,276,682,926 |
| |
| _Of Jupiter._ |
Jo | 267,380 2252 5,980,050,000 |
Europa | 425,160 2099 4,842,133,708 |
Ganymede | 678,390 3436 21,240,229,268 |
Callisto | 1,192,820 2929 13,157,027,273 |
| |
| _Of Saturn._ |
Mimas | 120,800 1000 523,600,000 |
Enceladus | 155,000 ? 65,450,000 |
Tethys | 191,000 500 65,450,000 |
Dione | 246,000 500 65,450,000 |
Rhea | 343,000 1200 904,780,417 |
Titan | 796,000 3300 18,816,606,060 |
Hyperon | 1,007,000 ? 3,053,634,965 |
| |
Japetus | 2,314,000 1800 3,053,634,965 |
| |
| _Of Uranus._ |
Ariel | 123,000 } Total mass taken at |
Umbriel | 171,000 } 1/15,000th of primary |
Titania | 281,000 } 1,724,977,600 |
Oberon | 376,000 } |
| |
| _Of Neptune._ |
----- | 220,000 } Mass taken at |
| } 1/40,000th of primary |
| 727,680,925 |
----------+----------+-----------------+-----------------+
| Density. |Volume at Density| Total Volume at |
Names. |(Water=1.)| of Water in |Density of Water |
| | Cubic Miles. | in Cubic Miles.|
----------+----------+-----------------+-----------------+
| |
| _Of the Earth._ |
Moon | 3·438 .. 18,141,236,000 |
| |
| _Of Jupiter._ |
Jo | 1·132 6,769,416,600 |
Europa | 2·141 10,367,008,269 |
Ganymede | 1·868 39,676,748,273 |
Callisto | 1·472 19,367,144,146 |
| ----------------- |
| 76,180,317,288 |
| |
| _Of Saturn._ |
Mimas | ... |
Enceladus | ... |
Tethys | ... |
Dione | ... |
Rhea | ... |
Titan | ... Total Volume |
Hyperon | ... in Cubic Miles. |
| |
Japetus | 0·7 36 26,548,606,407 19,539,774,315 |
-----------+----------------------------------------------+
PART III.--RINGS OF SATURN.
---------+-----------------------------+--------------------------+
| | |
Rings. | Diameters of Rings | Areas of Rings |
| in Miles. | in Square Miles. |
---------+-----------------------------+--------------------------+
Outer { | Outer | 172,240 | } 5,252,035,427 |
{ | Inner | 151,590 | } |
| | | |
Middle { | Outer | 148,100 | } 6,919,075,757 |
{ | Inner | 114,560 | } |
| | | |
Dark { | Outer | 110,060 | } 3,040,689,488 |
{ | Inner | 90,993 | } |
| | | |
| | Total | 15,211,800,672 |
---------+----------+------------------+---------+----------------+
|Thickness | | | Volume at |
Rings. | of Rings | Volume of Rings |Density. |Density of Water|
| in Miles.| in Cubic Miles. |(Water=1)|in Cubic Miles. |
---------+----------+------------------+---------+----------------+
Outer { | | | | |
{ | | | | |
| | | | |
Middle { | | | | |
{ | | | | |
| | | | |
Dark { | | | | |
{ | | | | |
| | | | |
| 90 | 1,369,062,060,480| ·0001425| 195,000,000 |
---------+----------+------------------+---------+----------------+
(4) All of these bodies, planets, satellites, and rings were supposed
to revolve around their primaries, and to rotate on their axes, in the
same direction viz., from right to left, in the opposite direction to
the hands of a watch.
In addition to the above definition it is necessary to give some sort
of description of the various parts of the machine or system which has
to be made out of the nebula, with their positions, dimensions, and
details. This we believe will be made plain enough, in the simplest
manner, by Table No. I., taken and calculated from the elements of the
solar system given in almost all astronomical works, from which we have
selected what we believe to be the most modern data.
The construction of this table requires some explanation on account of
its being made to show complete results from incomplete data. There has
been no difficulty with the sun, the major planets, and the satellites
of the earth and Jupiter, but for the minor planets, the satellites of
the three outer planets, and the rings of Saturn, we have been obliged
to exercise our judgment as best we could.
There being almost no data whatever of the dimensions and densities of
the minor planets, to be found, we have been driven in order to assign
some mass to them, to imagine the existence of one planet to represent
the whole of them (in fact Olbers's planet before it exploded), which
we have supposed to be placed at the mean distance of 260,300,000 miles
from the centre of the sun; and we have given to it a mass equal to
one-fourth of the mass of the earth, that being, in the opinion of some
astronomers, the greatest mass which the whole of them put together
could have. This assumption we shall explain more fully at a more
suitable time.
In the case of Saturn the diameters of two of the satellites are
wanting which we have assumed to be the same as those of the smallest
of those nearest to them, and thus have been able to compute the
volumes of the whole of them; but we have not been able to find any
statement anywhere of their densities, and to get over this difficulty
we have reasoned in the following manner.
The density of the moon is very little over two-thirds of that of the
earth, while that of the satellites of Jupiter varies from a little
more than the same to a little more than twice as much as the density
of their primary. Why this difference? To account for it we appeal to
the very general opinion of astronomers, that the four inner planets
are in a more advanced stage of their development, or existence, than
the four outer ones. In this way it is easy to conceive that the earth
has arrived at the stage of being more dense than its satellite; while
in the case of Jupiter, his satellites being of so very much less
volume than their primary, have already arrived at a higher degree of
development. Carrying this motion forward to Saturn, we have supposed
that from his being considerably less dense than any other of the
outer planets--quite possibly from having been formed out of material
comparatively (perhaps not actually) less dense than the others--his
satellites may not have condensed to a greater degree than his own
mass, and we have, therefore assumed their density, that is the density
of the volume of the whole of them, to be the same as that of their
primary.
To determine some mass for the rings of Saturn, is a much more
intricate matter than for his satellites, and presents to us some
ideas--facts rather--which had never before crossed our imagination.
The most natural way to look upon these rings is to suppose that they
are destined to become satellites at some future time. All the modern
cosmogonies that have come under our notice are founded upon the idea
that rings are the seed, as it were, of planets and satellites, and if
those of Saturn have been left, as it has been said, to show how the
solar system has been evolved, it cannot be said that the supposition
is not well founded. In this way we are led to speculate upon how many
satellites are to be made out of the rings before us. Considering,
then, that the nearest satellite is 120,800 miles from the centre of
Saturn, leaving only 83,500 miles between his surface and that of
Mimas, and also that the distances between satellites diminish rapidly
as they come to be nearer to their primaries, there is not room to stow
away a great number of satellites. On the other hand, seeing that there
are at least three distinct rings, we cannot reasonably do less than
conclude that three satellites are intended to be made out of them. But
let the number be what it may, all that we have to do with them for our
present purpose is to assign some mass to them. With this view, we have
given, arbitrarily, to each one of the three we have supposed, a volume
equal to that of one of the satellites of 500 miles in diameter, that
is, about 65,000,000 cubic miles, and we have supposed their density to
be the same as that of water, instead of that of the planet. Thus, in
the table, we have assigned to the three a mass of 195,000,000 cubic
miles at density of water, which would be more than sufficient to make
four other satellites for the system of 500 miles in diameter each, and
of the same density as the planet.
For the table referred to we have calculated the areas of the three
rings to be 152,110,800,172 square miles, and we have assumed the
thickness as 90 miles, that is about two-thirds of that estimated by
Chambers in his handbook of Astronomy, but almost the same as that
given by Edmund Dubois; nevertheless their total volume comes up to
1,369,062,060,480 cubic miles, which reduces their average density
to 0·0001425 that of water, to make up the mass of 195,000,000 cubic
miles at the density of water, which we have adopted for the three.
This density corresponds to very nearly one-tenth of that of air,
which, however strange it may appear to us, may be considered to be
a very full allowance, seeing that we shall find, later on, that the
planet itself was formed out of matter whose density could not have
been more than one twenty-six millionth part of that of air. All the
same, it is hardly matter that we could liken to brickbats. After being
driven to this low estimate of density, which startled us, we referred
to an article in "Nature" of Nov. 26, 1886, on Ten Years' Progress
in Astronomy, where we find what follows:--"He (Newcomb) finds the
mass of Titan to be about 1/12,000 that of Saturn. It may be noted,
too, that Hall's observations of the motions of Mimas and Enceladus
indicate for the rings a mass less than 1/10 that deduced by Bessel;
instead of being 1/100 as large as the planet, they cannot be more than
1/1000, and are probably less than 1/10,000." (We make them 1/791514).
Thinking over the numbers herein given we cannot help being surprised
by them. If Titan be 1/12500 of the mass of Saturn, we cannot conceive
how the mass of his rings can be so much greater than that of Titan. We
cannot pretend to fit even one satellite of that size, mechanically,
into a space of 83,500 miles wide, while Titan revels in an ample
domain with a width of 332,000 miles. But we shall not pursue this part
of our speculations any further. Astronomers may be able to demonstrate
that the rings are of a totally different nature to those out of which
the planets and their satellites are supposed to have been made, or
that the nebular hypothesis or anything resembling it is no better than
a foolish dream. All that we have pretended to do has been to give them
their due place in the hypothesis we are attempting to analyze, and to
look upon them in a practical and mechanical light, as an unfinished
part of the solar system.
To determine masses for the satellites of the two outer planets, we
have to be more empirical even than we have yet been. A little trouble
will show that the whole mass of all the satellites and rings of Saturn
put together is about 1/7820th of the mass of the planet, and we shall
avail ourselves of this proportion to assign masses for the satellites
of the remaining planets, the numbers and names of which are the only
data we have been able to find. Considering then, that Uranus has only
four satellites and no rings, we think if we give them 1/15,000th of
the mass of their primary, it will be a very fair allowance; and with
the same empiricism we have adopted for the solitary satellite of
Neptune 1/40,000th of the mass of its primary.
However rude and crude these approximations may be, we have the
satisfaction of thinking that the masses obtained by their means, can
have no appreciable effect upon the operations into which they are to
be introduced, whilst they enable us to deal with a complete system
or machine. But for these we have another Table No. II. to present, a
_résumé_ of the foregoing one, for greater facility of reference.
TABLE II.--VOLUMES OF THE VARIOUS MEMBERS OF THE
SOLAR SYSTEM AT THE DENSITY OF WATER.
---------+------------+-------------------+-----------------------+
| | Volume in | Total Volume in |
Name. |Designation.| Cubic Miles at | Cubic Miles at |
| | Density of Water. | Density of Water. |
---------+------------+-------------------+-----------------------+
Sun | | |482,169,000,000,000,000|
| | |-----------------------|
Mercury | Planet | | 92,735,000,000|
Venus | " | | 1,131,960,000,000|
Earth | " | 1,471,169,000,000| |
Moon | Satellite | 18,141,236,000| 1,489,310,236,000|
| |-------------------| |
Mars | Planet | | 160,728,460,000|
---- | Asteroids |One fourth of Earth| 367,792,000,000|
Jupiter | Planet |479,292,741,000,000| |
" |4 Satellites| 76,180,317,000| 479,368,921,317,000|
| |-------------------| |
Saturn | Planet |154,351,000,000,000| |
" |8 Satellites| 19,539,774,315| |
" | 3 Rings | 195,000,000| 154,370,734,774,315|
| |-------------------| |
Uranus | Planet | 25,874,664,000,000| |
" |4 Satellites| 1,724,977,600| 25,876,388,977,600|
| |-------------------| |
Neptune | Planet | 29,107,237,000,000| |
" |1 Satellite | 727,680,925| 29,107,964,680,925|
---------+------------+-------------------+-----------------------+
Total of Planets, Satellites and Rings | 691,966,535,445,840|
------------------------------------------+-----------------------+
Dividing 482,169,000,000,000,000 by 691,966,535,445,840
makes the mass ofthe whole of the members to be 1/696·86th
part of the mass of the sun, instead of 1/700th as
generally stated by astronomers.
CHAPTER V.
PAGE
83 Analysis of the Nebular Hypothesis. Separation from the nebula
of the rings for the separate planets, etc.
84 Excessive heat attributed to the nebula erroneous and impossible.
85 Centigrade thermometer to be used for temperatures.
86 Temperature of the nebula not far from absolute zero.
86 Erroneous ideas about glowing gases produced by collisions of
their atoms, or particles of cosmic matter in the form
of vapours.
87 Separation of ring for Neptune. It could not have been thrown
off in one mass, but in a sheet of cosmic matter.
88 Thickness and dimensions of the ring.
89 Uranian ring abandoned, and its dimensions.
90 Saturnian ring do. do.
91 Jovian ring do. do.
93 Asteroidal ring do. do.
94 Martian ring do. do.
95 Earth ring do. do.
96 Venus ring do. do.
97 Mercurian ring do. do.
98 Residual mass. Condensation of Solar Nebula to various diameters,
and relative temperatures and densities.
100 Unaccountable confusion in the mode of counting absolute
temperature examined and explained. Negative 274 degrees
of heat only equal 2 degrees of absolute temperature.
103 The Centigrade thermometric scale no better than any other,
and cannot be made decimal.
104 The sun's account current with the Nebula drawn up and represented
by Table III.
ANALYSIS OF THE NEBULAR HYPOTHESIS.
We may now proceed to take the original nebula to pieces, by separating
from it all the members of the solar system, in performing which
operation we shall suppose the divisions between the nebula and each
successive ring to have taken place at a little more or less than the
half distances between the orbits of two neighbouring planets, because
we have no other data to guide us in determining the proper places.
These divisions have manifestly been brought about in obedience to
some law, as is proved in great measure by what is called Bode's Law;
although no one has as yet been able to explain the action of that
law. It is no doubt certain that a division must have taken place much
nearer to the outer than the inner planet in each case, if we think of
what would be the limit to the sphere of attraction between the nebula
and a ring just detached from it--for the attraction of the abandoned
ring, and even of all those that were outside of it, would have
very little influence in determining the line where gravitation and
centrifugal force came to balance each other--but the data necessary
for calculating what these would be are wanting. Even if they existed
the calculations would become too complicated for our powers as the
number of rings increased; and for our purpose it is really of very
little importance where the divisions took place. The breadths of
the rings would be practically the same, whether they were divided
at the half distances between, or much nearer to, the outermost of
two neighbouring planets; and although the extreme diameters of the
consecutive residuary nebulæ would be somewhat greater, their densities
and temperatures would not materially differ from those we shall
find for them as we proceed in our operations. Their masses would be
the same in all cases, which is the principal thing in which we are
interested.
This premised, we shall first examine into the excessive heat
attributed to the nebula, that being the first condition mentioned in
our definition of the hypothesis.
The diameter of the sun being 867,000 miles, his volume is
341,238,000,000,000,000 cubic miles, and his density being 1·413 times
that of water, his volume reduced to the density of water would be
482,169,000,000,000,000 cubic miles. Now, astronomers tell us that the
whole of the planets, with their satellites and rings, do not form a
mass of more than 1/700th part of the mass of the sun. If, then, we add
1/700th part to the above volume, we get a total volume, for the whole
of the system, of 482,857,590,478,000,000 cubic miles at the density
of water, which corresponds to a sphere of about 973,360 miles in
diameter. On the other hand, the diameter of the orbit of Neptune being
5,588,000,000 miles, if we increase that diameter to 6,600,000,000
miles, so that the extreme boundary of the supposed nebula may be as
far beyond his orbit, as half the distance between him and Uranus is
within it, we shall still be far within the limit at which the process
of separation from the nebula, of the matter out of which Neptune was
made, must have begun. From these data we can form a very correct
calculation of what the density--tenuity rather--of the nebula must
have been. For, as the volumes of spheres are to each other as the
cubes of their diameters, the cube 973,630 is easily found to be to the
cube of 6,600,000,000, as 1 is to 311,754,100,720, or in other words,
the density of the nebula turns out to have been 1/311,754,100,720th
part of density of the whole solar system reduced to that of water.
Carrying the comparison a little further, we find that as water is
773·395 times more dense than air, and 11,173·184 times more dense
than hydrogen, the density of the nebula could not have been more than
1/403,000,000th part that of air, and 1/27,894,734th that of hydrogen.
But, confining the comparison to air, as it suits our purpose better,
we see that it would take 403,000,000 cubic feet of the nebula to be
equal in mass to 1 cubic foot of air at atmospheric pressure; and that
were we to expand this cubic foot of air to this number of times its
volume, the space occupied by it would be as nearly in the state of
absolute vacuum as could be imagined, far beyond what could be produced
by any human means. Now, were heat a material, imponderable substance,
as it was at one time supposed to be, we could conceive of its being
piled up in any place in space in any desired quantity; but it has been
demonstrated not only not to be a substance at all, but that its very
existence cannot be detected or made manifest, unless it is introduced
by some known means--friction, hammering, combustion--into a real
material substance. Therefore, we must conclude that if it existed at
all in the nebula, it must have been in a degree corresponding to the
tenuity of the medium, and the air thermometer will tell us what the
temperature must have been if we only choose to apply it.
Applying, then, this theory of the air thermometer, if we divide[B]
274° by 403,000,000--the number of times the density of the nebula
was less than that of air--we get 0·00000068°, as the absolute
temperature of the nebula, something very different to excessive heat,
incandescence, firemist, or any other name that has been given to its
supposed state. Furthermore, as a cubic foot of air weighs 565·04
grains, 403,000,000 divided by 565·04, which is equal to 713,223,
would be the number of cubic feet of the space occupied by the nebula,
corresponding to each grain of matter in the whole solar system, which
would be equal to a cube of very nearly 90 feet to the side. And as the
only means by which the nebula could acquire heat would be by collision
with each other of the particles of matter of which it was composed; to
conceive that two particles weighing 1 grain each, butting each other
from an average distance of 90 feet, could not only bring themselves,
but all the space corresponding to both of them--which would be
1,426,446 cubic feet, _of what_?--up to the heat of incandescence, or
excessive heat of any kind, is a thing which passes the wit of man.
Consequently, neither by primitive piling up, nor by collisions among
the particles, could there be any heat in the nebula at the dimensions
we have specified, beyond what we have measured above.
[B] Here we beg to state that in all our coming operations, we will use
the Centigrade Scale for temperatures without adding C to each number
specified, unless a different scale has to be referred to, in which
case the distinctive of the scale shall be given in the usual way. This
we do because it is the fashion, not because we think it possesses any
advantage over any other scale, but rather the contrary. Perhaps we
may have something more to say about scales after we have handled the
Centigrade a little more than it has been our lot to do hitherto.
Some people believe, at least they seem to say so, that meteors or
meteorites colliding would knock gas out of each other, sufficient
to fill up the empty space around them, and become incandescent, and
so pile up heat in nebulæ sufficient to supply suns for any number
of millions of years of expenditure. But they forget that gas is not
a _nothing_. It possesses substance, matter, of some kind, however
tenuous. Therefore, if the meteors knock matter out of each other in
the form of gas, they must end by becoming gas themselves, and we come
back to what we have said above; we have two grains, in weight, of gas
abutting each other at an average distance of 30 yards, instead of two
grains of granite or anything else, and things are not much improved
thereby. And if we compare 30 yards with M. Faye's 3000, where are we?
The next thing to deal with is the formation of the planets.
SEPARATION OF RING FOR NEPTUNE.
When the nebula was 6,600,000,000 miles in diameter its volume would
be 150,532,847,222^{18}[C] cubic miles, and we have just seen that
its density must have been 311,754,100,720 times less than that of
water, or 403,000,000 less than air, and its temperature 0·00000068°
above absolute zero. On the other hand, we find from Table II. that
the volume of Neptune and his satellite is 29,107,964,680,925 cubic
miles at the density of water. Multiplying, therefore, this volume by
311,754,100,720 we get 9,074,530^{18} cubic miles as the volume of the
ring for the formation of Neptune's system at the same density as the
nebula. Then, subtracting this volume from 150,532,847,222^{18}, there
remain 150,523,772,692^{18} cubic miles as the volume to which the
nebula was reduced by the abandonment of the ring out of which Neptune
and his satellite were formed.
[C] The exponent 18 in 150,523,772,692^{18} means that 18 cyphers have
to be added to complete the number. The same is the case with any other
number and exponent of large quantities.
Then the mean diameter of the orbit of Neptune being 5,588,000,000
miles, its circumference or length will be 17,555,261,000 miles, and if
we divide the volume of his system as stated above, by this length, we
get 516,912,620,000,000 square miles as the area of the cross section
of the ring, which is equal to the area of a square of 22,735,123
miles to the side. Again, if we divide the circumference of the orbit
by this length of side, we find that it is 1/772·165th part of it,
and therefore about 28 minutes of arc. Also if we divide the diameter
of the orbit by an arc of 22,735,123 miles in length, we find that it
bears the proportion of 1 to 246 to the diameter of the orbit. Thus the
cross section of the ring would bear the same ratio to its diameter
that a ring of 1 foot square would bear to a globe of 246 feet in
diameter. Here we find it difficult to believe that by rotating a ball
of 246 feet in diameter of cosmic matter, meteorites, or brickbats,
we could detach from it, mechanically, by centrifugal force a ring
of 1 foot square, and the same difficulty presents itself to us with
respect to the nebula. We cannot conceive how a ring of that form could
be separated by centrifugal force from a rotating nebula, and have
therefore to suppose it to have had some different form, and to apply
for that to the example of Saturn's rings--just the same as Laplace no
doubt did. We cannot tell how the idea originated that the ring should
be of the form we were looking for--perhaps it was naturally--but it
seems to have been very general, and in some cases to have led to
misconceptions. It is not difficult to show how a Saturnian or flat
ring could be formed, but we shall have a better opportunity hereafter
of doing so. We must try, nevertheless, to form some notion, however
crude it may be, of what might be the thickness of a flat ring of the
cross section and volume we have found for Neptune.
Let us suppose that the final separation of the ring took place
somewhere near the half-distance between his orbit and that of
Uranus, say, 2,290,000,000 miles from the centre of the nebula, the
breadth of the ring would be the difference between the radius of
the original nebula, i.e. 33,000,000,000 miles and the above sum,
which is 1,010,000,000 miles. Then if we divide the area of the cross
section of the ring by this breadth, that is, 516,912,620,000,000 by
1,010,000,000, we find that the thickness would be 511,794 miles;
provided the ring did not contract from its outer edge inwards during
the process of separation. This could not, of course, be the case,
but, as we have no means of finding how much it would contract in that
direction, we cannot assign any other breadth for it; and we shall
proceed in the same manner in calculating the thicknesses of the rings
for all the other planets as we go along. We can, however, make one
small approach to greater accuracy. We shall see presently that the
density of the ring would be increased threefold at its inner edge as
compared with the outer during the process of separation, which would
reduce its average thickness to somewhere about 341,196 miles at
density of water, of course. The nebula remaining after Neptune's ring
we may now call
THE URANIAN NEBULA.
The volume of the nebula after abandoning the ring for the system
of Neptune was found to be 150,523,772,692^{18} cubic miles at its
original density, but during the separation it has been condensed
into a sphere of 4,580,000,000 miles in diameter, whose volume would
be 50,303,255,814^{18} cubic miles; so that if we divide the larger
of these two volumes by the smaller, we find that the density of the
Uranian nebula would be increased 2·9923 times, and therefore it would
then be 311,754,100,720 divided by 2·9923, equal to 104,184,535,721
times less dense than water. Furthermore, if we compare it to the
density of air, which we can do by dividing this last quantity by
773·395, we find it to have been 134,710,620 times less than that
density; and if we apply the air thermometer to it, we shall find that
its absolute temperature must have been 274 divided by 134,710,620 =
0·000002034° or -273·9999796.°
We can now separate the ring for the system of Uranus from the
Uranian nebula, reduced as we have seen to 4,580,000,000 miles in
diameter, volume of 50,303,255,814^{18} cubic miles, and density
of 104,184,535,721 times less than water. Referring to Table II.,
we find the volume of the whole system of Uranus to have been
25,876,388,977,690 cubic miles at the density of water, but we have to
multiply this volume by the new density of 104,184,535,721 times less
than water in order to bring it to the same density as the nebula,
which will make the volume of his system to be 2,695,918,851^{15}
cubic miles at that density. Then, subtracting this volume from
50,303,255,814^{18}, we find that the nebula has been reduced to
50,300,559,895,149^{15} cubic miles in volume.
Then the diameter of the orbit of Uranus being 3,566,766,000 miles, its
circumference will be 11,205,352,065 miles, so that dividing the volume
2,695,918,851^{15} of his system by this length of circumference, the
area of the cross section of the ring would be 240,592,061,166,666
square miles. If we now suppose the diameter of the nebula, after
abandoning the ring for the whole system of Uranus, to have been
2,672,000,000 miles--dimension derived from nearly the half-distance
between the orbits of Uranus and Saturn--we find that the breadth of
the ring would be 954,000,000 miles, which would be the difference
between the radii of the Uranian and Saturnian nebulæ, respectively
2,290,000,000 miles, and 1,336,000,000 miles; so that if we divide the
area of cross section of Uranus' ring or 240,592,070,232,288 square
miles by this breadth we find the thickness of the ring to have been
252,193 miles. But the density of the inner edge of the ring would be
5·036 times more dense than the outer edge, for the same reason as in
the case of the Neptunian ring, which would make the average thickness
to have been about 100,553 miles.
SATURNIAN NEBULA.
We have seen that the volume of the nebula after the separation of
the ring for Uranus' system would be 50,300,559,859,149^{15} cubic
miles, but as we have reduced the diameter of the Saturnian nebula to
2,672,000,000 miles, its volume would also be reduced, or condensed to
9,988,700^{21} cubic miles, so that dividing the larger volume by the
smaller we find that its density must have been increased 5·036 fold.
Then dividing 104,184,535,721 by 5·036, we see that the density would
be reduced, or increased rather, to 20,689,000,000 times less than that
of water. This can be easily found to be 26,750,876 times less than the
density of air, and the air-thermometer would show that the absolute
temperature of the Saturnian nebula must have been 0·000010242° or
-273·99998976°.
We have just seen that the Saturnian nebula has been condensed to
2,672,000,000 miles in diameter, to volume of 9,988,700^{21} cubic
miles, and density of 20,689,000,000 times less than that of water.
Then from Table II. we get the volume of the whole of the system of
Saturn as 154,370,734,774,315 cubic miles at the density of water, and
multiplying this by 20,689,000,000 will give 3,193,775,478^{15} as its
volume at the same density as the nebula; and subtracting this from
9,988,700^{21} we find that the volume of the nebula had been reduced
to 9,985,506,224,522^{15} cubic miles.
Then the diameter of the orbit of Saturn being 1,773,558,000 miles its
circumference would be 5,571,809,813 miles in length, and if we divide
the volume of his system, viz. 3,193,775,478^{15} cubic miles, by this
length, we find the area of the cross section of the ring to have been
573,202,529,391,503 square miles. Now, supposing the diameter of the
nebula, after abandoning the ring, to have contracted to 1,370,800,000
miles and radius consequently of 685,400,000 miles, the breadth of the
ring would be 1,336,000,000 less 685,400,000 or 650,600,000 miles;
and if we divide the area of the cross section of the ring, that is,
573,202,529,391,503 square miles, by this breadth, we get 881,037 miles
for its thickness. But in the same way as before, the inner edge of the
ring would be 7·4037 times more dense than the outer edge, which would
reduce its average thickness to 238,000 miles.
JOVIAN NEBULA.
The volume of the nebula after separation of the ring for Saturn's
system having been 9,985,506,224,522^{15} cubic miles, this volume has
to be condensed into the volume of the Jovian nebula of 1,370,800,000
miles in diameter, which would be 1,348,720,186,335^{15} cubic miles.
Then if we divide the first of these two volumes by the second, we find
the density of the Jovian nebula to have been increased 7·4037 fold
over the previous one. But the density of the Saturnian nebula was
20,689,000,000 times less than water, dividing which by 7·4037 makes
the Jovian nebula to have been 2,794,417,420 times less dense than
water. Dividing this by 773·395 we get a density for it of 3,613,182
times less than that of air, which corresponds to the absolute
temperature of 0·00007583° or -273·99992417°.
From the Jovian nebula of 1,370,800,000 miles in diameter, volume of
1,348,720,186,335^{15} cubic miles, and density of 2,794,417,420
times less than water, we have now to deduct the whole of the system
of Jupiter, which, by Table No. II., is 479,368,921,317,000 cubic
miles at density of water. Multiplying this by 2,794,417,420 we get
the volume of 1,339,557,155^{15} cubic miles for his system at the
same density as the nebula; therefore, substracting this amount from
1,348,720,186,335^{15} we get 1,347,380,629,180^{15} cubic miles as the
volume to be condensed into the succeeding nebula which we shall call
Asteroidal, the dimensions of which we can determine in the following
manner, although only very approximately.
According to the nebula hypothesis, there must have been a ring
detached from the nebula for the formation of the Asteroids, as well as
the formation of the other planets. So, in order to be able to assign
elements for that ring, corresponding to those we have found for the
others, we shall suppose the whole of them to have been collected
into one representative planet, at the mean distance from the centre
of the nebula of 260,300,000 miles, more or less in the position
denoted by the number 28 in Bode's Law; also its mass to have been
one-fourth of that of the earth, or 367,792,000,000 cubic miles at
density of water, which, in the opinion of probably most astronomers,
is a considerably greater mass than would be made up by the whole of
them put together--discovered and not yet discovered. With the above
distance from the centre of the nebula, the divisionary line between
the Jovian and the Asteroidal nebulæ would be 372,000,000 miles from
the said centre, and the diameter of the latter 744,000,000 miles in
consequence.
We know that some of the Asteroids move in their orbits beyond this
supposed divisionary line, and it may be that when we come to determine
the divisionary line between the supposed Asteroidal and the Martian
nebulæ, some of them may revolve in their orbits nearer to Mars than
that line, but that will not interfere in any way with our operations,
because we are only dealing with the whole of them collected into one
representative.
For finding the dimensions of the ring for Jupiter's system, we have
the mean diameter of his orbit as 967,356,000 miles, which makes
its circumference to be 3,039,045,610 miles in length. Therefore,
dividing the volume of the ring as found above, viz. 1,339,557,155^{15}
cubic miles by this length, the area of its cross-section comes to be
440,782,188,524,000 square miles, which divided in turn by the breadth
of 313,400,000--the difference between the radii of the Jovian and
Asteroidal nebulæ, or 685,400,000 less 372,000,000--makes the thickness
of the ring to have been 1,406,771 miles. But, as before, the inner
edge of the ring had become 6·2484 times more dense than the outer
edge, so that the average thickness would be only 450,282 miles.
ASTEROIDAL NEBULA.
The volume of the nebula after the separation of the ring for the
system of Jupiter having been 1,347,380,629,180^{15} cubic miles,
this volume has to be condensed into the volume of the Asteroidal
nebula of 744,000,000 miles in diameter and consequently of volume of
215,634,925,373,133,820^{9} cubic miles. Then if we divide the first of
these volumes by the second, we find the density to have been increased
6·2484 fold, as used above for the average thickness of Jupiter's ring.
But the density of the Jovian nebula was 2,794,417,420 times less than
water, dividing which by 6·2484 makes the Asteroidal nebula to have
been 447,218,905 times less dense than water. This again divided by
773·395 makes it 578,254 times less dense than air, which will give us
0·00047384° as its absolute temperature--or the same as -273·99952616°.
Next, from the Asteroidal nebula 774,000,000 miles in diameter, volume
of 215,634,925,373,133,820^{9} cubic miles, and density 447,218,905
times less than water, we have to deduct the volume of the whole
of the system which in Table No. II. we have supposed to have been
367,792,000,000 cubic miles at density of water. Multiplying this
by 447,218,905 we get the volume to have been 164,482,717,200^{9}
cubic miles for the ring at the same density as the nebula; so,
deducting this quantity from 215,634,925,133,820^{9}, we get
215,634,760,890,416,620^{9} cubic miles as the volume to which the
nebula had been reduced by the separation of the ring.
For the dimensions of the ring we have the mean diameter of the orbit
of the representative Asteroid as 520,600,000 miles, that is twice its
distance from the centre of the nebula, which makes its circumference
to be 1,635,516,960 miles in length. Dividing then the volume of the
ring, which we found to have been 164,482,717,200^9 cubic miles by this
length, the area of its cross-section must have been 100,569,251,938
square miles, which divided by the breadth of 171,000,000 miles--the
difference between the radii of the Asteroidal and Martian nebula,
namely 372,000,000 less 201,000,000--makes the thickness of the ring to
have been 588 miles. But the inner having been 6·339 times more than
the outer edge, as we shall see presently, the average thickness would
be 185 miles.
MARTIAN NEBULA.
The volume of the last nebula after the separation of the ring for
the Asteroids was found to have been 215,634,760,890,416,620^{9}
cubic miles, which had to be condensed into the volume of the Martian
nebula of 402,000,000 miles in diameter, which would give a volume of
34,015,582,677,165,354^{9} cubic miles. Dividing then, the larger of
these volumes by the smaller, we find that the density of the Martian
nebula had been increased 6·339 times by the condensation. But we found
the density of the Asteroidal nebula to have been 447,218,905 times
less dense than water, dividing which by 6·339 makes the Martian nebula
to have been 70,547,110 times less dense than water. This divided again
by 773·395 makes it 91,259 times less dense than air, and consequently
its absolute temperature to have been 0·00300243° or -273·99699757°.
From the Martian nebula of 402,000,000 miles in diameter, volume
34,015,582,677,165,354^{9} cubic miles, and density 70,547,110 times
less than water, we have to deduct the volume of his ring, which by
Table II., was estimated at 160,728,460,000 cubic miles at density
of water. Multiplying this by 70,547,110 we find its volume to be
11,338,927,154^{9} cubic miles at the same density as the nebula,
deducting which from its whole volume we get 34,015,571,338,237,20^{9}
cubic miles as the volume after the separation of the ring.
For finding the dimensions of the ring we have 283,300,000 miles as
the mean diameter of the orbit of Mars, which makes its circumference
890,015,280 miles in length. Then dividing the volume of the ring
11,338,927,154^{9} cubic miles by this length, the area of its
cross-section comes to be 12,740,148,859 square miles, which, divided
by the breadth of 83,690,000 miles--that is one-half of the difference
between the diameters of the Martian and Earth nebula, respectively
402,000,000 and 234,620,000 miles--makes the thickness of the ring to
have been 152 miles. But as before, the inner having become through
condensation, 5·0302 times more dense than the outer edge, the average
thickness would be 61 miles.
EARTH NEBULA.
As the volume of the nebula was 34,015,571,338,237,200^{9} cubic miles
after the separation of the ring for Mars, we have to condense it into
the volume of the earth nebula, which at 234,620,000 miles in diameter
would be 6,762,303,076,923,031^{9} cubic miles. Dividing the larger of
these volumes by the smaller we find that the density of the nebula
has been increased 5·0302 times, as employed above. But we found the
density of the Martian nebula to have been 70,547,110 times less than
that of water, dividing which by 5·0302 makes the earth nebula to have
been 14,024,781 times less dense than water. Dividing this again by
773·395 we find it to have been 18,134 times less dense than air, and
274° divided by this density of air--the same as in all the respective
cases--gives 0·0151097° as the absolute temperature of the nebula and
corresponds to -273·9848903°.
From the earth nebula 234,620,000 miles in diameter,
6,762,303,076,923,031^{9} cubic miles in volume, and 14,024,781 times
less dense than water, we have to subtract the volume of the ring of
the earth's system, which, in Table II., appears as 1,489,310,236,000
cubic miles at density of water. Multiplying this by 14,024,781 we find
it to have been 20,887,249,553^{9} cubic miles at the same density as
the nebula. And subtracting this quantity from 6,762,303,076,923,031^9,
we get 6,762,282,189,673,478^9 cubic miles for the volume of the
previous nebula after the separation of the ring for the system of the
earth.
For finding the dimensions of the ring we have 185,930,000 miles for
the mean diameter of the Earth's orbit, which makes the circumference
584,117,688 miles in length, and dividing the volume of the ring for
the system, which was found to be 20,887,249,553^9 cubic miles, by
this length, the area of its cross section comes to be 35,760,344,109
square miles, which divided by the breadth of 37,205,000 miles--that
is one-half of the difference between the diameters of the Earth and
Venus nebulæ, respectively 234,620,000 and 160,210,000 miles--makes
the thickness of the ring to have been 961 miles. But the inner will
presently be seen to have been 3·141 times more dense than the outer
edge when its separation was completed, so that the average thickness
would be 612 miles.
VENUS NEBULA.
As the volume of the nebula was 6,762,282,189,673,478^9 cubic miles
after the separation of the ring for the system of the Earth, we
have to condense it into the volume of the Venus nebula, which at
160,210,000 miles in diameter would be 2,153,120,792,079,208^9 cubic
miles. Then dividing the larger of these two volumes by the smaller, we
find that the density of the Venus nebula had been increased to 3·141
times what that of the Earth nebula was. But we found the density of
that nebula to have been 14,024,781 times less than that of water,
dividing which by 3·141 makes the Venus nebula to have been 4,465,512
times less dense than water. Dividing this again by 773·395 we find
it to have been 5,774 times less dense than air, which would make its
absolute temperature to have been 0·04745486°, which corresponds to
-273·9525459°.
From the Venus nebula of 160,210,000 miles in diameter, volume
2,153,120,792,079,207,921^{6} cubic miles, and density 4,465,512
times less than that of water, we have now to deduct the volume of
her ring, which by Table II. is 1,131,960,000,000 cubic miles at the
density of water. Multiplying this volume by 4,465,512 we find the
volume of the ring to have been 5,054,780,604,651^{6} cubic miles
at the same density as the nebula, and subtracting this amount from
2,153,120,792,079,207,921^{6} we get 2,153,115,737,298,603^{6} cubic
miles for the volume to be condensed into the nebula following.
To find the dimensions of the ring we have 134,490,000 miles for
the diameter of the orbit of Venus, which makes its circumference
422,513,784 miles in length. Then dividing the volume of the ring,
i.e. 5,054,780,604,651^{6} cubic miles by this length, the area of its
cross-section comes to be 11,963,821,788 square miles, which, divided
by the breadth of 28,489,000 miles--that is one-half of the difference
between the diameters of the Venus and Mercurian nebulæ, respectively
160,210,000 and 103,232,000 miles--makes the thickness of the ring to
have been 420 miles. But the inner edge having become, in the process
of separation, 3·738 times more dense than the outer one (see below)
the average thickness would be reduced to 225 miles.
MERCURIAN NEBULA.
As the volume of the nebula was 2,153,115,737,298,603,270^{6} cubic
miles after the separation of the ring for Venus, we have to condense
it into the volume of the Mercurian nebula, which at 103,232,000 miles
in diameter would be 576,026,613,333,333,333^{6} cubic miles. Then,
dividing the larger of these two volumes by the smaller, we find that
the density of the Mercurian nebula must have been increased 3·738 fold
over that of its predecessor. But we find the density of the Venus
nebula to have been 4,465,512 times less than water, dividing which
by 3·738 makes the Mercurian nebula to have been 1,194,666 times less
dense than water. Dividing again this density by 773·395 we find it
to have been 1545 times less than air, and 274° divided by this air
density gives 0·1773463° as its absolute temperature, which corresponds
to -273·8226537°.
From the Mercurian nebula 103,232,000 miles in diameter, volume of
576,026,613,333,333,333^{6} cubic miles, and density of 1,194,666
times less than water, we have to deduct the volume of his ring,
which by Table II. is 92,735,000,000 cubic miles at density of water.
Multiplying this volume by 1,194,666 makes the ring to have been
110,787,355,300^{6} cubic miles in volume at the density of the nebula,
and subtracting this amount from 576,026,613,333,333,333^{6}, we get
576,026,502,545,978,033^{6} cubic miles for the volume to be condensed
into the nebula following.
To find the dimensions of the ring we have 71,974,000 miles for the
mean diameter of the orbit of Mercury, which makes its circumference
226,113,518 miles in length. Then dividing the volume of his ring,
i.e. 110,787,355,300^{6} cubic miles, as above, by this length, the
area of its cross-section comes to be 489,963,459 square miles. Here
we have to determine the breadth of the ring in a new way, that is
empirically. Seeing that the breadth of the ring for the earth's system
was 37,205,000 and of that for Venus 28,489,000 miles, we shall assume
20,000,000 miles for the breadth of the ring for Mercury. This will
make the residuary, now the Solar nebula, to have been 31,616,000 miles
in radius and 63,232,000 miles in diameter. Returning now to the area
of the cross-section of the ring, that is, 489,963,459 square miles,
and dividing it by the assumed breadth 20,000,000 miles, makes the
thickness of the ring to have been 25 miles. But, as before, its inner
edge having become 4·354 times more dense than the outer one during the
process of separation (see below) the average thickness must have been
only 11 miles.
SOLAR NEBULA.
Lastly, as the volume of the nebula was
576,026,502,545,978,033^{6}
cubic miles after the separation of the ring for Mercury, we have to
condense it into the volume of the Solar nebula, which at 63,232,000
miles in diameter would be
132,376,310,975,609,756^6
cubic miles. Then dividing the first of these two volumes by the
second, we find that its density must have been increased 4·3514 fold.
But we found that the density of the Mercurian nebula was 1,194,666
times less than that of water, dividing which by 4·3514 makes the Solar
nebula to have been 274,546 times less dense than water. Dividing this
in turn by 773·395 shows it to have been 355 times less dense than
air, and, still further, dividing 274° by this air density makes its
absolute temperature to have been 0·7718585° equal to -273·2281415°.
We might conclude our analysis here, but it will be more convenient
to carry our calculations a few steps further, to save the additional
trouble that might be occasioned by having to return to them later on.
First we shall condense the Solar nebula to 211,911 times less dense
than water, and therefore 274 times less dense than air, which we may
note will increase its density 1·2956 times. This supposed to be done,
its diameter would be 58,002,920 miles, its volume 102,176,129,412^{12}
cubic miles, and its density 1/274th of an atmosphere--about
_one-ninth_ inch of mercury--which would, in consequence, make its
absolute mean heat equal to _one degree_ of the ordinary Centigrade
scale, or, in another way of expressing it, equal to -273°.
Second. Let us condense this same nebula to 773·395 times less dense
than water, and consequently to the density of air at atmospheric
pressure, then its diameter will be 8,930,309 miles, volume
372,905,560,345^9 cubic miles, and the mean heat 0°, or the heat of
freezing water--which by some unexplained process of thought has
hitherto been considered to be 274° of absolute _temperature_.
Third. By again condensing the Solar nebula to the density of water,
corresponding to a pressure of more than 773 atmospheres, its diameter
becomes 972,285 miles, its volume 482,167^{12} cubic miles, and mean
heat 775°, including the 2° acquired in condensing it to the pressure
of 1 atmosphere, as is plainly shown in Table III.
Before going any further we must enter into a digression to examine
into the process of thought by which the absolute zero of heat has
come to be called the absolute zero of temperature, and absolute
temperature to be so many degrees of negative--less than 0° or
nothing--heat counted from the lower or wrong end, to be called
positive absolute temperature; thus making heat and temperature appear
to be two very different things, without giving any explanation of what
is the difference between them.
Science has, as it were, gone down a stair of 274 steps carrying along
with it the laws of gases, and has found, most legitimately, with their
assistance the total absence of even negative heat at the bottom of it;
and, leaving these laws there, has jumped up to the top of the stair,
thinking that it carried along with it 274° of absolute heat, which it
now calls temperature; instead of bringing the said laws up with it
and verifying, if not at every step at least at intervals, how much it
brought up with it of what it had taken down. Had it done so it would
have found that at the top of the stair it had got what was equal to
only 2° of positive heat as measured by the Centigrade scale, as has
been shown above, which might be called temperature, but that would
not mend matters. Science seems to have forgotten, for the time being
at least, all about the laws of gases; it had got something which it
thought would enable it to mount much higher, and was satisfied. It
will not be difficult to do away with the confusion of thought that is
thus shown to have occurred.
The laws of gases are founded upon the fact that in gases there is a
necessary interdependence between heat and pressure, and the starting
points adopted by science for calculating this interdependence in them
are 0° of heat and 1 atmosphere of pressure at 0° of heat. Obeying
these laws, we have argued, from the beginning of our operations, that
heat requires something to hold it in, and that the nebula from which
the Solar system was formed--if it was so formed--could only contain
heat in proportion to its density; that is being a gas, or vapour in
the form of a gas, it could not contain, i.e. hold in it, more than 2°
of positive heat when its density was equal to the pressure belonging
to 1 atmosphere of a gas; all as shown in the most irrefragable manner
in this chapter and in the accompanying Table III.
A gas can be easily compressed in a close vessel to a pressure of 100
atmospheres, which would enable it to hold 100° of heat due to that
compression; in fact, were it compressed to that degree by a piston in
a cylinder, without any loss of heat, it would be raised to that heat
by that act alone, but that would raise it to only 102° instead of 374°
of what is called absolute temperature according to present usage;
because as a gas it could not hold any more heat at that pressure. It
is, therefore, evident that this _usage_ has not been derived from the
laws of gases. Neither has it been derived from the other two states
of liquid and solid to which all gases can be reduced, as can be very
easily demonstrated.
To cool steam at atmospheric pressure from its gaseous to its liquid
state 519° of heat of one kind and another--as measured by the
Centigrade thermometer--have to be abstracted from it, which leaves
the liquid at its boiling point of 100°--a quantity that has been
arbitrarily adopted to mark the difference between the freezing and
boiling points of this liquid. In order, after this, to reduce the
liquid, now water, to the freezing, or what is called 0° of heat,
these 100 degrees of heat have to be extracted from it, which is not
very difficult to do because the heat put into it arbitrarily can be
extracted from it; but if it is now wanted to change the steam from
its liquid to its solid state, the work, or operation assumes a very
different character, because heat cannot be extracted from a substance
which contains none at all. It is well known that 80° of heat are
required to change one pound of ice at 0° into a pound of water also
at 0° of heat; but it is equally well known that 80° of heat cannot be
taken out of the pound of water which has none in it; how then, is the
water to be changed into ice?
Even in cooling water to 0° it has to be put into a bath of some kind,
either of cold water or some cold mixture of other substances at least
as cold; because, otherwise, extraneous heat from any source might find
its way into it, and prevent it from cooling down to zero of heat.
In the same manner, to change the water into its solid state of ice
it has to be put into a similar bath, not to extract heat from it,
because it has not any to extract, but to prevent extraneous heat from
getting into it. This being the case, it is evident that if water is
put into a bath at what is called -1° of heat, or even a fraction of
that amount, it will be converted into ice though very gradually, by
keeping extraneous heat from getting to it to sustain the collisions,
or vibrations, of its constituent atoms necessary to maintain it in
its liquid state. All for the very same reason why a stone, a piece
of metal, or of anything assumes the same degree of heat, or absence
of heat, as the medium by which it is surrounded; be it derived from
sun-heat, earth-heat, or heat produced chemically or mechanically, and
is not cooled down to a lower degree than the surrounding bath, be it
what it may.
The heat required to change a solid into a liquid is called _latent
heat_, which in the case of ice and water may be a fraction of
-1° or -80°, or _minus_ almost anything according to the time it
is necessary for it to act; so that no quantity of what is called
absolute temperature can be ascribed to ice without the element time
being involved in it. The absolute temperature of water and ice, just
changing from freezing to frozen, might be counted as the same, seeing
that a fraction of a degree of heat may make all the difference between
them; but no fixed absolute temperature can be applied to ice, as it,
in conjunction with all solid bodies, may have any degree of absolute
temperature between its melting point and the absolute zero of heat, as
far as is at present known. The same, of course, must be the case with
any gas or vapour, or nebulous matter changed into its liquid and then
solid state; and this fact enables us to go a little further.
We have seen that what, according to present usage, is called the
absolute temperature of solid hydrogen may be anything between -257°
and -274° of heat, that is, between the absolute temperature of 0° and
17°, which, of course, is no measure at all; and, therefore, absolute
temperature can only be looked upon as a conventional term, which,
when added to positive Centigrade, or other, heat, conveys no clear
idea to the mind, as it must always be mixed up with the concomitant
idea of latent heat and its time of action. This leads us to think of
what remains in the vessel, in which pure hydrogen has been changed
into its liquid and then solid state, after these operations have been
performed; and our first conclusion comes to be that there can be
nothing in it but a small piece of solid hydrogen; but from the limited
accounts we have seen of these operations, there does appear to be
something remaining, because it seems that by it the degree of negative
heat in the vessel can be measured. What that remaining something may
be can hardly be anything but a matter of conjecture. The first and
most probable idea that occurs is that it may be some lighter gas mixed
with the pure (?) hydrogen that was put into the vessel; the next is
that it may be the vapour of solid hydrogen; and the last refuge for
speculation is that it may be radiant matter, whatever that may turn
out to be. At one time it was supposed to be impurities mixed with the
gases operated upon, which in the case of common air, were found to be
removed to a certain extent by means of absorbents; but the numerous
components of common air discovered since that time, have gone far to
throw light upon that supposition, and we are thus led to think of what
a true gas really is. But we are not yet prepared to follow up this
thought.
This is not an inappropriate place to say that when we adopted the
Centigrade scale for our work, we thought that a special thermometer,
decimal throughout and consequently more handy, might be arranged for
science alone, leaving every man the free use of whatever scale he
liked best; but our experience acquired in this chapter put an end to
that thought, and has left us totally unable to see how any decimal
scale can be contrived, which will start from absolute zero of heat
and will admit of any combination with any existing scale, or will
assist humanity in any of its operations in connection with heat and
temperature, whichever science may choose to call it. We therefore see
that no known thermometer scale is superior to another, and end where
we began by saying that the Centigrade is the fashionable one at the
present time. It is decimal as far as boiling water and resulting steam
are concerned, but all the world is not boiling water; even steam has
to be complicated with latent heat.
TABLE III.--ABSTRACT OF MEASUREMENTS, ETC., RESULTING
FROM THE CALCULATIONS MADE IN CHAPTER V.
-------------+--------------+-------------------+---------------+-----
| | | |
| | Volume of the | |Incr.
Nebulæ | | Mass of each | Times less | of
---- |Explanations. | Separate System at| Dense than |Dens-
Diameter | | Density of Water | Water. | ity
in miles. | | in cubic miles. | | in
| | | |times
-------------+--------------+-------------------+---------------+-----
Original or | | | |
Neptunian | | | |
6,600,000,000| Volume of | |311,754,100,720|
| Neptune's | | |
| Ring | 29,107,964,680,925|311,754,100,720|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+-----
Uranian |Condensed from| | |
4,580,000,000| Neptunian | | |2.9923
| Nebula | | |
| | | |
| Volume of | | |
| Uranus' Ring | 25,876,388,977,000|104,184,535,721|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Saturnian |Condensed from| | |
2,672,000,000| Uranian | | |5.0357
| Nebula | | |
| | | |
| Volume of | | |
|Saturn's Ring |154,370,734,774,315| 20,689,000,000|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Jovian |Condensed from| | |
1,370,800,000| Saturnian | | |7.4037
| Nebula | | |
| | | |
| Volume of | | |
|Jupiter's Ring|479,368,921,317,000| 2,794,417,420|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Asteroidal |Condensed from| | |
744,000,000| Jovian Nebula| | |6.2484
| | | |
| Volume of | | |
| Asteroidal | | |
| Ring | 367,792,000,000| 447,218,905|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Martian |Condensed from| | |
402,000,000| Asteroid | | |6.3392
| Nebula | | |
| | | |
| Volume of | | |
| Martian Ring | 160,728,460,000| 70,547,110|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Earth |Condensed from| | |
234,620,000|Martian Nebula| | |5.0302
| | | |
| Volume of | | |
| Earth Ring | 1,489,310,236,000| 14,024,781|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Venus |Condensed from| | |
160,210,000| Earth Nebula | | |3.1410
| | | |
| Volume of | | |
| Venus Ring | 1,131,960,000,000| 4,465,512|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Mercurian |Condensed from| | |
103,232,000| Venus Nebula | | |3.7379
| | | |
| Volume of | | |
|Mercurian Ring| 92,735,000,000| 1,194,666|
| | | |
| Volume of | | |
| Nebula | | |
| less ring | | |
-------------+--------------+-------------------+---------------+------
Solar |Condensed from| | |
63,232,000| Mercurian | | |
| Nebula | | 274,546|4.3514
| | | |
|Volume @ 1/274| | |
58,002,920| of 1 atm. | | 211,911|1.2956
| | | |
|Vol. @ density| | |
8,930,309| of 1 atm. | | |274.000
| | | |
|Vol. @ density| | |
972,895| of water | | |773.395
-------------+--------------+-------------------+---------------+------
-------+---------------------------------------+-----------+-----------
| | |
| | |
| | |
| Volumes at Densities | Times | Absolute
| of Respective Nebulæ in | less Dense| Tempera-
| cubic miles. | than Air. | ture.
| | |
| | | (Degrees.)
| | |
| | |
-------+---------------------------------------+-----------+-----------
| | |
Neptun-|150,532,847,222,000,000,000,000,000,000|403,000,000| 0·00000068
ian | | |
| 9,074,530,000,000,000,000,000,000| .. | ..
-------+---------------------------------------| |
|150,523,772,692,000,000,000,000,000,000| |
Uranian| | |
| 50,303,255,814,000,000,000,000,000,000| |
| | |
| 2,695,918,851,000,000,000,000,000|134,710,620|0·000002034
-------+---------------------------------------| |
| 50,300,559,895,149,000,000,000,000,000| |
Saturn-| | |
ian | 9,988,700,000,000,000,000,000,000,000| |
| | |
| 3,193,775,478,000,000,000,000,000| 26,750,876| 0·00001024
-------+---------------------------------------| |
| 9,985,506,224,522,000,000,000,000,000| |
Jovian| | |
| 1,348,720,186,335,000,000,000,000,000| |
| | |
| 1,339,557,155,000,000,000,000,000| 3,613,182| 0·00007583
-------+---------------------------------------| |
| 1,347,380,629,180,000,000,000,000,000| |
Aster- | | |
oidal | 215,634,925,373,133,820,000,000,000| |
| | |
| 164,482,717,200,000,000,000| 578,254| 0·00047384
-------+---------------------------------------| |
| 215,634,760,890,416,620,000,000,000| |
Martian| | |
| 34,015,582,677,165,354,000,000,000| |
| | |
| 11,338,927,154,000,000,000| 91,259| 0·00300244
-------+---------------------------------------| |
| 34,015,571,338,237,200,000,000,000| |
Earth | | |
| 6,762,303,076,923,031,000,000,000| |
| | |
| 20,887,249,553,000,000,000| 18,134| 0·0151097
-------+---------------------------------------| |
| 6,762,282,189,673,478,000,000,000| |
Venus | | |
| 2,153,120,792,079,207,921,000,000| |
| | |
| 5,054,780,604,651,000,000| 5,774| 0·047454
-------+---------------------------------------| |
| 2,153,115,737,298,603,270,000,000| |
Mercur-| | |
ian | 576,026,613,333,333,333,000,000| |
| | |
| 110,787,355,300,000,000| 1,545| 0·1773463
-------+---------------------------------------| |
| 576,026,502,545,978,033,000,000| |
Solar | | |
| 132,376,310,975,609,756,000,000| 355| 0·771831
| | |
| 102,176,129,412,000,000,000,000| 274| 0·99635
| | |
| 372,905,560,345,000,000,000| 0| 2·0000
-------+-+---------------------------------+---+-----------+------+---
| At Density of Water. | At Air Density. |
+---------------------------------+---------------+------+
| Dimensions of Rings. |Space to Grain | |
| | of Matter. | |
+--------------+------------------+-------+-------+ I |
| | | Aver- | | Side | n |
| | Thick- | age | | of | c |
| Breadth | ness |Thick- | Cubic | Cube | h |
| in miles. |in miles.| ness | Feet. | in | e |
| | |in miles| | Feet. | s |
---------+--------------+---------+--------+-------+-------+------|
| | | | | | |
Neptunian| ... | ... | ... |713,223| 89·327| |
| | | | | | |
| | | | | | |
| 1,010,000,000| 511,794| 341,196| | | |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Uranian | | | | | | |
| | | | | | |
| | | | | | |
| 954,000,000| 252,193| 100,553|238,357| 61·994| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Saturnian| | | | | | |
| | | | | | |
| | | | | | |
| 650,600,000| 881,037| 238,000| 47,313| 36·168| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Jovian | | | | | | |
| | | | | | |
| | | | | | |
| 313,400,000|1,406,771| 450,282| 6,303| 18·472| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Aster- | | | | | | |
oidal | | | | | | |
| | | | | | |
| 171,000,000| 588| 185| 1,023| 10·075| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Martian | | | | | | |
| | | | | | |
| | | | | | |
| 83,690,000| 152| 61| 161| 5·445| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Earth | | | | | | |
| | | | | | |
| | | | | | |
| 37,205,000| 961| 612| 32| 3·178| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Venus | | | | | | |
| | | | | | |
| | | | | | |
| 28,489,000| 420| 225| 10·2 | 2·170| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Mercurian| | | | | | |
| | | | | | |
| | | | | | |
| 20,000,000| 25| 11| 2·734| 1·398| |
---------+--------------+---------+--------+-------+-------+------+
| | | | | | |
Solar | | | | | | |
| ... | ... | ... |0·6283 | 0·8565| 10·28|
| | | | | | |
| ... | ... | ... |0·4848 | 0·7856| 9·43|
| | | | | | |
| ... | ... | ... |0·00177| 0·121| 1·452|
---------+--------------+---------+--------+-------+-------+------+
Returning now to page 84, we see that the volume of the sun alone was
considered to be 482,169^{12} cubic miles, which corresponds to a
diameter of 972,869 miles. Comparing this with the volume 482,167^{12}
cubic miles, see page 99, left after all the members of the Solar
system have been separated from the original nebula, we find that
there is a remainder of 2,000,000,000,000 cubic miles _less_ than we
ought to have. But it will be remembered that we added only 1/700th
part to the mass of the sun for the mass of the whole Solar system,
whereas it will be seen, by referring to Table II., that we ought to
have added 1/696·86th part. Had we done so the sphere containing the
whole Solar system at the density of water would have been 973,361·31
miles in diameter with volume of 482,860,744^{9} cubic miles, which
would have added 3,153,681,000,000 cubic miles to the volume we started
with, and would have left us with 1,375,903,430,000 cubic miles _more_
than we ought to have had. Besides, for the sake of round numbers, we
made the diameter of the nebula containing the whole Solar system, at
the density of water, to be 973,360 instead of 973,359·208 miles, and
thereby really added more to the original volume than we should have;
so that the defects in accuracy at the beginning of our work partially
counterbalanced each other, which accounts so far for the difference
noted at the end not being much more than half of what it should have
been. Taking all this into consideration, and the really insignificant
magnitudes of the differences that would result from the corrections
that could be made, we have not thought it necessary to reform the
whole of our calculations. Besides, the data we have been working upon
are not so absolutely exact as to insure us that we should get nearer
to the truth by making the revision. The whole error would be much more
than obliterated were we to apply 5·67 instead of 5·66 for the mean
density of the earth to the debit side of the sun's account.
To simply describe arithmetical operations conveys no really
satisfactory meaning to the mind; of working them out in full there is
no end; and to partially represent them as we have done in these pages,
although showing how the results are arrived at, still leaves them so
mixed up together that it is difficult to compare them with each other,
and to note the sequences from the beginning to the end of the whole
operation. For these reasons we have compiled Table III., where the
whole of the principal and most important data, and results from them,
may be followed out and examined.
We may now say that we have taken our nebula to pieces, with the
exception of the parts belonging to the satellites of those planets
which have them; which would only be a tiresome repetition of what we
have done for each principal member of the system, provided we had the
necessary data, which we have not; and have thus acquired a certain
amount of knowledge of the primitive conditions of each one of them.
But we have still to examine into and draw conclusions from what we
have seen and learned during the operation; which in some points,
differ very much from our notions, formed from what we had previously
read on the subject.
CHAPTER VI.
PAGE
108 Analysis continued. Excessive heat of nebula involved condensation
only at the surface. Proof that this was Laplace's idea.
109 Noteworthy that some astronomers still believe in excessive heat.
110 Interdependence of temperature and pressure in gases and vapours.
Collisions of atoms the source of heat.
110 Conditions on which a nebula can be incandescent. Sir Robert Ball.
112 No proper explanation yet given of incandescent or glowing gas.
115 How matter was thrown off, or abandoned by the Jovian nebula.
116 Division into rings of matter thrown off determined
during contraction.
117 How direct rotary motion was determined by friction and collisions
of particles.
118 Saturn's rings going through the same process. Left to show
process.
120 Form gradually assumed by nebulæ. Cause of Saturn's
square-shouldered appearance.
120 A lens-shaped nebula could not be formed by surface condensation.
121 Retrograde rotary motion of Neptune and Uranus, and revolution
of their satellites recognised by Laplace as possible.
123 Satellites of Mars. Rapid revolution of inner one may be
accounted for.
124 Laplace's proportion of 4000 millions not reduced but enormously
increased by discoveries of this century.
ANALYSIS OF THE NEBULAR HYPOTHESIS--_continued_.
When Laplace elaborated his hypothesis, heat was considered to be an
imponderable material substance, and continued to be thought of as
such--though perhaps not altogether believed to be so--for somewhere
about half a century afterwards; so that it cannot be wondered at that
he thought the nebula could have been endowed with excessive heat, more
especially as it was looked upon as imponderable, and could in no way
have any effect on the mass of the nebula. He only accepted the idea
that was common to almost all astronomers of his time, that nebulæ were
masses of cosmic matter of extreme tenuity but self-luminous, and
consequently possessed of intense heat; they saw the sun gave light
and felt its heat, and very naturally thought the nebula must be hot
also. Without this idea he could not have formed the hypothesis at
all, because he could not have conceived that the condensation of the
nebula could only take place at its surface, or, as he terms it, "in
the atmosphere of the sun," as most assuredly would be the case with
an excessively hot body. And in order that there may be no doubt about
this being his idea, we quote his own words as guaranteed by M. Faye in
"L'Origine du Monde": "La considération des mouvements planétaires nous
conduit donc à penser qu'en vertu d'une chaleur excessive l'atmosphère
du soleil s'est primitivement étendu au delà des orbes de toutes les
planètes, et qu'elle s'est reserrée successivement jusqu'à ses limites
actuelles." And again: "Mais comment l'atmosphère solaire a-t-elle
déterminé les mouvements de rotation et de révolution des planètes et
des satellites? Si ces corps avaient pénétré profondément dans cette
atmosphère, sa résistance les aurait fait tomber sur le soleil. On
peut donc conjecturer que les planètes ont été formées à ses limites
successives par la condensation des zones de vapeurs qu'elle à dû, en
se refroidissant, abandonner dans le plan de son équateur." Proceeding
on these ideas Laplace was quite in order and logical in conceiving
that successive rings could be abandoned by the hot nebula, through the
centrifugal force of rotation, for the formation of planets, more or
less just in the way we have separated them. Having obtained his end
quite legitimately, as he thought, in this way, he had no occasion to
look any deeper into the affair, and consequently was not under the
necessity of taking any thought of what the interior construction of
the nebula might be, any more than so many others have not done since
his day.
That he should have conceived the nebula to have been endowed with
intense heat was, as we have already said, a natural consequence of the
mistaken notions of the nature of heat at that period; but that so many
astronomers should, up to the present day, think that the nebula must
have been intensely hot, even to the degree required to dissociate the
meteorites of which they conceive it to have consisted, seems to us to
be almost inconceivable. We believe we have shown abundantly plainly,
that there could have been almost no heat in the primitive nebula,
because there was hardly any cosmic matter to hold it in. We have given
as proof of this the laws of gases recognised and accepted by every
scientist, according to which a gas cannot contain a stated amount of
heat except it be at a pressure corresponding to that temperature,
that is, unless it is subjected to conditions foreign to its natural
state. Therefore we must either persist in maintaining that there was
almost no heat in the original nebula, or we must throw the laws of
gases to the winds, for they all depend one upon another. There may be
nebulæ possessed of very high temperature, that of incandescence for
example, but certainly the nebula out of which the solar system was
made, could not have contained more heat than what we have shown it had
at the various stages through which we have carried it. If there be
nebulæ at the temperature of incandescence, they must be possessed of
densities, or pressures, corresponding to that temperature. A few pages
back we have spoken of the impossibility of two grains of matter 90
feet apart, raising, by mutual collisions, their temperature and that
of the space occupied by each to the temperature of incandescence, and
if we now substitute for them meteorites of a pound weight each, the
space occupied by each of them will be a cube of 1670 feet to the side,
which does not help us in any way to believe that the spaces occupied
by them could be heated up by their collisions, so as to shine with the
temperature of incandescence. So we get no help from meteorites.
Some people evidently seem to think that nebulæ can be incandescent
and give the spectrum of incandescent gas, without their density or
pressure being increased to the corresponding degree. Sir Robert Ball
seems to be one of them, though at the same time he appears to be not
altogether sure of it. When discussing the self-luminosity of the
nebula in Orion, in his "Story of the Heavens," Ed. 1890, p. 465, he
says: "We have, fortunately, one or two very interesting observations
on this point. On a particularly fine night, when the speculum of the
great six-foot telescope of Parsonstown was in its finest order, the
skilled eye of the late Earl of Rosse and of his assistant, Mr. Stoney,
detected in the densest part of the nebula myriads of minute stars,
which had never before been recognised by human eye. Unquestionably
the commingled rays of these stars contribute not a little to the
brilliancy of the nebula, but there still remains the question as to
whether the entire luminosity of the great nebula can be explained, or
whether the light thereof may not partly arise from some other source.
The question is one which must necessarily be forced on the attention
of any observer who has ever enjoyed the privilege of viewing the great
nebula through a telescope of power really adequate to render justice
to its beauty. It seems impossible to believe that the bluish light of
such delicately graduated shades has really arisen merely from stellar
points. The object is so soft and so continuous--might we not almost
say ghost-like?--that it is impossible not to believe that we are
really looking at some gaseous matter."
Here we see that his own belief about the matter is not very firm. He
admits that the stars contribute not a little to the brilliancy of
the nebula, and the most he can say in favour of its shining with its
own light is, that it seems impossible to believe that the light has
arisen merely from stellar points. He then goes on to show how the
self-luminosity may be explained, as follows:--
"But here a difficulty may be suggested. The nebula is a luminous body,
but ordinary gas is invisible. We do not see the gases which surround
us and form the atmosphere in which we live. How, then, if the nebula
consisted merely of gaseous matter, would we see it shining on the far
distant heavens? A well-known experiment will at once explain this
difficulty. We take a tube containing a very small quantity of some
gas: for example hydrogen; this gas is usually invisible; no one could
tell that there is any gas in the tube, or still less could the kind of
gas be known; but pour a stream of electricity through the tube, and
instantly the gas begins to glow with a violet light. What has the
electricity done for us in this experiment? Its sole effect has been
to heat the gas. It is, indeed, merely a convenient means of heating
the gas and making it glow. It is not the electricity which we see, it
is rather the gas heated by the electricity. We infer, then, that if
the gas be heated it becomes luminous. The gas does not burn in the
ordinary sense of the word; no chemical change has taken place. The
tube contains exactly the same amount of hydrogen after the experiment
that it did before. It glows with the heat just as red-hot iron glows.
If, then, we could believe that in the great nebula of Orion there were
vast volumes of rarefied gas in the same physical condition as the gas
in the tube while the electricity was passing, then we should expect to
find that this gas would actually glow."
There is a great deal to be said about this explanation. We presume
that a very small quantity of hydrogen gas means that it was
considerably below atmospheric pressure. Even so we admit that by
introducing sufficient heat into the tube by means of electricity or
otherwise, the gas could be raised to the temperature of incandescence,
but its pressure would, at the same time, be increased to the
corresponding force measured in atmospheres; and we also admit that
when the gas was allowed to cool down to its original temperature, the
same quantity of hydrogen would be found in the tube; but how about
the tube? When the gas came to be at the temperature of incandescence
the tube would be the same, or very soon raised to it, and being
made of glass would be sufficiently plastic to be distorted, or even
burst by the pressure within, probably even before the gas reached
the temperature of incandescence. We must not forget that the first
appearance of incandescence begins with red heat whose temperature
is not far from 500° in daylight, and that white heat rises to above
1000°. If the experiment was made in an almost capillary tube,
sufficiently thick to prevent accidents, then it might appear to prove
a foregone conclusion, but nothing else; it might keep the idea of
pressure out of sight, but it could not prove that the gas inside was
in a rarefied state when incandescent. That the gas glowed the same as
a red-hot bar of iron has not been shown. The gas had to be shut up
in a tube to make it glow, but the bar of iron could glow outside of
the tube. Could a streak of hydrogen be put into a furnace along with
a bar of iron and heated to incandescence by its side, there might be
some fair comparison between them, as long as they were in the furnace
together, but the moment they were taken out the glow would disappear
from the gas, whereas the iron would glow for some time. On the other
hand we might _say_ that a stream of incandescent gas might be made to
heat a bar of iron in an oven to its own temperature, but the moment
the stream of gas and the iron bar were removed from the oven, the
former would disappear at once and the latter would continue to glow,
simply because it was dense enough to contain a very considerable
supply of heat compared to what the gas could, or rather, because the
pressure of the gas, even did it correspond to the temperature, would
disappear at once and the heat with it. So it is not always safe to
_say_ things. But it is quite safe to say that no gas--or substance
such as we are accustomed to look upon as gas--can abide in a state
of incandescence, and merely glow, unless its pressure, or density,
corresponds to the temperature of incandescence; which for red heat (in
the dark) would be 370° = 2·35 atmospheres, and for white heat at 1000°
= 4·65 atmospheres, above absolute zero of pressure in both cases. And
also, that if the self-luminosity of a nebula arises from incandescent
gas, the pressure in the gas of that nebula must be somewhere between 2
and 5 atmospheres above absolute zero of pressure. Now we have shown,
at page 85, that the density and pressure in the solar nebula, at the
stage there specified, could not have been more than the 403 millionth
part of those of our atmosphere, and consequently were justified in
asserting that in it there could be almost no heat whatever.
We have just been speaking of a streak of gas and a bar of iron being
heated in an oven to a red or white heat side by side, but everybody
knows that this could not be done; but everybody has not thought of
why it could not be done, otherwise Sir Robert Ball would not have
favoured us with his laboratory experiment of a streak, or remnant, of
hydrogen in a glass tube. We know that a plate, or bar, of iron can be
heated up to the temperature of incandescence in an oven, but it has
never occurred to anyone, who has seen the thing done, that the gas,
air, or vapour which heats them must be at a pressure corresponding
to that temperature. Multitudes of people may have thought of how the
thing is done, but apparently very few have thought that it is not the
gaseous part of the current of heated matter introduced into the oven,
that heats it and the metal in it, but the solid part which is the
distinctive and most important part of the constituents of the current.
The solid part of the matter--let it be gas or any other element--is
heated to incandescence in some furnace and carried along by the
gaseous part--that is the _stuff_ that fills the empty spaces between
the solid molecules--to give it out to the oven and iron. We are not
sure that the gaseous part even glows. We see plainly enough that
the walls of the oven glow, but with respect to the gas, or carrying
agent, we are inclined to think that it rather dims the glow of the
oven and iron than otherwise. In passing, we say it is not unreasonable
to suppose that the solid matter which contained the heat till it was
given out, consisted of the elements which were put into the furnace
to raise the heat, and of those which were drawn in by the draught--in
a word, the elements of combustion--but about the carrying constituent
there is a great deal to be said after we know more about it. It seems
to us from all this that the hydrogen gas in Sir Robert Ball's tube was
not made to glow by heating up to the temperature of incandescence,
but somehow by the electricity passing through it, if it did pass.
We, therefore, come to the conclusion that the light of nebulæ does
not come from gas--or what we call gas--heated up to be incandescent
merely to make it glow, and that it might be as cold as the light that
comes from the aurora, or as that of a glow-worm. Sir Robert Ball
refers to stellar points seen through the nebula, and acknowledges that
part of the glow may be due to them, which shows that the nebula must
have been excessively tenuous; for we know how thin a cloud will hide
Sirius from us, and we think that nobody will assert that two grains
of matter dispersed in 1,426,445 cubic feet of space, as we have seen
at page 86, would hide Sirius from us. Therefore, we must acknowledge
that the glow of nebula in Orion, observed by Sir Robert Ball, was
caused either by the stellar points, or by some other thing that most
assuredly could not be gas heated to the temperature of incandescence,
or in part from both. For we believe that the glowing of nebulæ,
fluorescence, phosphorescence, Will-o'-the-wisp, auroras, fire-flies,
fire-on-the-wave, etc., etc., all, all proceed from the same cause.
We may now proceed to say a few words about the separation of the rings
for the planets, brought about by the rotation of the nebula on its
axis, and the centrifugal force produced throughout it thereby. We have
shown, at page 88, that a ring could not be detached from the nebula
at once in one large annular mass, as it seems to have been the common
notion was the mode of separation; and we shall now try to show with
some detail what the process must have been, notwithstanding that it
has been in a general way described by others; because, like everything
else, there is something to be learnt from it. For this purpose we
shall select what we have called the Jovian nebula, because we can
suppose, for the present, it must have been more nearly in the form
of a sphere than either the original or any of the exterior nebulæ,
which may not have been properly licked into shape, as it were; and
also because we have found that the thickness and mass of the ring
for his, Jupiter's, system were vastly greater than those for any
other one of the planets. We have made the Jovian nebula to have been
1,370,800,000 miles in diameter, and the greatest thickness of the ring
detatched from it to have been 1,406,771 miles. Now in a circle of
that diameter, a chord of the length of that thickness would subtend
an arc of very little more than 7 minutes, one half of which we shall
suppose to be measured on each side of the equatorial diameter of the
nebula at right angles to the diameter; then, the middle ordinate of
a chord of 1,406,771 miles long, would be 359 miles long. This length
would be a very small fraction of the radius of the circle which
would be 685,400,000 miles long, but in a rotating sphere of the same
dimension, we must acknowledge that the centrifugal force at the middle
of the arc would be greater--however small the difference--than at
its ends, and would sooner come to balance the force of gravitation;
therefore we must admit that the process of separation would begin
there by abandoning a thin layer of matter, convex on the outer side
and in a measure concave on the inner side, for the reason just
given, much the same as a layer that could be peeled off from the
equator of an orange--the poles and equator of an orange are easily
distinguished. As the velocity of rotation increased another layer
would be abandoned following the first, so far curved on both sides,
i.e. convex and concave, and the same process would continue on and
on, according as the centrifugal force continued to balance that of
gravitation, till the whole of the matter for all the attendants of
the sun was abandoned; so that in the process itself no such division
of rings as we have been following could have taken place, but one
continuous sheet, as it were, would be formed from first to last.
Whether the thickness of the ring for Jupiter's system, or any other
system or planet, was limited to the length of the chord we have been
dealing with, or came to be many times greater or even less, makes no
difference on our explanation. After being abandoned in a sheet, as we
have shown it would be, the centrifugal force they had acquired would,
for a time at least, keep the particles of the sheet near the radial
positions they then occupied, and their mutual attraction would go on
diminishing its thickness, till finally the radial attractions among
the particles divided the sheet into entirely separate rings after the
manner of those of Saturn; which would in due course break up and form
themselves into the smaller nebulæ from which the planets were supposed
to have been made.
M. Faye has made it a great point against the nebula hypothesis that
when these rings broke up, the rotary motions of the planets resulting
from them would be retrograde, because the outer parts of them would
be travelling at a slower rate than the inner ones, and has taken the
trouble to construct a diagram to show how this would be the case;
but he himself has told us, in "L'Origine du Monde," that Laplace had
duly considered this point, and had shown how the friction of the
particles of the flat rings among themselves would, through course of
time, retard and accelerate each other, so that a ring would come to
revolve as if it were one solid piece, and consequently that the outer
edge of the ring would come to be travelling faster than the inner
one, which according to his (M. Faye's) own showing would produce,
on breaking up, a planet with direct motion of rotation. Laplace's
words, as cited by him, are:--"Le frottement mutuel des molécules de
chaque anneau a dû accélérer les unes et retarder les autres jusqu'à ce
qu'elles aient acquis une même mouvement angulaire. Ainsi les vitesses
réelles des molécules éloignées du centre de l'astre out été plus
grandes. La cause suivante a dû contribuer encore à cette différence
de vitesse: les molécules les plus distantes du soleil et qui, par les
effets du refroidissement et de la condensation, s'en sont rapprochées
pour former la partie supérieure de l'anneau out toujours décrit les
aires proportionnelles aux temps, puisque la force centrale dont elles
étaient animées a été constamment dirigée vers cet astre; or cette
constance des airs exige un accroissement de vitesse à mesure qu'elles
s'en sont rapprochées. On voit que la même cause a dû diminuer la
vitesse des molécules qui se sont élevées vers l'anneau pour former sa
partie inférieure."
In his method of bringing all the molecules of matter in a ring, to
revolve round the centre as if they formed one sole piece, Laplace does
not appeal to any accommodating force among them except friction, while
he might have called in that of the collisions of the molecules amongst
themselves. It is not to be supposed that each molecule would remain
fixed in the position it occupied when separated from the nebulæ,
and only went on rubbing against--and creating friction with--its
neighbours, and only creeping closer to the centre or farther from it,
as it was acted upon by the attraction of the other parts of the ring.
The molecules would be rushing against each other in all directions,
in spite of, although in the main obedient to, the law of attraction;
and we could conceive the possibility of molecules gradually working
their way from the extreme outer edge to the extreme inner edge of a
ring, or _vice versâ_, which would be a much more effectual means of
bringing about one period of revolution throughout the whole ring, than
the simple force of rubbing against each other. When physicists get a
gas shut up in a close vessel, they grant to its molecules the power of
committing exactly the same kind of freaks; and a planetary ring is,
to all intents and purposes, a closed vessel to our molecules; because
they have been placed in it by the laws of attraction and centrifugal
force, and there is no other force acting upon them sufficiently
powerful to liberate them from it. Therefore there is no reason why a
molecule in a ring should be always wedged up in one place, especially
after we have shown that each molecule of matter, in any of the rings
we have been dealing with, must have had a much greater free path to
move about in, than a molecule of gas shut up in any of the vessels
used by physicists.
We have no reason to look upon the rings of Saturn otherwise than
as in process of being converted into one or more satellites, most
probably more than one; because if the matter they are composed of has
been separated from the planet in the form of a sheet, the same as we
have seen must have been the case with the matter separated from the
original nebula for the planets, the sheet has been already divided
into at least three distinct parts, and surely that cannot have been
done without some object. If these rings have been left, as has been
said, in order to show us how the solar system has been formed, that
does not authorise us to conclude that they will always remain in the
form they have. There is no reason why the lesson should not be carried
out to the very end, through the breaking up of the rings, formation of
spherical nebiculæ, and finally satellites. It would be rash to assert
that the matter of which any one of them is composed--be it atoms,
molecules, meteorites, or brickbats--cannot, through friction and
collisions of its particles among themselves, come to revolve around
Saturn as if it were one solid piece. But should anyone do so, and
adopt M. Faye's condemnation of Laplace's mode of forming rings, he
must confess that when Saturn's rings are converted into satellites,
their rotations must be retrograde; and it might be, for him, an
interesting inquiry to find out whether the rotations of the existing
satellites are direct or retrograde.
Astronomers have learnt the lesson as far as it has gone, have
noted and registered the state of affairs as it is at present, and
their successors will no doubt do the same as changes succeed each
other. The day may be inconceivably remote, but it will inevitably
come for the rings to be changed into satellites, unless they are
disposed of in some other way. It has been said that were the rings
to break up, in consequence of their being in a state of unstable
equilibrium, they would fall back upon the planet, but that would
depend on circumstances. If the motion of their revolution were stopped
altogether, they would certainly fall back upon the planet; but if it
were not stopped then each molecule would retain its centrifugal force,
and would revolve around the primary on its own account, just as,
according to very general opinion, it does at present. We do not see
why, or for what purpose, these rings could have been separated from
Saturn merely to fall back upon him again. It would be rather a strange
way of giving a lesson if it were stopped, by a cataclysm of some
kind, just when the most interesting part of it was in a fair way of
being exhibited. Such a proceeding would assuredly not suit the ideas
of those who believe that the solar system has been self-formed by a
simple process of evolution.
During the whole process of separation of rings from the original
nebula, the nebulous matter would be abandoned in what we may call the
form of thin hoop-shaped rings, so that the equatorial region of the
nebula would be flat--as we have shown at p. 115--and when the nebula
came to be so much reduced that it could abandon no more matter through
centrifugal force, its form would be, in some measure, like that of a
rotating cylinder terminating at each end in a cap in the form of a
segment of a sphere. When explaining the formation of planetary rings,
we have seen that in the Jovian nebula the length of the flat part
would have come very soon to be nearly 1,500,000 miles, and that it
would increase rapidly. But, remembering that the flattening of the
equatorial part must have begun on the original nebula, we see that
the flat part must have increased vastly in length before it reached
Jupiter, and that by the time the residuary, or solar, nebula was
reached--which we made to be only a little over 63,000,000 miles in
diameter--the cylindrical part of it would bear no small proportion
to that diameter. Taking this form of the nebula into consideration,
and also the fact that the separation of matter from it by centrifugal
force could not always be absolutely equal all around it, the swaying
in its rotary motion produced by the all but inevitable inequality
of mass, at the two ends of the cylindrical part, and at the sides
of the segmental caps, may have been the cause of the differences in
the inclinations of the orbits of the planets to the ecliptic; and
especially of why the difference came to be so much greater in the case
of Mercury than in any of the others.
In connection with this very reasonable conclusion as to the form of
the nebula almost from the beginning, we may add that, when it ceased
to throw off rings, it would be very much in the same condition as
Saturn is at the present day. Therefore we may conclude with very great
safety, that the present form of Saturn is that of a cylinder with
segments of spheres forming the ends; and in this manner can account
for his square-shouldered appearance, which has puzzled more than one
astronomer.
The idea has been very general that in condensing and contracting, the
nebula would gradually come to assume the form of a lens of a very
pronounced character, from the circumference of which the rings would
be abandoned one after the other; but when thoroughly looked into, it
is difficult to see how this could be the case. In a sphere of cosmic
matter contracting equally all round towards the centre through the
force of attraction, it is more natural to suppose that the separation
of matter from its equator through centrifugal force, would have
a tendency to diminish the equatorial more rapidly than the polar
diameter, as we have been trying to show above, more especially as
the attraction of the matter in the rings as they were abandoned one
after the other would, in a constantly increasing degree, assist the
centrifugal force in facilitating the separation by drawing the matter
outwards. Matter falling in from the polar regions would afterwards
require to have its motion turned off at right angles before it could
be sent off by centrifugal force to the equator, an operation which
would be more easily effected in the equatorial regions, where the
gravitating motion had only to be retarded; and as very unequal amounts
of density could not be created in the interior parts of such a sphere
by gravitation, so as to cause pressure outwards, it is difficult to
show how the polar diameter could be more rapidly reduced than the
equatorial diameter, which was being continually shorn of its length.
It may be said that all that we have been writing in the last few pages
is absurd, because we have been proceeding on the supposition that
the condensation of the nebula was effected at or near its surface.
Laplace procured this condition by piling up imponderable heat in his
nebula, but he might have got it otherwise. Given a nebula such as
the one we are dealing with of 6,600,000,000 miles in diameter, where
would condensation be most active? Most undoubtedly where there was the
greatest mass of matter. Compare, then, the mass of 1,000,000 miles
in diameter at the surface with the mass of the same diameter at the
centre, and we cannot hesitate for a moment in concluding that the most
active condensation would not be very far from the surface. Not only
so, but the same would continue to be the case, at least until the last
ring was abandoned. Thus by working upon what may have appeared to
be an absurd foundation, i.e. condensation at the surface due to the
intense heat of the nebula, we have been able to acquire more correct
ideas than we had before, of how the solar system was elaborated. But
we shall have much more to say on the same subject hereafter.
There has been a great outcry raised about the rotation of the planets
Neptune and Uranus being retrograde, as is correctly concluded to be
the case from the revolution of their satellites being retrograde, but
we do not see that there has been any good reason for it. Laplace,
no doubt, concluded, wrongly, that the motions of all the bodies of
the solar system--as known to him--were direct, and therefore used
that conclusion in showing that there were 4000 milliards against 1 in
favour of his hypothesis being right; but at the same time it cannot be
concluded that he thought that it would be destroyed by the motion of
rotation of one or even several of the forty-three bodies turning out
to be retrograde; because, when discussing the hypothesis of Buffon,
he states, most distinctly, that it is not necessary that the rotation
of a planet should be in the same sense as that of its revolution, and
that the earth might revolve from east to west, and at the same time
the absolute movement of each of its molecules might be directed from
west to east. His words as cited by M. Faye in "L'Origine du Monde,"
at page 158, are: "A la verité, le mouvement absolu des molécules
d'une planète doit être alors dirigé dans le sens du mouvement de
son centre de gravité, mais il ne s'ensuit point que le mouvement de
rotation de la planète soit dirigé dans le même sens; ainsi la Terre
pouvait tourner d'orient en occident, et cependant le mouvement absolu
de chacune de ses molécules serait dirigé d'occident en orient, ce qui
doit s'appliquer au mouvement de révolution des satellites, dont la
direction, dans l'hypothèse dont il s'agit, n'est pas nécessairement la
même que celle de la projection des planètes." He seems to say, "This
would suit Buffon's hypothesis, but I do not require it for mine." Even
were this not so, it would not be very difficult to account for the
retrograde rotation of these two planets, but we are not yet prepared
to show, in a convincing manner, how these motions were produced. We
have to show first how the nebula itself was brought to the dimensions
at which we took it up, and there is a great deal to be done before we
can show that.
Should our belief in being able to explain how the retrograde rotations
of Uranus and Neptune were brought about turn out to be unacceptable,
we would not condemn the nebular hypothesis, because, as M. Faye
himself says, if we add the asteroids to Laplace's 43 we should have
somewhere about 500 bodies, all with direct motion, agreeing with the
hypothesis, against 4 that do not, that is about 125 to 1 instead of
43 to 1, which was all Laplace could claim. Moreover, we have not been
able to see that M. Faye's objections to it are well founded, rather
the contrary; nor can we agree with him when he says that when one
point in a hypothesis is found to be erroneous it ought to be abandoned
altogether, and something better sought for. Is his something any
better? All acquired knowledge has been built up from ideas collected
from all sides, and from errors reformed. What would a grammarian say
were we to return to him his grammar as useless, because we had found
one exception to one of his rules against 125 cases in which we had
found it to be right? Perhaps it would put him in mind of the name
of a tree. And grammar is not the only case in which we say that the
exception confirms the rule.
In taking the nebula to pieces, we have taken no notice of the
satellites of Mars, not only because they are so small that they would
have had no sensible effect on our calculations, but because we cannot
conceive that they could have been abandoned by the planet, when in a
nebulous state, in the same manner as the planetary rings are supposed
to have been by the parent nebula; and we might simply refer to the
dimensions, especially the thinness, we have found for the ring out
of which Mercury was formed, for proof of our assertion; but for
more satisfactory corroboration, we will go a little deeper into the
affair. Let us take the diameters of Mars and of the orbits of his
satellites, as they are stated in text-books of astronomy; that is
2957, 11,640 and 29,200 miles respectively, and suppose the diameters
of what--in the method we have applied to the planets--we would call
the Deimos and Phobos nebulæ to have been 40,000 and 20,420 miles also,
respectively; then these two diameters would make the breadth of the
ring for the formation of Deimos to have been 9790 miles. With these
data, if we go through a series of calculations with respect to this
outer satellite, in all respects similar to those we have made for each
of the rings of the planets, we shall find that the ring for Deimos
would have been only 5·64 _inches_ thick, without taking into account
its condensation during the process of separation. This, of course,
points out at once the impossibility of any such operation going on in
Nature. We can imagine the possibility of a ring of even millions of
miles broad, and of very great tenuity, holding together provided it
be hundreds of thousands of _miles_ thick, but to think of one 10,000
miles broad and less than 6 _inches_ thick holding together is another
affair altogether. With respect to Phobos, it is only necessary to say
that he revolves round Mars in considerably less than one-third of the
time that he ought to, and is therefore not a legitimate production
of the nebular hypothesis any more than Deimos can be. Here, then, we
have come upon two bodies, one of which has not been formed in the way,
and the other has not the proper motion, prescribed in the hypothesis;
but we do not think ourselves justified in declaring it to be worthy
of condemnation on that account, seeing that we have found no other
difficulty in working out the solar system from it.
Moreover, it is not impossible, nor do we think it at all improbable,
that through the course of time astronomers may discover that Phobos
is a captured asteroid--perhaps Deimos also--gradually working its
way into final annexation. And who can tell how many of these erratic
bodies Jupiter and Mars may have captured already? In the dark as it
were, for they may have been too small to be noticed when they were
being run in. Neither of these two worthies has ever been very much
celebrated in song or history for respect for his neighbour's property.
Jupiter is credited with sorting out the asteroids and arranging them
in bands, and perhaps he has been human enough to exact a commission
for his labour; and it might be more in his line, and certainly much
more easy for Mars, to take forcible possession of as many of them as
came within his reach.
CHAPTER VII.
PAGE
126 Analysis continued. No contingent of heat could be imparted to
any planet by the parent nebula.
127 Only one degree of heat added to the nebula from the beginning
till it had contracted to the density of 1/274th
of an atmosphere.
127 Increase in temperature from 0° to possible average of 274°
when condensed to 4,150,000 miles in diameter.
128 Time when the sun could begin to act as sustainer of life and
light anywhere. Temperature of space.
129 The ether devised as carrier of light, heat, etc. etc. What
effect it might have on the nebula.
130 First measure of its density, as far as we know.
133 The estimate _too_ high. May be many times less.
134 Return to the solar nebula at 63,232,000 miles in diameter.
134 Plausible reason for the position of Neptune not conforming
to Bode's Law. The ring being very wide had separated
into two rings.
135 Bode's law reversed. Ideas suggested by it.
137 Rates of acceleration of revolution from one planet to another.
138 Little possibility of there being a planet in the position
assigned to Vulcan.
138 Densities of planets compared. Seem to point to differences
in the mass of matter abandoned by the nebula at
different periods.
139 Giving rise to the continuous sheet of matter separating into
different masses. Probably the rings had to arrive at a
certain stage of density before contracting circumferentially.
140 Possible average temperature of the sun at the present day.
Central heat probably very much greater.
140 Churning of matter going on in the interior of the sun, caused by
unequal rotation between the equator and the poles.
Coming back to the period when we reduced the residuary nebula to the
density of our atmosphere with temperature of 0°, or freezing water, we
can with confidence affirm that none of the rings abandoned by it for
the formation of planets, could have carried with them any contingent
of heat to help them in their formation--any beyond the temperature
of space--for even if they did it would very soon be reduced to
that. Each one of them in condensing, breaking up, rejoining the
broken fragments, converting itself into a minor nebula, and finally
constituting itself as a planet, must have accumulated in the process
its own heat requisite to convert it into a molten liquid globe--a
stage of existence through which they are all, that is, the major
planets, acknowledged to have passed, or have to pass. During that
process its primitive annular form, and the multitude of fragments into
which each one of them broke up, would present sufficient radiating
surface, not only to dispose of all the heat it could have brought with
it from the nebula, but a considerable part of the little it could
create for itself while contracting and condensing. We may even go
farther and assert that no one of them would have any necessity for
being supplied with extraneous heat until it had, in a great measure,
exhausted the stock it had produced for itself, or so far as to cool
down from the molten liquid to the solid state, and to the stage when
vegetable and animal life could exist upon its surface. We have no
reason for supposing that an enormous supply of extraneous heat was
crammed into each nebula, merely to be radiated into space before
condensation could take place, and thus retard the execution of the
work in hand. If there are astronomers or physicists who believe that
the sun could not acquire by gravitation, all the heat he must have
expended during geological time, they must look for it in some other
source than that of useless and impossible cramming.
Hitherto we have said nothing of heat being radiated into space by the
nebula during our operations, because there could be almost absolutely
none to radiate from it at 0° of temperature. No doubt there is a
large range between this and the absolute zero of temperature which is
-274°; but we have seen, at page 99, that when the nebula was condensed
from 403,000,000 to 274 times less dense than air, only _one degree_
was added to its temperature--that is, it was raised from -274° to
-273°--and that these -273° of absolute temperature were added to it
in its condensation from being only 274 times less dense than air to
atmospheric pressure, when its temperature became 0° of the ordinary
Centigrade scale. Therefore the only period when there could be any
measurable radiation of heat into space would be between the times
when the diameter of the nebula was (see Table III.) between 58,000,000
miles and 9,000,000 miles. Even when the end of this period came, the
temperature, after a contraction of 49,000,000 miles in diameter, would
be only -1° raised to 0°--in other words -273° raised to 0°--and that
would not furnish much positive heat--heat such as we are accustomed
to deal with--to be radiated into space, whose temperature is without
doubt somewhat warmer, so to speak, than -273°. And let us repeat, and
fix it in our memory, that this -273° was equal to only 1° of positive
heat.
If we now suppose the nebula to be condensed to one-tenth of its
volume, with consequent density of 10 atmospheres, and corresponding
diameter of about 4,150,000 miles, its temperature would be 2740° of
the ordinary Centigrade scale--according to our mode of calculating
hitherto--provided no heat had been radiated from it into space in the
meantime. Of course this could not be the case, but we have no means of
calculating what the amount of radiation would be, and it will not make
much difference on our operations to take no notice of it. However,
it is here necessary to take into consideration that 2740° would be
the average temperature of the nebula; consequently, if condensation
was most active where the greatest mass was, which certainly could not
be at the centre or even near it, there also heat would be produced
most rapidly, from whence it would spread towards the centre and
surface. From the centre it would have no outlet, and would accumulate
there as condensation advanced; whereas from the surface it would be
radiated into space, and would tend to decrease in amount, so that we
may conclude that the surface must have been considerably colder than
the centre. If to this we add the fact that, in order to get to the
surface, heat would have to be conducted, or conveyed by currents; over
from one to two millions of miles, it becomes all the more certain
that the central heat would be very much greater than that of the
surface. How much less it would be at the surface we cannot pretend
to calculate, but we may suppose it to have been from one-fifth to
one-third of the average, or rather, somewhere between 370° and 1000°,
which we have taken, at page 110, to be the temperatures of red-heat
and white-heat. And thus we come to find that the nebula, which was
supposed to be endowed with excessive heat when it extended far beyond
the orbit of Neptune, could not have radiated either heat or light into
space to much purpose, until it had been condensed into not much more
than 4,000,000 miles in diameter. This then we must acknowledge to be
the earliest period at which the sun began to act as the life sustainer
of his system; because, even were it to be found that there are other
planets revolving within the orbit of Mercury, which we do not think
very probable, we have seen that he could have no light or heat with
sufficient vivifying power to radiate to them, till his diameter was
reduced to not far from what we have shown above. Even then the sun
would most likely be very much less brilliant than he is now, but the
light may have been sufficient to promote vegetation on Mars--or the
earth, if it was sufficiently cooled down from its molten state--and
not much heat would be required by him, as there would probably be
a remnant of his own interior heat, still sensible at the surface,
sufficient for vegetation at least.
We have had occasion to refer several times to the temperature of
space, and, though we cannot pretend to determine what it is, our
operations enable us to show that it must be very much less than
any estimate of it that has ever come under our notice. The nearest
approach made to absolute zero by M. Olzewski, in his experiments on
the liquefaction of gases, as reported in the "Scientific American" of
June 2, 1887, was -225°, or so-called 49° of absolute temperature,[D]
which would correspond to a density of 0·1788 of an atmosphere. This
could not be the density of space, because it can be easily shown that
our nebula, when at the same density, must have had a diameter of about
29,000,000 miles, and we must admit that were a globe of this diameter
rotating in a medium of its own density, the friction between the two
would have been so great as to put a stop to the rotation before very
long. We may even say that distinct rotation could never have been
imparted to it. Following the same reasoning, we must acknowledge that
the density of space must be much lower than that of our original
nebula, if that could be, and therefore we can assert with confidence
that the temperature of space must be far below -225°.
[D] From the same source, date June 6, 1896, we learn that the greatest
cold probably ever reached was -243·5° or 31·5° of so-called absolute
temperature, but that will have very little effect on our calculations,
and so it is not worth while altering them all to suit.
Here our operations put us in mind that we have said nothing yet about
the ether, or what effect it might have on our nebula and the bodies
formed out of it. We have not done so for the simple reason that, with
one exception, it has never been taken into account in any scientific
work that has come into our hands, except so far as its being called
upon to perform the offices of a dog that has been taught to carry
and fetch, and we have not known how to deal with it. But as we have
come along, we have seen that it must have had something to do with
the density, and consequent temperature, of all the bodies we have
been dealing with, and that, if properly studied, it may enable us to
account for some things that we have never seen, to our mind, properly
explained. We know that it was devised, or conceived of--somewhere
between thousands of years ago and the birth of modern astronomy--as a
medium for carrying light, heat, and anything that was hard to move,
through space, or to where it was wanted to be moved, by its vibrations
or undulations, in the same way that sound is conveyed by wave motion,
or vibration, through air, water, and a multitude of bodies; and we
understand that some time during that long period it began to be looked
upon as a material substance. We are told that it is supposed to
pervade all bodies of all classes, but we think this idea must be taken
in a limited sense, because, whether it is combined with electricity,
as some suppose, or is only a carrier of electricity, a good conductor
must have a larger supply of it than a bad one, and an absolute
non-conductor, if there be such a substance, must contain none at all,
always provided the ether is the conducting or carrying power. We are
told also, that it is neither of the nature of a gas nor a liquid, but
may be of the nature of a jelly, and of its nature we shall have more
to say hereafter. It was natural that it should be conceived to be a
material substance, because if light and heat were to be carried from
one place to another by wave motion, as sound is by water and air,
then the medium for carrying it must be of the same nature as air and
water--or any other carrier of sound--that is, it must be a material
substance and, in consequence, possessed of some density or specific
gravity. The only place where we have seen any density assigned to it
has been, in a series of articles on the "Origin of Motion," published
in "Engineering" of 1876, where it is estimated to be 1/5,264,800th[E]
of the density of air. How this estimate was formed is explained in the
number for December 1, 1876, page 461, from which we make the following
very long quotation, because we look upon it as of great importance.
[E] Years after this was written we have seen it stated that the
density of the ether has been calculated from the energy with which
light from the sun strikes the earth, and that to represent it there
are twenty-seven cyphers after the decimal point before the figures
begin. But as this gives something like one thousand quadrillionth part
of the density of water, we refuse to accept or even think of it.
"Steel of the best quality in the form of fine wire has been known to
bear a tensile strain represented by not less than 150 tons per square
inch before breaking, and even this cannot be said to be the limit to
the tensile strength of steel, since the tenacity increases as the
diameter of the wire is reduced. Rejecting 'action at a distance,'
therefore, these molecules of the wire must be controlled by some
external agent, and therefore, the pressure of the external agent must
_at least_ equal the static value of the strain. The pressure of the
ether therefore cannot be less than 150 tons per square inch. Now,
since it is a known fact that the strain required to separate molecules
in 'chemical union' would be very much greater than in a mere case of
'cohesion,' it follows that the ether pressure must be greater than
the above figure. If we suppose the strain required to separate the
molecules of oxygen and hydrogen combined in the state of water (one
of the most powerful cases of chemical union) to be only three times
greater than in the case of the molecules of steel, then this would
give 450 tons per square inch as the effective ether pressure. It may
be taken as certain that the strain required would be greater than
this, as it has not been found possible by any ordinary mechanical
means to separate molecules in chemical union. However, as it is only
our object to fix a limiting value for the ether pressure, or a value
that is less than the actual fact, we will therefore take in round
numbers 500 tons per square inch as the total ether pressure, having
thus valid grounds for inferring that this estimate is within the facts
as they actually exist. The existence of such a pressure as this might
well be sufficient to strike one with astonishment and legitimately
excite incredulity, if it were not kept in mind that this pressure
is exercised against _molecules_ of matter, a perfect equilibrium of
pressure existing, so that it may be deduced with certainty beforehand,
that, however great this pressure might be, it could not make itself
apparent to the senses. The air exercises a pressure of some tons
on the human body without such pressure being detected, how much
more cause, therefore, is there for the perfect concealment of the
ether pressure, which is exercised against the molecules of matter
themselves. This great pressure is the absolutely essential mechanical
condition to enable the ether to control forcibly the molecules of
matter in stable equilibrium, and to produce forcible molecular
movements when the equilibrium of pressure is disturbed (as exemplified
in the molecular movements of 'chemical action,' etc.).
"It is generally admitted that the ether must have a very low density,
one reason being the almost imperceptible resistance opposed by it
to the passage of cosmical bodies (the planets, etc.) at high speed
through its substance. The pressure of an aëriform body constituted
according to the theory of Joule and Clausius, being less as its
density is less, it will therefore be necessary to show that the ether
can exert so great a pressure as the above, consistent with a very low
density. From the known principles belonging to gases, the pressure
exerted by an aëriform medium is as the _square_ of the velocity of
its component particles, and as the density. We will, in the first
place, consider what the density of the ether would be, if it only gave
a pressure equal to that of the atmosphere (15 lb. per square inch).
From the above principles, therefore, it follows that for the ether to
give a pressure equal to that of the atmosphere, the ether density will
require to be as much less than that of the atmosphere, as the _square_
of the velocity of the other particles is greater than the square of
the velocity of the air molecules. The velocity of the air molecules
giving a measure of 15 lb. per square inch is known to amount to 1600
feet per second. Taking, therefore, the square of the velocity of the
ether particles in feet per second, and the square of the velocity of
the air molecules and dividing the one by the other, we have the number
of times the ether density must be less than that of the atmosphere, in
order for the ether to give a pressure of 15 lb. per square inch, or we
have
(190,000 × 5280)^{2}/1600 = 393,120,000,000.
This result shows therefore that the density of ether, if it only
gave a pressure equal to that of the atmosphere, would be upwards of
390,000,000,000 times less than the density of the atmosphere. This
result expresses such an infinitesimal amount of almost vanishing
quantity, that the ether density might be well much greater than this.
We will now, therefore, consider what the ether density would be to
give a pressure of 500 tons per square inch. Pressure and density being
proportional to each other, it follows that for the ether to give a
pressure of 500 tons per square inch, the ether density would require
to be as much greater than the above value, as 500 tons is greater than
15 lb. Multiplying, therefore, the above value for the density by this
ratio, we have
1/393,120,000,000 × (500 × 2240)/15 = 1/5,264,800;
or this shows that the density of the ether to give a pressure of 500
tons per square inch would be only 1/5,000,000th of the density of the
atmosphere. This value representing a density less than that of the
best gaseous _vacua_ is therefore quite consistent with the known fact
of the extremely low density of the ether. It follows, therefore, as a
mathematical certainty dependent on the recognised principles belonging
to gaseous bodies, that the ether could exert a pressure of not less
than 500 tons per square inch consistent with such an extremely low
density as to harmonize with observation."
If the ether is possessed of a density equal to that shown above, then
the density of our original nebula must have been greater than what we
have shown it to be. The density we found for it was 1/403,000,000th
that of air, or 0·000000002481 of an atmosphere, and 1/5,264,800th is
equal to 0·00000019 of an atmosphere; if then we add these two together
we get 0·0000001925 of an atmosphere as the density of our nebula.
This comes to be very slightly greater than the density of the ether,
and shows that the estimate in the foregoing quotation is too high;
unless it is asserted that the ether can exert no frictional action
at all, which, we believe, no one has ever done; while the absolute
temperature of the nebula at the new density would be 0·000053°,
which would be a very small addition indeed to the 0·00000068°, we
found for it at first. On the other hand, when the nebula was reduced
to 29,000,000 miles in diameter the density of the ether would have
increased its density from 0·1788, which we showed it then to have,
only to 0·17880019 of an atmosphere, which would make no appreciable
difference on its temperature, and would be so immensely greater than
the 0·00000019 of an atmosphere of the ether that it could hardly
be supposed to have any effect in retarding the rotation of so much
heavier a body. And should it be found that the density of the ether
is 1/4, 1/3, or 1/2 less, or even a great deal more, than that shown
in the above quotation, it would only have proportionately less effect
on our nebula, in every sense, than what we have just shown. We may,
therefore, conclude that the introduction of the element ether has not
vitiated our operations in any way up till now, and we shall leave it
until we have acquired more knowledge of its nature and effects.
Although we have already condensed our nebula to somewhere about
4,000,000 miles in diameter, where we have shown it might begin to
radiate light--radiation of heat may have begun when the diameter
was ten times as great, or even before that--we propose to return to
the period when it had just abandoned the ring for the formation of
Mercury and was 63,232,000 miles in diameter, and became what we have
called the Solar nebula; because there is a good deal to be learned
from a careful study of our operations up to that period, and of what
must have taken place during further condensation up till the final
establishment of the sun such as it is at the present time.
When the planet Neptune was discovered, Bode's Law fell into disrepute
for a time, because the new planet was found to be much nearer to the
sun than, according to it, it should have been. All the other planets
occupied the places assigned to them within 5 per cent. of the exact
appointed distance from the sun, but Neptune turned out to be 22·54
per cent. out of his exact place, and hence the discredit thrown
upon the law. It was hard treatment for a servant that had helped so
unmistakably--as we know to have been the case--to the discovery of
the first four asteroids, which has afterwards been followed by the
discovery of a whole host of them, and that had been pressed into the
service for the discovery of the very planet which was the cause of
its discredit--but such is the world. However, first offences against
the law are generally looked upon with merciful eyes, and the Series
of Titius seems to have been so far received into favour again that,
some astronomers are said to have been looking out for another planet
farther off than Neptune, being convinced that there must be some
reason why a law that has shown itself to be right in eight cases
should be altogether wrong in the ninth. Here, we think that the most
likely explanation that can be given is, that the ring out of which
Neptune was formed divided itself, after breaking up, into two planets
instead of one, and that this is the reason why, Bode's Law could not
point out the true position of either of them. It is hard enough to
believe that the ring out of which Uranus was made--which we have seen
may have been 954,000,000 miles broad, and over 3,400,000,000 miles
in extreme diameter--could have united its fragments, after breaking
up, into one planet, and the difficulty of belief becomes greater the
greater the diameter comes to be. We have, in our work, considered the
breadth of Neptune's ring to have been 1,010,000,000 miles, but then
we limited the diameter of the nebula to 6,600,000,000 miles--we had to
draw the line somewhere--whereas it may have been a thousand million
miles greater, which would very greatly increase the probability of
two planets, perhaps even more, having been formed out of the ring.
If it has been so, the law could not apply to the case. A new Act was
required. Besides, it is not a law, never has been, but only a register
of facts; and we know that truths are often discovered from similar
registers. It registers, and at the same time shows, that there is a
nearly fixed inter-relation, even proportion, in the distances of the
planets from the centre of the sun as far out as Uranus; and were we
to make a similar register, beginning at the (present) outside of the
planetary system, and registering the number of revolutions, beginning
with 1 for Neptune, rates of acceleration of revolution in number of
days, and densities of the planets, we may draw from it some useful
knowledge. But we shall first extend Bode's Law to embrace Neptune, and
show the discrepancies between the actual positions of the planets and
those pointed out by the law.
Here we see that, with the exception of the first step from Neptune
to Uranus which is only 1·9577, we have an average gradation of
acceleration of 2·5898 times, from one planet to another, from the
outermost as far in as Mars; and that had Neptune had the period
of revolution sought for by Leverrier in his discovery of that
planet, viz. 217·387 years, or 79,399·602 days, the average rate of
acceleration would have been 2·5896 times, from planet to planet,
as far in as Mars. This, we think, is pretty strong evidence that
one law of acceleration was in force from the beginning of the
separation of rings from the nebula up to the time when the ring for
Mars was separated--the departure from it in the case of Neptune,
notwithstanding--and goes far to prove that part of the nebular
hypothesis which implies that each of the planets is now revolving
round the sun in the orbit, and with the velocity, belonging to the
centre of gyration of the ring out of which it was formed. From
Mars to Venus the law--the areolar law, of course--had changed to a
variable decreasing law, as seen from the foregoing register, which
then again changed into an increasing one, till at Mercury the rate of
acceleration rose again to 2·5543 times from Venus, or very nearly the
same rate of increase that existed from Uranus to Mars. The causes of
these changes may or may not be able to be accounted for--we shall have
to return to them hereafter, in the cases of Neptune, the earth and
Venus--but there is one thing of some importance that is deducible from
the register, which we shall endeavour to make clear.
BODE'S LAW EXTENDED.
--------------+----------+----------+----------+-----------+-----------
---- | Mercury. | Venus. | Earth. | Mars. | Asteroids.
--------------+----------+----------+----------+-----------+-----------
Numbers in }| | | | |
progression }| 0 | 3 | 6 | 12 | 24
| | | | |
Add 4 to each}| | | | |
for distance }| | | | |
from sun, }| 4 | 7 | 10 | 16 | 28
Earth's = 10 }| | | | |
| | | | |
Distance from}| | | | |
sun according}|37,186,000|65,075,500|92,965,000|148,744,000|260,300,000
to the law, }| | | | |
(Miles) }| | | | |
| | | | |
Actual |35,987,000|67,245,000|92,965,000|141,650,000| ..
distance | | | | |
| | | | |
Percentage }| | | | |
of distance }| .. | 3.34 | .. | .. | ..
beyond law }| | | | |
| | | | |
Percentage }| | | | |
of distance }| 3.22 | .. | .. | 4.77 | ..
within law }| | | | |
--------------+-------------------------------------------------------
---- | Jupiter. | Saturn. | Uranus. | Neptune.
--------------+-----------+-----------+-------------+-----------------
Numbers in }| | | |
progression }| 48 | 96 | 192 | 384
| | | |
Add 4 to each}| | | |
for distance }| | | |
from sun, }| 52 | 100 | 196 | 388
Earth's = 10 }| | | |
| | | |
Distance from}| | | |
sun according}|483,418,000|929,650,000|1,782,114,000|3,607,042,000
to the law, }| | | |
(Miles) }| | | |
| | | |
Actual |483,678,000|886,779,000|1,783,383,000|2,794,000,000
distance | | | |
| | | |
Percentage of}| | | |
distance }| 0.05 | .. | 0.07 | ..
beyond law }| | | |
| | | |
Percentage of}| | | |
distance }| .. | 4.50 | .. | 22.54
within law }| | | |
--------------+-----------+-----------+-------------+-----------------
Our register as specified above will be the following:--
-----------+--------+-------+---------------------+-----------------+
Planet. | Rev. of Planet,|Accel. of revolution,|Density of Planet|
|(in solar days) |(Neptune taken as 1) | |
-----------+----------------+---------------------+-----------------+
Neptune. | 60,180.8600 | 1.0000 | 1.132 |
Uranus. | 30,688.3000 | 1.9577 | 1.302 |
Saturn. | 10,759.2198 | 2.8523 | 0.736 |
Jupiter. | 4,332.5848 | 2.4833 | 1.358 |
Asteroids.| 1,714.1876 | 2.5606 | ... |
Mars. | 686.9796 | 2.4629 | 4.188 |
Earth. | 365.2563 | 1.8808 | 5.660 |
Venus. | 224.7007 | 1.6255 | 4.810 |
Mercury. | 87.9692 | 2.5543 | 6.850 |
-----------+----------------+---------------------+-----------------+
A good deal has been written about planets or other bodies existing
between Mercury and the sun, especially about Vulcan whose existence
seemed to be so certain, that his distance from the sun and period
of revolution were calculated to be about 13,000,000 miles and 20
days respectively. Now, with what we have seen about the rate of
acceleration of planets as their orbits approach the sun, we may
endeavour to form some notion of where any within the orbit of Mercury
may be found. If we take the same rate of acceleration we have found
between Venus and Mercury--that is 2·5543, which may be looked upon
as almost the general rate for all the planets--we find that there
might be a planet revolving round the sun in 34·4436 days; but here we
must stop, because, though we could make no objection to the existence
of a planet with the period of revolution just shown, were we to
take another equal step towards the centre of the nebula, the same
acceleration of rotation would give us a planet, or ring for a planet,
revolving round the sun in 13·4454 days; not much more than one-half
the average of his rotation round his axis at the present day, which
would knock on the head most completely the theory that each planet
was detached from the nebula at the time that it was rotating with the
velocity of the planet's orbit, or we should have to conclude that the
nebula had passed, by a long way, its power to abandon matter through
centrifugal force. No one could suppose that a ring for a planet could
be formed within the body of the nebula and abandoned, or thrown out,
afterwards, because centrifugal force could not throw out the ring and
at the same time retain the surrounding matter.
Turning our thoughts now to the supposed planet Vulcan, which was
calculated to revolve round the sun in about 20 days, we have either
to conclude that it was formed in the body of the nebula and come to
the same breakdown of the nebular hypothesis, or we have to acknowledge
that the sun is now rotating much more slowly on its axis than the
nebula did at the time the ring for Vulcan was abandoned.
If we now direct our attention to the densities of the several planets,
we shall find some suggestive matter in their study. A general look
shows us at once that there are four periods of rise and fall in their
densities. There is one rise and fall (referring to our register)
from Neptune to Uranus and on to Saturn; then another rise to Jupiter
and fall to, we suppose, the asteroids, because we are told that the
quantity of matter in the region where the asteroids travel is less
than in any other zone of the solar system, and the general density
must in consequence have been less there than anywhere else; still
another rise from the Asteroids to the Earth, and fall to Venus; and
then a final rise to Mercury accompanied, without doubt, by a fall
after the planet was abandoned, because the centrifugal force of the
rotating nebula must have been decreasing, at the least, preparatory
to its ceasing to have the power to throw off more matter. The first
rise and fall would seem to indicate that there had been a much closer
mutual relation in the births of Neptune, Uranus and Saturn than is
indicated in any way in the nebular hypothesis. We could imagine that
at one time they formed one flat ring, which afterwards divided itself
into three, following the same law as we see dividing the rings of
Saturn at the present day. With respect to Jupiter, his enormous size
is sufficient to entitle us to believe that his ring was separated from
the nebula independently of any of the others, and to account for there
having been the rise and fall in the density that we have noted between
Saturn and the Asteroids. Then the rise and fall from Mars to Venus,
or further on towards Mercury as it would be, may indicate one ring
divided into three in the same manner as we have supposed for the three
outer planets. And the final rise to Mercury and subsequent fall to the
sun or to the solar nebula might be either due to one operation or to
complication with other unknown bodies that may be travelling between
Mercury and the sun.
In support of the foregoing ideas, we may also refer to our having said
on a previous occasion, that the whole of the matter separated from the
nebula in the form of thin hoop-shaped rings, would condense into one
continuous sheet, perhaps even up to the time when centrifugal force
could not throw off any more matter against the force of gravitation.
In that case we can conceive that the radial attraction, outwards
and inwards, of the particles of the matter forming the sheet would
gradually establish lines of separation, dividing off the matter into
distinctly separate rings, preparatory to their transformation into
planets; but we cannot explain how these separate rings came to be
more dense in one place than another. We must leave that for future
discovery. Meanwhile the idea of one continuous sheet of matter
extending from the sun out to Neptune, suggests the possibility of all
the rings having been in existence as rings, more or less advanced in
their evolution, at the same time; and if not so much as that, makes
it more easy for us to see how the four inner planets, being made out
of more condensed cosmic matter, and being of so much smaller volume,
have arrived at a much more advanced stage of their being than the
four outer ones. Going a little further, we can see how the cosmic
matter of the rings condensing from both sides in the direction of
their thickness, and falling in impeded, so to speak, the tendency to
contract in length, or circularly, until they arrived at a certain
stage of density, when they began to contract in their orbital
direction, to break up into pieces, each one of which would form itself
into a small, probably shapeless, nebula with a tendency to direct
rotation, as explained and shown by M. Faye in "L'Origine du Monde,"
chapter xiii., page 267, entitled "Formation de l'Universe et du Monde
Solaire"--an explanation which must have occurred to everyone who has
taken the trouble to think seriously, of how nebulous spheres could be
formed out of a flat nebulous ring endowed with a motion of revolution.
We have seen at page 127 that when the nebula was condensed to a little
over 4,000,000 miles in diameter, its average temperature might have
been 2740°, provided no heat had been radiated into space. In like
manner, we can see that the sun being now condensed to 1·413 times the
density of water, or 1093 times the density of air, in other words,
that number of atmospheres, its present average temperature might
be about 300,000°--as each atmosphere corresponds to 274°--provided
no radiation of heat into space had been going on. But this way of
estimating could not in any way apply to the nebula after it had
ceased to throw off planetary matter; because from that time, or at
all events from the time when it came to be of a density equal to one
atmosphere and temperature of 0°, or freezing point of water, that
would be accumulated within it, owing to the difficulty of carrying
to the surface, to be radiated into space, what was produced by
condensation in the interior, as we have shown before. Both heat and
pressure would increase from the surface towards the centre, the former
rising, in spite of surface radiation, to something far beyond what we
have stated above that it might be, aided by the increase of pressure
which near the centre must be enormously greater than the average of
1093 atmospheres, seeing that the pressure at the surface of the sun
is estimated to be not far from 28 atmospheres. The first cause of the
increase of pressure would be the condensation produced by gravitation,
which according to the areolar law would increase the rotary velocity
of the nebula in proportion as the centre was approached; and as this
would begin long before it had given up abandoning rings, or rather
from the very beginning of its rotation; from that time, there would be
different rates of rotation at different distances between the surface
and the centre, which would cause friction among the particles of its
matter, in other words a churning of the matter shut up in the interior
of the nebula, and thus produce heat over and above that produced by
the condensation of gravitation alone. If two particles of matter would
produce a given quantity of heat, in falling from the surface of the
nebula to any point nearer to the centre, they would surely produce
more if they were rubbed against each other by churning action during
their fall.
Reflecting on what we have written up till now, we see that the
analysis of the nebular hypothesis we have made, which at first may
have appeared to be unnecessary or even useless, has shown us and
made us think over many details, of which we had only a vague notion
previously. It has shown us that without condensation at or near the
surface of the nebula--which we have pointed out must have been caused
by its greatest mass being near that region, and which Laplace procured
by endowing it with excessive heat--the various members of the solar
system could not have been evolved from it in terms of the hypothesis.
From it we have been able to learn, by means of the register of the
acceleration of revolution from one planet to another, when, and for
what reason, the nebula ceased to be able to throw off any planet
nearer to the sun than the supposed Vulcan, or almost even so near.
Finally, and not to go into greater detail, it has so far given us some
ideas, that we had not before, of the internal structure of the sun,
and has made us believe that a great deal may be learnt by attempting
to find out what that structure really is. For this purpose, it appears
to us that a careful examination into, and study of, the interior of
the earth might be a great help, and to this we shall appeal, as we
cannot think of any other process by which our object can be attained.
This, therefore, we shall endeavour to do in the following chapters.
CHAPTER VIII.
PAGE
142 Inquiry into the Interior Construction of the Earth. What is
really known of the exterior or surface.
143 What is known of the interior.
144 Little to be learned from Geology, which reaches very few
miles down.
145 Various notions of the interior.
146 What is learnt from earthquake and volcanoes.
Igno-aqueous fusion, liquid magma.
147 Generally believed that the earth consists of solid matter
to the centre. Mean density. Surface density.
148 More detailed estimate of densities near the surface.
148 Causes of increased surface density after the crust was formed.
150 Calculations of densities for 9 miles deep, and from there to
the centre forming Table IV.
151 Reflections on the results of the calculations.
151 Notion that the centre is composed of the heaviest metals.
"Sorting-out" theory absurd.
152 Considerations as to how solid matter got to the centre.
153 Gravitation might carry it there, but attraction could not.
154 How the earth could be made out of cosmic matter,
meteorites or meteors.
THE INTERIOR OF THE EARTH AND ITS DENSITY.
Before attempting to inquire into the nature and structure of the
interior of the earth, it will be convenient to specify the bases on
which the inquiry is to be made, in other words, the data we have to
proceed with; which data should be denuded of everything whatever
having the semblance of a hypothesis or theory, and should consist of
simple facts. Anything founded upon theory must come to an end should
the theory be afterwards found to be erroneous, and all the labour
would be lost.
What we really know of the earth in this way may be stated as follows:--
Of the exterior or surface we know that it is of a spherical form,
surrounded by an atmosphere of probably 200 miles or even more, in
height, consisting of common air mixed with vapour of water in more or
less degree; that, of its surface, nearly three-fourths are covered
by water, and the remaining fourth consists of dry land, intersected
in all directions by rivers; that on the dry land there are elevated
tablelands and ranges of mountains from two to three miles high, with
occasional ridges and peaks rising up to altitudes of from five to
near six miles, and that in the part covered by water or sea, there
are depressions or furrows with depths in them probably exceeding
the heights of the highest mountains; that the sea does not remain
constantly at the same level but rises and falls twice in every
twenty-four hours, or thereby, in obedience to the attraction of the
moon and sun, forming what are called tides; and that its polar regions
are enveloped in dense masses of snow and ice, which the persevering
energy of man has not been able to penetrate in centuries of continued
and determined effort.
What we know of the interior of the earth is found in great measure
from the exterior, that is, from the construction of the rocks as seen
in deep ravines, in precipices, and on the sides of hills or mountains;
and also from what we have been able to learn from the exploration of
mines and from deep wells, the deepest of which have penetrated it
very little beyond one mile in depth; all of which knowledge may be
summarised as follows: That the substances which compose the earth
are manifold and of manifold nature--or, more appropriately speaking,
simply the elements of chemistry--varying in density, or specific
gravity, from the same as that of water, or in some cases much less,
to three or four times as much in some kinds of rock and earths
(disintegrated rock), to more than twenty times in the heaviest metals;
that from a depth great enough not to be affected by the changes of
seasons, the heat of the earth increases in descending towards the
centre, by one degree of Fahrenheit's thermometer for every fifty to
sixty feet in depth--that is about thirty metres for each degree of the
Centigrade scale--as far down as we have been able to penetrate; that
at the greatest of these depths abundant supplies of water are found,
which shows that it must exist at much greater depths than any that
have yet been reached; and that at unknown depths, as shown by the
eruptions of volcanoes, there are masses of matter in a molten liquid
state, or that, owing to their great heat, can be suddenly liquefied by
diminution of pressure.
Over and above what has been stated, little can be learnt from geology,
because the earth must have been formed and fashioned almost to its
present condition before geology could begin to exist, and all its
teachings are confined to a very few miles from its surface. Its first
lesson could only begin when the earth was so far cooled down that a
crust could be formed on its surface, and that crust could be deluged
by copious falls of rain on it. Some help or guidance may be obtained
however, from the ideas which astronomers and physicists have formed
on its interior, and it may be useful to have the principal of these
ideas specified, as they may help to strengthen arguments that may be
advanced, or conclusions that may be drawn.
When it was discovered that the temperature of the earth increases,
as we go downwards, at what may be considered a rapid rate, it was
calculated that at a depth of from twenty-five to thirty miles, the
heat would be great enough to melt any substances that have been found
near the surface; and it was immediately concluded that from that depth
to the centre the whole of the interior was a molten liquid mass, whose
temperature far exceeded any heat that could be produced upon the
surface. Even up to the present day, the belief in a liquid interior
has not disappeared.
Many years afterwards, the supposed liquid state of the interior of
the earth was taken advantage of, to frame a theory that earthquakes
and eruptions of volcanoes are caused by the attraction of the moon
on the liquid interior producing tides, in the same manner as it
produces tides in the sea, which in their turn act upon the crust,
cracking and rending it to produce the one, and forcing the liquid
matter out through the rents, or up through the vents of volcanoes to
produce the other, in some way that it is more easy to imagine than
to explain mechanically. Also when the effect of the attraction of
the moon on the liquid internal matter came to be duly considered, it
was concluded that the crust, with only 25 to 30 miles in thickness,
could not be rigid enough to resist the pressure brought upon it by
the movements of the interior tides; and it began to be thought that,
owing to the pressure of the superincumbent strata, the density of
the matter at that depth might be so great that it would become solid
at a much higher temperature than it does at the surface; and some
physicists went the length of supposing that the earth has a solid
crust and solid nucleus with liquid matter between them. On the other
hand Sir William Thomson, Lord Kelvin, looking more as it would appear
to the effects of the moon's attraction on the crust than on the liquid
interior, concluded that the earth must be a solid globe, contracting
through gravitation in the interior, and cooling at the surface,
because a crust so thin as 25 to 30 miles, or even 100 miles, would be
continually rent and broken up by the tidal action of the moon; but
Professor Clerk Maxwell and others have thought that the elasticity of
the crust would be great enough to admit of its accommodating itself
to all the changes of form that would be caused by the action of those
tides. Notwithstanding that they agree with Lord Kelvin in the main, in
his objections to the existence of a liquid interior, many scientific
men suppose that, through the effects of pressure, the liquid interior
of the earth may have been changed into a viscous state, as it went on
contracting through gravitation, which would, according to the degree
of viscosity, either annul, or almost annul, the tidal action on it of
the moon. To which it may be added that that action would not raise
such high waves in even perfectly liquid molten matter as it would upon
water; because it would be easier for the moon to lift a cubic mile of
water three or four feet high, than to lift a cubic mile of melted rock
or metal to the same height.
Other parties look upon the earth as mainly solid to the centre, but
with large reservoirs of liquid matter in various parts of it near the
surface, which furnish all the material for volcanic eruptions and
are the causes of earthquakes. There are others also who, believing
the earth to be altogether solid, consider that when any part of the
intensely heated and dense interior is relieved suddenly from pressure,
as, for example, by the convulsive action of an earthquake, it will
immediately assume the liquid state and become material for volcanic
eruptions; a theory which they consider to be substantiated by the
fact of these two phenomena generally accompanying each other. And Mr.
Mallet seems to have demonstrated that earthquake-shocks proceed from
centres not far from the surface, which would seem to point out that
if a liquid interior did exist at 25 to 30 miles from the surface,
it could have no part in causing earthquakes. There are others still
who consider earthquakes and volcanic eruptions to be caused by water
penetrating deeply into the interior, but it is difficult to understand
how water could penetrate into the interior to a greater depth than
where it would be converted into steam, that is to a greater depth than
from three to four miles.
Many other notions about the interior state and conditions of the earth
have been formed, more or less entertainable, more or less fanciful, to
provide liquid matter for volcanic eruptions. One of these, referred
to in "Nature" of December 12, 1889, takes for granted "that granite
has consolidated from a state of igneo-aqueous fusion, and that the
liquid magma from which all granitic intrusions have proceeded contains
water-substance," and proceeds, "It is, therefore, only a further step
to assume that this water-substance is an essential constituent of
the liquid substratum (assumed by the author), and to suppose that it
has been there since the consolidation of the earth." This mixture of
water, fire, and molten granite is one that does not agree with what
we have been taught of the nature of any of the three components, and
we cannot accept it. Why we refer to it more particularly than to the
other ideas we have cited, is because it so far comprehends some of
them, and that we shall have to return to it hereafter, when we think
it will be seen that it has not been properly thought out.
Bearing in mind all these ideas we have cited, and working with the
data we have considered as actual facts, we may now proceed with our
inquiry.
The belief that the earth is a mass of matter increasing, whether
liquid or solid, or part of both, in density from the surface to the
centre is so general that we shall look at it in that light first, and
endeavour to find out what must be its density at any place between its
surface and its centre.
Astronomers and geologists concur in telling us that the mean density
of the earth is very near to 5·66 times that of water: knowledge that
has been acquired by measuring the attraction of high and precipitous
mountains for plummets; by the attraction of masses of metals for each
other, measured by the torsion balance; and by the acceleration or
retardation of the vibrations of pendulums, as observed in the depths
of mines and on the tops of mountains, compared with each other. They
also tell us that the average density of the matter and rocks of which
the crust is composed is about 2-1/2 times that of water; and then,
in a general way, that the average density of the crust, taking into
consideration that so much of its surface is covered by the sea, is not
much more than 1-1/2 times that of water. This estimate is manifestly
incorrect, for it implies that the whole of the crust of twenty-five to
thirty miles is affected by the presence of water, when we know that
the depth of the sea at any place does not exceed one-fourth of that
thickness. Therefore, we shall endeavour to obtain some more accurate
computation, as it is the only datum we have to go upon, and has a
greater effect upon the result, and upon all things relating to the
interior, than might at first sight be supposed.
We find in "Nature," of January 19, 1888, that Mr. John Murray has
calculated that if the whole solid land of the earth were reduced to
one level under the sea, its surface would be covered by an ocean with
a uniform depth of about 2 miles. Here we have a very good beginning
for our calculations.
Without taking into consideration the increase of density in water
at 2 miles deep, at that depth we may suppose we have come to solid
matter, the specific gravity of which could not be less than twice that
of water, on account of the pressure of that depth of water upon it.
If we now go down 2-1/2 miles further we shall have the solid matter
subjected to a pressure proportioned to that depth; and if we take
its weight per cubic foot at an average between granite (at 163 lb.)
and earth (at 77 lb.), or 120 lb., the pressure at 2-1/2 miles deep
of solid matter alone will be about 700 tons per square foot, or just
about the crushing strain of our strongest granites, and therefore, the
density of the matter under it must be equal to that of granite, or
2·5 times that of water. We do not add the pressure of the water, at
present, because that may be looked upon by some people as of the same
nature as of the atmosphere upon a human body, which neither increases
the pressure upon it nor adds to its weight; but we see that at that
depth the solid matter must have a density equal to the average between
water on its surface and 2·5--that of granite; and if we choose to take
the average between 2 miles of water and 2-1/2 miles of solid matter,
we shall have 1·82 as the average density of the outer 4-1/2 miles in
thickness of the crust of the earth. For our purposes, however, and for
obvious reasons, we shall consider the average density of the 2-1/2
miles alone of solid matter to be 2·25 times that of water.
We shall now go down to 9 miles deep, because the diameter of 7918
miles we have adopted for the earth will there be reduced to 7900
miles, which will be convenient for our further operations. At that
depth we shall have a superincumbent pressure at the very least as
follows:--
Tons.
At 2 miles deep, 2 miles of sea at 150 tons per mile 300
2-1/2 " 2-1/2 " solid matter at spec. grav. 2·25
equal to 331·25 tons per mile 828
9 " 4-1/2 " of rock at 163 lb. per cubic foot 1730
----
Total pressure per square foot 2858
or just about 4 times the crushing strain of our best granites. Then,
as when crushing takes place compression begins, it will, we believe,
be far below the mark to estimate the general specific gravity of the
earth at 9 miles deep to be 3 times that of water.
We have now added the pressure of the 2 miles of water, because
there could be no water at the depth of 9 miles; for the critical
temperature of water is known to be 412°, beyond which temperature
water cannot be maintained in its liquid state by any amount of
pressure, however great; and 9 miles would give 483° temperature at 1°
for each 30 metres. At that depth there might be steam, although it is
difficult to see how it could penetrate so far, because the only force
to help it to penetrate would be gravitation, and that would have to
act against the increasing repulsion of heat.
There is another circumstance to be considered which would tend to
increase the density of the outer portion of the crust, if there be a
crust, and if not, of the outer portion of the earth itself.
When the earth was in the molten liquid state, it is generally supposed
to have been surrounded by vapours of a great proportion of the metals
and of some of the metalloids, in addition to the vapour of water, air,
and other gases, which floated above them higher up in the atmosphere.
In that case when the crust began to be formed through cooling, these
vapours would be precipitated on the surface and mixed with the
half-liquid half-solid matter there, but the proportion of condensed
vapours would be very small compared with what they fell upon, and the
specific gravity of the mixture would not be great enough to cause it
to sink much below the surface, because it would soon meet with matter
as dense as itself; consequently we must consider that all these metals
would remain near the surface--most likely much nearer to it than the
9 miles which we have as yet descended to--and whatever may have been
the proportion of their density it ought to be added to the weights and
pressures that have been taken into account above. We believe that it
will be shown later on that this estimate of a density of three times
that of water at 9 miles deep in the earth is very much lower than it
should be; because, when the pressure upon the matter there came to be
greater than its crushing strain, compression would go on more rapidly
than shortly afterwards, and it might so be that with a strain of
very much less than four times that of crushing, compression would be
reduced to its utmost limit. But more of this hereafter.
Having determined densities for the matter composing the earth at
2, 4-1/2, and 9 miles below the surface, that is, to where the mean
diameter comes to be 7900 miles, if we divide that diameter into
layers of 25 miles each in thickness, compute the volume of each layer
or shell, increase the density of each layer as we descend in direct
proportion from 3--the density we have fixed for 9 miles deep--to
13·734 times the density of water, at the centre, and multiply the
volume of each layer from the surface downwards by its respective
average density, we shall find a mass nearly equal to the mass of the
earth at the density of water--always taking its mean diameter at
7918 miles, and mean density at 5·66 times that of water, as already
premised. These calculations have been carefully carried out, and are
represented in detail in Table IV. for future reference. They terminate
in a deficiency of over 70,000,000 of cubic miles, a deficiency which
would be more than made up by making the central density 13·736 instead
of 13·734. Thus we see that if the density of the earth increases
regularly from the surface to the centre, and if the densities we have
given to the layers between the surface and 9 miles in depth are not
greater than those adopted, the central density must be exceedingly
near 13-3/4 times that of water. Of course, if the three surface
densities are in reality _less_ than those we have adopted, the central
density must be greater than 13-3/4 times that of water. The whole
being a result to our calculations which leads us to speculate on what
kind of matter there is at the centre of the earth.
We are acquainted with various kinds of rocks, stones and other solid
matter that have densities (specific gravities) of 2-1/2 to 3 times
that of water, and we have to conceive that a cubic foot of one of
these would have to be compressed into a height of 2-3/4 or 2-1/4
inches in order to have the density of 13-3/4 required at the centre,
a result which presents us with a substance which it is difficult
to imagine or to believe to exist. It may be that the centre of the
earth is occupied by the heaviest metals we know, arranged in layers
proportioned in thickness to the masses required of them, and that
they are laid one over the other according to their densities, or
mixed together until a distance from the centre is attained, at which
ordinary rocks compressed as highly as their nature would admit of, may
exist; but we do not derive much knowledge or satisfaction from such
a supposition. An examination of our table of calculations will show
that 500 miles in diameter of the central part might be filled up with
platinum, the few other rarer and heavier metals, and gold amalgamated
with mercury in due proportions. Then there might be a mixture of
mercury and lead to 1800 miles in diameter, followed by a mixture of
lead and silver to 2400 miles. After that might come a compound of
silver, copper, tin, and zinc to 4900 miles, and some compounds of
iron might finish the filling process up to 6000 miles in diameter,
or thereby; where the known rocks, compressed to half their volume at
first, but gradually allowed to expand, might complete the whole mass
of the earth. It will be seen, also, that by the time compressed rocks
could be used for this filling process, more than 43 per cent. of the
whole volume of the earth would be occupied exclusively by pure metals
mixed by rule and measure.
It would appear then that the "sorting-out theory"--about which a
good deal has been written--whereby, in suns and planets, the metals
on account of being heavier fall more rapidly to the centre, and the
lighter metalloids remain near the surface--a theory probably got up
to get over the difficulty we are in--is not a very happy one, as too
much metal would be required for the process, at least for the earth.
No doubt it might be applied differently to what we have done by mixing
metals with rocks, stones, earth, etc., forming metallic ores--very
rich they would doubtless have to be--from the centre outwards; but
however disposed it would seem that very much the same quantity would
be required to furnish the desired densities up to 6000 miles in
diameter, where we have supposed compressed granites, etc., might come
into play. Besides, such an arrangement would do away with the whole
beauty of the theory; there would be no law to invoke; it would be all
pick-and-shovel work.
The sorting-out theory is one of these notions that occur to
humanity and are accepted at once, without consideration of what the
consequences may be. If it is made to account for the four inferior
planets being so much more dense, and of coming so much sooner to
maturity--so to speak--than the four superior ones, it is hard to
understand why the sun up to the present day almost ranks in low
density with the large planets. If that theory holds good, it would be
most natural to suppose that the mean density of the sun should be very
much greater than that of Mercury. But it appears to be only carried
as far as it suits the theorist, and to be there dropped, or rather
ignored.
Having been defeated in our attempt to build up or construct an earth
solid to the centre by appealing to the metals to make up the weight or
density required for the foundation layers, and that even to somewhere
about three-fourths of the diameter of the whole structure, we are
forced to fall back upon our known rocks, earths, etc., in order to
compound out of them the dense material we require, and of course we
feel that we have in hand a more hopeless task than we had with the
metals. How are we to compress the everlasting hills into one-fourth or
one-fifth of their volume? Some solution of the difficulty, or mystery,
must be found somewhere; but at the same time the mountains of gold,
silver, and less precious metals required have shown us how absurd,
even laughable, it is to appeal to them.
Let us suppose that we have a cubic foot of matter of any kind of
13-3/4 times the density of water, and that we place it in one of
the scales of a balance at the centre of the earth; we shall find
that it does not depress the scale one hair-breadth, for the very
good reason that it has nowhere to depress it to; it would be already
at what may be called the end of gravitation or tendency to fall
lower. As it could not get any lower it would have a tendency to fly
off anywhere--provided it was free to do so--and drag the scale and
balance along with it, in obedience to its own attractive power and
the attraction of all the matter of the earth surrounding it, except
that the attraction might be so equally distributed all around it that
it would not move in any direction. It would, however, be in a state
of very unstable equilibrium, and if by some means the attraction
were increased a little on one side more than the others, and it were
at liberty to do so, it would abandon the centre and fly off in that
direction never to return. Now, this being the case, we are forced to
consider how a cubic foot of matter, such as the one we are dealing
with, could ever have found its way to the centre of the earth; and
the law of gravitation, or rather of attraction, does not in any way
help us out of the difficulty. We know that we put our cubic foot of
extremely dense matter there for an experiment, but we do not know of
any process of nature that could place there any equal mass of matter
of that density.
Gravitation and attraction are generally used as synonymous terms,
more especially gravitation--somewhat after the manner of the likeness
between the two negroes, Cæsar and Pompey, the latter being most
especial in the likeness--but there is a very appreciable distinction
between them, if we want to use each of them in its proper and strict
sense. Gravitation implies the conception of a weight of some kind
falling to a fixed centre, while attraction gives the idea of two
weights, or masses, drawing each other to a common centre, which when
properly looked at is a different thing; because the centre may be
anywhere between the two, depending entirely on the difference, if
any, in the weights of the masses. The confounding of the two, or
rather the almost universal adoption of the less correct term, name,
expression--whichever it may be called--has been the cause of wrong
conceptions being formed of the construction of almost all--probably
all--celestial bodies, and of that most absurd expression, _attraction
of gravitation_, used by all our most eminent physicists. The
_gravitation_ of _attraction_ might be excused, but putting cause for
effect is hardly scientific. A name is nothing as long as what is meant
by it is understood and taken into consideration, but that is not
always the case, as we shall proceed to show.
The term gravitation may be applied with almost, but not absolutely,
perfect strictness to the attraction between the sun and the planets,
because the common centres of their attractions and the centre of the
sun are so near each other that they may be looked upon as one and
the same thing, or point; but it is not so with the attractions of the
planets for each other where there is no common fixed centre, or if
there is something approaching to it in a far off way, it is constantly
varying, so that the term gravitation cannot be strictly applied to
them, nor even to the sun, to speak truly. Planets sometimes _gravitate
away_ from each other and from the sun, otherwise Adams and Leverrier
could not have discovered Neptune from the perturbations of Uranus.
Neither can it be properly applied to the different masses of matter
in the sun or in the earth--although it was no doubt notions connected
with the earth that gave rise to the term, from all ponderable matter
falling upon it--because _per se_ they could have no tendency to fall
to the centre, for _at the centre_ there is no sufficient attractive
force to draw them towards it. Gravitation was a known term long
before the days of Newton, who had the glory of enlightening the
world by showing that attraction was the cause of it; and, perhaps
unfortunately, the name was continued to represent what it in reality
does not.
Let us suppose that we have an empty earth to fill up; if we place one
mass of matter at London and another at Calcutta, they could have no
tendency of themselves to fall to the centre, but if left alone would
go for each other in a straight line and meet half-way between the two,
provided they were equal in mass, and attraction, not gravitation,
would be the proper term to apply to them. But supposing that two
equal masses were placed at their antipodes and the four were left to
themselves, they would gravitate towards and meet at the centre in the
usual meaning of the word, but the force that drew them there would
be really that of attraction. We could, however, place four similar
and equal masses at the centre, and give the outer ones just and good
reason for gravitating or falling down to it, because those at the
centre being equally attracted in the four directions might remain
stationary there, but would be in a state of unstable equilibrium. We
may now suppose that when the masses had just left London and Calcutta
to meet the others, a goodly number of other equal masses were added to
those at these two places and began to attract the two bound towards
the centre, they would prevent the two from proceeding, or at least
retard them on their journey inwards. Moreover, the larger numbers at
these two places would attract the four masses at the centre with more
force than would the two at the antipodes, and would draw the whole of
the four away from the centre and outwards towards themselves; but we
might also suppose that at the same moment an equal number of equal
masses were added to those at the antipodes, which would again equalize
the attractions at the four outer posts, and things would continue as
they were at the first; with this difference, that the four at the
centre would not be able to balance the attractions at the four outer
posts, and the consequence would be--seeing that the forces at the four
outer stations were equal to each other, and far superior to the four
at the centre--that each one of the four at the centre would be drawn
away from it towards one of the outer stations--provided the law of
attraction acted impartially--and so the centre would be left without
any of the masses at it, that is empty. No doubt when the four outgoing
masses met the larger ones coming in, they would all then move towards
the centre; but the four places where they met would be immensely
nearer the places occupied at first by the outer masses than half-way
between them and the centre--proportioned, in exact conformance with
the law of attraction, to the excess of the numbers of the masses at
the outer stations over those at the centre--and they would be moving,
all of them together, to a remote and void space. We may now increase
the four outer stations to thousands or millions, with the security
that the mode of proceeding would be the same with the whole of them;
that is, that the first tendency of the masses at each one of the
millions of stations would be to draw away the filling we were pouring
into the hollow earth--provided we did it equally and impartially all
over the hollow--from the centre, and to leave a void there.
We are accustomed to look upon the earth as a solid body in which
there are no acting and counteracting forces, no movements of matter
from one place to another, similar to those we have been calling into
play, and as if there was only one force acting upon its whole mass
and driving it to the centre; we have, in our ideas, got the whole
mass so compressed and wedged in that it cannot move, and never has
been able to move in any direction except towards the centre, and
this is no doubt the case at the present day. We never stop to think
with sufficient care how this compression and wedging-in were brought
about, and we only accept what we have been accustomed to believe to
be facts, and trouble ourselves no more about it; but there must have
been a time, according to any cosmogony we may choose to adopt--even to
the vague one that the solar system was somehow made out of a nebula
of some kind--when the matter of the earth was neither compressed nor
wedged in, nor prevented from moving in any direction towards which it
was most powerfully attracted--before superincumbent matter came, so to
speak, to have any wedging-in force--and we must go back to that period
and study it deeply, if we want to acquire an accurate knowledge of the
construction of the earth.
TABLE IV.--CALCULATIONS OF THE VOLUMES AND DENSITIES
OF THE EARTH BETWEEN THE DIAMETER SPECIFIED,
REDUCED TO THE DENSITY OF WATER.
-----+------+---------------+-------+-----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+-------------+
| | | | |{Total volume|
7918| |259,923,849,377| 5·6600|1,471,168,987,476|{of the earth|
| |---------------+-------+-----------------|{at density |
| | | | |{ of water. |
| | | | | |
| | | | |{Density at |
| | | | |{7914 miles |
7914|2·0000| 393,724,522| 1·0000| 393,724,522|{in diameter.|
| | | | |{The 2 miles |
7909|2·5000| 491,596,266| 2·2500| 1,106,090,598|{above being |
| | | | |{at density |
| | | | |{of water. |
7900|3·0000| 883,309,189| 2·7500| 2,429,097,520| |
| |---------------+-------+-----------------|{Volume to |
| | 1,768,628,977| | 3,928,912,640|{9 miles deep|
| | | | |{at density |
| | | | |{of water. |
7850|3·0679| 4,870,723,550| 3·0339| 14,777,288,178| |
| | | | | |
7800|3·1359| 4,809,069,650| 3·1019| 14,917,253,147| |
| | | | | |
7750|3·2038| 4,747,808,450| 3·1698| 15,049,403,225| |
| | | | | |
7700|3·2717| 4,686,939,950| 3·2377| 15,174,905,476| |
| | | | | |
7650|3·3397| 4,626,464,150| 3·3057| 15,293,702,541| |
| | | | | |
7600|3·4076| 4,566,381,050| 3·3737| 15,405,599,748| |
| | | | | |
7550|3·4756| 4,506,690,650| 3·4416| 15,510,226,541| |
| | | | | |
7500|3·5435| 4,447,392,950| 3·5095| 15,608,125,558| |
| | | | | |
7450|3·6114| 4,388,487,950| 3·5775| 15,699,815,651| |
| | | | | |
7400|3·6794| 4,329,975,650| 3·6454| 15,784,493,235| |
| | | | | |
7350|3·7473| 4,271,856,050| 3·7132| 15,862,255,885| |
| | | | | |
7300|3·8152| 4,214,129,150| 3·7812| 15,934,465,142| |
| | | | | |
7250|3·8832| 4,156,794,950| 3·8492| 16,000,335,122| |
| | | | | |
7200|3·9511| 4,099,853,450| 3·9172| 16,059,945,934| |
| | | | | |
7150|4·0191| 4,043,304,650| 3·9851| 16,112,973,361| |
| | | | | |
7100|4·0870| 3,987,148,550| 4·0531| 16,160,311,788| |
| | | | | |
7050|4·1549| 3,931,385,150| 4·1210| 16,201,238,203| |
| | | | | |
7000|4·2229| 3,876,014,450| 4·1889| 16,236,236,930| |
| |---------------| |-----------------| |
| | 80,329,049,377| | 285,717,488,335| |
-----+------+---------------+-------+-----------------+-------------+
-----+------+---------------+-------+----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+------+---------------+-------+----------------+-------------+
| | | | | |
7000|4·2229| 80,329,049,377| 4·1889| 285,717,488,335| |
| | | | | |
6950|4·2908| 3,821,036,450| 4·2568| 16,265,387,960| |
| | | | | |
6900|4·3587| 3,766,451,150| 4·3248| 16,289,147,934| |
| | | | | |
6850|4·4267| 3,712,258,550| 4·3927| 16,306,838,133| |
| | | | | |
6800|4·4946| 3,658,458,650| 4·4606| 16,318,920,654| |
| | | | | |
6750|4·5625| 3,605,051,450| 4·5285| 16,325,475,491| |
| | | | | |
6700|4·6305| 3,552,036,950| 4·5965| 16,326,937,841| |
| | | | | |
6650|4·6984| 3,499,415,150| 4·6645| 16,323,022,067| |
| | | | | |
6600|4·7664| 3,447,186,050| 4·7324| 16,313,463,263| |
| | | | | |
6550|4·8343| 3,395,349,650| 4·8004| 16,299,036,460| |
| | | | | |
6500|4·9022| 3,343,905,950| 4·8682| 16,278,802,946| |
| | | | | |
6450|4·9702| 3,292,854,950| 4·9362| 16,254,190,604| |
| | | | | |
6400|5·0381| 3,242,196,650| 5·0042| 16,224,600,476| |
| | | | | |
6350|5·1060| 3,191,931,050| 5·0721| 16,189,793,479| |
| | | | | |
6300|5·1740| 3,142,058,150| 5·1400| 16,150,178,891| |
| | | | | |
6284|5·2140| 962,684,511| 5·2080| 5,013,660,933| |
| |---------------| |----------------| |
Half volume}| | | |{0·352507 of |
of earth }|129,961,924,688| | 518,596,945,467|{whole volume|
| | | | |{of the earth|
| | | | |{at density |
| | | | |{of water. |
6250|5·2420| 2,129,893,439| 5·2080| 11,092,485,030| |
| | | | | |
6200|5·3098| 3,043,490,450| 5·2759| 16,057,151,265| |
| | | | | |
6150|5·3778| 2,994,795,650| 5·3438| 16,003,588,994| |
| | | | | |
6100|5·4457| 2,946,493,550| 5·4118| 15,954,833,794| |
| | | | | |
6050|5·5137| 2,898,584,150| 5·4797| 15,883,371,567| |
| | | | | |
6000|5·5816| 2,851,067,450| 5·5477| 15,816,866,892| |
| |---------------| |----------------| |
| |146,826,249,377| | 609,405,243,009| |
-----+------+---------------+-------+----------------+-------------+
-----+------+---------------+-------+----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+------+---------------+-------+----------------+-------------+
| | | | | |
6000|5·5816|146,826,249,377| 5·5477| 609,405,243,009| |
| | | | | |
5950|5·6495| 2,803,943,450| 5·6156| 15,745,824,838| |
| | | | | |
5900|5·7175| 2,757,212,150| 5·6835| 15,670,605,255| |
| | | | | |
5850|5·7850| 2,710,873,550| 5·7515| 15,591,589,223| |
| | | | | |
5800|5·8533| 2,664,927,650| 5·8194| 15,508,275,967| |
| | | | | |
5750|5·9213| 2,619,374,450| 5·8873| 15,421,043,199| |
| | | | | |
5700|5·9892| 2,574,213,950| 5·9553| 15,330,206,336| |
| | | | | |
5650|6·0572| 2,529,446,150| 6·0232| 15,235,360,051| |
| | | | | |
5600|6·1251| 2,485,071,050| 6·0912| 15,137,064,780| |
| | | | | |
5591-1/2 | 412,281,190| 6·1591| 2,539,281,080| |
| |---------------| |----------------| |
0·647819 } | | | |{Half mass of|
of whole } |168,383,592,967| | 735,584,493,738|{whole earth |
volume of} | | | |{at density |
the earth} | | | |{of water |
| | | | | |
5550|6·1930| 2,028,807,460| 6·1591| 12,495,628,024| |
| | | | | |
5500|6·2610| 2,397,498,950| 6·2270| 14,929,225,962| |
| | | | | |
5450|6·3289| 2,354,301,950| 6·2950| 14,820,330,775| |
| | | | | |
5400|6·3968| 2,311,497,650| 6·3628| 14,707,597,247| |
| | | | | |
5350|6·4648| 2,269,086,050| 6·4308| 14,592,038,570| |
| | | | | |
5300|6·5327| 2,227,067,150| 6·4988| 14,473,263,994| |
| | | | | |
5250|6·6006| 2,185,440,950| 6·5667| 14,351,135,086| |
| | | | | |
5200|6·6686| 2,144,207,450| 6·6346| 14,225,958,748| |
| | | | | |
5150|6·7365| 2,103,366,650| 6·7026| 14,098,025,308| |
| | | | | |
5100|6·8045| 2,062,918,550| 6·7705| 13,966,990,043| |
| | | | | |
5050|6·8724| 2,022,863,150| 6·8385| 13,833,349,651| |
| | | | | |
5000|6·9403| 1,983,200,450| 6·9064| 13,696,775,588| |
| |---------------| |----------------| |
| |194,473,849,377| | 905,774,812,734| |
-----+------+---------------+-------+----------------+-------------+
-----+------+---------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+------------+
| | | | | About |
5000|6·9403|194,473,849,377| 6·9064| 905,774,812,734| density |
| | | | | of iron |
4950|7·0083| 1,943,930,450| 6·9743| 13,557,554,137| |
| | | | | |
4900|7·0762| 1,905,053,150| 7·0423| 13,418,813,378| |
| | | | | |
4850|7·1441| 1,866,568,550| 7·1102| 13,271,675,704| |
| | | | | |
4800|7·2121| 1,828,476,650| 7·1781| 13,124,988,241| |
| | | | | |
4750|7·2800| 1,790,777,450| 7·2461| 12,976,152,480| |
| | | | | |
4700|7·3479| 1,753,470,950| 7·3140| 12,824,887,528| |
| | | | | |
4650|7·4159| 1,716,557,150| 7·3819| 12,671,453,226| |
| | | | | |
4600|7·4838| 1,680,036,050| 7·4499| 12,516,100,569| |
| | | | | |
4550|7·5518| 1,643,907,650| 7·5178| 12,358,568,931| |
| | | | | |
4500|7·6197| 1,608,171,950| 7·5858| 12,199,270,778| |
| | | | | |
4450|7·6876| 1,572,828,950| 7·6537| 12,037,960,935| |
| | | | | |
4400|7·7556| 1,537,878,650| 7·7216| 11,874,883,784| |
| | | | | |
4350|7·8235| 1,503,321,050| 7·7896| 11,710,269,651| |
| | | | | |
4300|7·8914| 1,469,156,150| 7·8575| 11,543,894,449| |
| | | | | |
4250|7·9594| 1,435,383,950| 7·9254| 11,375,991,957| |
| | | | | |
4200|8·0273| 1,402,004,450| 7·9934| 11,206,782,371| |
| | | | | |
4150|8·0953| 1,369,017,650| 8·0613| 11,036,061,982| |
| | | | | |
4100|8·1632| 1,336,423,550| 8·1295| 10,864,454,250| |
| | | | | |
4050|8·2311| 1,304,222,150| 8·1972| 10,690,969,808| |
| | | | | |
4000|8.2991| 1,272,413,450| 8.2651| 10,516,624,406| |
| |---------------| |-----------------| |
| |226,413,449,377| |1,147,552,171,299| |
-----+------+---------------+-------+-----------------+------------+
-----+------+---------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+------------+
| | | | | About |
4000|8·2991|226,413,449,377| 8·2651|1,147,552,171,299| density |
| | | | | of copper |
3950|8·3670| 1,240,997,450| 8·3331| 10,341,355,851| |
| | | | | |
3900|8·4349| 1,209,974,150| 8·4010| 10,164,992,834| |
| | | | | |
3850|8·5029| 1,179,343,550| 8·4689| 9,987,742,590| |
| | | | | |
3800|8·5708| 1,149,105,650| 8·5369| 9,809,800,023| |
| | | | | |
3750|8·6387| 1,119,260,450| 8·6048| 9,631,012,320| |
| | | | | |
3700|8·7067| 1,089,807,950| 8·6727| 9,451,577,408| |
| | | | | |
3650|8·7746| 1,060,748,150| 8·7407| 9,271,681,355| |
| | | | | |
3600|8·8426| 1,032,081,050| 8·8086| 9,091,189,137| |
| | | | | |
3550|8·9105| 1,003,806,650| 8·8766| 8,910,390,109| |
| | | | | |
3500|8·9784| 975,924,950| 8·9445| 8,729,160,715| |
| | | | | |
3450|9·0464| 948,435,950| 9·0124| 8,547,684,156| |
| | | | | |
3400|9·1143| 921,339,650| 9·0804| 8,366,132,559| |
| | | | | |
3350|9·1822| 894,636,050| 9·1483| 8,184,398,976| |
| | | | | |
3300|9·2502| 868,325,150| 9·2162| 8,002,658,247| |
| | | | | |
3250|9·3181| 842,406,950| 9·2842| 7,821,074,605| |
| | | | | |
3200|9·3860| 816,881,450| 9·3522| 7,639,638,697| |
| | | | | |
3150|9·4540| 791,748,650| 9·4200| 7,458,252,283| |
| | | | | |
3100|9·5219| 767,008,550| 9·4880| 7,277,377,122| |
| | | | | |
3050|9·5899| 742,661,150| 9·5554| 7,096,424,353| |
| | | | | |
3000|9·6578| 718,706,450| 9·6239| 6,916,759,004| |
| |---------------| |-----------------| |
| |245,786,649,377| |1,320,251,473,643| |
-----+------+---------------+-------+-----------------+------------+
-----+------+----------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+----------------+-------+-----------------+------------+
| | | | | |
3000| 9·6578|245,786,649,377| 9·6239|1,320,251,473,643| |
| | | | | |
2950| 9·7257| 695,144,450| 9·6918| 6,737,200,981| |
| | | | | |
2900| 9·7937| 671,975,150| 9·7597| 6,558,275,871| |
| | | | | |
2850| 9·8616| 649,198,550| 9·8276| 6,380,063,674| |
| | | | | |
2800| 9·9295| 626,814,650| 9·8956| 6,202,697,051| |
| | | | | |
2750| 9·9975| 604,823,450| 9·9635| 6,026,158,444| |
| | | | | |
2700|10·0654| 583,224,950|10·0315| 5,850,621,086| |
| | | | | |
2650|10·1334| 562,019,150|10·0994| 5,675,940,204| |
| | | | | |
2600|10·2013| 541,206,050|10·1674| 5,502,658,393| |
| | | | | |
2550|10·2692| 520,785,650|10·2353| 5,330,397,363| |
| | | | | |
2500|10·3372| 500,757,950|10·3032| 5,059,409,310| |
| | | | | |
2450|10·4051| 481,122,950|10·3712| 4,989,822,340| |
| | | | |{ About |
2400|10·4730| 461,880,650|10·4391| 4,821,618,293|{ density |
| | | | |{of silver. |
2350|10·5410| 443,031,050|10·5070| 4,654,927,242| |
| | | | | |
2300|10·6089| 424,574,150|10·5750| 4,489,871,636| |
| | | | | |
2250|10·6768| 406,509,950|10·6429| 4,326,444,747| |
| | | | | |
2200|10·7448| 388,838,450|10·7108| 4,164,770,870| |
| | | | | |
2150|10·8127| 371,559,650|10·7798| 4,005,338,715| |
| | | | | |
2100|10·8807| 354,673,550|10·8467| 3,847,037,595| |
| | | | | |
2050|10·9486| 338,180,150|10·9147| 3,691,134,883| |
| | | | | |
2000|11·0165| 322,079,450|10·9826| 3,537,269,768| |
| |---------------| |-----------------| |
| |255,735,049,377| |1,422,103,132,109| |
-----+-------+---------------+-------+-----------------+------------+
-----+-------+---------------+-------+-----------------+------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at |Observations|
in | ties. | in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+-------+---------------+-------+-----------------+------------+
| | | | | |
2000|11·0165|255,735,049,377|10·9826|1,422,103,132,109| |
| | | | | |
1950|11·0845| 306,371,450|11·0505| 3,385,557,708| |
| | | | | |
1900|11·1524| 291,056,150|11·1185| 3,236,107,805| |
| | | | | |
1850|11·2203| 276,133,550|11·1864| 3,088,940,344| |
| | | | | |
1800|11·2883| 261,603,650|11·2543| 2,944,165,858| |
| | | | | |
1750|11·3562| 247,466,450|11·3223| 2,802,888,487|} About |
| | | | |} density |
1700|11·4242| 233,721,950|11·3902| 2,662,139,545|} of lead |
| | | | | |
1650|11·4921| 220,370,150|11·4582| 2,525,045,253| |
| | | | | |
1600|11·5600| 207,411,050|11·5261| 2,390,640,503| |
| | | | | |
1550|11·6280| 194,844,650|11·5940| 2,259,028,872| |
| | | | | |
1500|11·6959| 182,670,950|11·6620| 2,130,308,620| |
| | | | | |
1450|11·7638| 170,889,950|11·7299| 2,004,522,025| |
| | | | | |
1400|11·8318| 159,501,650|11·7978| 1,881,768,566| |
| | | | | |
1350|11·8997| 148,506,050|11·8658| 1,762,143,088| |
| | | | | |
1300|11·9676| 137,903,150|11·9337| 1,645,694,821| |
| | | | | |
1250|12·0356| 127,692,950|12·0016| 1,532,519,609| |
| | | | | |
1200|12·1035| 117,875,450|12·0696| 1,422,709,531| |
| | | | | |
1150|12·1715| 108,450,650|12·1375| 1,316,319,764| |
| | | | | |
1100|12·2394| 99,418,550|12·2055| 1,213,453,112| |
| | | | | |
1050|12·3073| 90,779,150|12·2734| 1,114,168,820| |
| | | | | |
1000|12·3753| 82,532,450|12·3413| 1,018,557,725| |
| |---------------| |-----------------| |
| |259,400,249,377| |1,464,439,812,165| |
-----+-------+---------------+-------+-----------------+------------+
-----+-------+---------------+-------+-----------------+------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at |Observations|
in | ties. | in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+-------+---------------+-------+-----------------+------------+
| | | | | |
1000|12·3753|259,400,249,377|12·3413|1,464,439,812,165| |
| | | | | |
950|12·4432| 74,678,450|12·4093| 927,507,290| |
| | | | | |
900|12·5111| 67,217,150|12·4772| 838,681,824| |
| | | | | |
850|12·5791| 60,148,550|12·5451| 754,569,575| |
| | | | | |
800|12·6470| 53,472,650|12·6132| 674,461,229| |
| | | | | |
750|12·7149| 47,189,450|12·6820| 598,456,605| |
| | | | | |
700|12·7829| 41,298,950|12·7489| 526,516,184| |
| | | | | |
650|12·8508| 35,801,150|12·8169| 458,859,759| |
| | | | | |
600|12·9188| 30,696,050|12·8848| 395,512,465| |
| | | | | |
550|12·9867| 25,983,650|12·9528| 336,561,022| |
| | | | | |
500|13·0546| 21,663,950|13·0207| 282,079,794| |
| | | | | |
450|13·1226| 17,736,950|13·0886| 232,151,644| |
| | | | | |
400|13·1905| 14,202,650|13·1566| 186,858,585| |
| | | | | |
350|13·2584| 11,061,050|13·2245| 146,276,856| |
| | | | | |
300|13·3264| 8,312,150|13·2924| 110,488,423| |
| | | | | |
250|13·3943| 5,955,950|13·3604| 79,573,874| |
| | | | | |
200|13·4623| 3,992,450|13·4283| 53,611,816| |
| | | | | |
150|13·5202| 2,421,650|13·4963| 32,683,315| |
| | | | | |
100|13·5981| 1,243,550|13·5642| 16,867,761| |
| | | | |{ About |
50|13.6661| 458,150|13.6321| 6,245,547|{ density |
| | | | |{of mercury.|
0|13·7340| 65,450|13·7001| 896,672| |
| |---------------| |-----------------| |
| |259,923,849,377| |1,471,098,672,405| |
| | | | | |
|True volume at density of water|1,471,168,987,476| |
| |-----------------|{ About |
| Deficiency | 70,315,071|{1/21,000th |
| | |{ part. |
-----+-------------------------------+-----------------+------------+
CHAPTER IX.
PAGE
165 Inquiry into the Interior Construction
of the Earth--_continued_.
166 The earth gasiform at one period. Density including the moon
may have been 1/10,000th that of air. Must have been a hollow
body. Proofs given.
169 Division of the mass of the earth alone into two parts.
171 Division of the two masses at 817 miles from surface.
172 Reasons why the earth cannot be solid to the centre.
172 Gasiform matter condensing in a cone leaves apex empty.
173 Proportions of the matter in a cone.
174 Calculations of the densities of the outer half of the hollow
shell of the earth. Remarks upon the condensation.
175 Calculations of inner half of the hollow shell.
177 Remarks upon position of inner surface of the shell.
179 Calculations of the same.
THE INTERIOR OF THE EARTH AND ITS DENSITY--_continued._
When, according to the nebular hypothesis, the ring for the formation
of the earth and moon had been thrown off by the nebula, and had
broken up and formed itself into one isolated mass--rotating or not on
an axis, as the case may have been--it must have been in a gasiform
state. What was its density, more or less, may be so far deduced from
Table III., where it will be seen that when it had condensed to about
one-half of its volume, it must have had a density of only 1/9000th
part of our atmosphere, and in which each grain of matter would have
for its habitat 16 cubic feet of space, or a cube of 2·52 feet to the
side. So that, with an average distance from its neighbours of 2-1/2
feet, a grain of matter could not be looked upon as wedged-in in any
way, and would be free to move anywhere. Now, supposing this earth-moon
nebula to have been in the form of even an almost shapeless mass,
and that it was nearly homogeneous--as it could hardly be otherwise
after the tumbling about it had in condensing from a flat ring--its
molecules would attract each other in all directions, and as the
mass--without having arrived perhaps at the stage of having any well
defined centre--would have an exterior as well as an interior, the
individual molecules at the exterior would draw those of the interior
out towards them, just as much as those at the interior would attract
those of the exterior in towards them; but as the number of those
at the exterior would--owing to the much greater space there, being
able to contain an immensely greater number--be almost infinitely
greater than of those nearer to the central part, the latter would
be more effectually attracted, or drawn, outwards than the former
would be inwards, and there would be none left at the interior after
condensation had fairly begun. The mass would speedily become a hollow
body, the hollow part gradually increasing in diameter. But let us go
deeper into the matter.
Let us suppose that the whole mass had assumed nearly the form of a
sphere. We have already shown that, although the general force of
attraction would cause all the component particles of the sphere to
mutually draw each other in towards the centre, yet the more powerful
tendency of the particles at the exterior--due to their greatly
superior number--would at first be to draw the particles near the
centre outwards towards them, and that there would consequently be
a void at the centre, for a time at least. Of course it is to be
understood that each part of the exterior surface would draw out to it
the particles on its own side of the centre, just in the same manner as
the four masses we placed at the centre were shown to be drawn out by
those at London, Calcutta, and their antipodes. Now we must try to find
out what would be the ultimate result of this action; whether it would
be to form a sphere solid to the centre, or whether the void at first
established there would be permanent.
In order to show how the heat of the sun is maintained by the
condensation and contraction of that luminary, Lord Kelvin--in his
lecture delivered at the Royal Institution, on Friday, January 21,
1887--described an ideal churn which he supposed to be placed in a
pit excavated in the body of the sun, with the dimension of one
metre square at the surface, and tapering inwards to nothing at the
centre. In imitation of him, we shall suppose a similar pit of the
same dimensions to be dug in the spherical mass, out of which we
have supposed the earth to have been formed; only we shall call it
a pyramid instead of a pit. This we shall suppose to be filled with
cosmic matter, and try to determine what form it would assume were it
condensed into solid matter, in conformity with the law of attraction.
The apex of our imaginary pyramid would, mathematically speaking, have
no dimension at all, but we shall assume that it had space enough to
contain one molecule of the cosmic matter of which the sphere was
formed. This being so arranged, we have to imagine how many similar
molecules would be contained in one layer at the base of the pyramid
at the surface of the sphere, and we may be sure that when brought
under the influence of attraction, the great multitude of them would
have far more power to draw away the solitary molecule from the apex,
than the single one there would have to draw the whole of those in
the layer at the base in to the centre of the sphere. A molecule of
the size of a cubic millimetre would be an enormously large one,
nevertheless one of that size placed at the apex of the pyramid would
give us one million for the first layer at the base, and shows us what
chance there would be of the solitary one maintaining its place at the
apex. At the distance of one-twentieth of the radius of the sphere
from the centre, the dimension of the base of the pyramid would be
one-twentieth of a square metre, and the proportion of preponderance of
a layer of molecules there would be as 25 to 1, so that the molecule at
the centre would be drawn out almost to touch those of that layer; at
one-tenth of the radius from the centre, the preponderance of a layer
over the solitary central molecule would be as 10,000 to 1; and so on
progressively to 1,000,000 to 1, as we have already said.
Following up this fact, if we divide the pyramid into any number of
frusta, the action of attraction will be the same in each of them;
the molecules in the larger end of each will have more power to draw
outwards those of the small end, than they will have to draw inwards
those of the larger end; and then the condensed frusta will act upon
each other in the same manner as the molecules did, the greater mass of
those at the larger end, or base, drawing down, or out--whichever way
it may seem best to express it--a greater number of the frusta at the
smaller end of the pyramid, until, in the whole of it, a point would
be reached where the number of molecules in the various frusta drawn
down from the apex would be equal to those drawn up from the base,
leaving a part of the pyramid void at each end, because we are dealing
with attraction, not gravitation, and there would be no falling to
the base or apex, but concurrence to the point, just hinted at, where
the outwards and inwards attractions of the masses would balance each
other. This point of meeting of the two equal portions of cosmic matter
may be called the plane of attraction in the pyramid. The whole pyramid
would thus be reduced to the frustum of a pyramid, whose height would
be as much more than double the distance from the plane of attraction
to its base, as would be required to make the upper part above the
plane of attraction equal in volume, or rather in number of molecules,
to the lower part. It would be impossible for us to explain how, in a
pyramid such as the one we have before us, the action of attraction
could condense, and at the same time cram, the whole of the molecules
contained in it into the apex end.
We must not, however, forget that there are two sides to a sphere, as
well as to a question, and that we must place on the opposite side to
the one we are dealing with, another equal pyramid with apex at the
centre and base at the surface, at a place diametrically opposite to
the first one, and that the tendency of the whole of this new pyramid
would be to draw the whole of the first one in towards the centre of
the sphere. But in the second, the law of attraction would have the
same action as in the first; the molecules of the matter contained in
it near the base would far exceed, in attractive force, those near the
apex, and would draw them outwards till the whole were concentrated
in a frustum of a pyramid, exactly the same as the one in the first
pyramid. And while the whole masses of matter in the two pyramids were
attracting each other at an average distance, say, for simplicity's
sake, of one-half the diameter of the sphere, the molecules in each
of them would be attracting each other from an average distance of
one-quarter the diameter of the sphere; their action would consequently
be four times more active, and they would concentrate into the frusta
as we have shown, before the two pyramids had time to draw each other
in to the centre. There would be then two frusta of pyramids attracting
each other _towards_ the centre with an empty space between them. Here
then we have two elements of a hollow sphere, one on each side of the
centre, and if we suppose the whole sphere to have been composed of
the requisite number of similar pyramids, set in pairs diametrically
opposite to each other, we see that the whole mass of the matter out of
which the earth was formed must have--by the mutual attractions of its
molecules--formed itself into a hollow sphere.
All that has been said must apply equally well whether we consider the
earth to have been in a gasiform state, or when by condensation and
consequent increase of temperature it had been brought into a molten
liquid condition. For up to that time it must have been a hollow
sphere, and we must either consider it to be so still, or conceive that
the opposite sides have continued to draw each other inwards till the
hollow was closed up; in which case, the greatest density would not be
at the centre, but at a distance therefrom corresponding to what has
been called the plane of attraction of the pyramid. That the opposite
sides have not yet met will be abundantly demonstrated by facts that
will meet us, if we try to find out what is the greatest density of the
earth at the region of greatest mass or attraction, wherever that may
be.
Seeing that the foregoing reasoning forces us to look upon the earth as
a hollow sphere, or shell, in which the whole of the matter composing
it is divided into two equal parts, attracted outwards and inwards by
each other to a common plane, or region of meeting, we shall divide its
whole volume into two equal parts radially, that is, one comprising a
half from the surface inwards, and the other a half from the centre
outwards--that is to say, each one containing one-half of the whole
volume of the earth. Referring now to our calculations, Table IV., we
find that the actual half volume of the earth is comprised in very
nearly 817 miles from the surface, where the diameter is 6284 miles,
because the total volume at 7918 miles in diameter is 259,923,849,377
cubic miles. This being the case, we cannot avoid coming to the
conclusion, after what has just been demonstrated by the pyramids that
if one-half of the whole volume is comprehended in that distance from
the surface, so also must be one-half of the mass.
But for further substantiation of this conclusion let us return to the
table of calculations. There we find that from the surface to the depth
of 817 miles--where the diameter would be 6284 miles--which comprehends
one-half of the volume--the mass at the density of water is shown to
be only 518,596,945,467 miles instead of 735,584,493,738 cubic miles,
which is the half of the whole mass of the earth reduced to the density
of water. That is, the outer half of the volume gives only 70·5 per
cent. of half the mass, while the inner half of the volume gives not
only one-half of the mass but 29·5 per cent. more; or, to put it more
clearly, the mass of the inner half-volume is 1·84 times, nearly twice
as great, as the mass of the outer half-volume. On the other hand, we
have to notice that the line of division of the mass into two halves
falls at 1163·25 miles from the surface, where the diameter is 5591·5
miles; so that on the outer half of the earth, measured by mass, 64·74
per cent. of the whole volume of the earth contains only one-half of
the mass, whereas on the inner portion, measured in the same way, 35·26
per cent. of the same whole contains the other half. All these results
must be looked upon as unsatisfactory, or we must believe that two
volumes of cosmic matter which at one time were not far from equal, had
been so acted upon by their mutual attractions that the one has come to
be not far from double the mass of the other; that the vastly greater
amount of cosmic matter at the outer part of a nebula has only one-half
of the attractive force of the vastly inferior quantity at the centre.
This we cannot believe if the original cosmic, or nebulous, matter was
homogeneous; and if it was not homogeneous we have, in order to bring
about such result, to conceive that the earth was built up, like any
other mound of matter, under the direction of some superintendent who
pointed out where the heavier and where the lighter matter was to be
placed.
We shall now proceed to find out what would be the internal form, and
greatest density of the earth, under the supposition that it is a
hollow sphere divided into two equal volumes and masses--exterior and
interior--meeting at 817 miles from the surface; but before entering
upon this subject we have something to say about the notion of the
earth being solid to the centre.
We are forced to believe that, according to the theory of a nucleus
being formed at the centre as the first act, the matter collected there
must have remained stationary ever since, because we cannot see what
force there would be to uniform the nucleus just formed; gravitation,
weight falling to a centre, would only tend to increase, condense, and
wedge in the nucleus more thoroughly. Attraction, as we have shown,
would not allow the matter to get to the centre at all. Convection
currents, or currents of any kind, could not be established in matter
that was being wedged in constantly. Moreover, when in a gasiform
state, it would be colder than when condensed by gravitation to, or
nearly to, a liquid or solid state, and heat would be produced in
it in proportion to its condensation, that is, gradually increasing
from the surface to the centre in the same manner as density, which,
when the cooling stage came, would be conducted back to the surface
to be radiated into space, but could not be carried--by convection
currents--because the matter being heavier there than any placed above
it, and being acted upon by gravitation all the time, would have no
force tending to move it upwards; and above all, when solidification
began at the surface, it is absurd to suppose that the first formed
pieces of crust could sink down to the centre through matter more dense
than themselves; unless it was that by solidification they were at
once converted into matter of the specific gravity of 13·734. Even so
the solid matter would not be very long in being made liquid again
by meeting with matter not only hotter than itself, but constantly
increasing in heat through continual condensation, which would act
very effectively in preventing any convection current being formed to
any appreciable depth, certainly never to any depth nearly approaching
to the centre. If solidification began first at the centre--as some
parties have thought might be the case--owing to the enormous pressure
it would be subjected to there, before it began at the surface, then,
without doubt, the central matter must have remained where it was
placed at first, up to the present day. This would suit the sorting-out
theory very well, as all the metals would find their way to the centre
and there remain; but judged under a human point of view, it would be
considered very bad engineering on the part of the Supreme Architect to
bury all the most valuable part of His structure where they could never
be availed of; or that He was not sufficiently fertile in resources
to be able to construct His edifice in a way that did not involve
the sacrifice of all the most precious materials in it. Man uses
granite for foundations--following the good example He has actually
given we believe, and are trying to show--and employs the metals in
superstructures; but some people may also think that it was better to
keep the root of all evil as far out of man's reach as possible. What
a grand prospectus for a Joint Stock Company might be drawn up, on the
basis of a sphere of a couple of thousand miles in diameter of the most
precious metals, could only some inventive genius discover a way to get
at them!
Returning to our pyramids. We know that the centre of gravity of a
pyramid is at one-fourth of its height, or distance from the base,
and if we lay one of 3959 miles long (the radius of the earth) over a
fulcrum, so that 989-3/4 miles of its length be on one side of it and
2969-1/4 miles on the other, it will be in a state of equilibrium. This
does not mean, however, that there are equal masses of matter on each
side of the fulcrum, for we know that the mass of the base part must
be considerably greater than that of the apex part, and that it must
be counterbalanced by the greater leverage of the apex part, due to
its greater distance from the point of support. This being so, in the
case of a pyramid consisting of gasiform, liquid, or solid matter,
the attractive power of the 989-3/4 miles of the base part would be
greater than that of the 2969-1/4 miles of the apex part, and the plane
of equal attraction of the two parts would be less than 990 miles from
the base of the pyramid. This is virtually the same argument we have
used before repeated, but it is placed in a simpler and more practical
light, and shows that the plane of attraction in a pyramid will not be
at its centre of gravity but nearer to its base, and that it must be
at or near its centre of volume. Thus the plane of attraction in one
of the pyramids we have been considering of 3959 miles in length, and
consequently the radial distance of the region of maximum attraction of
the earth, would not be at 990 miles from the base or surface, but at
some lesser distance.
Now, if we take a pyramid, such as those we have been dealing with,
whose base is 1 square and height 3959, its volume would be the square
of the base multiplied by one-third of the height, that is 1^{2} ×
3959/3 = 1319·66, the half of which is 659·83. Again, if we take the
plane of division of the volume of the pyramid into two equal parts
to be 0·7937 in length on each side, and consequently (from equal
triangles) the distance from the plane to the apex to be 0·7937 the
total height of 3959, which is 3142·258; then, as we have divided it
into a frustum and a now smaller pyramid, if we multiply the square
of the base of this new pyramid by one-third of the height we have
0·7937^{2} × 3142·258/3, or 0·62996 × 1047·419 = 659·83, which is
equal to the half-volume of the whole pyramid as shown above. Thus we
get 3959 less 3142·258 = 816·74 miles as the distance from the base
of the plane of division of the pyramid into two equal parts, which
naturally agrees with the division of the earth into the two equal
volumes that we have extracted from the table of calculations, where we
have supposed the earth to be made up of the requisite number of such
pyramids. So that it would seem that we are justified in considering
that the greatest density of the earth must be at the meeting of the
two half-volumes, outer and inner, into which we have divided it.
Considering, then, that one-half of the volume and mass of the earth
is contained within 817 miles in depth from the surface, this half
must have an average density of 5·66 times that of water, the same as
the whole is estimated to have. Also, as we have seen already, that,
taking its mean diameter at 7918 miles, its mass will be equivalent
to 1,471,168,987,476 cubic miles, one-half of this quantity, or
735,584,493,738 cubic miles will represent the half-volume of the earth
reduced to the density of water. With these data let us find out what
must be the greatest density where the two half-volumes meet, supposing
the densities at the surface and for 9 miles down to remain the same as
in the calculations we have already made, ending with specific gravity
of 3 at 7900 miles in diameter.
Following the same system as before when treating of the earth as
solid to the centre, and using the same table of calculations for the
volumes of the layers: If we adopt a direct proportional increase
between densities 3 at 7900 miles and 8·8 at 6284·5 miles in diameter,
multiply the volumes by their respective densities, and add about 31
per cent. of the following layer, taken at the same density as the
previous or last one of the number, we shall find a mass (see Table
V.) of 735,483,165,215 cubic miles at the density of water, which is
as near the half mass 735,584,493,738 cubic miles as is necessary for
our purpose. It would thus appear that if the earth is a hollow sphere,
its greatest density in any part need not be more than 8·8 times that
of water, instead of 13·734 times, if we consider it to be solid to the
centre.
Let us now try to find out something about the inner half-mass of
the earth, and the first thing we have got to bear in mind is, that
where it comes in contact with it, its density must be the same as
that of the outer half-mass at the same place, and continue to be
so for a considerable distance, varying much the same as the other
varies in receding from that place, and diminishing at the same rate
as it diminishes. This being the case--and we cannot see how it can be
otherwise--if we attempt to distribute the inner half-mass over the
whole of the inner half-volume, and suppose that its density decreases
from its contact with the outer half--where it was found to be 8·8
times that of water--to zero at the centre, in direct proportion to
the distance; then, it is clear that at half the distance between
that place and the centre, the density must be just 4·4 times that of
water. Now, if we divide the outer moiety of the inner half-mass of the
earth--that is, the distance between the diameters of 6284·5 miles and
3142·25 miles--into layers of 25 miles thick each, take their volumes
from Table IV., and multiply each of them by a corresponding density,
decreasing from 8·8 to 4·4, we shall obtain a mass far in excess of
the whole mass corresponding to the inner half of the earth. This
shows that a region of no density would not be at the centre but would
begin at a distance very considerably removed from it. It is another
notice to us that the earth must be a hollow sphere. But why should
there be a zero point or place of no density? And what would a zero of
no density be? It would represent something less than the density of
the nebulous matter out of which the earth was formed; and all that
we have contended for, as yet, is that there is a space at the centre
where there is no greater density than that corresponding to the earth
nebula; but we must now go farther.
If the earth is a hollow sphere, it must have an internal as well as
an external surface. But how are we to find out what is the distance
between these two surfaces? Let us, to begin, take a look at the hollow
part of the sphere. From the time of Arago it began to be supposed that
there is a continual deposit of cosmic matter upon the earth going on,
and since then it has been proved that there is a constant and enormous
shower of meteors and meteorites falling upon it. But although this is
the case on the exterior surface, it may be safely asserted that on
the interior surface, where the supply of cosmic matter must have been
limited from the beginning, there can be no continual deposit of such
matter going on now; nor can there have been from, at least, the time
when the earth changed from the form of vapour to a liquid state. We
may, therefore, be sure that there is no undeposited _cosmic_ matter
of any kind in the hollow of the sphere, and that, as far as it is
concerned, there is an absolute vacuum.
TABLE V.--CALCULATIONS OF THE VOLUMES AND DENSITIES OF
THE OUTER HALF OF THE EARTH--TAKEN AS A HOLLOW
SPHERE--AT THE DIAMETERS SPECIFIED, AND REDUCED
TO THE DENSITY OF WATER.
With mean diameter of 7918 miles. Diameter of half-volume at
6284·5 miles, and density there of 8·8 times that of water.
-----+-------+---------------+-------+----------------+--------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at | Observations.|
in | ties. | in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+-------+---------------+-------+----------------+--------------+
| | | | |{ Half-volumes|
| | | | |{ of the earth|
7918 | ... |129,961,924,377| ... | 735,584,493,738|{ actual and |
| |---------------| |----------------|{ at density |
| | | | |{ of water. |
| | | | | |
| | | | |{ Density at |
| | | | |{ 7914 miles |
| | | | |{ in diameter.|
7914 | 2·0000| 393,724,522 | 1·0000| 393,724,522|{ The 2 miles |
| | | | |{ above being |
| | | | |{ at density |
| | | | |{ of water. |
7905 | 2·5000| 491,596,266 | 2·2500| 1,106,090,598| |
| | | | | |
7900 | 3·0000| 883,309,189 | 2·7500| 2,429,097,520| |
| |---------------| |----------------| |
| | | | |{ Volume to |
| | 1,768,628,977 | | 3,928,912,640|{ 9 miles deep|
| | | | |{ at density |
| | | | |{ of water. |
7850 | 3·1823| 4,870,723,550 | 3·0912| 15,056,380,638| |
| | | | | |
7800 | 3·3625| 4,809,069,650 | 3·2724| 15,737,199,523| |
| | | | | |
7750 | 3·5437| 4,747,808,450 | 3·4531| 16,394,666,359| |
| | | | | |
7700 | 3·7250| 4,686,939,950 | 3·6343| 17,023,745,860| |
| | | | | |
7650 | 3·9062| 4,626,464,150 | 3·8156| 17,652,736,611| |
| | | | | |
7600 | 4·0875| 4,566,381,050 | 3·9969| 18,251,368,419| |
| | | | | |
7550 | 4·2688| 4,506,690,650 | 4·1781| 18,829,404,185| |
| | | | | |
7500 | 4·4500| 4,447,392,950 | 4·3594| 19,387,964,826| |
| | | | | |
7450 | 4·6312| 4,388,487,950 | 4·5486| 19,926,368,386| |
| | | | | |
7400 | 4·8125| 4,329,975,650 | 4·7219| 20,445,712,022| |
| | | | | |
7350 | 4·9938| 4,271,856,050 | 4·9031| 20,945,337,398| |
| | | | | |
7300 | 5·1750| 4,214,129,150 | 5·0844| 21,426,318,250| |
| | | | | |
7250 | 5·3562| 4,156,794,950 | 5·2656| 21,888,019,489| |
| | | | | |
7200 | 5·5375| 4,099,853,450 | 5·4469| 22,331,491,757| |
| | | | | |
7150 | 5·7187| 4,043,304,650 | 5·6281| 22,756,152,901| |
| | | | | |
7100 | 5·9000| 3,987,148,550 | 5·8093| 23,162,542,072| |
| | | | | |
7050 | 6·0813| 3,931,385,150 | 5·9907| 23,551,749,018| |
| | | | | |
7000 | 6·2625| 3,876,014,450 | 6·1719| 23,922,373,584| |
| | | | | |
6950 | 6·4438| 3,821,036,450 | 6·3532| 24,275,808,774| |
| | | | | |
6900 | 6·6250| 3,766,451,150 | 6·5344| 24,611,498,395| |
| | | | | |
6850 | 6·8062| 3,712,258,550 | 6·7156| 24,930,043,518| |
| | | | | |
6800 | 6·9875| 3,658,458,650 | 6·8968| 25,231,657,617| |
| | | | | |
6750 | 7·1688| 3,605,051,450 | 7·0782| 25,517,275,173| |
| | | | | |
6700 | 7·3500| 3,552,036,950 | 7·2594| 25,785,657,035| |
| | | | | |
6650 | 7·5312| 3,499,415,150 | 7·4406| 26,037,748,365| |
| | | | | |
6600 | 7·7125| 3,447,186,050 | 7·6218| 26,273,762,636| |
| | | | | |
6550 | 7·8938| 3,395,349,650 | 7·8032| 26,494,592,389| |
| | | | | |
6500 | 8·0750| 3,343,905,950 | 7·9844| 26,699,082,667| |
| | | | | |
6450 | 8·2562| 3,292,854,950 | 8·1656| 26,888,136,380| |
| | | | | |
6400 | 8·4375| 3,242,196,650 | 8·3468| 27,061,966,998| |
| | | | | |
6350 | 8·6188| 3,191,931,050 | 8·5282| 27,221,426,381| |
| | | | | |
6300 | 8·8000| 3,142,058,150 | 8·7094| 27,365,441,252| |
| | | | | |
6284½| 8·8000| 962,684,511 | 8·8000| 8,471,623,697| |
| |---------------| |----------------| |
| |129,961,924,688| | 735,484,165,215| |
| | | | | |
True half-volume at density of water | 735,584,493,738| |
-------------------------------------+----------------+--------------|
Deficiency | 100,328,522| |
-------------------------------------+----------------+--------------+
As to how far the internal surface is from the centre, it may be
possible to designate a position, or region, from which it cannot be
very far distant, although we can never expect to be able to point out
exactly where it is. Going back to the time when the whole earth was
in a molten liquid state, and just before the outer surface began to
become solid, it is certain that the interior surface must have been
in the same liquid condition, whatever may have been the condition of
the mass of matter between the two surfaces, owing to the pressure
of superincumbent matter; nay, we may be sure that whatever may be
its state now, it continued liquid long after the other became solid,
because it had no outlet by which to get rid of its melting heat by
radiation, nor weight of superincumbent matter to consolidate it; and
it would always be much hotter than the outer surface. At that time we
have every reason to believe that the outer surface was at least as
dense as it is now, there being no water upon it to lower its average
density, as is the case at the present day; and we have equal reason
to consider that the density at the inner surface, whether liquid or
solid, is now at least equal to what the outer surface was then. Duly
considering, therefore, the absence of water from the interior surface,
we shall suppose that the first layer of 25 miles thick upon it will
have an average density of 2-1/2 times that of water, terminating at
3 times, which is the density we have taken for the outer surface
at 9 miles deep. But there is another contingency, which it will be
necessary to take into consideration before going any farther.
It has been understood--as it is certainly the truth--in the
calculations made with respect to the outer half of the mass of the
earth, that the increase of density in descending was due to the
pressure of the superincumbent matter, caused by the attraction for it
of the inner half, as well as that of the whole of both the outer and
inner halves on the other side of the hollow interior. In the case of
the inner half we have now to consider that the attraction of the outer
half alone would be the effective agent, and that the superincumbent
pressure--that is, of course, the pressure acting from the centre
outwards--would be interfered with, or perturbed, by the attraction of
the mass on the other side of the hollow interior, so that it would
not exert its full power in that direction. But that does not mean
that the density would be in any way diminished. The attractions of
the planets for each other perturb them in their revolutions around
the sun, accelerating or retarding each other, but do not increase
or diminish their density or mass; only it will lead us to expect
that the same depth of 817 miles will not produce the same amount of
pressure outwards at the meeting of the two halves as it does inwards,
and that to obtain an equal pressure a greater depth will be required.
We believe that an expert mathematician, taking as bases two opposite
pyramids in a sphere, similar to those we have used in a former part
of our work, could point out, with very approximate accuracy, what
ought to be the distance of the inner surface of the shell from the
centre--provided a maximum density were determined for the earth--but
that goes beyond our powers, and we shall limit ourselves to the use of
our own implements; which will cause us to depart from the statement
we have made, that the density of the inner half must decrease from
the place of meeting of the two halves, at the same rate as the outer
half had increased. It must decrease much more rapidly than the other
increased. All this premised, and having established a density of 3 for
the interior surface, we may proceed to calculate where that surface
ought to be, so as to give for the interior half of the earth a mass
equal to 735,584,493,738 cubic miles of water.
If we begin our operations with a density of 8·8 times that of water
at the meeting of the two halves of the shell, and diminish it for any
considerable distance at the same rate as it increased when we were
finding the mass of the outer half, that is 0·1812 for each layer, we
soon find that before we could make up the whole mass of the inner
half of the shell, the density would be decreased to at least that of
water, which cannot be, as there can be no liquid or solid matter of
any kind of so low density anywhere in the interior half of the shell.
Furthermore, if we decrease it at the same rate as the volumes of the
different layers of the earth decrease as they approach the centre, it
involves a mass of calculation that serves no useful purpose, as such
calculations bring no contingent of satisfaction with them; because
all the densities with which we are dealing have to be brought to a
rational form before we can frame a proper approximate idea of what
the interior construction of the earth is, as will be seen hereafter;
and because it takes no account of the perturbation--above alluded
to--produced by the attraction of the matter on the opposite side of
the hollow. But, in order to get such a result as we can with our
limited powers, if we begin with a density of 8·8 at the diameter of
6284·5 miles and fix the density of 3--which we have adopted above--at
the diameter of 3200 miles, we shall get a mass somewhat less than
one-half of the earth; and with a density of 2·91 at 3150 miles
diameter we get a mass of 735,713,884,116 cubic miles of water, which
is rather greater than one-half of the mass required (see operations
of Table V.). This density of 2·91 reduced to 2·5, as we mentioned,
might be done when we were fixing the number 3, would make very little
difference on the resulting mass, compared with what we have been in
quest of.
Here we may state that we found that, had the calculations been made
with documents of density proportioned to the decrease of the volumes
of the layers of the earth as they approached the centre, the density
would have been reduced to 2·25 at 3150 miles in diameter; which tends
to show that should that process be considered to be more accurate, it
would not have made any great difference on the result.
With all, we may consider that it has been demonstrated, that the
greatest density of the earth is not necessarily greater at any part of
its interior than 8·8 times that of water.
TABLE VI.--CALCULATIONS OF THE VOLUMES AND DENSITIES
OF THE INNER HALF OF THE EARTH, ON THE SAME
DATA AS THOSE FOR THE OUTER HALF.
------+---------------+---------+----------------+--------------+
Diam. | Volumes |Densities| Volumes at | Observations.|
in | in Cubic | |Density of Water| |
miles | Miles. | | in Cubic Miles.| |
------+---------------+---------+----------------+--------------+
6284½|129,961,924,688| | 735,584,493,737|}Half-volumes |
|---------------| |----------------|}of the earth.|
6250 | 2,129,893,439| 8·800 | 18,743,062,263| |
| | | | |
6200 | 3,043,490,450| 8·705 | 26,493,584,367| |
| | | | |
6150 | 2,994,795,650| 8·610 | 25,785,090,546| |
| | | | |
6100 | 2,946,493,550| 8·515 | 25,089,392,578| |
| | | | |
6050 | 2,898,584,150| 8·420 | 24,406,078,543| |
| | | | |
6000 | 2,851,067,450| 8·325 | 23,735,136,521| |
| | | | |
5950 | 2,803,943,450| 8·230 | 23,076,454,654| |
| | | | |
5900 | 2,757,212,150| 8·135 | 22,429,920,840| |
| | | | |
5850 | 2,710,873,550| 8·040 | 21,795,423,342| |
| | | | |
5800 | 2,664,927,650| 7·945 | 21,172,850,179| |
| | | | |
5750 | 2,619,374,450| 7·850 | 20,562,089,432| |
| | | | |
5700 | 2,574,213,950| 7·755 | 19,963,029,182| |
| | | | |
5650 | 2,529,446,150| 7·660 | 19,375,557,509| |
| | | | |
5600 | 2,485,071,050| 7·565 | 18,799,562,493| |
| | | | |
5550 | 2,441,088,650| 7·470 | 18,234,932,216| |
| | | | |
5500 | 2,397,498,950| 7·375 | 17,681,554,755| |
| | | | |
5450 | 2,354,301,950| 7·280 | 17,139,318,196| |
| | | | |
5400 | 2,311,497,650| 7·185 | 16,608,110,615| |
| | | | |
5350 | 2,269,086,050| 7·090 | 16,087,820,094| |
| | | | |
5300 | 2,227,067,150| 6·995 | 15,578,334,714| |
| | | | |
5250 | 2,185,440,950| 6·900 | 15,079,542,555| |
| | | | |
5200 | 2,144,207,450| 6·805 | 14,591,331,697| |
|---------------| |----------------| |
| 56,339,575,889| | 442,428,177,291| |
-------+---------------+---------+----------------+--------------+
5150 | 2,103,366,650| 6·710 | 14,113,590,222| |
| | | | |
5100 | 2,062,918,550| 6·615 | 13,646,206,207| |
| | | | |
5050 | 2,022,863,150| 6·520 | 13,189,067,738| |
| | | | |
5000 | 1,983,200,450| 6·425 | 12,742,062,891| |
| | | | |
4950 | 1,943,930,450| 6·330 | 12,305,079,748| |
| | | | |
4900 | 1,905,053,150| 6·235 | 11,878,006,390| |
| | | | |
4850 | 1,866,568,550| 6·140 | 11,460,730,897| |
| | | | |
4800 | 1,828,476,650| 6·045 | 11,053,141,349| |
| | | | |
4750 | 1,790,777,450| 5·950 | 10,655,125,828| |
| | | | |
4700 | 1,753,470,950| 5·855 | 10,266,572,412| |
| | | | |
4650 | 1,716,557,150| 5·760 | 9,887,369,184| |
| | | | |
4600 | 1,680,036,050| 5·665 | 9,517,402,223| |
| | | | |
4550 | 1,643,907,650| 5·570 | 9,156,565,611| |
| | | | |
4500 | 1,608,171,950| 5·475 | 8,804,741,426| |
| | | | |
4450 | 1,572,828,950| 5·380 | 8,461,819,751| |
| | | | |
4400 | 1,537,878,650| 5·285 | 8,127,688,665| |
| | | | |
4350 | 1,503,321,050| 5·190 | 7,802,236,249| |
| | | | |
4300 | 1,469,156,150| 5·095 | 7,485,350,584| |
| | | | |
4250 | 1,435,383,950| 5·000 | 7,176,919,750| |
| | | | |
4200 | 1,402,004,450| 4·905 | 6,876,831,827| |
| | | | |
4150 | 1,369,017,650| 4·810 | 6,584,974,897| |
| | | | |
4100 | 1,336,423,550| 4·715 | 6,301,237,038| |
| | | | |
4050 | 1,304,222,150| 4·620 | 6,025,506,333| |
| | | | |
4000 | 1,272,413,450| 4·525 | 5,757,670,861| |
|---------------| |----------------| |
| 96,451,524,689| | 671,704,075,372| |
-------+---------------+---------+----------------+--------------+
| | | | |
3950 | 1,240,997,450| 4·430 | 5,497,618,693| |
| | | | |
3900 | 1,209,974,150| 4·335 | 5,245,237,939| |
| | | | |
3850 | 1,179,343,550| 4·240 | 5,000,416,652| |
| | | | |
3800 | 1,149,105,650| 4·145 | 4,763,042,919| |
| | | | |
3750 | 1,119,260,450| 4·050 | 4,533,004,823| |
| | | | |
3700 | 1,089,807,950| 3·955 | 4,310,190,441| |
| | | | |
3650 | 1,060,748,150| 3·860 | 4,094,487,859| |
| | | | |
3600 | 1,032,081,050| 3·765 | 3,885,785,163| |
| | | | |
3550 | 1,003,806,650| 3·670 | 3,683,970,405| |
| | | | |
3500 | 975,924,950| 3·575 | 3,488,931,696| |
| | | | |
3450 | 948,435,950| 3·480 | 3,300,557,106| |
| | | | |
3400 | 921,339,650| 3·385 | 3,118,734,715| |
| | | | |
3350 | 894,636,050| 3·290 | 2,943,352,605| |
| | | | |
3300 | 868,325,150| 3·195 | 2,774,298,854| |
| | | | |
3250 | 842,406,950| 3·100 | 2,611,461,545| |
| | | | |
3200 | 816,881,450| 3·005 | 2,454,728,757| |
| | | | |
3150 | 791,748,650| 2·910 | 2,303,988,572| |
|---------------| |----------------| |
|113,596,348,539| | 735,713,884,116| |
| | | |{ True |
| | | 735,584,493,738|{ half-volume |
| | |----------------| |
| | | 129,390,378| Excess |
-------+---------------+---------+----------------+--------------+
CHAPTER X.
PAGE
184 Inquiry into the interior construction
of the earth--_continued_.
185 Density of 8·8 times that of water still too high for the
possible compression of the component matter of the
earth as known to us.
186 Reasons for this conclusion drawn from crushing strains
of materials.
187 A limit to density shown thereby.
188 The greatest density need not exceed 6·24 of water.
189 Gases shut up in the hollow centre. Their weight must so far
diminish the conceded maximum of 6·24.
190 Density of inner half of earth at 3000 miles diameter. Greatest
density may be less than 5·833 of water.
191 Supposed pressure of inclosed gases very moderate.
193 Meaning of heat limit to density. Temperature of interior half
of shell and inclosed gases must be equal.
194 State of the hollow interior.
195 Results of the whole inquiry.
INQUIRY INTO THE INTERIOR CONSTRUCTION OF THE EARTH--_continued_.
It may be well to revert here to the experiment we made of putting
a cubic foot of rock, of specific gravity 13·734 in the scale of a
balance at the centre of the earth, where we saw that it could not
depress the scale one hair-breadth, and make the same experiment by
placing a cubic foot of rock of 8·8 specific gravity in the same scale,
at what we have called the region of greatest density of the earth,
that is, at 817 miles from its surface. Here, also, we shall find that
the scale is not depressed for the very same reason as in the former
case, that is because it had nowhere to be depressed to; and it might
be argued that for the same reasons advanced formerly there can be no
matter at that place, but the cases are entirely different. In the
first case, there is nearly the whole mass of the earth drawing the
matter away from the centre were it at liberty to move; whereas, in
the second case, the meeting of the two halves of the shell, at the
region where there is the greatest mass of matter, is also the meeting
place of the action of attraction in its greatest force; the place to
which matter is attracted from all sides, remains stationary, and it
is held there both by attraction and weight of superincumbent matter
or gravitation. The attraction of the whole earth acts as if it were
concentrated at its centre, but that is for external bodies. That kind
of attraction on the inner half of the shell would be far inferior to
that outwards of the outer half, owing to its greater distance and
conflicting nature, and would perturb, as we have said, but not do
away with it. The same could not occur at the centre, because it is
not the centre of the mass, that is, it is not the place where the
greatest quantity of matter existed originally, or is now to be found,
and consequently never was, nor can now ever be, the actual centre of
interior attraction.
It has been said when treating of the earth as being solid to the
centre, that it is not easy to comprehend what may be the nature of
the rocks we are acquainted with, when compressed to one-fourth or
one-fifth of their volume, and we do not find ourselves much better off
when we contemplate them as reduced to one-third or one-fourth of their
bulk, that is, when a cube of one foot is reduced to three or four
inches in height, as would be the case with it at a maximum density of
8·8 times that of water when placed at a depth of 817 miles from the
surface of the earth. We find, therefore, the idea thrust upon us that
there may be a limit to density, perhaps not an absolute limit, but a
practical one; in which case, the greatest density of the earth may not
greatly exceed 5·66 times that of water. For, if we conceive that it
increases to its maximum at 100 miles from the surface, and continues
nearly uniform thereafter, a little calculation will show that the
greatest density of the outer half of the shell need not much exceed
6 times that of water; and, of course, the same will be the case with
the inner half should its density be almost uniform till 100 miles from
the inner surface is reached. It might even so happen that at a depth
of 25 to 30 miles the practical limit might be reached; for a column
of granite of one foot square and 25 miles high would weigh, and exert
a pressure upon its base of 10,000 tons, a pressure equal to nearly
fifteen times what would be sufficient to crush it into powder; in
which case the greatest density of the earth might not much exceed the
5·66 that we are accustomed to think of--without thinking.
It may be deemed absurd to think that there is even a practical
limit to the density of matter, but on the other hand it is much
more absurd to suppose that there is not an absolute limit to it. We
cannot conceive of density being other than the result of compression,
and we cannot believe that matter can be compressed more and more
continually for ever. There must be some end to compression. Perhaps it
was the difficulty in conceiving of rock being compressed to so small
a fraction of its volume as would enable it to take its place at the
centre of the earth--where it has been said that, "it must weigh like
lead"--that originated the idea of its centre being occupied by the
metals, arranged as they would be in a rack in a store, the heaviest
pieces at the bottom of the rack, and the lighter ones higher up.
When fairly looked at, density would really seem to have a limit,
except in so far as it may be combined with heat. We know that water
is compressed 0·00005 part of its volume for every atmosphere of
pressure to which it is subjected. But 0·00005 for round numbers, is in
fractional numbers 1/20,000; therefore a pressure of 20,000 atmospheres
would compress a cubic foot of water into 1/20,000 of a foot in height,
or practically into nothing. We know, also, that as a column of water
33·92 feet high balances one atmosphere, one mile in height will be
equal to 155·66 atmospheres, and 20,000 atmospheres will produce a
pressure equal to a column of water 128 miles high; therefore, a cubic
foot of water, subjected to such a pressure, would be compressed into
virtually nothing. Again, supposing that we have a column of liquid
rock, of 2-1/2 times the density of water, of the same height of 128
miles, we should have a pressure of 2-1/2 times that of the column of
water; and as we have no reason to believe that granite in a liquid
state has to obey a different law of compression to the one obeyed by
liquid ice; then a column of granite 51 miles high would be sufficient
to squeeze its own base, not only off the face of the earth but out of
the bowels thereof. It will be seen, therefore, that at 100 miles deep
from the surface, the density of the earth might well be equal to not
only 5·66 times the density of water but to a great deal more; and that
our estimate of 3 times the density of water, at 9 miles deep, was far
within the mark.
The authors of text-books on the strength of materials tell us that
"the Modulus of Elasticity of any material, is the force that would
lengthen a bar of that material of 1 inch square to double its length,
or compress it till its length became zero; supposing it possible to
stretch or compress the bar to this extent before breaking." This is
neither more nor less than a counterpart of the law of gases, upon
which the air thermometer is constructed, applied to solid matter, and
may be used in the same manner. But we can never produce a perfect
vacuum, and so annihilate a gas and temperature; neither can we
annihilate matter, nor easily reduce it to one half of its volume. Now,
we have seen, a little way back, that a column of granite 25 miles high
would exert a pressure at its base 15 times as great as would crush it
to pieces; so that a column of 25÷15, or 1·66 miles high would destroy
the elasticity of the material, because, when crushing takes place,
all elasticity is gone. We cannot, therefore, get much satisfaction
out of any calculations made upon the theory of the strength of
materials; still, by them, we can make more plain the absurdity of any
notion of the indefinite compressibility of matter. But if, in the
face of contravening its conditions, we follow the reasoning used for
the formation of the theory, and take the modulus of elasticity for
granite as 2,360,000 feet, then the same modulus would compress a bar
of granite of 1 inch square in section till its height became zero. And
as that length is equal to 447 miles, at that depth from the surface of
the earth, granite or any other rock or stone of a similar nature would
be compressed out of existence by the weight of the superincumbent
matter.
Thus we have arrived at two measures of force which would compress
to zero the rocks that are known upon the earth. One where rocks are
looked upon as in a molten, liquid state, and analogous to water, where
the force is equal to that exerted by a column of the material 51 miles
high; and the other where the column requires to be 447 miles high.
In either case the same method of calculation will show that columns
one-half of these heights, will compress the material into at least
one-half of its volume--that is half-way between what it is at the
surface and would be at the specified depths--and consequently into
double its density. So we find in the one case that the density of the
earth ought to be about 5·66 times that of water at a depth of 25-1/2
miles; and, in the other, at somewhere less than 225 miles deep. But,
before proceeding to use and reason upon these depths, we must recall
to mind that the calculations from which we have derived them, in the
second case, have been made in violation of the theory that was adduced
for the purpose, and that in consequence the latter depth must be
excessive. For, were we to erect a structure of any kind, calculating
the stresses it would have to bear, under the same violation of the
theory, we should inevitably find that the structure would give way
under the strains that would be brought upon it; that is the columns
25-1/2 and 225 miles high would compress the same kind of matter
composing them into very far below one-half of its volume.
This premised, let us go back to our layers of 25 miles thick with
their respective volumes. Nine of them counted from the diameter of
7900 miles inwards, will be equal to 225 miles and will bring us to
234 miles deep, which at the same time that it leaves us the same
volume and mass that we have always retained for the first 9 miles in
depth, will facilitate our calculations considerably without making
any appreciable difference in them. We shall then have to find for the
9 layers 9 corresponding densities increasing from 3 to 5·66, and if
we multiply these together respectively, and add the numbers of the
volumes and masses of the outer 9 miles in depth, we shall get, at
the diameter of 7450 miles, a simple volume of 43,418,587,327 cubic
miles, and mass volume of 195,312,523,450 cubic miles. Deducting this
latter sum from 735,584,493,738 cubic miles, which represents the
half mass of the earth at the density of water, we have a remainder
of 540,271,970,288 cubic miles. On the other hand we find that the
simple volume of the earth comprehended between the diameters of
7450 and 6284·5 miles is 86,543,337,361 cubic miles; so that if we
divide 540,272,970,288 by this sum, we find that a density of 6·24
times that of water over the whole intervening space--between the
two diameters just cited--will make up the whole half-volume, at the
density of water, from the surface of the earth to the diameter of
6284·5 miles. Then, for the inner half-mass:--If we multiply the simple
volume between the diameters of 6284·5 miles, and 3150 miles, which
is 113,596,348,539 cubic miles by 6·24, we get 708,841,214,870 cubic
miles at density of water; and if from there we run down the density to
3 at 2700 miles in diameter we get 27,400,652,354 cubic miles, which
added to the last mentioned amount gives 736,241,867,224 cubic miles,
somewhat in excess of the inner half-mass of the earth at density of
water. Thus we see that in order that the average density of the earth
of 5·66 may be made up, there is no necessity for appealing to matter
of any kind with a density of more than 6·24 times of water. And there
is still something else of importance to be taken into consideration
before we can bind ourselves to a density even so great as that.
We have said, a few pages back, that there can now be no undeposited
cosmic matter in the interior of the hollow earth, and that as far
as such matter is concerned the hollow part may be a perfect vacuum.
This is not absolutely true, for gases may be cosmic matter, just the
same as any others of the elements out of which the earth is formed,
but what is generally meant by cosmic matter is solid--at least, we
have always looked upon it in that light--and all solid matter must
have been deposited upon the interior surface at an immeasurably long
period of time before the nebula forming the earth came to have even
the density of water; certainly before it came to be in a molten liquid
state; and we did not want to introduce any posterior evolutions in
order not to complicate our calculations, and also to obtain some
tangible bases to which the consequences of these evolutions might be
applied. But as we have now both form and density to work upon we may
take them into account, and it will be found that neither of these two
bases will be very materially altered by them.
When the earth was in a molten liquid state, it is believed--as we
have said on a former occasion--to have been surrounded by a dense
atmosphere, composed of gases and vapours of metals, metalloids, and
water, and we have no reason to doubt that the hollow of the sphere
was filled with a similar atmosphere, only the vapour of water would,
most probably, be dissociated into its elements of oxygen and hydrogen.
Also we have every reason to believe that even at the present day
gases are being produced in the interior, one part of which find their
way to the surface and are dissipated into the atmosphere in the same
manner as the gases from the chimney of a furnace; and another part
into the interior, where they could not escape but would be stored
up in the hollow. Thus at the present day there may be an atmosphere
there, composed near the surface of vapours of the elements with gases
above them, so to speak, at a very high degree of pressure. These gases
could not have gone on accumulating always, but must have found an
exit in some particular place, or places, when the pressure exceeded
the resistance, or when this was diminished by some convulsion such
as an earthquake; but we do not want to define too much, or make more
suppositions on this point than what present themselves to us in a
reasonable way. All that we need say is, that the resisting power
of some thousands of miles of solid, or even viscous, matter must
be enormous, and the pressure necessary to force its way through it
must have been equal to many thousands of atmospheres. We know that a
pressure of 773·4 atmospheres condenses air to the density of water,
and it must be the same with any similar gas; so we have only to
suppose that the pressure is 4827 atmospheres--which is equal to 773·4
multiplied by 6·24--in order to bring the whole of the gases, and
vapours of elements, in the hollow to the same density of 6·24 times
that of water, which we have shown need not be exceeded in any part of
the earth. And such being the case, we can place the division between
solid and gasiform matter in any point of the radius that may seem to
us reasonable, only we must always have as much solid matter in the
inner as in the outer half-mass of the earth.
Following nearly the result we have obtained in another way, by
placing the division of the hollow part at 3000 miles in diameter,
the volume of which is 14,137,200,000 cubic miles, and multiplying
this by 6·24, we get a mass equal to 88,216,128,000 cubic miles at
density of water, composed of vaporous and gaseous matter in the hollow
centre, and consequently much greater than is required to make up the
total mass of the earth at the density of water; which shows that the
density of the mass between the diameters of 7450 and 3000 miles must
be less than 6·24 times that of water. How much less is very easily
found, by dividing the surplus of 88,216,128,000 cubic miles over the
whole volume between 7450 miles in diameter and the centre, because
in this way we shall include the whole mass arising from both solid
and gasiform matter. This whole volume--that of a globe 7450 miles in
diameter--is 216,505,262,050 cubic miles, which, divided by the surplus
gives the amount 0·407 as the density to be deducted from 6·24 on its
account, and therefore the greatest density of any part of the earth
need not be over 5·833 times that of water.
This result derived from our operations will be acknowledged, we doubt
not, to be much more satisfactory, we might say, more comprehensible,
than to have to believe that our known rocks and stones could be
compressed till they were 13·734 or even 8·8 times heavier than water.
At first sight 4827, say 5000, atmospheres or 75,000 lb. on the square
inch, appears to be an enormous pressure, but it is nearly almost as
nothing compared to the pressures we have been dealing with. A column
of granite 1 mile high would exert a pressure upon its base of 6050 lb.
per square inch, and one of 25 miles high of 151,200 lb., or double the
number of atmospheres we have applied to the gases in the hollow of
the earth. If we take a column 225 miles high, such as we considered
to be the least that would be necessary to compress granite into
one-half of its volume, we get 1,360,860 lb. per square inch, or over
90,000 atmospheres of pressure; and if we go into thinking of columns
of 447 and 817 miles--this last being the depth from the surface of
the division of the matter of the earth into two equal portions--we
could have gases compressed to 174,600 and 326,700 atmospheres or,
dividing the numbers by 773·4, 222 and 422 times the density of water;
so there is no cause to stumble over high pressure. With even 10,000
atmospheres, more than double the number assumed, we should have gases
as heavy as the material we found at the centre of the earth, when we
were looking upon it as solid to the centre--which was 13·734 times the
density of water--and so get rid of burying the precious metals where
they would be "matter in the wrong place," and according to D'Israeli's
definition, justly entitled to the epithet applied to them, sometimes,
by people who have never been blessed with a superabundant supply of
them. At the same time, we find out what we knew before, viz. that we
may have gases heavier than the heaviest metals and as rigid as steel,
if we can only find a vessel strong enough to compress them in, along
with the means of doing it; and also that the thousands of miles of
highly compressed matter, between the hollow centre and the surface of
the earth, are far more than sufficient to imprison gases of far, very
far, greater elasticity than our modest measure of 5000 atmospheres.
And we hope to be able to show presently good reason for believing that
the gases compressed in the hollow, at what may really be considered
as very high pressures, have had, and may probably still have, a very
important part to play in the evolution of the earth.
We have just seen that the pressure produced by a column of granite 1
mile high would be 6050 lb. per square inch, consequently one of double
the height, or 2 miles, would exert a pressure of 12,100 lb. per square
inch at its base, equal to the crushing strain of the very strongest
granite we know, while at the same time that strain would not amount to
one-sixth of 4827 atmospheres; so that if the gases in the hollow of
the earth were at a pressure of only 800 atmospheres, their pressures
would be able to crush granite of that class to pieces, and therefore
the estimate of specific gravity of 3 for the density of the interior
surface--which we made at the beginning of our calculations for the
hollow sphere--cannot be looked upon as by any means exaggerated.
We might now reform our calculations of the two halves of the interior
of the earth, giving a more rational and curve-like form to the
densities, under the supposition that at much less distance than 234
miles from the surface, matter might be compressed to its utmost limit;
but as, according to our demonstration, the solid matter of the earth
must have been divided into two equal parts at the place where the
greatest mass was, long before it could have been condensed into a
state to compress gases; and as the total mass of solid matter must,
in order to make up the total mass of the earth, depend to some extent
on the mass of imprisoned gases; we are unable to make any reform much
different to what our calculations show. Besides, as the difference
between average densities of 5·66 and 5·67 makes a difference of
2,600,000,000 cubic miles on the mass of the earth reduced to the
density of water, very approximate accuracy cannot be attained in any
calculations.
What is meant by a limit to density except in so far as it is combined
with heat, is that whatever density may be given to matter by
compression when it is in a heated state, a greater density will be
found in it when it is deprived of that heat; that whatever may be the
density of any part of the interior of the earth in its present state,
that density will be increased when the earth becomes cooled down to
the temperature derived from the heat of the sun, or to absolute zero
of temperature, if such there be, on account of shrinking in cooling;
and that therefore there can be no absolute limit to density as long as
there is any heat in matter.
It may not be unnecessary for us to recognise now that the weight of a
column of granite would decrease as the depth increased, for the force
of gravitation would be diminished by having a part of the attraction
of the earth above instead of below it; but at 100 miles in depth the
diminution would be only about one-eighth--if distance is taken into
account--of the 817 miles down to the plane of greatest density, and
1/2200th part if the mass left above is considered; differences that
would make extremely little alteration on our calculations.
It will not be out of place either to take a look at what may be
the temperature of the interior of the shell, and of the gases shut
up in the hollow part of the earth; and we have not much to say on
the subject, because we shall not depart from the system we have
followed up till now, with considerable strictness, of not theorising
or speculating on what may be; but will restrict our observations
to theories that have been very generally adopted by astronomers,
geologists, and scientists in general. The air thermometer will be
of no use to us, for whatever may have been the temperature when
the earth was in the process of formation, it must have diminished
very greatly during the cooling process it has undergone since, and
we know that gases heated in a closed vessel in such manner that
pressure and temperature will agree to the theory on which the air
thermometer is constructed, may be cooled down afterwards to almost
any degree required, and the relation between temperature and pressure
destroyed thereby. At one time it was thought that the earth had only
a solid crust, and that, under it, the whole of the interior was in
a molten liquid state. Then some physicists thought that, through
pressure of superincumbent matter, solidification must have begun at
the centre; others that it began almost simultaneously at the surface
and centre, and that there may still be a liquid mass between the two
solidifications--this is repeating what we have said before, but it is
done only to bring it to mind. We, at present at least, do not want
to have anything to do with any of these theories, only we believe
that we have shown in an indisputable manner that there could be no
solidification at the centre, because there could be no matter there
capable of being solidified--gases could not be solidified under such
pressure, and at all events heat, as there must have been there. We
believe at the same time that no one will deny that the heat of the
earth increases as the centre is approached, and that the temperature
of the interior may be very great. The crust of the earth was at one
time supposed to be only 25 to 30 miles thick, because the increase of
heat at that depth would be sufficient to melt any of the substances
we are acquainted with on the surface--repetition again; but for many
years past it has been deemed necessary to increase the thickness to
even hundreds of miles, for reasons some of which will be alluded to in
due time; and if, even at these depths, the increase of heat were only
sufficient to fuse all the substances we know, it is very certain that
at the interior surface of the shell it must be very much greater, as
heat from there could only be _conducted_ outwards, and the difference
required to cause conduction, of any considerable degree of activity,
through more than 2000 miles must be enormous, according to the
experiments made by various physicists upon metals, which have a very
much higher conducting power than rocks, and especially strata, of any
kind. Therefore there can be no doubt, we think, that the inner surface
of the shell must be at a very much higher temperature than what would
preserve it in its liquid state, and that the matter composing it is
liquid to a depth where it might be solidified by the pressure of
superincumbent matter. We do not see how convection currents could be
instituted, much less kept up, in melted matter, under the viscosity,
and, at least quasi-solidity, sure to be produced by pressure of tens
of thousands of pounds on the square inch, and therefore we do not take
them into account. Any way, whatever may be the temperature of the
interior surface of the shell, the same must be that of the imprisoned
gases, because there convection currents could and must exist--were
they even only created by the rotation of the earth and attraction
of the moon--and cannot fail to keep the whole of the hollow part at
the same temperature. It would be absurd to suppose that these gases
could be at a lower temperature than the upper layers, counted from the
region of greatest density, of the interior surface of the shell.
This section of our work may now be brought to a close by stating the
conclusions at which we have arrived, leaving the results involved
by them to be discussed separately, which we shall proceed to do
immediately without binding ourselves so strictly, as we have done
hitherto, to the avoidance of anything that may be looked upon as
theorising or speculating. We believe we have conducted our operations
in the most strict conformity to the law of attraction, and have no
doubts whatever about the form of the interior of the earth resulting
from them; but there may be some room for small variations in the
details of the various densities, and the position of the interior
surface of the shell, arising from the pressure of the gases in the
hollow centre, and the weight they will, in consequence, add to the
general mass of the earth. The conclusions are as follows:--
(1) That the earth is not solid to the centre, nor is it possible that
it could be, according to the law of attraction, but is a hollow sphere.
(2) That its greatest density must be at the region where the greatest
mass of matter is to be found--as must have been always the case from
the time it was a globe revolving on its axis, whether gasiform,
liquid, or solid--which is now at 817 miles deep from the surface; and
that the greatest density may not be much more than the mean of 5·66
times that of water ascribed to it by astronomers.
(3) That the inner surface of the shell of the hollow globe cannot be
much over or under 2000 to 2200 miles from the outer surface.
(4) That the hollow part of the globe must be filled by an atmosphere
consisting possibly in part of vapours of the chemical elements, and by
gases at a very high degree of pressure.
(5) That the region of greatest density, and the position of the
interior surface of the shell, may be expressed with very approximate
accuracy as follows:--The former must be at 0·7939 of the mean radius
of the earth, and the latter at 0·5479 of the same; both counted from
the centre.
(6) That if the earth is a hollow sphere, the same must be the case
with all the major planets and their satellites, the sun, and all the
suns, or stars, that are seen in the heavens; and that their interior
proportions and form must be in much the same ratios to their radii as
those we have found for the earth.
CHAPTER XI.
PAGE
197 The Earth. The idea entertained by some celebrated men,
and others.
199 Difficulties of forming a sphere out of a lens-shaped nebula.
200 Various studies of the earth's interior made for special purposes.
Difficulty some people find in conceiving how the average
density of little over 5·66 can be possible, the earth being
a hollow sphere.
201 What is gained by its being a hollow shell.
202 Geological theories of the interior discussed. Volcanoes and
earthquakes in relation to the interior.
206 Liquid matter on the interior surface of the shell, and gases
in the hollow, better means for eruptions than magma layers.
207 Focal depths of earthquakes within reach of water,
but not of lavas.
209 Minute vesicles in granite filled with gases, oxygen and hydrogen,
but not water.
211 The Moon. A small edition of the earth.
212 Rotation stopped. Convulsions and cataclysms caused thereby.
Air, water, vapour driven off thereby to far off hemisphere.
Liquid matter in hollow interior would gravitate to the inside
of the nearest hemisphere.
213 Form and dimensions during rotation. Altered form after
it stopped.
214 Agreeing very closely with Hansen's "curious theory."
CONSEQUENCES OF THE EARTH AND MOON BEING HOLLOW BODIES.
_The Earth._--The idea that bodies such as those of the solar system,
even of the whole universe, have their greatest density where the
greatest mass is and are hollow spheres, is so natural and logical,
more especially if it is supposed that they have all been formed out of
some kind of nebulæ, that it seems strange it has never been brought
forward prominently before. We say prominently because we know that the
earth has been considered to be a hollow sphere by very eminent men,
such as Kepler, Halley, Sir John Leslie, and by others of less name
long after them. In support of this last remark, we shall make a few
extracts--with comment on them--from an article on the "Interior of
the Earth" in "Chambers's Journal" for February 1882, which have some
interest in connection with our work.
1. "The great astronomer Kepler, for instance, in seeking to account
for the ebb and flow of the ocean tides, depicted the earth as a
living monster, the _earth animal_, whose whalelike mode of breathing
occasioned the rise and fall of the ocean in recurring periods of
sleeping and waking, dependent on solar time. He even, in his flights
of fancy, attributed to the earth animal the possession of a soul
having the faculties of memory and imagination."
If it could be believed that Kepler had any idea of the earth being
formed out of a nebula, whether hollow, or solid to the centre, the
idea of a breathing animal was almost a consequence, because the
attraction--a thing he is supposed to have known nothing about--of
the original nebula for the earth one, on matter so light as nebulous
matter, would raise enormous tides and make the earth, in its then
state, not far from like an enormous primitive bellows made out of
goatskins. No one knows what dreams may have passed through his brain.
The last part of his notion was altogether fanciful.
2. "Halley was opposed to the idea of the globe being solid, 'regarding
it as more worthy of the Creator that the earth, like a house of
several storeys, should be inhabited both without and within.' For
light, too, in the hollow sphere, he thought provision might in some
measure be contrived." This notion appears to be altogether fanciful,
the fruit of an enthusiastic, exuberant imagination, leaving no trace
of scientific thought upon the subject.
3. "Sir John Leslie, like Halley, conceived the nucleus of the world
to be a hollow sphere, but thought it filled, not with inhabitants,
but with an assumed 'imponderable matter having an enormous force of
expansion.'" It would be interesting to know on what bases he formed
his ideas, as the filling of the hollow with imponderable matter seems
to show more method than the former cases, but we have never seen
any allusion made to his theory anywhere, except in the article we
are quoting from. There may have been some reasons given for such a
supposition in his "Natural Philosophy," but when we began to read that
work in times long past, a more modern one was recommended to us, and
we lost the chance, never to return.
There are other theories referred to in the article, but we shall take
notice of one more only.
4. "A certain Captain Symmes, who lived in the present century, was
strongly convinced of the truth of Leslie's theory. He held that near
the North Pole, whence the polar light emanates, was an enormous
opening, through which a descent might be made into the hollow sphere,
and sent frequent and pressing invitations to A. von Humboldt and Sir
Humphrey Davy to undertake this subterranean expedition! But these
imaginative conceptions must one and all be set aside, and the subject
treated on more prosaic, though not less interesting, lines."
This conception of Captain Symmes will probably be looked upon as the
most absurd of the whole lot, but to us it seems to give evidence of
more thought than any one of them. One would think that he must have
formed some notion of how a hollow sphere, with an opening out to the
surface at each one of its two poles, could be formed. We must note
that he lived in, possibly after, the time of Laplace.
We doubt whether anyone has ever studied out thoroughly how even a
solid sphere could be ultimately elaborated from a nebula. It has
always been a very general idea that a condensing and contracting
nebula would, under the areolar law, assume the form of a lens rather
than of a sphere. If this be so in reality, we may ask: How can the law
of attraction produce a sphere out of a lens-shaped mass of rotating
vaporous or liquid matter? It seems evident that to bring about
such a result attraction must cease to act altogether in the polar
directions, and only continue to draw in the matter from the equatorial
directions of the lens, till the desired sphere was formed; and, How
were the action and inaction of the law of attraction to be regulated
meanwhile? Or, when the time came that a sphere of a pre-arranged
diameter could be formed, a goodly part of the lens must have been
cut off and abandoned; in which case we have again to ask: What was
done with the surplus, the cuttings? No doubt they could be used up in
meteor swarms, comets, or something; but Captain Symmes's theory has
opened up a field for a good deal of thought, and our present knowledge
of polar matters prevents us from being sure that strange discoveries
may not be made as to the condition of the earth at the poles, although
there may not actually be holes into the hollow interior. With regard
to the last sentence of the quotation, we fully agree and are doing our
best to comply with it. And in so doing, we shall have to return to
the formation of globes out of nebulæ, elaborated into something more
advanced than even lens-shaped discs.
There is no doubt that the reasons assigned by most, if not all, of
the authors of the notions above cited are very fanciful, but one can
hardly believe that the true reason--why the earth must be hollow--has
not occurred to some of them; and that they did not follow it out
because it involved too much work, and they did not feel inclined to
undertake it, or had not time. On the other hand, modern astronomers
and physicists have been so fascinated by the discoveries they have
made, and in following them up, that the temptation to go on in the
same course has been too great to allow them to spend time on the
investigation of sublunary and subterranean affairs. Some of them
have indeed studied the interior of the earth for special purposes,
such as the thickness of the crust, solidity or liquidity, stability,
precession of the equinoxes, the action of volcanoes, etc., etc.; but
they never, apparently, examined into any of these features to the
very end, otherwise, we believe, they would have come long ago to the
same conclusion as we have. And withal it seems wonderful how near
some of them have come to it. To most people it would appear absurd
to think that any part of the earth of any great magnitude can be
hollow, if in order to make up its mass its average specific gravity
must be 5·66--more especially, if we tell them that the greatest
specific gravity at any place need hardly exceed 5·66--forgetting that
weight or mass can be taken from the interior where the volume per
mile in diameter is small, and be distributed near the exterior where
the volume per mile in diameter is comparatively immensely greater.
But in whatever light we look upon the conclusions we have arrived
at, a change in the construction of the bodies in space from solid to
hollow spheres must produce changes in our ideas of them, and have
consequences of great importance, too numerous to be all taken account
of; we shall, therefore, only take notice of the most prominent.
Looking at the earth as a hollow sphere, we get rid of the difficulty
of conceiving that matter can be compressed to three or four times less
than the volume it has as known to us; and also of the misplacement of
metals to the incredible degree we have shown to be necessary to make
up its whole mass according to the sorting-out theory. And if we can
only be bold enough to look upon gases as ponderable matter that can be
compressed to great density, and so added to the weight of the whole
mass, we may not be under the necessity of compressing the known matter
composing it to even the half of its volume.
Somewhere in the first quarter of this century (see "Edinburgh Review,"
January 1870) Mr. Hopkins argued that the solid crust of the earth
must be at least 800 to 1000 miles thick, in order to account for the
precession of the equinoxes and nutation, but about a quarter of a
century afterwards M. Delaunay demonstrated before the French Academy
by actual experiment that the thickness of the crust had no bearing
whatever on the problem. And about the same time Lord Kelvin inferred
from the same thickness of crust that "no continuous liquid vesicle at
all approaching to the dimensions of a spheroid 6000 miles in diameter
could possibly exist in the earth's interior without rendering the
phenomena of precession and nutation sensibly different from what they
are"; and that the earth, as a whole, must be far more rigid than glass
and probably more rigid than steel, "while the interior must be on
the whole more rigid, probably many times more rigid, than the upper
crust." With the theory of a hollow shell, a better foundation is
given for Mr. Hopkins's argument than a solid crust at about the same
depth as he assumed, while at the same time the liquid vesicle of 6000
miles in diameter is removed, which Lord Kelvin showed would change
the phenomena of precession and nutation. We have seen that imprisoned
gases may have a high degree of density, and consequently rigidity, and
may in some measure supply what was required by Lord Kelvin, who knows,
also, very well that a structure with some degree of elasticity in it
is stronger than one that is absolutely rigid. Moreover, the shell of
the earth, composed of solid materials at a very high temperature, and
consequently so far plastic, could not fail to accommodate itself to
any variation of centrifugal force that could take place. Variations
in rotation of the earth could only have come on extremely slowly, and
even the most rigid matter we know will gradually yield to extreme
pressure long continued. But this subject of the plasticity of the
most solid part of the interior was discussed and, it may be said,
demonstrated during the meeting of the British Association of 1886, as
reported in "Nature" from July to September of that year. Any way, the
possibility of plasticity is most patently shown by the hollow-sphere
construction of the earth.
We do not know what were M. Delaunay's proofs that the thickness of
the crust has no bearing whatever on precession and nutation, but if
they were complicated with the fluidity, or even viscosity, of a liquid
interior beyond a depth of 800 to 1000 miles, they must be entirely
changed under the notion of a hollow sphere where there could be no
really liquid molten matter, except near the inner surface. One thing
we may be certain of, and that is, there must be something to account
for precession and nutation, and we believe that the hollow shell,
with the greatest density where the mass is greatest, is a much more
rational cause for these phenomena than the bulging out of the earth to
the extent of 13 miles or so at the equator.
It is very difficult to find out what geologists consider to be the
nature of the interior of the earth in its details, but for our
purpose no particular knowledge is required. However, it is necessary
to allude to the principal features of their theories in order to
note and remark how far they will agree to, or be facilitated, or the
reverse, when applied to a hollow sphere. It would seem that almost
all geologists are agreed that the central part is solid, and possibly
extremely rigid owing to the enormous pressure of superincumbent
matter; that it has a solid crust of several hundreds of miles in
thickness; and that under this there is a sub-crust divided into two
or more layers of different densities, partially liquid or at all
events plastic, extending all over the solid interior matter; the chief
purpose for which it is required being apparently to supply matter for
volcanic action and surface movements.
Under the theory we are advocating, the place of greatest density of
the interior is calculated to be at 817 miles from the surface, and
its greatest approach to solidity will be there also; consequently,
if geologists consider that it will have sufficient plasticity there
to provide matter for volcanic eruptions, they will be at one with us
so far. But should they consider that they require, for volcanoes,
matter more liquid than is likely to be found at that depth, they
will have to place their magma layers either much deeper or somewhere
between that depth and the surface, in which case they will encroach
on the requirements of astronomers, without liberating themselves from
a difficulty in which they must find themselves involved under their
present ideas. They say that these plastic layers exist under the solid
crust all round the interior of the earth, so that if one of the duties
they have to perform is to keep the various chains of volcanoes in
communication with each other, their lateral movements must extend to
some hundreds of miles in the cases of the enormous volumes of matter
that are sometimes thrown out in even modern eruptions, and they have
to provide the means for procuring that lateral motion. Shrinkage from
cooling, or falling in of part of the solid crust, might bring about
these enormous outbursts of lava, but they would be more likely to
produce simple overflows than the explosive ejection of such masses
as are now being recorded from time to time. We have brought into
remembrance, page 148, that water cannot penetrate into the interior
of the earth to a greater depth than 9 miles, more or less, as water,
and that beyond that depth it can only exist in the form of steam, or
dissociated into its elements of hydrogen and oxygen. As long as it
continued in the form of water it could be suddenly flashed into steam,
of not far from two thousand times its volume, by relief from pressure
or sudden application of heat, and thus be converted into a violent
explosive almost instantaneously; but when it came to have the form of
a gas, it could only be heated gradually the same as any other gas. It
is clear, therefore, that water cannot be looked to for producing the
force, explosive or otherwise, that is required to raise even molten
matter from depths of hundreds of miles to overflow from the summits or
outlets of volcanoes.
A pressure of 400 atmospheres would be required to balance a column of
average rock of _one mile_ high. A mass of water, through shrinkage
of the crust, might get introduced to the vent of a volcano, or some
cavity connected with it, a few miles under the surface of the earth
and cause an earthquake--it might be introduced by an earthquake--or
eruption or both, abundantly formidable and destructive, no doubt, but
only comparatively superficial, such as those of Naples and Charleston,
where the extreme depth was calculated to be only a few miles; but it
seems to us to be totally inadequate to produce those outpours that
last for days and weeks, covering leagues of land, and filling up bays
of the sea, with floods of lavas. It may be the principal agent or ally
in producing the horrors and devastation of a grand eruption that has
invaded the regions of water, but it is not to be conceived as possible
that it can be the prime cause. The volumes of steam, water, and mud
thrown out on such occasions, only tend to distract our attention from
looking deeper for the true cause of the eruption. Geologists are
therefore thrown back upon their magma layers to look for the motive
power for producing these grand eruptions, and they cannot get water
down deep enough to do it.
Tides produced by the sun and moon cannot be appealed to, otherwise the
eruptions would be more or less uniform in their periods of occurrence.
Sudden evolution of gases in the magma layers could not be accounted
for in any way known to us, and accumulation of gases would involve
the idea of immense cavities, to serve as reservoirs to be gradually
filled till the pressure was sufficient to force a way out, and would
imply a formation of the interior in compartments specially adapted for
particular purposes, and altogether too fanciful to be entertained.
Where could such enormous masses of matter, as those thrown out, come
from at only a few miles from the surface? The great eruption at the
Sandwich Islands, of about a century ago, after flowing over a distance
of many miles of land, on which it left enormous quantities of lava,
filled up a bay of the sea twenty miles long, and ran out a promontory
of three or four miles into the sea; and we cannot conceive it to
be possible that such a quantity of matter could be blown out from
something less than 9 miles deep by water suddenly flashed into steam.
The critical temperature of water--that temperature at which it changes
into steam under any pressure however great--being 412°, its pressure
in the state of steam will be somewhere about 7150 lb. per square inch,
let us say 500 atmospheres; then, if 400 atmospheres are required to
balance 1 mile in depth of average rock, as we have stated above, the
pressure of steam just cited would balance only 1-1/4 miles of rock.
We can, therefore, see how inadequate it would be to force a column of
lava up from even the depth of 9 miles. At that depth 3600 atmospheres
of pressure are required to balance a column of lava, and there are
only 500 available. It has been said that the downward pressure of
steam would force up the lava through the vent of a volcano, but an
arrangement of that kind would require a downcast shaft as well as
the upcast one of the vent like as there are in collieries; but the
downcast would have to go very deep to compress the steam--a gas
now--to the required number of atmospheres. Far more likely that the
steam itself would put an end to any increase of water, by driving it
back through the channels by which it was descending; for if they are
supposed to exist under a solid crust of 800 miles thick the pressure
required would be 320,000 atmospheres, and with a crust of only 100
miles thick 40,000 would be required. The only way, therefore, in which
volcanic eruptions can be produced in the earth, if solid or liquid,
or partially solid and partially liquid, to the centre--in other
words, from magma layers--is by the shrinking of the crust squeezing
out the lava. With a hollow earth and shell of more or less 2200
miles in thickness, liquid to some depth on the interior surface the
difficulty becomes very much less. The communication between the vents
of volcanoes would be complete and simple, without any lateral forcing
of the lava through magma layers made expressly for the purpose; it
would be an open and natural flow from one place to another. That
there are such volcano vents connected with each other has been very
generally believed, and even almost proved by observation of eruptions
taking place in two or more almost simultaneously, or at the least
showing signs of violent agitation, the motive forces for which would
be the gases which we have concluded must be imprisoned in the hollow
centre. When their pressure came to be sufficient to blow or force out
the liquid, or semiliquid matter, bubbling and boiling in the vents in
constant activity, there would be an eruption, during and after which
the gases would escape till their pressure was greatly reduced, when
the volcanoes would return to their semi-active state. The gases would
naturally be those of the many kinds that are found in eruptions, by
reason of their being generated in the earth, mixed with steam and
water in the manner we have already shown.
Let it not be supposed that the gases would require to have force
enough to raise lavas from depths of over 2000 miles from the surface.
According to our arguments for a hollow earth, at 817 miles from the
surface the two halves--outer and inner--of the matter composing it
meet and balance each other, so that all the pressure required would be
what is necessary to overcome the inertia, viscosity, or cohesion of
the matter in the vents. What that would be we do not pretend to be
able to calculate, but we believe that it would be very much inferior
to that required to balance a column of lava of even 100 miles high. We
have seen that gas compressed to 4835 atmospheres would be 6-1/4 times
more dense than water, and of equal specific gravity to the heaviest
matter required in any part of the earth to make up its average density
to 5·66 that of water, and we cannot assume any greater pressure than
this, without diminishing that maximum. If that, or any lesser degree
of compression, would supply the necessary force, then all difficulty
is removed further than pointing out the means of keeping the volcano
vents open or openable; and the quality of openable may be facilitated
by the contraction of the interior from cooling. If a greater pressure
be necessary, we need not be afraid of greatly increasing it, for the
only consequence would be to diminish the maximum density of solid
matter required in any part of the earth, to make up the general
average to 5·66, which means less compression of the matter. If the
idea of the accumulation of gases in the hollow centre, or of the
hollow centre itself, is inadmissible, then scientists in general can
continue as before with their magma layers--aqueo-igneous if they
like--but they must abandon the notion of lavas being expelled from
them by steam pressure. We repeat that steam could never get down in
the form of steam to the depths they require. The temperature there
would be more than sufficient to resolve it into its elements of oxygen
and hydrogen, and it would behave very much like the gases we have
supposed to be in the hollow; there might be accumulation, but there
could be no sudden flashing into existence like steam from water.
In support of our observation--if it needs support--that water as
water cannot penetrate into the earth to a greater depth than where it
meets a temperature of 412° we may refer to reports on earthquakes of
comparatively recent occurrence. We learn from the "London Quarterly
Review" of January 1869, that in the Neapolitan earthquake of 1857, Mr.
Mallett found the greatest focal depth to have been 8-1/8 geographical,
or 9·35 statute miles, which agrees very well with the depth to which
water could penetrate and be suddenly flashed into steam. (We say
nothing, for the present at least, about how the water and the heat
managed to meet so instantaneously.) The shock of the instantaneous
generation of steam might be felt much lower, but it would tend to
interrupt, not to produce, the eruption of lavas. In speaking of the
pressure on the walls of the cavity, where the shock was produced,
being 640,528 millions of tons, the reviewer says, "it may have been
greater because the steam might be supposed to have acquired the
temperature of the lava," and that is 2000°F.; but that could not well
be. In order to meet lava of that temperature the steam would have
to descend to from 20 to 25 miles deep; on the other hand, if the
lava is assumed to have entered the cavity, it could only do so at a
comparatively low velocity and would not reach more than a fraction
of the steam at a time, and even for that reason there could be no
flashing, as steam is only a gas, and cannot be heated otherwise
than as a gas. Here the spirit of facilitating the meeting of the
lava and the steam, is as apparent as in bringing about the meeting
of the water and the lava noticed above. On the whole, therefore, we
think that we were right in saying that steam or water cannot be the
cause of volcanic eruptions, but that the invasion of the domains of
water by the lavas may be the cause, in the main, of the explosive
part of eruptions, and of the most disastrous effects of earthquakes.
Moreover, the focus of the Neapolitan earthquake was 75 miles distant
from Vesuvius, and therefore far removed from anything like direct
connection with the vent of the volcano, so that water from it in any
form could have no effect upon the magmas of scientists.
"The Scientific American" of July 16, 1887, tells us that Captain E.
D. Dalton has calculated that the depth of the Charleston earthquake
was 12 miles; statute miles, it is to be supposed, as nothing is said
to the contrary. To reach the temperature of 412° this would give
an increase of 1° in 45 metres in depth, which is a considerably
greater depth than what we have estimated, but does not invalidate our
reasoning, as it has always been known that the gradient of increase
of heat varies considerably from one place to another. Besides, and
more especially, Charleston being a seaport, and, consequently, not
far from the level of the sea, it is to be supposed that, owing to the
presence of water, the cooling of the earth has penetrated to a greater
depth there than in the heart of Italy. The same authority states that
in the formidable Yokohama earthquake of 1880, the mean depth was only
3-1/4 miles. The mention of mean depth here makes us notice that the
12 miles may have been the extreme depth to which the earthquake, or
shock, was felt at Charleston, and that the focal depth may have been
considerably higher up than that. Be that as it may, there is no proof
existing that water or even steam can penetrate into the earth more
than a very few miles, much less to hundreds of miles.
Having referred pretty freely to the aqueo-igneous magmas, supposed by
some scientists to exist deep down in the interior of the earth, it is
but fair to give our reasons for refusing to believe that there can be
any such mixture in any part of it, or anywhere else. In order to do
so, we shall first cite some of the bases upon which such ideas have
been founded. In "Nature" of December 12, 1889, we find what follows:--
"Let us now consider the alternative theory suggested by Mr. Fisher. He
claims that geologists furnish him with a certain amount of positive
evidence for the idea that water is an essential constituent of the
liquid magma from which the igneous rocks have been derived. Passing
over the proofs of the existence of water in the crystals of volcanic
rocks, and in the materials of deep-seated dykes, let us come at once
to the granite, a rock which can only have been formed at great depths
and under great pressures, and which often forms large tracts that are
supposed to have been subterranean lakes or cisterns of liquid matter
in direct communication with still deeper reservoirs. Now, all granites
contain crystals of quartz, and these crystals include numerous minute
cavities which contain water and other liquids; and the quartz of some
granites is so full of water-vesicles that Mr. Clifton Ward has said:
'A thousand millions might easily be contained within a cubic inch of
quartz, and sometimes the contained water must make up at least 5 per
cent. of the whole volume of the containing quartz.' This amount only
represents the water that has been as it were, accidentally shut up in
the granite, for some was doubtlessly given off in the form of steam
which made its way through the surrounding rocks."
We cannot follow Mr. Fisher in "passing over the proofs of the
existence of water in the crystals of volcanic rocks and in the
materials of deep-seated dykes"; because the presence of water in
these crystals when examined in a laboratory is no proof that water
was present in them when they were liquid, and before they put on the
form of crystals. There is no analogy between them and General Wade's
read. Any crystals that a man can pick up anywhere, even from the
mouth of a volcano, are quite capable of absorbing vapour of water
from the atmosphere before he can carry them to his laboratory. All
matter is supposed to be pervaded, more or less, by the ether, and
there is always an open road for it, i.e. the vapour of water to enter
by. Nature dives more rapidly into a piece of rock than a man can walk
or drive down from the summit of a volcano, so that getting water out
of it when he is in his laboratory, is no proof that the water was
there when the piece of rock was at the bottom, not the mouth, of the
volcano. The minute so-called water-vesicles in granite have only
served the purpose of a snare to facilitate his deceiving himself,
by the help of Mr. Clifton Ward, to further his speculations. For we
think it would have been far more natural for him to have supposed that
these vesicles were originally filled with the all-pervading ether.
Or, are we to prohibit the ether from being present anywhere, except
where it suits us? Even the dimensions given to the vesicles of a
thousand millions of them being contained in a cubic inch makes us at
once think of something more ethereal than water. And the whole object
of Mr. Fisher's argument is to show how the depth of the ocean may be
increased by water expelled from such magmas.
A hollow planet, with compressed gases in the centre, raises the idea
of the possibility of explosion. It would have furnished Olbers, or
any follower of his, with the bursting force to shatter into fragments
the planet, out of which he supposed the asteroids to have been made.
It need not cause any alarm with respect to the earth, whose shell is
very much thicker than that of the exploded planet, seeing that its
whole mass has been estimated not to have exceeded one-fourth of that
of the earth (see Table I.). The 5000 atmospheres of pressure we have
spoken of could have no such effect on so thick a shell as the earth's;
and we cannot increase the number without diminishing its average
density, as we have shown. When we see Mars blown up, whose diameter,
and consequent thickness of shell, are not much more than half those of
the earth, we may begin to think of getting out of the way.
THE MOON.
This satellite is supposed, according to the nebular hypothesis, to
have been at one time neither more nor less than a smaller edition
of the earth itself, endowed with atmosphere, plains, mountains,
volcanoes, rivers, seas, rotary motion, etc.; previous to which it had
passed through the same stages of gasiform, molten-liquid, and solid as
its parent had done. One would think that its almost perfectly round
form proves to demonstration that it must have rotated rapidly on its,
or an, axis at one time; but there are some astronomers who think that
it has never rotated at all, an opinion in which we cannot concur by
any means. When it arrived at the stage of having seas, the tides
raised in them by the attraction of the earth must have acted like a
brake on its rotation--in the same manner as its attraction is supposed
to be now doing on the earth--and gradually reduced it until it ceased
altogether; from which time forward it must have always presented the
same side to the earth. It has been thought that the tides raised in it
by the earth would be so tremendous that they would prevent anything
like rotation having ever existed; but everything requires to be
accounted for, and the only way to account for its perfectly circular
form is by its having rotated.
Considering, then, the moon as having been dispossessed, absolutely,
of rotation and reduced to the single motion of revolution round the
earth--as far as we are at present concerned, at least--we can go back
to the period when this change came over it, and consider what would
happen about the time, and immediately after the rotation came to an
end.
When a fly-wheel is made to revolve rapidly and is then allowed to run
until it stops, it very seldom comes to rest all at once, and generally
swings backwards and forwards something like a pendulum, until it
finally stops; because it is always a little heavier on one side than
the opposite, even should the difference of weight be only that of
the handle by which it was set in motion; so we may suppose it would
be with the moon when at last it failed to turn the centre, as it is
called--the tides, the retarding cause, giving origin to the difference
of weight on opposite sides--and we can conceive what commotions
would be created on its surface by the wobbles it would make. We can
imagine how the seas would rush backwards and forwards over the lower
land and hills, levelling them down to the flat plains that are seen
spread abroad among the innumerable volcanoes which cover the side
turned towards the earth, until it finally came to rest. When the
commotions ceased and the centrifugal force of the moon's revolutionary
motion round the earth--which is over 38 miles per minute-came to act
freely, we know that the atmosphere and seas, being the mobile parts
of it, would be pretty nearly all driven off very quickly to the side
farthest from the earth, perhaps even before it came to the final
state of comparative rest, whose translation would involve mighty
rushings of waters there as well. Also, that all the liquid matter in
its interior, being so much heavier and more difficult to be moved by
centrifugal force, would gravitate towards the side nearest the earth,
whose attractive force would soon put an end to anything in the form of
interior tides of molten matter, which very probably existed up till
that period. If the moon came to a stop without any wobbling, then the
transference of atmosphere and seas to the farthest off hemisphere,
and the gravitation of the liquid matter of the interior to the side
nearest to us, might be more gradual but would finally and certainly
come to pass. And here we must specially note that if it made one
rotation for each revolution, or one rotation in any length of time or
under any circumstances whatever, these transferences of matter from
one hemisphere to the other could not have taken place, because there
would be no stationary region to which they could be transferred by
centrifugal force, as each part of its circumference would in its turn
occupy that region. And above all--be it specially marked--because the
moon would not, in that case, always present its same side to the earth.
Looking upon the moon as a hollow sphere of somewhat the same
proportions as we have made out for the earth, the region of greatest
density would be at about 234 miles deep from the outer surface, the
interior surface of the shell at the depth of 692 miles, and the
hollow centre 776 miles in diameter, as long as it continued to rotate
upon its axis. When that motion ceased and the seas were transferred
to the hemisphere farthest off from the earth, and the liquid matter
in the interior had gravitated towards the nearest, as we have just
said above, its conditions would be very materially altered. Lest it
should be supposed that with a very thin crust, nearly its whole mass
would gravitate to the side nearest to the earth, let us always bear
in mind that the moon would be virtually solid to not far from the
inner surface of the shell, through the pressure of superincumbent
matter, both from without and from within, in the same manner as we
have considered the earth to be. Whatever water had been absorbed by
the crust when it was still rotating on its axis--which, at most,
could have penetrated only a few miles--and even whatever lakes or
inland seas might have been left on the surface always seen by us,
would be soon evaporated by the internal heat, and the heat radiated
by the sun--which Sir John Herschel has calculated to be greater than
boiling water--and driven off in the shape of vapour in the same
manner as the atmosphere had been. These transferences would lead to
two consequences, each one of its own nature, which we must not fail
to notice particularly, as in great measure they explain to us the
constitution, or rather the construction, of the moon. (1) All air and
vaporous matter being translated to the unseen hemisphere would tend to
cool it more rapidly and deeply than the other, not only on account of
the cooling powers of the water, but from the atmosphere and vapours
preventing the heat of the sun from acting so powerfully upon it. (2)
On the other hand, owing to the accumulation of melted, or liquid,
matter in the interior of the side now turned permanently towards the
earth, the formerly solid part of that side would tend to increase in
temperature, which, joined to the heat from the sun not intercepted by
any atmosphere, and continuing without interruption for a fortnight at
a time, would produce a great difference in the temperatures of the two
hemispheres. Thus it is natural to suppose that the thicker and cooler
solid shell on the one side would tend to weaken and drive down the
volcanic forces to a greater depth; while the greater temperature and
thinner solid shell on the other, the down side--the one next to the
earth--would have an exactly opposite tendency and would bring them
nearer to the surface. In this manner we seem to find a very plausible
reason for the great exuberance of the volcanic forces displayed on the
surface of the moon always presented to us.
Both the interior construction and exterior form of the moon, as
modified by losing its rotary motion, would no doubt be very different
to that of a hollow sphere rotating on its axis; but Hansen's "curious
theory" has prepared us for this, by showing that some anomaly in its
construction had been noted and commented upon, although the existence
of the anomaly was not attributed to the atmosphere on its having been
driven away to the far-off hemisphere. But with this subject we have
dealt pretty fully already in Chapter II., which may be referred to for
further explanation if required.
CHAPTER XII.
PAGE
215 Some of the results arising from the sun's being a hollow sphere.
216 Repetition of the effects of condensation on the temperature of
the nebula.
217 Ideas called up by the apparently anomalous increase
of temperature.
218 How heat is carried from the sun to the earth.
219 The sun supposed to radiate heat only to bodies that can receive
and hold it, and not to all space. The heat of the sun
accumulated in a hot box to considerably beyond the boiling
point of water.
220 The heat accumulated in this way supposed to be due to a peculiar
function of the ether, as it is a fact that heat can be
radiated from a cold to a hot body.
221 The sun must be gaseous, or rather gasiform, throughout.
No matter in it solid or even liquid. Divisions and
densities of shell.
222 The hollow centre filled with gases, whose mass naturally
diminishes the mean density of the whole body.
223 The amount of this reduction so far defined. The presence of
gases or vapours in the hollow a natural result
of condensation.
223 The hollow centre filled with gases not incompatible with
the sun's being a hollow sphere. The temperature at the
centre may be anything, not depending on any law of gases.
224 Further exposition of hollow-sphere theory put off till after
further development of the construction of the sun.
In the last chapter we have endeavoured to point out how much our
knowledge of the interior construction of the earth and moon has been
increased, and how many difficulties in the comprehension of their
construction are overcome by the fact demonstrated in previous parts
of our work that they are hollow bodies; and we now proceed to show
some part of what may be learned from studying the sun under the same
conception of its being a hollow body. We say part of what may be
learned, because the whole seems to us to be so great that it would
take much more time and space, not to speak of knowledge, than we can
devote to the subject to make even a proper beginning to such a study.
To our sight it takes away the necessity for guessing in the dark at
what the construction may be, which is all that has hitherto been done;
and furnishes the means of discovering, with intelligent study and
investigation, what most probably is the actual constitution of the sun.
In Chapters V. and VII. we have followed up the contraction and
condensation of the residue of the original nebula, after it had thrown
off all the known planets; first, to the diameter of 58,000,000 miles,
with density of 1/274th of an atmosphere and temperature of -273°,
or _one degree_ of absolute temperature; second, to about 9,000,000
miles diameter, with density equal to air at atmospheric pressure, and
temperature represented by zero of the centigrade scale, or what has
been hitherto called 274° of absolute temperature; third, to 4,150,000
miles diameter, with density equal to ten atmospheres and temperature
of 2740° of actual, or 2742° of absolute temperature; and fourth, to
972,895 miles diameter, with density equal to water and temperature
which we do not venture to express. All these stated densities and
temperatures are understood to be average, the temperatures being those
the various stages would have had, had no heat been radiated into space
by them.
Here, then, we might go on to set forth what might be the interior
dimensions, various densities, and conditions of each one of the four
stages, under the conception of their being all hollow spheres, and
afterwards carry on a _résumé_ of the whole of them and apply it to the
sun as it is at the present day; but this, in addition to involving
an immense deal of difficult work, subject to errors and omissions in
operation, would not do much towards enabling us to explain in a more
simple way what may be, most probably is, its interior construction. We
shall, therefore, look upon the four stages as represented by a model
having the diameter and other known measurements of the sun in its
present state.
To begin what we propose to do we believe it is necessary to repeat,
as a thing that has to be borne in mind, that when we had contracted
the original nebula from 6,000,000,000 miles in diameter to
58,000,000 miles, its density was only equal to a barometric pressure
of _one-ninth_ of an inch of mercury, and its mean temperature had
been increased only _one degree_, that is, from -274° to -273°; and
we can add that, although we had given the original nebula ten times
that diameter, the result both in density and temperature would have
been the same when it was condensed to 58,000,000 miles in diameter.
Then, again, we believe it necessary to repeat that by contracting the
nebula from 58,000,000 to 9,000,000 miles in diameter its mean density
was raised from 1/274th to full atmospheric pressure, and its mean
temperature from -273° to zero of the ordinary centigrade scale, i.e.
to the temperature of freezing water. These two results strike us,
at first sight, as somewhat remarkable, seeing that what looks like
almost unlimited condensation to 58,000,000 miles diameter produced
only one degree of temperature, while the comparatively insignificant
condensation of from 58,000,000 to 9,000,000 miles in diameter produced
273° of heat, _in the way we are accustomed to measure heat_.
Following up these two facts gives rise to ideas that have been borne
in upon us ever since we stumbled upon them when making the analysis
of the nebular hypothesis. One of these notions was that, were it
practicable, the most effectual mode of liquefying gases would be by
putting any one of them into a sealed vessel, and confining it in
another vessel in which a vacuum of 1/274th part of an atmosphere could
be produced; no difficult matter as far as the vacuum is concerned,
for a good exhausting air-pump would be all that is required. But
the practicability? The vessel in which the vacuum is produced would
have to be protected so that no extraneous heat could be conveyed or
conducted into it in any way whatever. How this could be, or is, done
without cutting off every possibility of manipulating the enclosed
vessel, we do not see; but it seems evident that some method is
available because something presenting the same difficulties has been
actually done, as everybody knows. The only degree of vacuum of any use
in the exterior vessel would be about one-ninth of an inch of mercury,
because that would as we have just said, furnish a temperature of
-273°. There would be no necessity for applying pressure to the gas
experimented upon. In fact pressure would be an obstacle to the
experiment, according to the theory of the air thermometer; and could
only be of use by furnishing a larger quantity of liquid to be handled
and examined.
Another idea is that there can be no such condition as absolute zero of
temperature of what we are accustomed to think of as a gas, as far as
science is concerned; as on arriving at that condition, perhaps long
before, any gas would slip out of its hands altogether. But there is a
much more rational reason than this, which we have brought forward on
a former occasion. We are taught that heat is a mode of motion, which
means that as long as there is heat there will be motion to account for
it, so that motion would have to be annihilated on the earth before
absolute zero of temperature could be reached. We have, then, to come
back to what we said when treating of the heat of space, and look upon
the temperature of the vibration of the ether as being the lowest that
can be measured by science. We said then that it must be far below
-225°. Since then a temperature has been reached of within 23° or 24°
of absolute zero, according as that condition is measured by 273 or 274.
This, of course, leads us to think of the ether as a carrier of light,
heat, etc., and of how it can carry heat to the earth without becoming
heated itself, as there can be no doubt about its being a material
substance. How it can bring what may be called considerable heat to
the earth and still have little or no heat in itself; even should it
turn out, which we do not believe possible, that the estimates of the
heat of space of -150° and -142°, made about the beginning of this
century by Sir John Herschel and Pouillet, turn out to be near the
truth. We have seen, in "Nature" of July 15, 1886, a monograph by
Captain Ericsson, in which he shows that the heat radiated by the sun
to where his rays strike our atmosphere is somewhere about 83°F., and
it is not easy to see how radiated heat can be transmitted through 90
million miles of space at a temperature of much lower than -225°, and
reach the confines of our atmosphere with the heat of 83°F. There is
one supposition that occurs to us under which this can happen, and that
is, that the sun only radiates heat to bodies which can receive it,
and does not radiate it into all space where there is nothing but the
ether to hold it. This, of course, implies that the ether acts the same
part--the part for which it was really invented--with respect to heat
that a telegraph wire does with respect to electricity; in which case,
we could imagine that it starts from the sun with the maximum heat
radiated by him, and that this goes on decreasing in the ratio of the
square of the distance it travels through, the same as is understood
to be the case with all radiated heat; and that the part of space not
occupied, for the time necessary, by these connexions might be supposed
to form the return current which we believe must exist, just the same
as the earth does for electricity. For that there is a return current
is demonstrated by the fact that the earth radiates heat into space
when the sun is not shining upon it. Again, even in this case, we
have another difficulty thrown upon us, over and above that cited by
Captain Ericsson, of the heat delivered at the bounds of our atmosphere
being about 83°F., by our being informed in "Engineering" of December
4, 1885, that: "A hot box, contrived to observe the temperature which
could be attained by the unconcentrated solar rays, was used on Mount
Whitney, 12,000 feet above the sea"--well within the limits of our
atmosphere--"and that the enclosed thermometer rose to 233·3°F. on
September 9, 1 p.m., 1881, the shade thermometer then reading 59·8°F."
How are we to comprehend these two facts? We have seen a way of
getting over part of the first fact as far as to the boundary of our
atmosphere, but from there we have to carry 83°F. to the top of Mount
Whitney, through the atmosphere there and present it along with the
other lot in the hot box at 233·3°F.
We may get the beginning of what may be an explanation of all the
facts from another part of Captain Ericsson's monograph, where he
says: "Engineers of great experience in the application of heat
for the production of motive power and other purposes deny that
the temperature of a body can be increased by the application of
heat of a lower degree than that of the body whose temperature we
desire to augment." The soundness of their reasoning is apparently
incontrovertible, yet the temperature of the mercury in the instrument
just described raised to 600°F. by means of the parabolic reflector,
increases at once when solar heat is admitted through the circular
apertures, although the sun's radiant intensity at the time may not
reach one-tenth of the stated temperature. It should be mentioned that
the trial of this new pyrheliometer has not been concluded, owing to
very unfavourable atmospheric conditions since its completion. For
our present purpose the great fact established by the illustrated
instrument is sufficient, namely, that the previous temperature of a
body exposed to the sun's radiant heat is immaterial. The augmentation
of temperature resulting from exposure to the sun, the pyrheliometer
shows, depends upon the intensity of the sun's rays.
A little study shows us that the steam engineers are perfectly right
in their doctrine. The heat of steam can only be called a variety of
the temperature of water. At 300 lb. pressure per square inch the heat
of steam is 417·5°F., while at 20 lb. pressure it is only 228·0°F.,
and therefore the steam engineer has good reason to say that steam at
the lower pressure--or derived from heat that can only produce that
pressure--can add no heat to the higher; on the contrary, the only
possible means of applying the heat of the lower to that of the other
would be by mixing them, and we know what the result of that would
be. This brings before us the fact that the steam engineer's heat is
very limited, and can only be communicated in certain ways, while the
sun's heat is comparatively unlimited, and can only be communicated
to anything through the medium of the ether. But it probably teaches
more than that. Were the engineer's heat unlimited in quantity at
low pressure it can easily be believed that it could be transmitted
to another body at any temperature by radiation, the same as it is
radiated from the sun to a hot box; but it is not, and we thus seem
to find that radiation is a mode, possessed by the ether alone, of
conveying heat from one body to another. It has nothing whatever to do
with mixing, conduction, convection, or anything, except in so far as
the ether is mixed in a more or less limited quantity with all matter.
In support of this idea we can refer to Professor Tait's treatise
on heat, where we find it stated that "heat does pass (though on an
infinitesimal scale) from colder to hotter bodies"; and we can easily
understand that the infinitesimal quantity so passed is due to the
comparatively infinitesimal quantity of ether there is in either of the
two bodies to perform the work of transference. Professor Tait has not
told us how heat is carried from a cold to a hot body, but there can
be no doubt about its being a function of the ether which can only be
found out by a careful and analytical study of that agent. Such a study
we propose to undertake presently without much expectation of being
successful, but still with the hope of helping in some measure to find
out how the ether operates. Meanwhile we shall return to what we had
begun to say about the sun being a hollow sphere, and to our proposal
to treat of the nebula contracted from 58 million miles to its present
diameter, as if it were a model representing a _résumé_ of all the
effects produced on the nebula by that amount of condensation.
We know from all our work that the sun must be a gasiform body, which
means that all the cosmic matter contained in it must be in the form
of vapour, even although its consistence should outrival a London
fog--notwithstanding that some physicists have supposed that it may be
solid at the centre through extreme pressure--and it is not altogether
correct to compare its construction to that of a solid body such as the
earth; but as we have no other we shall begin to make a comparison with
it, which, it will be found, can lead us into no appreciable error.
Considering then the sun to be 867,000 miles in diameter, with mean
density of 1·413 that of water, the hollow part being still completely
empty, and applying to it the same proportion we have deduced for the
earth, we find that the region of greatest density would be at 0·7937
of the radius of the sphere--a proportion really derived from the
line of division into two equal parts of the volume of a sphere--from
the centre, or 89,431 miles from the surface; and the inner surface
of the shell at 0·548--a proportion derived from our calculations for
the earth--of the radius of 433,500 miles, or 237,558 miles from the
centre; which in turn makes the shell to be 195,942 miles thick, and
the hollow centre to be 475,116 miles in diameter. On the other hand,
still following the proportions derived from the earth, we find that
the density at the surface might be one-third of the mean density or
0·471; that it might be one-fifth greater than the mean, or 1·7 at the
region of greatest density and one-half, or 0·71 at the inner surface
of the shell--all of these three densities being in terms of water.
Now, the hollow centre of 475,116 miles in diameter would have a
volume of one-sixth of the whole volume of the sun, which, filled
with gases, would diminish all these densities just in proportion to
what may be considered the degree of compression and condensation
the gases might be subjected to. That there should be gases in the
interior hardly requires to be more than stated, as there can be no
doubt that the degree of heat to which the shell had arrived by the
time it came to have the dimensions above mentioned, would be amply
sufficient to excite chemical action among the elements of which the
sun is composed; and the gases or vapours produced by that action would
flow as naturally towards the interior of the hollow centre as towards
the space beyond the outer surface of the shell, until they were
stopped by increase of pressure, which of course would mean increase
of density in this case. We see then that if the hollow centre has a
volume of one-sixth of the whole volume of the sun and we multiply this
volume by 6, we have a mass equal to the whole mass of the sun, were
its mean density only the same as that of water. Consequently, if we
multiply the said volume by 6 and by 1·413, that is by 8·478, we get
a mass equal to the whole mass of the sun at its known mean density.
Again, were we to suppose the hollow centre to be filled with gases
of the same specific gravity of air, condensed to a pressure of 6560
atmospheres--which would correspond in density to 8·478 times the
density of water--we should have in the hollow centre alone a mass
equal to another sun, in addition to the one made up by the dimensions
and densities stated above. We see then that if we fill the hollow
centre with gases at the pressure, and with the density just stated,
we have a sun of twice the mass it should be. But if we leave the
specified gases in the hollow with one-half of the above density, and
deduct the equivalent mass of the other half density of the gases from
the shell, as estimated for the hollow centre, we should have a sun of
the mass required by astronomy. In this way we should have the three
specified densities reduced from 0·471, 1·70 and 0·71 to 0·236, 0·85
and 0·355, for the outer surface, the region of greatest density, and
the inner surface of the shell, respectively; and the pressure and
density of the gases in the hollow centre reduced to 3280 atmospheres.
Thus, from what has just been shown, which at first sight may be
thought very irrelevant matter, we discover that it is not necessary
that there should be any matter in the sun even so dense as water. And
still we have to think of what an insignificant pressure three or four
thousand atmospheres would be in the centre of the sun.
No one will pretend to allege that no gases can be produced in the
shell of the sun, or to say anything against those formed in the
inner half of it finding their way to the hollow centre, and going on
increasing there till they were able to force their way out through
the shell; that is, until their pressure was equal to the resistance
offered by the gaseous body of the sun, or against their temperature
increasing until it came to correspond to their density and most
probably rising to a much higher degree. Such, then, must even now be
the construction of the sun, as reduced to its present diameter and
density. That is, a hollow sphere consisting of cosmic matter combined
with gases and having a hollow centre filled with chemically formed
gases or vapours.
Here it may be argued that the sun ceases to be a hollow sphere, but
that is not so. The most that can be said about it is that it is a
hollow sphere with the empty part filled up. It would only be in much
the same condition as a hollow globe of iron filled with melted
antimony or bismuth. Its construction would be in no way changed by
the empty hollow being filled up, so long as its condition remained
gaseous--not changed to liquid or solid. The only difference in our
sphere would be that its density would virtually be the same from what
we have called the region of greatest density to the centre, which
would not only involve a greater distance of that region from the
surface of the sphere, but another reduction of the above mentioned
densities of the sun; for we cannot in any way imagine that the
pressure in its interior can be less than many thousands of atmospheres.
Whatever may be the relative densities of the shell and the gases in
the hollow, they will have no necessary effect upon the temperature
of the latter, because, let the densities be what they may, the gases
might be cooled down to absolute zero of temperature, or raised to
any imaginary degree without any change being made in their weight as
long as their volume was maintained the same. This has been proved by
laboratory experiments almost as far as possible. Gases at very high
degrees of pressure and consequent densities have been cooled down
to not far from the absolute zero of temperature, while others under
very low pressures have been heated up to nearly as great heat as the
enclosing vessel would bear, without their weight being altered in
either case; but in the sun there is a larger laboratory in which we
can place no limit to pressure or temperature. We know, however, that
pressures are required sufficiently great to blow out jet prominences
with velocities of 100,000 miles per second or more, to heights 200,000
and even 350,000 miles above the photosphere; and if we knew what these
pressures are we might be able to learn something about the minimum
temperatures of the gases. To obtain these pressures we have--in the
construction we are advocating--a real containing receptacle with sides
195,942 miles thick, in the outer half of which we have the compressing
force, due to the gravitation of the whole mass of the sun acting at
the centre, and over and above, both in it and the inner half, we have
the cohesive force of the matter of which it is composed. In fact we
have a sun whose construction we can understand, in which we have
gases shut up without their expansive forces being impaired in any
way, ready to be exerted with full energy whenever they are relieved
from compression by any commotions in any part of the whole body, and
taking their part in keeping the whole of the matter composing it in
constant motion. How these commotions are produced it is not difficult
to explain to a very considerable extent at least, but this we must
leave over until we have reconstructed the original nebula, and shown
how the solar system could be elaborated from it, almost exactly in the
way conceived by Laplace in his nebular hypothesis. We shall then also
be able to extend our exposition of what is to be learnt from our mode
of construction, and to still further reduce our estimate of the mean
density of the sun.
Meanwhile we have to go into another long digression, with the view of
trying to find out something about what the nature of the ether is or
may be, which we think to be quite necessary before we go any farther.
CHAPTER XIII.
PAGE
226 The ether. Its nature considered. Behaves like a gas.
227 Can be pumped out of a receiver.
228 Light and heat do not pass through a tube _in vacuo_.
Laboratory experiments examined.
229 Light and darkness in a partial vacuum, though high.
230 Electricity not a carrying agent.
232 Why there are light and dark strata in a high vacuum.
233 The real carrying agent through a high vacuum is the residue
of ether left in it. Digression to consider the aurora.
234 How air may be carried to extraordinary heights. Zones of air
carried up are made luminous by electricity.
236 Comparison of this method with experiments quoted.
237 Experiment suggested to prove whether light passes freely
through a vacuum tube.
238 The ether does not pervade all bodies freely.
239 It must be renounced altogether or acknowledged to be a material
body, subject to expansion, condensation, heating or cooling.
239 How light and heat pass through glass.
240 Temperature of the ether variable. Zodiacal light, cause of.
THE ETHER A MATERIAL SUBSTANCE, PROVED BY ITS BEHAVIOUR.
We have said in a former part of this work, pages 153 and following,
that if the ether is capable of performing all the functions that
are attributed to it, it must have some consistence or substance
of some kind; that it must be matter of some kind in some form,
and consequently must have density in some degree however low; and
we might, for the same reasons, suppose that it must have some
temperature; but as long as we believe that without motion there can
be no heat, we cannot conceive it to have any temperature. No doubt we
might suppose it to be in a constant state of vibration, and to have
the temperature corresponding to that state, whatever that may be; but
this, in addition to leaving us just where we were, would only entail
upon us the task of supplying temperature as well as density to a body
of whose existence no positive proof has hitherto been given, whatever
we may believe about it. At the same time, the evident necessity of
taking its temperature into consideration, seems to supply another
reason for concluding that it is a material substance, over and above
those we have cited now and before.
The general belief regarding the ether has been, ever since it was
invented, that it is a substance of some kind (imponderable and
impalpable?) which fills and pervades all space and matter; but
a little consideration will show that this belief requires to be
modified. The ether is supposed to be the connecting link of the
universe, and the agent for carrying light, heat, electricity, and
magnetism from the sun to the earth and planets, and all over space;
but it has been found that electricity will not pass through a vacuum,
such as has been produced by experimenters, unless it be with a very
powerful current. This, of course, would seem to prove that there must
be almost no ether in such a vacuum; because if there was ether in
it, of the same density as there is in space, electricity would pass
through it with the same ease as it does from one body to another
on the earth or in space; it would seem, also, to justify us in
inferring that electricity would not pass through an absolute vacuum
at all, however powerful the current might be, because there would
be absolutely no ether to carry it; and, likewise, that the quantity
of ether remaining in the experimenter's receiver had as much to do
with the passing of a very powerful current of electricity through
it--perhaps a great deal more--as the small quantity of air, or gas,
or dust not altogether exhausted from it, to which the experimenters
attribute its passage. Moreover, it would appear that when air or any
gas is pumped out of a receiver, the ether mixed with it is pumped out
along with it; consequently it must be a material, tangible substance,
possessing density in some degree, however low it may be. Here, then,
we have, it would appear, proof positive that there is such a carrying
substance as the ether has been supposed to be. It is a thing which we
have not to conceive of, fabricate, or build up in our minds. It is a
thing we can pump out of a tube, and is as much a material substance,
in that respect, as air or any other gas that is as invisible as
itself--yet nevertheless in the tube until it is pumped out.
Against this idea of the nature of the ether, and what may be done with
it, it may be argued that light and heat pass freely through a tube or
receiver _in vacuo_, when electricity refuses to pass; but are we sure
that they do pass? It would be a much more difficult matter to prove
that they do, than to prove that electricity does not, because our
eyesight gives us evidence in the latter case. Besides, there are facts
which, when thoroughly looked into, induce us to believe that light
actually does disappear gradually from a vacuum as it is being formed.
In an article on "The Northern Lights," in "Science for All," Vol.
II., reference is made to a well-known laboratory experiment in the
following words: "We take a glass cylinder, covered at the ends with
brass caps, one of which is fitted with a stop-cock, which we can
screw to the plate of an air-pump. To the brass caps we now attach
the terminals of a powerful induction coil, but as yet we perceive no
result. We now begin to exhaust the air from the cylinder, and as the
exhaustion goes on we soon see a soft tremulous light beginning to play
about the ends of the cylinder; and this, when the air is sufficiently
rarefied, gradually extends right through the cylinder. As we continue
the exhaustion these phenomena will be reversed, the light gradually
dying away as the exhaustion increases. We shall at once perceive how
very much this resembles an aurora on a small scale, and so we have
electricity suggested to us as the agent which produces the aurora."
Farther on in the same article we find that: "Aurora displays usually
take place at a great height--sometimes so high as 300 miles--while
their average height is over 100 miles. At such heights the air must
be extremely rarefied, and we should be disposed to expect that the
electric discharge could not take place through it."
Now, at the beginning of this experiment, it must be granted that light
was passing freely through the glass cylinder from side to side, and
also that, when the electric current was turned on, the electricity
was passing freely through the air in the cylinder though it was not
visible. It could not pass through the glass on account of its being
a non-conductor. Then, when the air had been partially exhausted from
the cylinder, and the "soft tremulous light" began to appear about its
ends, it is clear that some interference with, or change in, the free
passage of light through it must have been produced, both transversely
and longitudinally, which occasioned the difference in the appearance
of the light and caused its tremulous motion. And as change in the
appearance of the light extended through the length of the cylinder
as the exhaustion increased, and finally died away--light, change and
all--when it approached more nearly that of an absolute vacuum, we
cannot help concluding that the light disappeared because there was no
medium left in the cylinder, of sufficient density at least, through
which it could pass; which, of course, means that light cannot pass
through a vacuum any more than electricity can.
The experiment we have cited above may be considered antiquated, but
similar results are presented to us in Professor Balfour Stewart's
"Elementary Physics," where he says at page 399 of the Reprint of 1891:
"Another peculiarity of the current is the stratification of the light
which is given out when it traverses a gas or vapour of very small
pressure. We have a series of zones alternately light and dark, which
occasionally present a display of colours. These stratifications have
been much studied by Gassiot and others, and are found to depend upon
the nature of the substance in the tube." [The ether?] "If, however,
the vacuum be a perfect one, Gassiot has found that the most powerful
current is unable to pass through any considerable length of such a
tube."
[In passing, we take the opportunity to assert, with confidence, that
there can be no perfect vacuum on the earth.]
Here we see the gas or vapour in the tube divided into zones
alternately light and dark, which occasionally present a display of
colours, and are led to infer, from the colours depending upon the
nature of the substance in the tube, that they disappear altogether
when the exhaustion is sufficiently great; and are finally told that
the most powerful current is unable to pass through such a tube of
any considerable length. In this case also, we can say with perfect
confidence that there can be no ether left in the tube, in sufficient
quantity, or else it would be able to carry the electricity through it
much more easily than from the sun to the earth, or from one part of
the earth to another. If we refuse to acknowledge that the ether has
been removed from the tube or cylinder, we are forced to conclude that
it is not the carrying agent, for which alone it has been called into
existence by the imagination of scientists; and we have to invent new
theories, new methods for explaining what we have been accustomed to
think we thoroughly understood. We have to look for a new dog to carry
and fetch. Furthermore, all that has been said about electricity is
equally applicable to light, whether we can prove it or not. If light
could pass freely through the experimental cylinder from side to side,
as it was certainly doing before the exhaustion was begun, we cannot
understand why there should be, first tremulous light which finally
disappeared, and why dark strata were displayed in it by the forced
passage of electricity; unless it was that the carrier of the light was
removed, and then we naturally think of why there should be dark strata
in the tube. We can understand electricity lighting up darkness, but
not its darkening light--it lightens up midday--and we must conclude
that both the one and the other were driven through the cylinder, or
similarly conducted through it, by the same force, or were left behind.
Following up the quotations we have already made from "Science for
All," Vol. II., we now add another for further illustration of what we
have been saying, to wit: "Let us now return to the laboratory, and
see whether we can make any experiment which will throw light upon
this difficulty. If we send the electric discharge through one of the
so-called vacuum tubes--choosing one which consists, through part of
its length, of tube which is much narrower than the main portion--we
find that when the discharge is passing the pressure is greater in the
narrow part of the tube, showing that in some way gas is being carried
along by means of the current, and Professor A. S. Herschel suggests
that in some similar way air may be electrically carried up to these
great heights." This quotation, of course, refers to the Northern
Lights, but it serves to illustrate what we are seeking to show with
respect to the ether.
In this experiment, the explanation of the pressure being greater in
the narrow part of the tube, is exactly the same as that for water
passing through a conduit which is narrower at one place than another.
The same quantity of water has to pass through the narrow as through
the wide part, consequently the velocity and pressure (head) have to
be greater than in the wide part--the water arranges that for itself;
and the seeming difficulty of explanation arose from the idea "that in
some way gas is (was) being carried along by the current," when it was
only the gas that was being lighted up more vividly by the electricity
passing through it, because the same amount of electricity had to be
carried through the narrow part as the wide one. No portion of the
gas could be carried along with the electricity, else it would very
soon have been all accumulated at one end of the tube, or a reverse
current must have been set up to restore the balance, which would
speedily have shown itself. Had the said tube been filled with copper
instead of gas, the experimenter must have known that the electricity,
in passing through it, would have spread itself all through the wide
part, and contracted itself to pass through the narrow part, spreading
itself out again through the other wide part, thus giving rise to
differences of pressures and velocities at the different widths of the
tube; but, of course, he would not have been able to see this, because
the electricity could hardly be in sufficient quantity to light up the
copper, or to impart to it sufficient heat to make it visible. Neither
would the electricity carry with it part, or the whole, of the copper
when passing through the narrow part. It would be the gas lighted up
more vividly, not set in motion, by the electricity that the operator
saw in the experiment under discussion, and, no doubt, if the tube had
been sufficiently exhausted of gas, the light would have disappeared
the same as in the first quoted experiment, and the electricity would
have ceased to pass because there was nothing, in sufficient quantity
at least, to carry it along, not even the universally commissioned
monopolist the ether. Let us ask here: Does not all this seem to prove
that electricity is a carried, not a carrying, agent?
In the quotation made, at page 229, from "Elementary Physics," we are
told that when electricity passes through a gas or vapour of very small
pressure, "We have a series of zones alternately light and dark." Now
we ask, Why should part of these zones be dark? and the only answer
to be given is--simply because there is no light in them, nothing in
them to carry or hold light. Otherwise, we cannot understand why they
should appear to be dark. We cannot imagine a glass tube with light
and dark zones in it longitudinally--we have understood the zone to
be longitudinal; transverse sections would not be zones--at the same
time that light is passing freely through it transversely, i.e. from
side to side, unless it is that in the dark zones there is nothing, not
even the all-pervading ether, to carry or hold light in; therefore, we
conclude again that there is no light where there is no ether.
For an explanation of the existence of light and dark zones in the
almost exhausted cylinder or tube, we refer to Professor Tait's
treatise on "Heat," where he says, in section 358, "What happens at
exceedingly small pressures is not certainly known. In fact, if the
kinetic gas theory be true, a gas whose volume is immensely increased,
cannot in any strict sense be said to have one definite pressure
throughout. At any instant there would be here and there isolated
impacts on widely different portions of the walls of the containing
vessel, instead of that close and continuous bombardment which (to our
coarse senses) appears as uniform and constant pressure." Admitting
the truth of the kinetic theory of gases, we can see that in a vacuum
so rare that only electricity at a very high pressure could be forced
(carried?) through it, we have the prescribed conditions in which
there cannot be "one definite pressure throughout" the whole tube; in
other words, we shall have some places in a vacuum tube where there
is no gas at all, or perhaps even ether, and others where the gas is
so rare that it takes a powerful stream of electricity to light it
up in passing through, whether the lighted-up zones be composed of
gas, or of ether, or part of both. If it did not pass, there would be
no light-streak even. And further, we have to notice that the light
and dark streaks would be changing places constantly, owing to the
collisions of the small number of atoms or molecules of the gas, still
not exhausted from the tube, driving each other from place to place.
All this makes us think of what is the real carrier of electricity
through a partial vacuum, through a gas, or through a substance of any
kind whatever, and we can only imagine it to be the ether. In that
case the conductivity of any substance would depend upon the quantity
of ether contained in it, and we can give no other reason for there
being conductors and non-conductors of electricity. All matter has been
thought to be pervaded by the ether, but we have said before that this
must be the case in a limited sense only. It can be shown that glass
is permeable to ether, and is therefore not an absolute non-conductor.
Metals are supposed to consist of atoms bombarding and revolving around
each other under the control of ether. Intermediate conductors may have
the quantity in them of ether corresponding to their conductivity;
and the compressibility of water, or any liquid, may depend upon the
quantity of the ether mixed with its ultimate atoms.
Although we consider it to be going rather beyond the course we had
laid out for ourselves, we cannot help returning to the article on the
"Northern Lights" in "Science for All," quoted above in connection with
electricity in the presence of a vacuum; because it helps to illustrate
the subject we are dealing with.
In the regions where these Lights are seen, we know that there can be
no want of ether, because it is supposed to pervade all space; but we
know that there must be a very great want of air, or vapour of any
kind, due to the height above the earth at which they are seen. Here,
then, we have a great field for differences of pressures being caused
all through it, by the collisions among themselves of the molecules
or atoms of the extremely attenuated air; we have the higher or lower
pressed zones of the laboratory experiment spread out before us, and
if we suppose currents of electricity to be passed through them, we
have an aurora in the high heavens, a counterpart of what was seen in
the vacuum tube. The bombardment of the molecules continually shifting
their positions and creating zones of different pressures, when lighted
up by electricity, would easily account for the flashes, coruscations,
and changes of the aurora; but, how does the air get up so high as is
stated in the quotation at page 228?
We cannot accept the supposition of Professor A. S. Herschel that
the air is carried up to the height of from 100 to 300 miles by
electricity. We must believe, till evidence is given to the contrary,
that electricity is a carried, not a carrying, power. Conductors of
sound are all material substances; sound is not. It seems logical,
therefore, to conclude that the ether is a material substance, because
it conducts light, heat, etc. etc., which are not material substances.
Proof is therefore required that electricity is a material substance,
before it can be called a carrier. That air does somehow get up so high
there can be little doubt, as is satisfactorily proved by the burning
of meteorites when they come into our atmosphere at heights said to be
more than 300 miles. How it does mount up so high is not so wonderful
as it seems, when we take into consideration the causes of the trade
winds, which are: The upward currents of the air created by the heat of
the sun; the centrifugal force inherent in it at the time of leaving
the earth; and its angular motion, which may be, at a guess, from 10 to
16 miles per minute, seeing that the equator has an angular velocity
of over 1000 miles per hour. Then, from the time it leaves the earth,
the air must begin to lose its angular velocity, the impelling power
being cut off, and form a bank higher up, opposing the motion forward
of all the air following it, so that immediately above the tropics
there must be forward motion and obstruction, producing whirlwinds
of which we can see or know really nothing, though they must exist,
and which may carry air or vapours up to very great heights, carrying
with them densities far beyond what would correspond to the simple
attraction of the earth. At these heights this attraction would be very
much diminished, and almost the only way in which the density of the
whirlwinds could be diminished would be by expansion, which would not
be very active in bodies already very considerably attenuated, as the
whirlwinds would naturally be. Their movement towards the poles would
be the same as that of the trade winds has always been supposed to be;
and we can now see how there can be air at great heights in the aurora
regions, not carried up by electricity. In fact, the air may, or rather
must, have carried the electricity up with it, as we shall, we believe,
presently see.
We have not supposed that all the air, raised from the earth by the
heat of the sun, is carried up to such altitudes and to its polar
regions, but only a very small part of it; and we have to add that
there is perhaps not always electricity present in sufficient quantity
to illuminate the air when it is carried up, which would, from the
nature of its ascent, be undoubtedly divided into zones, streams, or
belts at different degrees of tenuity. We do not doubt, or rather we
believe, that electricity is always present in the atmosphere; but we
are not sure that it is always so in sufficient force to make itself
manifest. A very homely example of this is: Stroke a cat's back in
ordinary circumstances, and it will only arch it up in recognition of
the caress; but stroke it on a frosty night and it will emit sparks of
electricity. The cat's hair does not shine--perhaps fortunately for the
cat--because the electricity in it is not present in sufficient force,
and only shows itself when the hand acting like a brush collects it
into sparks. This shows not only that electricity is more abundant in
the air at one time than at another, but that it is more so in cold and
dry than in warm and moist air. It also shows one of the reasons why
auroras of great brilliancy and extent are not continually in play in
their own special regions, which is the want of a sufficient supply of
electricity; another reason being, the absence of the requisite zones,
or masses of air in cyclonic motion at different pressure and in
sufficient quantity. We understand from what we have read that the glow
of the aurora is seldom awanting in clear weather in the far north, and
can imagine that there is always a sufficient supply of electricity
and attenuated air to maintain the glow constantly; and also that the
brilliant displays are only made when there is a sufficient influx of
whirlwinds of air at low and varying pressures, and of electricity in
sufficient force to light them up. We should suppose that the bright
flashes would take place where the pressure was greatest, and the
illuminated darkness, so to speak, where it was least. Electricity does
not carry up air to these heights, neither does magnetism bring it down
from the sun; still a magnetic storm produces brilliant auroras.
Confronting these reflections with the laboratory experiment we have
cited at page 228, we see that they are very fully confirmed by it;
perhaps it would be more true to say that they were originated by
it. When the current of electricity was first turned into the glass
cylinder, no result was perceived. This must undoubtedly be construed
into showing that the light in the cylinder, passing through it
from side to side, was more powerful than the diffused light of the
electricity passing through it from end to end; which was the reason
why there was no result. By diffused, we mean that the electricity,
turned into the cylinder through a thin wire, would immediately spread
out over the whole of its width (or cross section) and thus very much
weaken its light-giving power. When exhaustion had proceeded to a
sufficient extent to produce the soft tremulous light, we can only
conceive that the transverse light had decreased so far that the
diffused light of the electricity, passing longitudinally, had begun
to balance it, which caused the tremulous appearance on account of the
one beginning to disappear and the other to take its place. And when
the light extended through the whole length of the cylinder and the
phenomena were reversed; and when the light died away altogether, when
the vacuum became sufficiently pronounced; we can only believe that
there was no light at all in it; neither natural light passing through
it transversely, nor light of electricity passing longitudinally.
Should any one object to this demonstration, as we may call it, we
refer him to the quotation, made at page 229, from Professor Balfour
Stewart's "Elementary Physics," and ask him, How could there be dark
zones in a tube, through which light ought to pass freely from side
to side? The thing appears to be tremendously absurd. There were dark
streaks in the tube and other streaks of gas, or vapour of some kind
at very low pressures (see also quotation from Professor Tait at page
232) that were lighted up to some extent by the current of electricity,
but even these died away. We do not pretend to impugn the idea that the
stratification of light and dark zones depended upon the nature of the
substances in the tube, we only want to insist that the substances left
in it were so extremely rare that electricity could not pass freely
through it longitudinally, nor daylight transversely, else there could
have been no dark zones in it; and that even the ether was in such
small force that it could not perform the carrying duties assigned to
it.
We have often wondered whether any experiments have ever been made
to ascertain whether any changes, as far as the presence of light is
concerned alone, have been brought about by producing a vacuum in a
tube. The gradual dying away of light, and its final disappearance,
are certainly suggestive of changes, and may have excited curiosity to
know what actually happens. That there are changes cannot be denied,
and it would be satisfactory to know what they are. It appears to us
that one simple and easily made experiment would give a good deal of
information on the subject. Let a glass tube of cylindrical form--one
of those prepared for vacuum experiments--be placed in a slit in the
window-shutter of a dark room, so that absolutely no light can pass
into the room except through the hollow part of the tube; which might
be effectually managed by burying two opposite sixth parts of its
circumference in the wood of the shutter, and there would still be left
one-third of its diameter for the free passage of light from side to
side. When so arranged, and when still full of air, let a spectrum be
taken of sunlight passing through it, to serve for comparison. Then
let a high vacuum be produced in the tube, and another spectrum taken
and compared with the first. This will at once show whether any change
has been produced or not. Should the difference we expect be found,
the experiment might be extended by spectra being taken at different
degrees of exhaustion, from which some useful information might be
derived.
We have said, at page 129, that the ether does not pervade all
bodies of all classes, and such must be the case in some measure at
least, otherwise there would be no non-conductors of electricity, no
insulators for our electric telegraphs and deep sea cables. Were glass,
for instance, pervaded freely by the ether, and the ether is in reality
the carrier of electricity, then electricity could pass freely through
glass, but it does not; therefore, there can be no, or at all events
very little, ether in glass or any other insulator. We can see, then,
the possibility of the ether being removed from a glass tube, provided
it is a material substance, by shutting up one end of it with a stopper
of glass and passing a perfectly-fitting glass piston through it to
the other end. Suppose this done, it would be quite safe to say that
electricity could not pass through the tube, because there would be
nothing--absolutely nothing--to carry it, not even the piston-rod, for
we could have that not only made of glass but on the outside of the
piston. In this case the result would be exactly the same as when the
contents of the tube were pumped out of it, and the residue left, if
any, would be the same, that is, an immeasurably small quantity of the
ether which had filtered through the glass. It may be argued that it
would be impossible to make such an experiment as we have proposed,
but that does not damage in the slightest degree the correctness of
the consequences deduced from it; any more than the impossibility of
constructing a perfect heat engine destroys the deductions drawn by
Sadi Carnot, from the study of such an ideal machine. We can grant that
glass being not an absolute non-conductor, the ether might, in course
of time, ooze through it and fill the tube again, while gas, air, or
dust could not so ooze through it, and thus re-establish the current
of electricity that was stopped for want of it; but we cannot grant
that there was any very perceptible quantity of ether in the tube, when
the electric current could not pass through it without dismissing the
ether altogether, and dropping back into the difficulties out of which
it has in many cases lifted us.
The evident fact that the ether cannot pass through glass freely,
and therefore cannot carry electricity with it, may be disputed by
referring to the free passage of light, and also of heat, through glass
and other substances, in virtue of transparency and diathermancy, two
terms that have the same meaning, at least, as nearly as that light
and heat mean the same thing; but we believe that this free passage,
instead of invalidating our reasoning, only tends to prove that the
ether is a material substance; because, if it is not, it might pass
through transparent bodies just as easily as light and heat do. Of
course, this belief obliges us to show how light and heat do pass
through a transparent body such as glass, and the mode is exactly the
same as of heat passing through any other body that is a conductor
of heat. Glass is a substance that is known to be a bad conductor,
but it is also known that it is not an absolute non-conductor of
heat; therefore, there is no difficulty in supposing that it, and
its companion light, can be conducted through glass with velocity
proportioned to its thickness. We know that in the case of a pane of
glass in a window it is practically instantaneous, but that does not
mean that it is absolutely so. We know also, that in passing through,
both are refracted, and that comparatively little heat is imparted to
the glass, even under bright sunshine, which may be very well accounted
for by the ether on the other side of the window pane carrying them
(light and heat) off, in the same direction they were going, quite
as fast as they could be conducted through the glass. But, supposing
there was no ether in the room to which the window gave light, or gas,
or elementary matter of any kind--a condition which could be obtained
by making the room of glass and pumping out its contents as was done
with the vacuum tube--What would be the result? There would be no wave
motion to carry on light and heat into the room, and it would be
in the same state as the exhausted tube, except that there would be
no electricity in the room--no current being passed through it--nor
anything in sufficient quantity to be lighted up if there was; the
light would be stopped and reflected back from the glass, and nothing
inside the room could be seen; not even that it was dark, because there
would be no electricity to make dark zones visible. The window, or
rather the whole room, would become a many-sided mirror, for reasons
almost identical with those that account for a sheet of glass being
made into a mirror.
We confess that all these deductions have startled us, but we can see
no flaw in the reasonings which have led to them. If it is not for
want of ether--in sufficient quantity at least--and the admission of
variable quantity is to admit that it is a material substance, that
electricity will not pass through a highly exhausted tube, we cannot
imagine what can be the reason why it does not; simply accepting it as
a fact is by no means satisfactory. In the dilemma between renouncing
the ether altogether or acknowledging its disappearance--effective at
least--it occurred to us that it might be for want of heat, and that
in terms of the inter-dependency of temperature and pressure in a gas,
heat disappeared in proportion to the decrease of pressure in the air
or gas that was being exhausted from the tube, or from cold being
applied to it from without; but that notion has already been disposed
of by our own work, when we have seen that a gas in a close vessel can
be heated or cooled to any degree, altogether independently of pressure.
When, acknowledging that the ether ought to have some temperature as
well as density, we have said that it might have the temperature of
vibration whatever that might be, thereby admitting that we could not
pretend to determine what it is; nevertheless, we may take a look at it
from a distance, and at least see what it cannot be, anywhere within
the limits of our system. We have shown, at page 220, that when the
original nebula was about 29,000,000 miles in diameter, its density
must have been 0·179 that of air at atmospheric pressure, and its
temperature -225°, and that these could be neither the density nor
temperature of space. With this temperature, then, it is evident that
there was still heat enough and to spare in the ether--considering it
to be a material substance--to cause it to vibrate and perform its
assigned offices; and, therefore, it could not be for want of heat that
neither it, nor light, nor electricity could be carried through the
vacuum tube, but for want of the ether in due quantity; consequently,
the temperature of vibration cannot be so great as -225°. Turning
back now to page 129, we find the density of the ether estimated at
1/5,264,800th of an atmosphere, which corresponds to an absolute
temperature of 0·000052° or -273·999948°; but on the following page we
expressed our opinion--well founded, we believe--that the estimate was
too high, i.e. too dense, and that it might be 2, 3, or 4 times, or
more, too great. Be this as it may, we can see that if the ether alone
occupies space--beyond a comparatively very limited distance from any
body belonging to the solar system--it must be almost absolutely free
from temperature of any degree, for the difference between -273·999948°
and -274° is virtually nothing; or it must have a special temperature
derived from the collisions of its own atoms, or from the sun. We have
said more than once that the temperature of space cannot be so high
as _minus_ 225°, and now we cannot believe that it can be so low as
absolute zero, because the ether in it is credited with the motion of
vibration, which must be either the cause or effect of heat. What then
shall we say? We can only speculate.
We can suppose that when the chemical elements were created, or evolved
by some process, and began to attract each other, they had the ether
to carry them into collision and produce heat; and that it, being also
a material substance, became heated to the same degree as the other
matter, always increasing in proportion to its state of condensation,
the ether mixed with the other matter being also, of course, condensed.
Then, following up this supposition, we can see that when the sun came
to be condensed to its present state, the ether must have had the same
degree of heat as itself at its surface, and be of the same density as
it would in our air at the earth's surface condensed to the pressure
of nearly 28 atmospheres; knowing as we do that the attraction of the
sun at the surface of its photosphere is almost 28 times greater than
that of the earth at its surface. Under this supposition, therefore,
the ether might emit light just as surely as any other matter that may
exist, or can be seen, in the corona or atmosphere of the sun, and
might be the cause of the Zodiacal Light, probably more naturally than
any other cause that has been imagined for it.
Mr. Proctor, in his "Sun," has given us a most elaborate description of
how the Zodiacal Light could be produced by the swarms of meteorites
and meteors, that are generally supposed to be floating around the sun
and continually showering in upon it, and we confess that his reasoning
is very plausible; but it, along with other similar hypotheses, has one
very serious defect which it is hard to get over, under our existing
ideas about matter and its origin. If there is a constant rain of
meteorites and meteors falling into the sun now, and the same has
been going on during the multitude of millions of years that it is
supposed to have existed, we have to acknowledge that it must either
come to an end some day, or that there is going on a constant creation
or evolution of matter to keep up the supply. It will not suffice to
accept the hypothesis that the supply comes from other suns, or any
idea of that kind, because each one of them would finally find itself
alone with its planets, etc., if it has any, in its domains the same
as our sun. Neither would it suit the ideas of those who consider that
matter has existed from all eternity and has _made itself_ into all
sorts of bodies or systems to suit them. Without continued creation,
or evolution, matter must end in condensation into one mass. There can
be no self-evolution to keep up the supply of matter. It would require
another and exactly opposite power to unmake the final mass, and
another change to original matter to start anew on the old course.
But we are speculating too soon. It may be said that if the Zodiacal
Light is caused by the ether, and if the ether is a material substance,
it must be exhausted sooner or later, just the same as all other
matter and the whole universe to one mass the same as before; and also
that we have no authority for supposing that the ether can be heated
and cooled or condensed and expanded. But we think that with what we
have done in this chapter, and what we will be able to show in the
following one, we shall be able to get over all these difficulties,
and also show how the universe might be dissolved and renewed by the
ordained process of evolution.
CHAPTER XIV.
PAGE
244 The ether considered and its nature explained. Further proofs
given by Dr. Crookes's work, of its material substance.
246 Highest vacuum yet produced. Absorbents cannot absorb the ether.
247 Dr. Crookes's definition of a gas. Not satisfactory. Why.
248 A fluid required to pump matter out of a vessel.
249 Gas as described by Dr. Crookes would not suit.
250 The ether the only elastic fluid we have.
The only real gas, if it is a gas.
250 A possible measure of the density of the ether.
251 Causes of dark and light zones in high vacua.
252 The real conductor of light in a high vacuum.
254 How a vacuum tube glows, when electricity passes through it.
255 Conclusions arrived at through foregoing discussions.
256 Some exhibitions of light explained.
257 Gases can be put in motion, but cannot move even themselves.
258 The ether shown to be attraction. And primitive matter also.
259 All chemical elements evolved from it. Its nature stated.
259 Action at a distance explained by the ether and attraction
being one and the same.
The idea that the ether can be pumped out of a tube of any kind,
along with the air or gas that has been shut up with it therein, will
very probably be declared to be absurd, by reference to Dr. Crookes's
experiments with his Radiometer, and investigations into the nature
of radiant matter; but when duly considered his work seems to confirm
it, and our reasonings in support of it, in a very convincing manner.
Radiant heat, or light, is shown, no doubt, to penetrate into an
exhausted bulb and to cause a radiometer to revolve, but we have to
consider what is the state of exhaustion at which its force is shown to
be greatest, and why that force decreases rapidly when the exhaustion
is progressively increased beyond a certain point; for a certain amount
of exhaustion is required first of all to diminish the resistance of
the air or gas to the vanes of the radiometer, before the radiant heat
gathers force enough to make them revolve at all. Its greatest power
to produce revolution is shown to be when the exhaustion is at from
30 to 60 millionths of an atmosphere, according to the gas or medium
in the bulb--see "Engineering," Vol. XXV., page 155--and decreases
from that point, often rapidly, as the exhaustion is increased, till
at last it ceases altogether. Everybody who has taken any interest
in the subject, knows that Dr. Crookes has exhausted radiometers to
such a degree that they could not be influenced by the radiation of
a candle placed a few inches from the bulb. We are not told at what
degree of exhaustion this took place, nor at what degree repulsion,
by radiation of heat, is supposed to have ceased altogether, but that
does not matter, even though it should only cease when the vacuum
comes to be absolute--most probably a stage to which it is impossible
to attain. What concerns us is the fact that repulsion by radiation
does reach a maximum at a certain degree of exhaustion, and then falls
off as the exhaustion is increased; and what we have got to consider
is what is the cause of the falling off. We are told it is caused by
the attenuation of the matter, gaseous or material, contained in the
bulb, and we are satisfied with the explanation. But in order to be
thoroughly so, we must insist on believing that it is part of the whole
of the matter that has been operated on; not only of the gas and other
matter to the exclusion of the ether, but of the whole, ether and
all. If the ether is left behind intact, it must perform the offices
it was created for by the imagination of man, or man must discard it
altogether. If it ceases to carry light and heat through a vacuum, it
is of no more use than we found it to be in the case of electricity,
and man is bound to dismiss it as a useless operative, who will strike
work for no reason whatever. Some people have supposed the ether to
be an absolute non-conductor of electricity, because it does not
convey that agent through a vacuum. Will they also declare it to be a
non-conductor of light and heat? If they will not, then they--and we
presume everyone else--must admit that it can be pumped out of a bulb,
in the same way as a gas or any other fluid matter.
Here we are led into another consideration, viz., whether the ether
is exhausted from a receiver by pumping alone, or by the help of
absorption. In his lecture, "On Radiant Matter," delivered at the
British Association, at Sheffield, August 22, 1879, Dr. Crookes said:
"By introducing into the tubes appropriate absorbents of residual
gas, I can see that the chemical attraction goes on long after the
attenuation has reached the best stage for showing the phenomena now
under illustration, and I am able by this means to carry the exhaustion
to much higher degrees than I get by mere pumping;" and that when
working with absorbents: "The highest vacuum I have succeeded in
obtaining has been 1/20,000,000th of an atmosphere, a degree which
may be better understood if I say that it corresponds to about the
hundredth of an inch in a barometer column three miles high." (We quote
from "Engineering," Vol. XXVIII., page 188.)
Now, what are we to think? Are we to suppose that the ether was in
part removed by the absorbents? We think we are justified in saying
that the absorbents had not anything to do with the exhaustion of the
ether, because Dr. Crookes used different kinds of absorbents for the
different kinds of gases he dealt with, and it is hard to believe
that all the _media_ he used were equally effective in absorbing the
ether as they were with the gases. On the other hand, if we consider
that the pumping was the only agent in removing the ether, we ought to
acknowledge that it must have been more effective with regard to it
than to the gases before absorption was resorted to with them; or that
a stage had been reached at which the pump could not extract any more
ether from the bulb. We shall have more to say of this presently. It
is a difficult matter to determine, but there is one thing we can see
clearly; when the exhaustion of the bulb was raised to 1/20,000,000th
of an atmosphere, the density of the ether--of itself--must have been
at a lower degree than that. Consequently if we assume its normal
density to be 1/5,264,800th of an atmosphere, in terms of the estimate
we quoted from "Engineering," it must have been diminished to less than
one-fourth of that when the above high vacuum was obtained; because it
must have been the density of the residual gas, or matter, and of the
ether, added together which amounted to 1/20,000,000th; the same as we
have argued with regard to the solar nebula when at 6,600,000,000 and
29,000,000 miles in diameter.
One thing leads to another, and we have again to repeat our
question--What is a gas? And all the answers we have been able to get
to it hitherto have been far from satisfactory.
A little earlier in the same lecture, referred to a few pages back,
Dr. Crookes, after telling us, very elaborately, what would have been
the definition of a gas at the beginning of this century, goes on to
say: "Modern research, however, has greatly enlarged and modified
our views on the construction of these elastic fluids. Gases are
now considered to be composed of an almost infinite number of small
particles or molecules, which are constantly moving in every direction
with velocities of all conceivable magnitudes. As these molecules are
exceedingly numerous, it follows that no molecule can move far in any
direction without coming in contact with some other molecule. But if
we exhaust the air or gas contained in a close vessel, the number of
molecules becomes diminished, and the distance through which any one of
them can move without coming in contact with another is increased, the
length of the mean free path being inversely proportional to the number
of molecules present. The farther this process is carried, the longer
becomes the average distance a molecule can travel before entering into
collision; or, in other words, the longer its mean free path, the more
the physical properties of the gas or air are modified."
Of course, what we have looked upon as Dr. Crookes's definition of
a gas, ends with the second sentence of the above quotation, and
is far from being sufficiently complete to be satisfactory; but we
have continued to quote from the lecture, because it contains matter
which demands consideration, and helps very powerfully to support the
conclusions we have been arriving at.
Why the definition is not satisfactory, is that it does not tell us
what there is in the spaces between the molecules of what is called the
gas. If there is room for them to move in every direction there must
be spaces between them, and these spaces must either be absolutely
empty, or filled with something. If they are supposed to be empty, then
the molecules being actually small pellets, like diminutive marbles,
or snipe-shot, we immediately begin to think why gravitation does not
make them, being ponderable bodies, fall down to the bottom of the
bulb; and seeing that, by the definition, they are evidently considered
not to do so, we think of what can keep them from falling, and of how
they can be pumped out of a bulb or any sort of vessel. If we fill
a vessel with marbles, snipe-shot, wheat flour, or dust, and set a
pump to work on it, we shall find that we make very little progress
in pumping them out of it. At first we might extract a puff or two of
flour or dust--marbles or snipe-shot by no means--carried into the
pump by any air there might be mixed with them, but that would very
soon come to an end; besides, there would be air, gas, something, in
the interstices--if any--of the flour or dust to drive them into the
pump when a vacuum was formed in it, and the puffs would cease when the
air, which would be in exceedingly small quantity, was all extracted.
But independently of all this, we have supposed the spaces between the
gas pellets or molecules to be absolutely empty, and there would be
nothing to push them into the vacuum created in the pump. There is no
possibility of pumping marbles, sand, flour, or dust out of a vessel
without the assistance of a fluid agent of some kind, water, gas, or
air; and even then it would be done with much difficulty.
Let us, then, suppose there is some such agent filling the spaces
between the atoms of the gas and think of what it must be. Were we to
ask the question we have a strong suspicion the first impulse of many
people would be to reply--With gas of course. But this reply could
not satisfy us. We should immediately be led to think of that gas
also consisting of atoms with vacant spaces between them filled with
something--some more gas; and were we to follow up that thought through
a sufficient number of stages, it is easy to see that in the end the
whole space occupied by any gas would come to be filled up with its own
solid atoms, without any empty spaces between them through which they
could move; and so rendered quite incapable of pushing each other into
a vacuum formed by any pump that might be applied to extract them from
any vessel of any kind; or we must suppose that each particle would
fly of its own good will into the vacuum made by the pump--as it were
on the wings of the morning. But we recall to memory that the wings of
the morning do not always carry us to rest, and we see that filling the
spaces with gas would only end in choking up the vessel altogether. It
might be said: Nobody imagines that the molecules of the gas in the
spaces would be sufficient to fill them up altogether; and then we
have only to ask, What then would there be in the spaces between the
molecules of these successive gases to prevent the whole of them from
gravitating to the bottom of the vessel? And to add that there would
still be empty spaces left, absolutely empty, that would have nothing
in them to help in any way to force the molecules or atoms of any gas
or vapour into a vacuum anywhere. It is clear then that a gas, such as
Dr. Crookes has described a gas to be, could only end in filling the
spaces left between its molecules or atoms. It would be an obstruction
to their collisions and bombardments which form an essential part of
the description or definition.
We must, therefore, have recourse to something else for filling up the
spaces between the molecules of a gas, and the only thing we can lay
hold of is our _limited liability_ agent the ether, which we allow to
do all we want it to do and nothing more. Vapours of solid or liquid
matter would be of no use, for they would only condense into solid
or liquid matter; unless always maintained at their temperatures of
evaporation or ebullition, and that would at the best be only another
form of a gas--nobody would use a liquid to assist in pumping air out
of a vessel--and, besides, we should still have to show what keeps
their particles apart, what fills the spaces between them, which would
force us to appeal to the ether as the only source, just as before. If
there are no spaces between the particles there can be no vapours.
If by pumping air out of a close vessel the number of its particles is
diminished, and we acknowledge that the ether pervades all space and
matter, in a greater or smaller degree, then we must either recognise
that a pump is able to separate the particles of the air from the ether
which pervades it in the vessel, and extract them alone; or we must
acknowledge that along with the particles of the air, the pump extracts
a corresponding portion of the ether. Which of these two consequences
of the pumping we have to choose cannot for a moment be doubtful. It
would be as reasonable to suppose that we could pump the colouring
matter out of a pond of muddy water, or the mud itself, and leave the
clear water behind, as to suppose that the molecules of air, or of a
gas, could be extracted from a close vessel, by a pump, and the ether
left behind in it.
We have called attention two or three pages back to the fact that a
fluid agent of some kind is required, in order to be able to pump
matter of any description out of any kind of vessel. For solid matter
a non-elastic fluid will suit, but for gaseous or vaporous bodies
an elastic fluid is required; but we have just seen that what have
hitherto been considered to be elastic fluids, that is, gases and
vapours, have no elasticity whatever of their own, but are undoubtedly
and in reality solid matter; and that in order to become elastic fluids
they have to be mixed with the ether, or something that has yet to
be discovered, invented, or imagined. If, then, until such a body is
found we take the ether as a substitute, we have to acknowledge that it
must be not only an elastic fluid but a material substance, capable of
being compressed and expanded, and heated and cooled; for nobody could
conceive clearly the existence of an elastic fluid that is not subject
to these conditions. He could not understand how the molecules of a gas
could be contracted, expanded, heated and cooled in a vessel, while the
elastic fluid which gave them liberty to move or to be moved, remained
constantly at one density and temperature. Furthermore, until such a
substitute is found, we have to acknowledge that it is the only thing
we have any idea of corresponding to a gas as described by Dr. Crookes;
that is, a multitude of molecules colliding with and bombarding each
other or their prison walls. But even beyond this we can uphold it to
be the only real, independent gas there is; because, being an elastic
fluid, there is no necessity for there being empty spaces between its
molecules, or even having molecules in the common acceptation of the
term. We have no reason to think that there are empty spaces between
the molecules or particles of indiarubber; and if there are, the ether
is the only substance we can properly conceive them to be filled with.
The law of Avogadro is, that "Equal volumes of gases and vapours
contain the same numbers of molecules, and consequently that the
relative weights of these molecules are proportioned to the densities."
Therefore we must always bear in mind that it is the _weights_, not
the _volumes_, which are equal, and that the volumes may be very
different. On this earth of ours, then, we may say with certainty that
an atmosphere of gas is composed of a definite number of its special
kind of molecules, mixed with a definite quantity of the ether, in
such proportion that the sum of their densities shall be equal to the
density of the air, at atmospheric pressure at sea level, and at 0°
of temperature. Holding this belief, we can see that each molecule,
or rather atom, of each gas must have its own amount of displacement
to enable it to float in the ether with which it is mixed. This would
account in the most satisfactory manner for the diffusion of gases,
whereby any molecule, or atom, may float wherever it is driven by
collisions with its neighbours, be it above, or below, or on a level
with, a molecule of a lighter or heavier gas. Therefore, were it
possible to determine with sufficient accuracy the dimensions of the
atoms of all gases, perhaps even of a limited number of them, it would
be possible to calculate the real density, or specific gravity, of the
ether.
We have not forgotten that when, by pumping, the ether was reduced to
at least one-fourth of its normal density, its buoyant power would be
reduced in the same proportion, nor that, when in a state of rest, the
displacement of a molecule, which enabled it to float in the ether,
would not be sufficient to make it float at one-fourth of that density;
but it might be supposed that when so far relieved from pressure, the
molecule could expand in proportion to the relief, especially if its
form were that of a vortex ring, or of a hollow sphere. However, should
this supposition not be admissible, we shall see presently that it is
not necessary. We know that as long as any degree of heat remains in
a gas collisions of its molecules will continue, dependent on their
attraction for each other, which may drive them to any part of the
containing vessel; and that it can only be when they are cooled down
to the absolute zero of temperature that they can come to be at rest.
But as we believe that the ether can never be reduced to this absolute
absence of temperature, nor completely extracted from any vessel, we
cannot acknowledge that the molecules of any gas, left along with it in
the vessel, could ever come to be absolutely at rest, even although the
molecules did not increase in volume with the diminution of pressure.
And we think this conclusion will agree with the opinion of Professor
Tait, expressed in the quotation, made at page 232, from his work on
"Heat," where he says: "In fact, if the kinetic gas theory be true, a
gas whose volume is immensely increased, cannot in any strict sense be
said to have one definite pressure throughout." This, of course, is
tantamount to saying that the diffusion of gases cannot continue to be
always exactly regular at extremely low pressures, and must vary as the
vacuum is increased; so that the volumes of the atoms and consequent
displacements may continue always the same under all pressures. We see,
then, from this quotation, that in all probability the molecules of a
gas are not always equally buoyed up by the ether in a high vacuum;
which very likely is the reason why there are dark streaks in it;
streaks without any visible molecules of gas in them, because the ether
was not dense enough to keep them afloat.
We have still something to add in support of what we said, at page 238,
of glass not being pervaded by the ether, in the common acceptation of
the word, and of our acknowledging that the ether might, in the course
of time, ooze through it and fill up the bulb again, while air, gas
and dust could not so ooze through it--nor even the larger particles
of the ether; should we be forced to acknowledge that it consists of
particles.
In one of a series of articles in "Engineering," Vol. XXV., on
Repulsion from Radiation, we find, at page 155, what follows: "With
the same apparatus, Mr. Crookes conducted a long series of experiments
for determining the conductivity of the residual gas to a spark from
the induction coil. In air he found, at a pressure of 40 millionths
(1/25,000th) of an atmosphere, which will be seen from the diagram,
is the pressure at which the force of repulsion is at a maximum,
that a spark whose striking distance at the normal pressure of the
atmosphere is half an inch will illuminate a tube whose terminals are
3 millimetres apart. By pushing the exhaustion farther, the half-inch
spark ceases to pass, but a one-inch spark will illuminate the tube,
and as a vacuum is approached more electromotive-force is required to
force the spark to cross the space separating the terminals within
the tube, until at still higher exhaustion a coil capable of giving a
6-inch spark in air at the pressure of the atmosphere is required to
show any indication of conductivity in the residual air. It was found,
however, in experimenting with so powerful a spark that occasionally
the glass was perforated by the discharge taking place through the
bulb; but it is a remarkable fact that the perforation in such cases
was so excessively small that several days were occupied before
equilibrium of pressure was established between the inside and outside
of the bulb."
Here we notice first--and it was the reason why we have made the first
and longest part of the quotation--that the spark whose striking
distance was half an inch at the normal pressure of the atmosphere,
fell to under one-fourth of its power in a vacuum of only 1/25,000th of
that pressure; that when a one-inch spark was required to illuminate
the tube, it must have decreased to one-eighth in a vacuum of
1/50,000th; and, if it be admissible to follow the same proportion,
the 6-inch spark must have been exhibited in a vacuum of 1/250,000th
an atmosphere at least. Perhaps all this experiment was carried on
in _vacua_ produced by pumping alone, and the final vacuum may have
reached a greater height than that which we have just mentioned; but
the most interesting part of it is the perforation of the bulb by the
6-inch spark. In it we have to consider what was the conveyer which
carried the electric spark through the glass of the bulb, instead of
to the other terminal of the coil so close at hand, and it is a very
difficult problem to solve. We naturally recur for some solution to the
stratification of light given out when an electric current traverses
a gas at very low pressure and gives rise to zones alternately light
and dark as noted in the reference we made, at page 229, to Professor
Balfour Stewart's experiments. We cannot think it unreasonable to
suppose that the dark zones contained no matter at all that could be
lighted up, and that it was the lighted zones alone which contained
carrying matter for the electricity. If so, we can easily imagine
one of these zones or strata carrying the perforating spark from the
induction terminal to the nearest part of the glass of the bulb, for it
was as possible for it to lie in that direction as in the direction of
the other terminal, and the difference of distance between the first
terminal and the glass, and between the two terminals, would not be
so great as it appears to be on simply reading the accounts of the
experiments; but we have still to think of how it managed to force
itself through the glass of the bulb.
To get over this difficulty, we can refer to what we have said, that
is, that glass may be thoroughly pervaded by the ether in an almost
infinitesimal degree, and suppose that the electricity may have
discovered, or rather been led to, the ether contained in the glass
tube or bulb, and so found its way to one of the oozing holes we have
said might exist in the glass; even the oozing hole may not have passed
quite through the glass, and there might remain a very thin film to be
burst open before perforation was complete. Also we may note that the
zone which performed the office of carrier to the side of the bulb was
much more probably composed of residual ether than residual air or gas,
or at the least formed a preponderating part of the carrying element.
The fact of the hole being so minute "that several days were occupied
before equilibrium of pressure was established between the inside and
outside of the bulb" on such occasions, goes far to prove that the
carrying agent through the glass must have been the natural carrier
of electricity, light, and heat. We cannot conceive that an eruptive
force could open such a small passage through the glass of the bulb,
but we can conceive that it should be able to force itself through
a very minute passage already open, and even join two or more such
passages into one. This conception makes us think of the many oozing
passages there may be through a glass bulb; passages so minute that
the ether might pass through them, but nothing so gross as any of our
known gases; in fine, so minute that glass, for all the compact look
it presents to us, may be only as a very fine sponge in respect to the
ether. However, that the perforations related in the above quotation
were large enough for air to pass through them there can be no doubt,
otherwise the equilibrium between the pressures on the inside and
outside of the bulb could not have been re-established even after many
days; for there still remains the idea that the oozing holes might be
so small that nothing but the ether could pass through them.
Should the glass of a vacuum tube or bulb be pervaded by the ether in
the manner we have supposed it to be, and we believe there can be no
doubt that it is so, it is obvious that its glowing when a current of
electricity is passed through it must be caused by the electricity and
consequently of its light, being carried into the body of the glass by
means of the ether imbedded in, and forming a constituent part of, it.
In connection with this we have to remember that the air in the tube
does not glow when it is at full atmospheric pressure, but only when
a certain degree of vacuum has been produced in it; and therefore it
is equally obvious that it is only when the ether enclosed in the tube
is reduced to the same degree of tenuity as that imbedded in the glass
forming the tube, that the light of the electricity can be carried by
it into the glass and make it glow. But to show this more clearly, it
is necessary to refer to the steps by which we believe we have made
very plain what must undoubtedly be the nature of the ether.
(1) First of all we have shown that, if there be such a thing as the
ether, it can be pumped out of a close vessel of any kind; which
proves that it must be a material substance, and in consequence can be
expanded, or rarefied, and compressed the same as any other material
substance; and that if there is no such thing, something else, having
these qualities, has to be invented to take its place. (2) In showing
this it has been made abundantly clear by the example of the hair
of a cat in variable weather, to which we may add the exhibition of
lightning in daylight, that it cannot make electricity visible, or
illuminate any matter, unless the quantity of electricity it has to
carry bears some certain proportion to the density of the ether in the
matter that is illuminated. (3) In proof of this we have shown how,
through its carrying power it can convey electricity of adequate force
up to very great heights, so as to illuminate very rarefied air and
cause auroras; the conveying being done either directly from the earth
or by means of the ether mixed with the air carried up by whirlwinds to
those great heights; and (4) how electricity is carried into the body
of a tube of glass and makes it glow.
With these examples we can extend our ideas to other exhibitions
of light, which, otherwise, we could hardly avoid looking upon as
mysterious. We can see how marsh gas, rising up from boggy ground,
becomes mixed with common air till it reaches a certain density, and
forms the Will-o'-the-wisp when there is sufficient electricity in the
air to make the diffused marsh gas visible, through the medium of the
ether always mixed with it; or, perhaps, rather when the density of
the diffused gas corresponds to the density of the ether. Then we have
the phenomena of films of matter on the surfaces of certain liquids
glowing with appropriate colours; which films must be pervaded by the
ether in proportion to their conducting powers, the same as we have
seen must be the case with all kinds of matter, the light given off
corresponding as is natural to the composition of the films; and of
course this same reasoning, or exposition, applies to the films formed
on, or near, the surface of the sea which produce what sailors call
"fire-on-the-wave." Lastly, and akin to the glowing caused in a vacuum
tube, we cite the case of the glow-worm, the radiation from which must
of necessity contain a certain amount of the ether in it, and may
either glow constantly or intermittently according to its capacity for
carrying electricity or light of any kind, constant or inconstant. Or
if there is no radiation from it, its skin may possess the properties
of a film on the surface of a liquid. We have seen in the "Times" of
September 21, 1896, in its report for that day of the Meeting of the
British Association at Liverpool, that in experimenting with glow-worms
Dr. Dawson Turner had found some difficulty in getting them to glow
when he wanted, but found they gave off the radiation whether glowing
or not. Perhaps his interference with them destroyed the balance of
force between the electricity present and the density of the ether in
it without stopping the radiation.
Hitherto the light given out by a nebula, and any light of the kind
not easily accounted for, has been attributed to incandescent gas not
burning or being consumed, but only glowing. Now it is time to look
upon it as belonging, at least in part, to the ether, and to look upon
the bright line in the spectrum of a nebula as the _Ether Line_. We
shall have to return to this later on.
We said, at page 248, that a fluid of some kind, elastic or not
elastic, is necessary to enable us to pump solid matter out of a
vessel of any kind, and went on to show that a gas as described by
Dr. Crookes, or that can be described, in its own independent state
of existence, by anybody, could not supply the want; because it
consists of particles, molecules, atoms--any name that can be given
to them--which have no power in themselves to move or to give motion
to anything; they can be moved but cannot impart motion to anything,
even to one another, until they are first set in motion by attraction.
This in its turn led us to see that the only elastic fluid we have is
the ether, and our work since then has taught us that we were wrong
in saying at page 250 that a non-elastic fluid would suit for pumping
solid matter out of a vessel; for we now see that what we have been
in the habit of looking upon as non-elastic fluids, must owe their
fluidity, such as it is, to the ether, which, in proportionate degree,
pervades them the same as it does all other matter. In this way we are
run down to the only conclusion we can come to, namely, that the ether
is the only connecting medium and carrying agent of matter that we
have, or even initiator of motion, except attraction; and being matter
of the nature of an elastic fluid, there is no reason why we should not
at once consider it to be attraction itself. It has been looked upon,
for no one can exactly tell how long, as the connecting mechanism of
the universe, thus having, in reality, assigned to it the attributes of
the law of attraction, and all that we have to do is to put it in its
right place. We are, in a manner, taught to look with suspicion on two
agents being required to do one kind of work, or even two kinds of work
that are so closely allied that we cannot separate them in a way that
satisfies us; and this is precisely a case in which we can have one
agent that can connect matter, and at the same time carry immaterial
elements from one place to another.
Having got this length we have still to go one step farther. We
cannot now doubt that the ether is a material substance, and if it
is, there is nothing to prevent us from considering it to be the
primitive matter; in fact it would be absurd to look upon it in any
other light. We cannot conceive of anything having been created before
the ether, or ordained before the law of attraction, and thus we have
the two coeval and one. It is long years since physicists, chemists
especially perhaps, began to think that the great number of chemical
elements cannot all have existed from the beginning of things, and
that it is far more probable that they have all been evolved from
one primitive substance, and this idea must now be gathering more
strength from day to day in view of the new elements that are being
constantly discovered; the unknown is being made known, and the air we
breathe instead of being one in four elements, as in former times it
was considered to be, is now not far from double that number in one.
Adopting this notion, then, the ether is much more likely to have been
the primitive element than any other material substance that can be
thought of. If it has never been thought of in this light, it has come
to be very remarkably near it, as may be seen by referring to the long
quotation we made in Chapter VII., beginning at page 129, where the
idea of the ether being the connecting _medium_ of matter is made use
of to compute its density. Little thought we of this when we made the
quotation, but there was the idea whether the author saw or not all
that was implied in it.
Having broached the notion of the ether being the primitive element
of the universe, or at all events, of the solar system, we might be
expected to show how all the other elements were formed from it; but
that has been done for us in a very much more able manner than we could
have done it. Anyone who chooses to refer to "Nature" of September
2, 1886, will find--in Dr. Crookes's opening address, on Chemical
Science in Section B, at the meeting of the British Association for
that year--a very detailed explanation of how all the chemical elements
might have been elaborated from one that he called Protyle; in which
explanation he will only have to change this word into Ether to
comprehend the process much more easily than by any exposition we could
pretend to draw up. To quote the whole address would be altogether out
of place, and besides, our notes of it are only fragmentary. But for
present satisfaction of those who cannot immediately refer to "Nature,"
we may say that in the same report it is clearly stated that Sir George
B. Airy was of opinion that all bodies may not be subject to the law of
gravitation; and have no cause to think it strange we do not see that,
were the ether and attraction one and the same, the whole universe
would be finally collected into one mass, itself included. They will
have better authority than ours for believing that the ether may
connect matter evolved from itself, without being materially confounded
with it. At the same time we acknowledge the necessity for expressing
our idea of what we consider to be its nature, and in compliance with
this obligation we say we have conceived it to be of the nature of
indiarubber, not an elastic fluid as we have called it before, but
rather an elastic substance like a jelly, as some people have conceived
it to be; not a gas, because it does not require any medium to connect
its particles.
Looking upon it in this light, action at a distance can be accounted
for in a very natural manner. When a stretched indiarubber band is
relieved from strain, the relief must be felt instantly throughout
every part of its length; for, although the band may take time to
contract, no time is required for the relief from strain being felt. In
like manner an alteration in strain between the sun and the earth--and
these alterations of strain are taking place every instant--connected
by an indiarubber ether will be felt instantly in both bodies;
and should anyone stand out for time being required to convey the
attraction, let him remember that the difference of its power would be
felt first at the two ends of the connecting medium, for the very good
reason that even attraction itself could not prefer one extreme to the
other. And that is all that is meant by action at a distance.
Here are some other things that could be explained more easily than
they can be at present, through the ether and attraction being
considered to be one and the same, than under any other conception
we can form; but although we have a dim vision of such explanations
in some cases, our knowledge of the sciences involved in them is not
sufficient to warrant us in letting our dim conceptions see the light.
Therefore all that remains for us to add is, that some things we have
said of the ether may have to be so far modified now, but as they have
had their part in leading us to the conclusions we have arrived at,
they cannot be altogether suppressed.
CHAPTER XV.
PAGE
261 Construction of the solar system. Matter out of which
it was formed.
262 Domains of the sun out of which the matter was collected.
263 Stars nearest to the sun. Table VII. showing distances.
265 Remarks on Binary Stars. Table VIII. showing spheres of
attraction between the sun and a very few.
266 Sirius actually our nearest neighbour. Form of the sun's
domains of a very jagged nature.
267 Creation of matter for the nebulæ, out of which the whole
universe was elaborated. Beginning of construction.
267 The law of attraction begins to operate through the agency
of evolution.
268 Form of the primitive solar nebula. The jagged peaks probably
soon left behind in contraction.
269 How the nebula contracted. Two views of the form it might take.
Comparison of the two forms, solid or hollow.
272 The hollow centre form adopted. The jagged peaks left behind.
273 The nebula assuming a spherical form. Shreds, masses, crescents
separated from one side.
274 Probable form of interior of nebula. Compared with envelopes
in heads of some comets.
275 Reflections on the nebula being hollow. Opinions of others quoted.
276 The matter of a sphere solid to the centre must be inert there.
277 Further proofs of the nebula being hollow.
278 How rotary motion was instituted.
279 Such a nebula might take one of two forms.
280 The form depending on the class of nebula. Planetary in the case
of the solar system. A similar conception of how rotary motion
could be instituted.
In this chapter we proceed to consider how the original nebula was
formed, and whether the solar system could be evolved therefrom in the
manner shown in the analysis of Chapter V.
The usual way of treating the solar system has been to suppose it
to have been formed out of a nebula extending far beyond the planet
Neptune, generally in a vague way; although some writers have specified
a limit to the distance, in order to give some definite idea of what
must have been the density of the nebula at some particular period
of its existence. In the first part of our work we have adopted the
same plan and we mean to follow it out, because it gives us a greater
degree of facility for expressing our ideas, and making them more
intelligible, than by adopting a new method. But we shall previously
endeavour to show where the nebula itself came from and how it was
formed, which seems to us to be as necessary as to show how it was
transformed into the solar system.
We understand Laplace to have supposed the nebula to have been formed
out of cosmic matter in its simplest condition, and in its most
primitive atomic state, collected from enormously distant regions
of space by the power or law of attraction. In this we shall follow
him, because we do not see the necessity for matter having to be
created in the form of meteorites or meteors, or any other form, to
be afterwards dissociated and reduced to the atomic state, by heat
produced by collisions amongst the dissociated atoms. Surely it would
show more prescience, more simplicity of work, and economy of labour,
to create matter in this primitive state, than in one which required
it to be passed through a mill of some kind, as it were, before it
was manufactured into nebulous matter; in fact, to make brickbats in
order that they should be afterwards ground down--dissociated--into
impalpable powder, to render them fit to be worked up into bricks. But
our first effort will be to attempt to define the collecting grounds
of this cosmic matter, somewhat more particularly than has been done
hitherto, as we believe that even a superficial study of them will
assist us greatly in forming a more comprehensive idea of the whole
solar system than anything we have met with in any of the books which
we have had the opportunity of applying to for information.
The collecting grounds, then, are clearly the whole region of space
to which the attractive power of the sun extends, or what astronomers
would call within the sphere of his attraction. These domains, like
those of any other proprietor, are limited by the domains of his
neighbours. At first sight, it would seem that his neighbours are
infinite in number, but a little thought will show that the number
may be very limited indeed. On this small earth of ours, it is a very
common thing for a landed proprietor to be able to look over the
domains of his neighbours, and see those of proprietors more remote;
even to look over the domains of his neighbours' neighbours, and see
properties so remote that he does not even know to whom they belong nor
how they are named. With much more reason, the same must be the case
with the sun, more especially as he, from his own mansion-house, sees
nothing of the domains, but only the mansion-houses of others, there
being no landmarks, hills, fences or woods to cut off his view, as
there are upon the earth; the only interruption possible to his view
being that another mansion-house should come to be exactly between
his and that of a farther-off neighbour. For our purposes, we will
assume that his nearest neighbours are those the distances of whose
mansion-houses have been measured, and will adopt the following list
of them, taken from Mr. George Chambers's "Hand-Book of Astronomy,"
part 3, page 10, 5th edition, 1889, and forming Table VII. All that we
can learn from this table is that the boundary between the sun and any
one of the stars mentioned in it must be somewhere on a straight line
connecting the two, but that does not furnish us with any information
as to the extent of the sun's domains, although it does help to give
us some idea of their form. For some knowledge of their extent, we
require to know how far the lordship of each one of the proprietors
extends from his mansion-house; which, very much the same as it does
upon the earth, depends upon the power he has to take and keep it; it
depends on the mass of each neighbour who actually marches with the sun
when compared with his own mass. The list referred to does not help us
in any way to determine this, as we have just said, but we have found
in Professor Charles A. Young's "Lessons in Astronomy," of 1891, page
270, the masses of six binary stars whose distances, calculated from
the parallaxes given in it, furnish us with data from which we can
calculate the distance from the sun of the boundary between him and any
one of them. The number is very small, but still from them we can gain
some notion of what was the form of the domains from which the original
nebula was collected; that is, always under the supposition that the
sun and his system were evolved from a nebula. From these data, Table
VIII. has been drawn up, which shows the distances of the six stars
from the sun, and the limits of his sphere of attraction in relation
to them expressed in terms of radii of the earth's orbit, and also in
radii of Neptune's orbit, which gives numbers more easily comprehended
by us.
TABLE VII.--LIST OF STARS WHOSE DISTANCES FROM THE SUN
HAVE BEEN MEASURED, AND WHICH ARE ASSUMED
TO BE HIS NEAREST NEIGHBOURS.
--------------------+-----+------+----+------------------+-----------+
| M | P | | Distance. | |
| a | r | P |---------+--------| |
Star. | g | o | a | Sun's |Time of | Observers |
| n | p M | r |Distance | its | |
| i | e o | a | = 1. | Light | |
| t | r t | l | |reaching| |
| u | i | l | | Earth. | |
| d | o | a | | | |
| e | n | x | | | |
| | (") | (")| |(years) | |
--------------------+-----+------+----+---------+--------+-----------+
[Greek: a] Centauri | 1 | 3·67 |0·75| 275,000| 4·34 |Gill. |
| | | | | | |
61 Cygni | 6 | 5·14 |0·50| 412,500| 6·51 |O. Struve. |
| | | | | | |
21185 Lalande |7-1/4| 4·75 |0·50| 412,500| 6·51 |Winnecke. |
| | | | | | |
Sirius | 1 | 1·24 |0·38| 543,000| 8·57 |Gill. |
| | | | | | |
[Greek: m] Cassiopeiæ| | |0·34| 606,000| 9·57 |O. Struve. |
| | | | | | |
34 Groombridge | 8 | 2·81 |0·29| 711,000| 11·23 |Auwers. |
| | | | | | |
9352 Lacaille |7-1/2| 6·95 |0·28| 737,000| 11·62 |Gill. |
| | | | | | |
21258 Lalande |8-1/2| 4·40 |0·26| 793,000| 12·52 |Krüger. |
| | | | | | |
Ö Arg. 17415 | 9 | 1·27 |0·25| 825,000| 13·02 |Krüger. |
| | | | | | |
[Greek: s] Draconis | 5 | 1·87 |0·25| 825,000| 13·02 |Brunnow. |
| | | | | | |
[Greek: e] Indi |5-1/4| 4·68 |0·22| 938,000| 14·80 |Gill. |
| | | | | | |
[Greek: a] Lyræ | 1 | 0·31 |0·20|1,031,000| 16·27 | |
| | | | | | |
O^2 Eridani |4-1/2| 4·10 |0·17|1,213,000| 19·15 |Gill. |
| | | | | | |
[Greek: r] Ophiuchi |4-1/2| 1·00 |0·17|1,213,000| 19·15 |Krüger. |
| | | | | | |
[Greek: e] Eridani |4-1/2| 3·03 |0·14|1,473,000| 23·24 |Elkin. |
| | | | | | |
[Greek: i] Ursæ Majoris 3 | 0·52 |0·13|1,586,000| 25·04 |C.A.F. |
| | | | | | Peters.|
[Greek: a] Boötis | 1 | 2·43 |0·13|1,586,000| 25·04 |C.A.F. |
| | | | | | Peters.|
[Greek: g] Draconis | 2 | 0·06 |0·09|2,292,000| 36·17 | |
| | | | | | |
1830 Groombridge | 7 | 7·705|0·09|2,292,000| 36·17 |Brunnow. |
| | | | | | |
Polaris | 2 | |0·07|2,947,000| 46·50 |C.A.F. |
| | | | | | Peters.|
3077 Bradley | 6 | 2·09 |0·07|2,947,000| 46·00 |Brunnow. |
| | | | | | |
[Greek: s] Foucani | 6 | 2·05 |0·06|3,438,000| 54·25 |Elkin. |
| | | | | | |
85 Pegasi | 6 | 1·38 |0·05|4,125,000| 65·10 |Brunnow. |
| | | | | | |
[Greek: a] Aurigæ | 1 | 0·43 |0·04|5,157,000| 81·37 |C.A.F. |
| | | | | | Peters.|
Canopus | 1 | |0·03|6,875,000|108·50 |Elkin. |
--------------------+-----+------+----+---------+--------+-----------+
TABLE VIII.--MASSES OF A FEW BINARY STARS SHOWING THE LIMIT OF
THE SUN'S SPHERE OF ATTRACTION WITH RESPECT TO THEM,
IN RADII OF THE EARTH'S ORBIT, AND DISTANCES OF THEIR
BOUNDARIES WITH THE SUN IN THE SAME MEASURE,
AND ALSO IN NEPTUNE DISTANCES.
-----------+-----+------+-------------+------------+---------------+
| P | |Distance of |Distance of | |
| a | Mass |Star from Sun| Limit of | Distance of |
| r | |in radii of |Sun's Sphere|Limit in radii |
Name of | a |Sun's |the Earth's |of Attract'n| of Neptune's |
Star. | l | Mass | Orbit |in radii of | Orbit |
| l | = 1. | | Earth's | |
| a | |(93,000,000 | Miles. | |
| x | | Miles.) | |= 2,794,000,000|
| (") | | | Orbit = 1. | |
-----------+-----+------+-------------+------------+---------------+
[Greek: a] | | | | | |
Centauri | 0·75| 2·14 | 275,000 | 128,505 | 4,277 |
| | | | | |
61 Cygni | 0·43| 0·23 | 479,686 | 369,358 | 12,294 |
| | | | | |
Sirius | 0·38| 4·26 | 543,000 | 127,465 | 4,243 |
| | | | | |
[Greek: a] | | | | | |
Geminorum | 0·20| 0·30 | 1,031,325 | 721,927 | 24,030 |
| | | | | |
70 Ophiuchi | 0·16| 5·00 | 1,289,150 | 257,830 | 8,582 |
| | | | | |
[Greek: ê] | | | | | |
Cassiopeiæ | 0·15| 3·00 | 1,375,100 | 458,366 | 15,257 |
------------+-----+------+-------------+------------+---------------+
But there is still something to be said with respect to the Binary
Stars of Table VIII., and any others whose masses may be met with later
on. If those forming a pair revolve around each other, or a common
centre, in orbits, it must happen that they will be sometimes more or
less in conjunction, opposition, and quadrature with regard to the sun;
also the angles of the planes of their orbits to direct lines between
them and the sun, whatever these angles may be, will cause variations
in the separate and combined forces of attraction they exercise in
the domains of the sun, at different periods of their revolutions;
so that these powers of attraction will be constantly increasing and
diminishing, and causing the boundaries of their domains to approach
and recede from the sun; thus introducing between their domains and
those of the sun a debatable land, which will reduce celestial to be
very much like terrestrial affairs, where each proprietor, or power,
takes the pull when an opportunity presents itself. No doubt all such
invasions, or claims, between proprietors will be settled by the law of
attraction, without lawsuit, arbitration or conflict; but as law gives
right, and might is right--most emphatically in this case--we come back
to the old seesaw of earthly matters. Well, therefore, many astronomers
teach that the whole universe is formed out of the same kind of
materials, and governed by the same laws that we are having good reason
to know something about on this earth of ours.
Accustomed to look upon [Greek: a] Centauri as the star nearest to
us, on account of its light-distance being so much smaller than any
other noted in our text-books, we were not prepared to find that, when
measured by his sphere-of-attraction distance, Sirius is actually a
rather nearer neighbour to the sun than it; nor that his, apparently,
next nearest neighbour, when measured in the same way, is twice as far
away as either of them; and thus we have the conviction thrust upon us
that they must have made deep hollows in the solar nebula when it was
being formed. On the other hand, when we think of three of the other
stars mentioned in the list of six, being practically from three to
six times farther off than either of them, we come to the conclusion
that the form of the nebula, when in its most primitive state, must
have been of a very jagged character; a conclusion which is very
considerably strengthened when we look at Table VII., and see that the
stars noted in it run up to from twice to not far from thirty times
more distant from the sun than [Greek: a] Centauri. And now, having
got a somewhat definite idea of the form of the sun's domains, we may
attempt the construction in them, first of a nebula and afterwards of a
solar system, such as our text-books describe to us; introducing into
the construction, as a matter of course, the variations from existing
theories which, we believe, we have demonstrated to be necessary.
Perhaps we ought to confine our operations to these domains, and so
we will almost exclusively; but the sun has been so long considered
as one of many millions of stars, and as part of what is now looked
upon as our universe, that we cannot help looking upon the whole as
having been the result of one act of creation; more especially as we
have no reason whatever for supposing it to have been built up piece
by piece; and whatever ideas we may form of our own little part of it,
we are bound to apply them to the whole. We may, therefore, lay the
foundations of our undertaking in the following manner. By creation we
mean only creation of nebulæ.
We shall suppose all space--if we can comprehend what that means--to
have been filled with the ether, and the law of attraction to have
been in force previous to the time when our operations are supposed to
have commenced. These we may consider to have been the first acts of
creation, or to have existed from all eternity. Then, in that part of
space occupied by our universe--even though it should extend infinitely
beyond the reach of our most powerful telescopes--we shall suppose the
work of creation to have begun by filling the whole of that space with
what are known as the chemical elements, reduced to their atomic state.
We do not want to have molecules or particles of matter, or meteorites
or meteors; because they involve the idea of previous manipulation or
agglomeration, but matter in its very simplest form, if there is any
more simple than the atomic. At this stage the most natural idea is to
suppose that the whole of this matter was at rest, without motion of
any kind, because we cannot understand how motion could be an object
of creation, but can very easily see how it might be of evolution; and
because, under the law of attraction, matter had the elements of motion
in itself. Under that law it is quite possible for us to comprehend
that all the suns of our universe could have been formed just as they
are, with all their movements of rotation, revolution in the cases of
multiple stars, and translation or what is called proper motion. And it
is within the bounds of possibility that future astronomers may be able
to show how these movements have been brought about, should it ever be
possible for them to find out and define with sufficient accuracy what
the translatory, or proper, motions are. Then, as for the temperature
of this newly created matter, we have no resource left but to suppose
that it must have been that of space, whatever that may have been then,
even as we have been obliged to say before.
Once created, the atoms of the cosmic matter would immediately begin
to attract each other in all directions, and form themselves into
groups. At first thought it might be supposed that these groups, and
suns formed from them, ought to have been all of the same size, being
formed from the same material under the same conditions, but nature,
or evolution, seems never to be disposed to produce the same results
in its manipulations of matter, whatever they may be. When the water
is drawn off from a pond, and the mud left in the bottom of it allowed
to dry in the sun, it breaks up into cakes of very various shapes and
sizes. No doubt there are physical causes for this being the case,
but, though perhaps not altogether impossible, it would be a hard task
to find them out. Much more so would it be with originally created
matter, and we have only to accept the fact. Moreover, there can be
little doubt but that the universe was formed, evolved, according to
some design--not at hap-hazard--and that the cosmic matter was created
with the distribution necessary to carry out the plan. That the stars
differ from each other in magnitude is the best proof of design; for no
one can believe that inert matter could determine into what shapes and
sizes it could arrange itself. But we have now nothing more to do with
the universe, and will confine our operations to the domains of the sun.
Notwithstanding the vagueness and dimness of the description we have
been able to give of the part of space to which our work is now to
be confined, we can conceive it to resemble in some degree--not a
comparatively flat but--a round starfish, with arms more unequal in
length, and irregular in position than the kind we are accustomed to
see. In such an allotment of space we can easily conceive that the work
of attraction and condensation, of the newly created cosmic matter, in
forming itself into a nebula, would be most active in the main body;
that in the arms, or projecting peaks as they may be called, it would
go on more slowly in the direction towards the centre, the quantity
being smaller; and that on account of the greater distance in each from
the centre of attraction, and of its being more under the influence of
the still existing counter-attraction of the matter in the domains of
the sun's neighbours, they might become almost, or rather altogether,
detached from the more rapidly contracting main body.
We shall, then, suppose that all this has taken place in our incipient
nebula. The centre of attraction would at first be the centre of
gravity of the whole region occupied by the cosmic matter, which would
be ruled in due measure by the projecting peaks, and the indentations
or hollows produced in it by the attractive force of the most powerful
neighbours; which hollows would gradually disappear as the process of
condensation went on, and the main mass would assume the figure of a
nebula of some shape. From this stage we may reasonably conclude that,
as it was contracting towards the common centre of gravity of all its
parts, it would gradually assume a somewhat globular form, and we may
now suppose it to have contracted to, say three times the diameter of
the orbit of Neptune. Here, then, we may take into consideration what
was the interior construction of the main mass which we may now look
upon as a nebula; and we have only two states in which we can conceive
it to have been. Either that the whole was condensing to the common
centre of gravity, in which case its greatest density would be at the
centre; or that it was condensing towards the region of greatest mass,
in which case its greatest density would be at that region, and its
least density at the exterior of the nebula, and also at, or at some
distance from, its centre; that is, that the nebula was hollow and
without any cosmic matter at all at its centre.
In the first case we must recognise that, from that period of time
at least, the cosmic matter that was at, or even near, the centre of
gravity then, must be there still all but inert, and being gradually
compressed to a greater and greater degree of density. There would, no
doubt, be attraction and collisions going on amongst the particles,
with condensation towards the centre and production of heat--as long
as the particles retained the gasiform condition--which might be
increased in activity by the pressure, or superincumbent weight, of the
whole exterior mass, but there would be no tendency in them to move
outwards--provided their gravitation was always towards the centre; and
any motion amongst them would be of the same kind as the vibration of
the particles of air shut up in a cylinder and gradually compressed by
a piston forced in upon them, and not allowed to escape owing to the
sides of the cylinder exerting upon them a pressure increasing exactly
in the same proportion as the pressure on the piston was increased.
And if this was the case with the matter at or near the centre, it
would be the same with that of the whole mass, with the exception,
perhaps, of the outer layer, which might act the part of the piston in
the cylinder. There could be no motions among the particles, except
those of collisions and of falling down towards the centre. The outward
impacts of collisions would be less strong than those inwards, on
account of gravitation acting against them, and the general tendency
of all matter would be to move towards the centre. Even were we to
assume that the whole mass was endowed with a rotary motion, the result
would be much the same, that is, increasing stagnation of the matter
as it approached to the centre. The areolar law teaches us, however,
that the increase of condensation at the centre would increase the
rotation there; but in that case we have to acknowledge that this
increase of rotation would have to be propagated from near the centre
to the circumference, which would be by far the most difficult mode of
propagation, and we are forced to think of what would be the rate of
rotation at the centre, of a nebulous globe, of some sixteen thousand
million miles in diameter, required to produce a rotation at the
circumference of even once in four or five hundred years; and from that
to think of what must be the speed of rotation at the centre of the
sun, at the present day, to produce one rotation at the circumference
of twenty-five to twenty-seven days. We should also have to think
seriously of how the rotary motion was instituted, and we could only
appeal either to simple assumption, or to the impact theory, which,
applied to a mass of the dimensions of the one we are dealing with,
would require more explanation than the whole formation of the nebula
itself.
In the second case, that is, looking upon the nebula as a hollow
sphere--when it was of the dimensions we have just supposed it to
be--we get rid of all the difficulties, and we may add impossibilities,
that we encountered in the first case. In such a formation there
could be no particle of matter in a state approaching to inertness,
not one that could not work its way, through force of attraction and
collisions, from the outer to the inner surface of the hollow shell,
or _vice versâ_, or all through and round it and from pole to pole--if
it had poles then; it might increase or decrease in density, according
to the density of the particles with which it came into collision, as
it moved from one place to another, but it would find no spot where
it could stand still or be imprisoned. Even arrived at the region of
greatest density, it could change places with its neighbours and move
all over that region, if it were condemned to remain with one density
once it had acquired it; if not, by acquiring or loosing a little
density--_i.e._ by being compressed or allowed to expand a little--it
could work its way outwards or inwards, as we have just said, and be as
free as the law of attraction would admit of, and as active as that law
would oblige it to be. It must be borne in mind that gravitation would
act in two opposite directions depending on whether it was acting on
the outside or inside of the region of greatest density. We do not go
the length of supposing that it could escape altogether from the nebula
were its progress outwards; because, as it approached the border, it
would meet with plenty of other particles coming in, which would reduce
its velocity and prevent its escape. Besides, the law of attraction
would take good care to prevent it from passing over to a neighbour
nebula or sun.
It may be argued that in the first case--_i.e._ condensation to the
centre--the particles would have the same facilities for changing
place, in so far as moving all round the interior of the nebula, or
across it, on their way to quasi stagnation, as their densities and
the superincumbent weight concentrated and increased; but there could
be no motion outwards because the _attraction of gravitation_ would not
permit it; nothing could _fall upwards_, all must _gravitate_ to the
centre. Thus the power of motion in the particles would be limited to
very much less than half what they would have in the case of the hollow
sphere.
It will not do to argue that the increasing heat at the centre would
create an upward current. It might create repulsion and prevent the
farther-out particles from so soon reaching their final resting or
vibrating place, but it could not create an upward convection current
of any magnitude; because the colder particles falling down to replace
those rising up--that is, if the warmer ones did rise up--being greater
in number because occupying greater space, would soon cool down the
centre and put an end to the upward current, that is, if it ever came
to be set in motion. The greater weight of the greater number would be
sure to keep the lesser number in their prison. If any one should say
that those nearest the centre would be the heaviest, let him remember
that the heaviest liquid or fluid does not rise to the surface. There
could be no furnace at the centre to heat the cold particles as they
came down to replace those that had just risen up; and if there was, it
would be gradually cooled and extinguished. In fact, the centre region
would become colder than that immediately outside of it, and so on
until the greatest heat would be at the surface of the nebula. Should
it be argued that the vastly greater number of particles in the outer
regions would help those at the centre to rise up, we agree; but it
would be because the attraction would be greater outwards than inwards,
as we have shown all along, and not because the pressure forced them
out--against itself. But, it must be added, this means that if there
was still a plenum at the centre the particles that had once left the
centre could never come back again, nor any others to replace them, and
that no convection current could ever be formed for carrying heat or
matter from the centre, or its immediate neighbourhood, outwards.
In view of the above comparison of the two cases--added as a complement
to what we believe we have demonstrated in a former part of our
work--we shall adopt the second as being most in harmony with the
laws of attraction, and of nature in general, and shall endeavour to
describe in some detail, the construction of the nebula out of the
matter belonging to the domains of the sun, as we have marked them out.
We have already said that on account of being at the greatest distance
from the main body, and at the same time nearer than all other parts
of it, to the attractive force in the domains of the neighbouring
stars or nebulæ--which attraction continues to be exerted upon the
solar system up to the present day--the matter in the high peaks which
we have shown would form part of the sun's domains, would come to be
completely separated from the rest of the nebulous matter. We shall
now assume this to have come about, the detached pieces, somewhat in
the shape of cones, occupying positions distant from the main body, in
some sort of proportion to their altitudes and masses. This separation
would naturally make some alteration on the centre of gravity of the
remaining mass. It would come to be nearer to the deep hollows, made
in the mass by the attraction of the most powerful of the nearest
neighbouring stars; and as we have seen that the hollows made by Sirius
and [Greek: a] Centauri would be the deepest, and also for greater
simplicity in description, we shall suppose that the centre of gravity
would come to be nearer to these hollows than it had been before. Then,
as the condensation and contraction proceeded, the tendency would be
to fill up these hollows, and, as a consequence, the matter at the
opposite side of the nebula would at the same time tend to lag behind
in approaching the centre--for the same reasons we have given in the
case of the peaks--and might easily come to be detached from the main
body altogether, first in the form of shreds, then in larger masses,
and afterwards in concave segments of hollow spheres, as contraction
advanced; and the whole seen from a sufficient distance, would have
the appearance of a nebula with crescents, perhaps almost rings, of
nebulous matter and detached masses on one side of it; all very much
like what we know to be the figures presented by some nebulæ.
When contraction had continued till the hollows caused by Sirius
and [Greek: a] Centauri were filled up, we might suppose that the
nebula had come to be somewhat of a spherical form, although far from
being very pronounced, and we have now to consider what its internal
structure might be and most probably was.
In describing the construction of the earth-nebula we showed that
particles of matter placed at different parts of its interior, even not
very far from the surface, would be drawn out, in the first place by
the greater number coming in from a greater distance from the centre,
and that when they met they would all be drawn in towards the centre by
the conjoint attraction of the whole mass; and now we can apply this
fact to the larger solar nebula, and consider what might be the result.
Let us fix upon a certain number of equidistant zones in a sphere of
cosmic matter, extending from the centre at _a_ to _b_, _c_, _d_ and
_e_, at the surface. We know that, according to our former reasoning on
particles, and the law of attraction, part of the matter of the zone at
_a_ will be drawn outwards by that at _b_, while part of that at _b_
will be drawn inwards by that at _a_, and that the same will take place
with all the other zones out to the surface at _e_; and thus there
might come to be congested layers between these equidistant places,
and there might even be formed hollow spheres within hollow spheres,
independent of each other, all through the nebula from near the centre
to the surface. This idea is by no means fanciful, as is witnessed
by the accounts given in Chambers's "Handbook of Astronomy," already
referred to, Vol. I., and the Figs. 215, 222 and 223, showing the form
and appearance of the remarkable comets of 1874 and 1882. If different,
almost concentric, zones or layers of cosmic matter can be constituted
in the hemisphere forming the head of a comet, there is no reason why
concentric layers of the same matter should not be formed in a nearly
spherical nebula. In fact, we can appeal to what is seen in the heads
of the two comets cited, Donati's also represented in the same work,
Figs. 199-203, as convincing proof of the correctness of our contention
and demonstration that all satellites, planets, suns, and stars are
hollow bodies. Even the tails of comets, at least of the larger ones,
are acknowledged to be hollow bodies.
When steadily looked into we find the notion that all fluid bodies
are hollow to be much more common than is perhaps generally believed.
Beginning with the smallest, we find what follows in the Rev. Dr.
Samuel Kinn's work, entitled "Moses and Geology," Edition 1889, page
86: "A mist, whether in the form of a cloud or fog, is composed of
small bodies of water obeying the laws of universal gravitation by
forming themselves into spherules, which Halley and other eminent
philosophers thought to be hollow. As water is heavier than air,
scientists were for a long time seeking for a good reason to account
for clouds floating. It may be that Kratzenstein has somewhat solved
the problem. He was examining in the sunshine some of the vesicles of
steam through a magnifying glass when he observed upon their surface
coloured rings like those of soap-bubbles, and some of the rays of
light were reflected by the outside surface, others penetrated through
and were reflected by the inner surface; he concluded, therefore, that
the envelope of the sphere must be excessively thin to admit of this
taking place. We may, therefore, suppose that these vesicles are filled
in some way with rarefied air, and are so many little balloons whose
height in the atmosphere varies in proportion to the density of the
air they contain. How this enclosed air should become rarefied on the
formation of the tiny globule is a problem still to be solved."
Dr. Kinn says nothing of _how_ the spherules of cloud or fog were
formed by the laws of universal gravitation, nor _why_ Halley and the
other eminent philosophers thought them to be hollow, and only states
the fact that Kratzenstein found the vesicles of steam to be hollow;
and only one cause can be assigned for such being the case, namely, the
manner in which we have shown how hollow spheres can alone be formed.
That the vesicles of steam examined in the sunshine were hollow it
would seem there can be no doubt; and if so, there can be as little
that Halley and the others were right in thinking the spherules of
clouds to be hollow. The steam vesicles could not come into existence
at once in the air, in form large enough to be examined through a
magnifying glass, but must have been built up out of a multitude of the
very smallest atoms of water turned into vapour; and would follow the
same law as the atoms of cosmic matter and so form the little balloons.
In their formation the hollow space would be filled with air, which
would expand when heated and contract when cooled, and so regulate
their height in the atmosphere. And thus the problem of the last
sentence of the quotation is solved.
We shall now go to the opposite extreme of matter, and see what Mr.
Proctor says when treating of the formation of a Stellar System; but
we must state that it is not very clear to us, whether he is exposing
Mädler's ideas or his own, although we think they are his own or, at
least, adopted. He says in "The Universe of Stars" at page 112: "He
(Mädler) argues that if a galaxy has a centre within the range of the
visible stars, a certain peculiarity must mark the motions of the
stars which lie nearer to the centre than our sun does. As has already
been mentioned, the neighbourhood of the centre of a stellar system is
a scene of comparative rest. In the solar system we see the planets
travelling faster and faster, the nearer they are to the great ruling
centre of the scheme; and the reason is obvious. _a._ The nearer a body
is to a great centre of attraction like the sun, the greater is the
attraction to which it is subject, and the more rapid must its motion
be to enable it to maintain itself, so to speak, against the increased
attraction; but in a vast scheme of stars tolerably uniform in
magnitude and distribution, _the outside of the scheme is the region of
greatest attraction, for there the mass of all the stars is operative
in one general direction_. (The italics are ours.) As we leave the
outskirts of the scheme, the attraction towards the centre becomes
counterbalanced by the attractions towards the circumference; and at
the centre there is a perfect balance of force, so that a body placed
there would remain in absolute rest. It is clear, then, that the
nearer a body is to the centre, the more slowly will it move." (Compare
this last sentence with the one beginning at _a_ above.)
Here we have recognised, the principle that in a star system the
immensely greater number of stars at the outside of the scheme would
produce a perfect balance of force, and that a body placed at the
centre would remain in absolute rest. This agrees wonderfully well with
what we have been arguing, a few pages back, with respect to a sun
solid to the centre. Matter at the centre would be at absolute rest,
_dead_, that nearest to it would be nearest to dead, and so on through
a sun or planet, gradually coming to life as it came nearer to the
surface; exactly as we have shown it would be, having in it little more
than rotary motion. When once acknowledging the immense superiority
of attractive force of the stars at the outskirts of the system, over
the very few there could be at its centre, Mr. Proctor seems to have
stopped short with the idea and to have contented himself with one body
at the centre in absolute rest. Had he gone one step further he must
have seen that one, or even a very few, could not maintain themselves
near the centre with such an immense number pulling them away in every
direction. There could be no perfect balance of force. And had he
applied the same idea to the earth, and followed it out to the end, he
could not have written as he has done, in "The Poetry of Astronomy," at
page 354, "that the frame of the earth is demonstrably not the hollow
shell formerly imagined, but even denser at its core than near the
surface." He would have found some difficulty in fixing his first dead
particle at the centre, when there were such infinite hosts of near and
far-off neighbours endeavouring to annex it. He would have found that
the absolute rest was neither more nor less than absolute vacuum. It
is utterly impossible to show how any body could be built up out of a
nebula of cosmic matter, or even meteorites, from a solid centre, under
the law of attraction. We repeat that any foundation laid there would
be in a state of unstable equilibrium, and would be hauled away out of
its place never to return; unless the cosmic matter around it were so
perfectly arranged on all sides that its attraction on the foundation
would be absolutely equal in all directions; a condition which cannot
be imagined by any one who takes the trouble to think of it. And we
think we may add, that no body could be established at the centre of a
system of any kind unless it were of sufficient magnitude to control
the whole matter within range of it, exactly as we see in the solar
system; and that the central body could be no other than a hollow
sphere. Thus we have either to look upon the sun with his planets and
their satellites as hollow bodies or to conclude that the solar system
was not formed out of a nebula.
Coming back to our nebula after the hollows in it, caused by the
attraction of Sirius and [Greek: a] Centauri, were filled up, and
when we showed that it might have had the interior form of a series
of hollow spheres one within the other, and also might be accompanied
by crescents and shreds of cosmic matter on the opposite side to the
hollows--a supposition we put forward more in explanation of what is
to be seen in some nebulæ and comets, than as in any way necessary for
our purposes--then, even although it had been separated interiorly
into different layers or concentric shells of spheres, these layers
continuing to attract each other, would finally come to form one hollow
sphere with its greatest density at the region where the inwards and
outwards attractions came to balance each other. Long previous to this
stage--even from the very beginning--the atoms gradually coalescing
into larger bodies, would be attracting, colliding with, repelling
and revolving around each other, sometimes increasing in dimensions,
at others knocking each other to atoms again; but there would be a
tendency in them to combine into larger masses as they approached the
region of greater density, where the attraction was greatest.
Now, if the collisions and encounters amongst the masses, great and
small, always exactly balanced each other, the whole mass of the nebula
would gradually contract towards the region of greatest density,
and the whole would ever remain without any other kind of motion in
it than what can be seen in a mity cheese--a kind of congeries of
particles heaving in every, and at the same time in no, direction.
But as an absolute balance of collisions could not be maintained for
ever, especially where they would be constantly varying in force and
direction, a time would come when movements of translation, as well as
of collision, would be instituted on a large scale, in many directions,
which, if they also did not manage to balance each other--an affair
equally as impossible as in the other case--would ultimately resolve
themselves into motion in one predominating direction through the whole
nebula.
We do not forget that we are dealing with the shell of a hollow sphere,
not with a ring, or section of a cylinder, and we can conceive that
there would be, from the first, partial motions of translation in
multitudes of directions, radial, angular, transverse, etc. etc.,
constantly changing, even being sometimes reversed, but also constantly
combining with each other, and gradually leading on to decided, though
partial, uniformity in one direction. As a matter of course this
motion of translation would be controlled by its own constituent parts
attracting each other to some extent, and thus a rotary motion would
be established in the interior of the nebula in the region of greatest
density. We can also conceive that when the motions of translation
had become nearly uniform, the plane of that uniform motion might be
in any direction through the whole mass of the nebula, and might be
continually varying until final uniformity was attained, when the
greater part of the mass was moving in combination, and the rotation
was thereby firmly established in one direction, though still not
embracing the whole.
We have to take into account also that when the rotary movement had
settled down into one plane, it would be most active at the distance
of the region of greatest density of the nebula from its centre; in
fact it would be instituted at that region and be, therefore, most
active there; and then the most active part of the matter would be in
the form of a rotating ring, still surrounded by an immense mass of
nebulous matter, both inwards and outwards, to which it would gradually
communicate its own motion, until the whole mass would rotate, in one
direction, on an axis. But it is evident that in the whole rotating
mass there would be different degrees of velocity of rotation at
different places, decreasing from the supposed ring inwards towards
the centre, and outwards to the surface at what would thus become the
equatorial region; and also decreasing from the equatorial plane to
the poles. Following up this idea, we have a more reasonable manner of
accounting for the different velocities of rotation observed on the
surface of the sun, between the equator and the poles, than we have
seen suggested in any speculations on the cause that have come under
our observation. Until rotation was fully instituted, the areolar law
could have no power over the multitudinous movements going on in the
nebula, but from that time it would begin to act, and condensation
would increase it at the region where it began; and as all increase had
to be propagated from there, inwards, outwards, and in all directions,
the differences in velocity of rotation throughout the sun must endure
as long as he continues to contract. In this we find an immense field
for producing heat in the sun, from the eternal churning which must be
going on in the interior.
A rotary motion produced in this way might have two different results:
in one case the rotation might be continued until the matter at the
polar regions had all fallen in towards the centre, and had been thrown
out afterwards by centrifugal force and the whole mass converted into a
nebular ring, in the form of the annular nebula in Lyra. In the other
case we could conceive that, in a smaller nebula, the centrifugal force
of rotation caused zones to be abandoned at the equatorial surface, in
the manner set forth by Laplace in his hypothesis, and that the matter
from the polar regions fell in more or less rapidly for the formation
of the different members of a system like the sun's; and that the
dimensions of the planets would be determined by the rapidity with
which the matter fell in as the process went on. Such a conception
would help to account for the outer planets of the solar system being
so much larger than the inner ones, because there would be more matter
falling in; and make us think that the nebula in Lyra is destined to
form a system of multiple stars.
Some years after this mode of instituting rotary motion in a
nebula was thought and written out, and also an extension of it to
which we may refer later on, we came upon a kind of confirmation
of the correctness of our views in an article in "Science Gossip"
of January 1890, on the nebular hypothesis, where it is said: "We
have established, then, the existence of irregular nebulæ which are
variable--that is, the various parts of which are in motion.... Now,
with the parts of the nebula in motion, whether the motion is in the
form of currents determined hither and thither according to local
circumstances, or in any other conceivable way, such motions bearing
some reference to a common centre, unless the currents exactly balanced
each other--a supposition against which the chances are as infinity
to one--one set must eventually prevail over the other, and the mass
must at last inevitably assume the form peculiar to rotating bodies in
which the particles move freely upon each other. It must have become
an oblate spheroid flattened at the poles and bulging at the equator,
rotating faster and faster as it contracted. In some such manner has
our solar system acquired its definite rotation from west to east."
The writer in "Science Gossip" has taken the irregular motions in the
nebula as made to his hand, and has come to the same conclusion as we
have, namely, that they would all resolve themselves into motion in one
direction only, always subject to the general attraction towards the
centre of gravity of the nebula, which means motion round a centre,
perhaps not necessarily rotary motion. However, the only difference
between his ideas and ours is that we deal with a hollow nebular shell,
in which, it will be acknowledged, it would be much more easy for the
law of attraction to produce marked and distinct motions of any kind,
and which would lead to one motion in one direction throughout, than
in a nebula homogeneous, or nearly so, from the surface to the centre.
Whether it would lead to the formation of an oblate spheroid is another
question, as that might depend on a variety of circumstances, one or
more of which we shall have to touch later on; in fact, we have already
shown how the very reverse might be the case.
CHAPTER XVI.
PAGE
282 The sun's neighbours still exercise their attraction over him.
283 Regions of greatest density in the 9 nebulæ dealt with; compared
with the orbits of the planets made from them.
287 Results of comparison favourable to the theory.
289 Differences of size in the planets have arisen from variations
in the quantity of matter accumulating on the nebulæ.
290 Causes of the retrograde motions in Neptune, Uranus, and
their satellites.
292 Probable causes of the anomalous position of Neptune.
293 Rises and falls in the densities and dimensions of the
planets explained.
295 The form of the nebulæ must have resembled a dumb-bell.
296 More about rises and falls in densities.
297 Reason why the Asteroid nebula was the least dense of the system.
298 Not necessary to revise the dimensions given to the 9 nebulæ.
299 Causes of the anomalies in the dimensions, densities, etc.,
of the Earth and Venus.
299 The strictly spherical form of the sun accounted for.
But it may yet be varied.
300 Repetition that a spherical body could not be made from a
lens-shaped nebula by attraction and condensation.
TESTING THE PRACTICABILITY OF THE HOLLOW SPHERE THEORY. RETROGRADE
MOTIONS, POSITIONS, DENSITIES, MASSES, ETC. ETC., CONSIDERED.
Before going any farther it will be convenient to try to find out
whether the solar system could have been constructed from a hollow
nebula such as we have been describing gradually contracting as the
matter for the formation of one planet after another was abandoned
until--as we have put it--the nebula could abandon no more matter, and
finally resolved itself into the sun. For this purpose we may suppose
it to have been condensed and contracted until its extreme diameter was
6,600,000,000 miles; the same as we supposed it to have been, when we
began the analysis of the nebular hypothesis. We will not now, however,
suppose it then to have contained the whole of the cosmic matter out
of which the system was formed, as we did before; because we have seen
as we have come along that a very considerable part of that matter
must have been left behind, almost from the moment that contraction
commenced. We have already given the reasons for this in describing the
domains of the sun; and, leaving the peaks out of account altogether
for the present, we will only deal with the regions of what we have
called the main body.
Although we have fixed a limit beyond which the neighbouring stars
could not draw off any cosmic matter from the domains of the sun,
that does not mean to say that their attractive powers would cease at
that limit; because we have had to acknowledge that each one of them
continues, even now, to exert its attractive power up to the very
centre of the sun. They would still have power to counteract, in some
measure, the sun's attraction of the matter of the nebula towards his
centre, and the result would follow that there would be one or more,
even many, fragments of the main body which would be left more or less
behind, and in varied forms, when the more central part had contracted
to the dimensions to which we have now reduced the nebula--all much the
same as we have already said a few pages back.
When the nebula was 6,600,000,000 miles in diameter its volume would
be 150,533^{24} cubic miles--as we have seen at page 87--the half
of which is 75,266^{24} cubic miles, corresponding to a diameter of
5,238,332,000 miles, or radius of 2,619,166,000 miles. Now, according
to our theory, it would be at this distance from the centre that the
greatest density and activity of the nebulous matter would be, where we
have just been showing how a movement of rotation could be generated,
and where, in consequence, its motive power, so to speak, originated
and existed. Here we find by dividing 5,238,332,000 by 6,600,000,000
that the region of greatest density in such a nebula would be at 0·7937
of its diameter. In our calculations about the earth, as it is, the
proportion was found to be 0·7939, but the densities of the outer
layers were empirically arranged by us; and, besides, almost the whole
of the mass was supposed to be solid matter, so that no accurate result
could be expected from that operation. There also we found that the
inner surface of the hollow shell was at 0·5479 of the whole diameter,
which we may adopt for the nebula we are about to deal with, as that
dimension may be varied considerably--so may the other also--without in
any way vitiating our theory.
Having found these proportions, which can only be considered as
distantly approximate, let us go back to the 9 nebulæ--excluding the
final solar one--into which we supposed the original nebula to have
been divided--in the analysis just alluded to--and see how the regions
of greatest density in them would correspond to the orbits of the
planets formed out of them. This examination requires a good deal of
calculation and accompanying description, which it might be found
tiresome to follow, and would really answer no good end were it written
out; so we shall suppose it to be made and the results obtained from
the calculations to be represented in the form of Table IX., where they
can be seen at a glance almost, and compared without much trouble. This
arrangement will also furnish a readier means of reference for the
remarks we shall have to make on, and the information obtained from,
the examination. And we have still to add that the extreme diameters of
the 9 nebulæ are the same as those we used for the analysis; as also,
that we make use of only the first of the proportions just cited, viz.,
0·7937, it being the only one required for determining the positions of
the regions of greatest density in the nebulæ.
TABLE IX.--DIMENSIONS OF THE NINE NEBULÆ, WITH THEIR
DIAMETERS AND REGIONS OF GREATEST DENSITY
COMPARED WITH THE DIAMETERS OF THE ORBITS
OF THE PLANETS FORMED FROM THEM.
----------+--------------+---------------------------+
| Nebula. |Region of greatest Density.|
| | |
Name of |--------------+-------------+-------------+
Planet. |Outer Diameter| Diameter | Radius |
| in Miles. | in Miles. | in Miles. |
----------+--------------+-------------+-------------+
| | | |
Neptune | 6,600,000,000|5,238,332,000|2,619,166,000|
| | | |
Uranus | 4,580,000,000|3,635,146,000|1,817,573,000|
| | | |
Saturn | 2,672,000,000|2,120,766,400|1,060,383,200|
| | | |
Jupiter | 1,370,800,000|1,088,003,960| 544,001,480|
| | | |
Asteroids | 744,000,000| 590,512,800| 295,256,400|
| | | |
Mars | 402,000,000| 319,067,400| 159,533,700|
| | | |
Earth | 234,620,000| 186,217,894| 93,103,947|
| | | |
Venus | 160,210,000| 127,158,677| 63,579,339|
| | | |
Mercury | 103,230,000| 81,933,651| 40,966,825|
+------------------------------------------+
| Had the position of Neptune been normal, |
| the above data for him and Uranus would |
| have been as under. More or less. |
+------------------------------------------+
Neptune | 8,299,786,830|6,587,540,800|3,293,270,000|
| | | |
Uranus | 5,144,439,613|4,083,042,000|2,041,521,000|
----------+--------------+-------------+-------------+
---------+---------------------------+------------------------------+
| Orbit of Planet. | Region of greatest Density |
| | compared with Orbit. |
Name of |-------------+-------------+-----------+-----------+------+
Planet. | Diameter | Radius | Within, | Without, | Per |
| in Miles. | in Miles. | (Miles.) | (Miles.) | cent.|
---------+-------------+-------------+-----------+-----------+------+
| | | | | |
Neptune |5,588,000,000|2,794,000,000|174,734,000| | 6·26|
| | | | | |
Uranus |3,566,766,000|1,783,383,000| | 34,190,000| 1·92|
| | | | | |
Saturn |1,773,558,000| 886,779,000| |173,604,200| 19·58|
| | | | | |
Jupiter | 967,356,000| 483,678,000| | 60,323,480| 12·47|
| | | | | |
Asteroids| 520,600,000| 260,000,000| | 35,256,400| 13·56|
| | | | | |
Mars | 283,300,000| 141,650,000| | 17,883,700| 12·63|
| | | | | |
Earth | 185,930,000| 92,965,000| | 138,947| 0·15|
| | | | | |
Venus | 134,490,000| 67,245,000| 3,665,660| | 5·45|
| | | | | |
Mercury | 71,974,000| 35,987,000| | 4,979,825| 13·84|
+----------------------------------------------------------+
|Had the position of Neptune been normal, the above data |
|for him and Uranus would have been as under. More or less.|
+----------------------------------------------------------+
Neptune |5,588,000,000|2,794,000,000| |499,270,000| 17·86|
| | | | | |
Uranus |3,566,766,000|1,783,383,000| |258,138,800| 14·48|
---------+-------------+-------------+-----------+-----------+------+
From the table we see that the region of greatest density of our
original nebula was at 6·26 per cent. _within_ the distance of
Neptune's orbit from the sun, a state of matters which precludes the
idea of condensation during, at least, a great part of the act of
abandoning the ring for the formation of that planet. But it will be
remembered that we gave it the diameter of 6,600,000,000 miles without
assigning any adequate reason for doing so, and, we can say with
truth, with the idea, more than anything else, of not increasing the
almost unimaginable tenuity of the matter composing the nebula; and
the position of Neptune in the system is so peculiar compared with the
other planets, that it cannot be properly used as a standard for any
kind of inquiry. The result obtained above can therefore be of no use
for the investigation we have undertaken. Not only so, but the almost
similar result in the case of Uranus is also rendered useless from the
same cause, in which we find that the region of greatest density of the
nebula is only 1·92 per cent. beyond the orbit of the planet. If the
mean distance from the sun of Neptune's orbit had been what was used
by Leverrier in the calculations which led to his discovery, namely,
36·152 radii of the earth's orbit, the region of greatest density of
the Uranian nebula would have been 14·48 per cent. beyond his orbit, as
may be seen from the addition to Table IX., in finding which we have
used the same system as in all our work.
In the next four nebulæ of the table--including the one we introduced
to represent the Asteroids--we see that their regions of greatest
density are respectively 19·58, 12·47, 13·56 and 12·63 per cent.
farther out from the centre of the sun than the orbits of the planets
formed from them. Here, then, we see a very apparent approach of
uniformity, and can say with much reason that planets could certainly
be formed out of the matter abandoned, through centrifugal force, by
hollow nebulæ similar in construction to what we have demonstrated
that of the original nebula to have been; each of them occupying the
position corresponding to its orbit.
Following these come the Earth and Venus nebulæ. In the former, the
region of greatest density almost coincides with the orbit of the
planet, being only 0·15 per cent. beyond it, instead of something like
12 per cent. as it ought to be to conform with the four preceding
cases; and in the latter it is 5·25 per cent. within the orbit of the
planet to be made from it. But in this case we have to note that the
orbit of Venus is 3·33 per cent. beyond the position pointed out for
it by Bode's law, and that it is the only one of the whole number of
planets whose orbit is farther removed from the sun than the distance
assigned to it by that law. Also we see from our reversal of Bode's
law, that the rates of acceleration of rotation for these two planets
are 1·880 for the earth and 1·626 for Venus, instead of the average of
2·5896 of the four preceding planets; that the density of Venus is less
than that of the Earth, instead of being greater as it is successively
in all the other planets from Saturn inwards; and we may add that
the diameters are nearly equal. All showing that influences had been
at work in the formation of these two planets, different to those in
the preceding four; and that until we know what these influences have
been, we cannot account for any anomalies produced by them. Neither
are we called upon to consider that our theory is destroyed by these
anomalies, any more than it can be by the anomaly in the case of
Neptune's position.
Lastly, we have in Mercury the region of greatest density of his nebula
at 13·55 per cent. beyond his orbit, and the rate of acceleration of
revolution over Venus 2·5543 times, both of which conform fairly well
with the same noted facts; in relation to Mars, the Asteroids, Jupiter,
Saturn, and, we may add, Uranus. But, in justice, we must not omit to
add that there may be some error in the excess of 13·55 per cent. in
the distance from the sun beyond his (Mercury's) orbit, arising from
the fact that there may have been some difference from what we made it
to be, in the line of separation between his nebula and that of Venus;
and also that we had to guess at the line of separation between his
and the residuary nebula. Moreover, it has to be taken into account
that his orbit is 3·22 per cent. within the position assigned to it by
Bode's law.
From the Table IX., and an examination of it, we learn that out of the
9 nebulæ into which we divided the original one, in the analysis of the
nebular hypothesis, we have five--four of which are consecutive--which
may have been almost of the same construction, and not far from
the same proportions; that the original nebula cannot, for reasons
assigned, be looked upon as either similar, or the reverse, to the five
just classed; that one, the Uranian, is practically similar to the
five, and might be exactly similar could the anomaly in the position
of Neptune be explained; and that the remaining two, the Earth and
Venus nebulæ, seem to show that they have been abandoned in a manner
different from the others. Perhaps we may be able, later on, and in a
different way, to give a reasonable explanation of the anomalies in the
positions occupied by Neptune, the Earth, and Venus, and also of the
peculiarities of their dimensions. So far, we believe we are justified
in concluding that out of the 9 nebulæ, 6 may really be considered as
supporting our theory, and the remaining 3 as, in all probability,
capable of being shown to be, at least, not opposed to it. To this we
may add that on several occasions we have stated our opinion, that
the divisions between the nebulæ we have established, could not have
taken place at the half-distance between the orbits of any two planets,
but much nearer to the outer one. It is evident, then, that if we had
made the divisions at any distance farther out, say at three-fourths
of that distance from the inner orbit, the extreme diameter of each
one of the nebulæ would have been just so much greater, the region of
greatest density farther out from the centre of the sun, and even that
of Neptune would have been beyond his orbit. All this could be done,
yet but it would serve no good purpose, as will be seen presently; and
we might be accused of cooking our data in order to produce a result
favourable to our theory.
We have made the foregoing examination because, when we began our work,
the general idea was that, according to the nebular hypothesis, the
material for the formation of each planet was abandoned by the ideal
nebula in a distinct and separate mass from any other--we are not at
all sure, however, that this was Laplace's idea. This, we found out,
could not be the case when we attempted to give some sort of separate
or distinct form to the matter out of which Neptune was supposed to
have been formed; and when we became convinced that all the matter
abandoned by the nebula, from first to last, must have been thrown off
in one continuous and, most probably, uninterrupted sheet. This, of
course, makes us think of how the division of the sheet into separate
rings was brought about, for there must have been absolute separation
between them, otherwise separate planets could not have been made out
of the sheet; and the only explanation that can be given is, that
it must have depended on the quantity of matter that was abandoned,
in nearly equal times, at different periods of the operation; for
the areolar law precludes the idea of there having been very rapid
changes in the rate of rotation of the nebula, and certainly of its
decrease at any period as long as condensation and contraction went
on. Whereas, although the sheet thrown off may have been continuous,
we have no reason to suppose that it was of constant volume or density
from beginning to end of the operation; in fact, we have already
seen that its density was constantly increasing, and have suggested,
in the reversal of Bode's law, that the differences in dimensions
and densities of the planets have arisen, from irregularity in the
quantities of matter abandoned from time to time. This irregularity
could only arise from the mode of construction of the nebula, and from
the forms it assumed during condensation, as we shall attempt to show
in due time. Meanwhile we can conclude that the region of greatest
density in any of our nebulæ had no influence whatever on the position
of the orbit of the planet that was formed out of it.
We have shown, very clearly we believe, at page 109, from
quotations--at second hand--from his own exposition of his hypothesis,
that Laplace considered that condensation could only take place at
the surface, or in the atmosphere as he called it, of his nebula,
on account of its being possible only after radiation into space of
part of its excessive heat; and that consequently there could be
no acceleration of rotation in the nebula, due to the areolar law,
except where there was condensation. On the other hand, in our cold
hollow-sphere nebula, condensation could only take place at the region
of greatest density, or greatest mass, which must be always very much
nearer to the surface than to the centre; so that in both cases,
equally, the abandoning of matter under the influence of centrifugal
force would be virtually the same, and no further remarks are called
for, on our part, on that head.
Neither is it necessary for us to show how planets could be formed out
of the rings abandoned by their respective nebulæ, for everybody seems
to agree that when they broke up, the fragments could not do otherwise
than form themselves into small nebulæ, which in the course of time
condensed into planets. M. Faye's explanations are good for that.
With respect to their motions of rotation being direct or retrograde,
we have seen, at page 116, and following, that Laplace's description of
how the former motion could be brought about is mechanically correct;
and, at page 121, that he did not consider that the direction of
revolution of a ring necessarily demands that the rotation of a planet
formed from it should be in the same direction. As already said, he has
shown how direct rotation could be produced, and we have no doubt that
he could have shown how retrograde rotation could also be produced, had
he found it to be at all necessary. Be that as it may, however, it is
a very simple matter to show how, following our method of construction
of the primitive nebula, the retrograde rotation of Uranus and Neptune
could, or rather must, have been determined.
It will be remembered that when we were "getting up" the original
nebula in the domains of the sun, whose form we described as well as
our limited means would admit of, we said that when the cosmic matter
contained in them began to contract, not only the parts contained in
the peaks and promontories would soon be left behind, and come in at
a slower rate, but also large masses of the outer part of the main
body, especially of what was on the sides opposite to the deep hollows
made in the domains by the most powerful of the sun's neighbours, in
the form of fragments, crescents, and parts of hollow segments. Let
us now, then, suppose the operation of planet-making to have advanced
so far that the whole nebula was rotating on its axis, and abandoning
matter through centrifugal force, from its equatorial regions in a
continuous sheet, as we have said several times that it must have
done, and that the matter destined for Neptune and Uranus has not only
been abandoned, but divided into two distinct rings--a supposition
made in this case only for facility of description. Then some of the
matter which had been left behind, but still being gradually drawn in,
would be almost totally intercepted in the equatorial regions of the
nebula by these two rings, and would fall in greater quantity upon
their outer edges than anywhere else, more especially in the case of
the outer one. These adventitious additions would come in without
any angular, or tangential, movement whatever, because rotary motion
was not yet established in them, and would retard the revolutionary
movement of the rings--in decreasing degree from their outer to their
inner edges--while acquiring angular motion themselves; and would also
intensify the original difference in revolutionary motion already
existing at these edges. At the same time these additions of extraneous
matter would seriously impede the contraction of the rings in the
radial direction on account of their volume, but would have little
or no effect on contraction in the circumferential direction; the
consequence of which would be that they would break up before friction,
and the mutual collisions of their particles, had time to produce a
uniform revolving motion throughout their whole breadth; that is, while
their inner edges would be still revolving with more rapid velocities
than the outer ones; and the rotary motions of the planets derived from
them would be retrograde, according to M. Faye's demonstration--or
that of any other who has taken the trouble to think over the matter.
And we may add that this mode of reasoning, applied with a little more
detail, will very fully account for the rotation of Neptune being
more decidedly retrograde than that of Uranus, because the quantity
of matter so deposited on the outer flat ring in this process would
unquestionably be greater than on the inner one, and consequently the
difference of velocity between the outer and inner edges of the two
rings also greatest on the outer one.
We take it to be unnecessary even to say that, the revolution of the
satellites of these two planets being retrograde and anomalous, the
rotation of their principals must be retrograde and anomalous also.
Before going any farther we have something to say about the anomalous
position of the orbit of Neptune, which is certainly not the position
sought for by M. Leverrier; in fact, the elements employed by him in
his calculations to discover a perturbing planet--whose existence
may be said to have been known--are so different from the elements
of the one actually discovered, that there would be nothing out of
reason in saying that Neptune is not the perturber that was sought
for, but only an instalment of the perturbing force. It may raise a
storm in some quarters to say so, but the fact remains the same, or
it must be confessed that mathematics is a more elastic science than
it professes to be. He has not the power of attraction required to
produce the perturbations in the movements of Uranus which gave rise
to the search for an outer planet. M. Leverrier made his calculations
under the belief that a planet of 1/9300th part of the mass of the sun
was required to produce the perturbations that had been observed in
the orbital motion of Uranus; whereas the planet discovered has only
1/20,000th of that mass--not one-half of what was required. On the
other hand, the semi-axis major of the orbit of the planet discovered
is found to be 30·037 instead of 36·154 (Bode's law measures) used for
the search; which greater proximity to the sun, it is true, increases
its power of attraction 1·449 times, but as its mass is only 0·465 per
cent. of what was expected, the attractive force would amount to less
than 0·68 per cent. of what was required. Then the question comes to
be, Where did the wanting 0·32 per cent. of attractive force come from?
And the answer is that some astronomers have been searching for another
planet to make up the weight, with more or less diligence, ever since
the deficiency came to be recognised. But all that we want to have to
do with the question is to suggest a very plausible reason for the
anomalous position of the orbit of Neptune.
If there is another planet beyond Neptune, the ring (perhaps the
rings) out of which he and the others were made, must have been much
greater in breadth than what we have assigned to it at page 88, viz.
1,010,000,000 miles; perhaps even one-half more, as may be deduced from
the addition made to Table IX., and what we have said in connection
with the semi-axis major adopted for the sought-for planet, by M.
Leverrier in his calculations. Now, that a ring of such enormous
breadth should have held together in one piece, until it finally broke
up through condensation and contraction, requires an extraordinary
effort of imagination, after seeing what has taken place with the
rings of Saturn; even the breadth of 954,000,000 miles appropriated
to the Uranian ring (see page 90) demands an elastic imagination to
conceive its holding together; so that the outer ring of the system
may very well have been divided into two, as we have said at page 134,
and two not very unequal planets made out of it--one into Neptune, and
the other into one as far beyond M. Leverrier's adopted distance of
36·154, and of such mass as would make up the missing 0·32 per cent. of
deficient attractive power. No doubt the outer ring may have broken up
into several planets, or even into a swarm of asteroids, but we prefer
to think of only two planets; because it seems to us that to draw
Uranus into the position he occupied when Neptune was discovered, the
two planets must have been operating in conjunction; an idea that is
not so easily entertained when there are several planets, or a host of
asteroids, to be taken into account.
We have already discussed, at page 115, the mode of formation of the
sheet of matter abandoned by the nebula, its posterior division into
separate rings, and how the part of these rings from Saturn inwards
could revolve themselves into planets having direct motion, so it is
not necessary to go over the same ground again, merely because we are
dealing with a hollow nebula instead of one full of cosmic matter to
the centre.
We have also shown, at page 119, that the nebula must have been
somewhat in the form of a cylinder terminated at each end by what
may be looked upon as a segment of a sphere, although it would more
probably be an almost shapeless mass of cosmic matter, because the
greater part of it would be very slowly brought under the influence
of centrifugal force as it fell in from the polar directions; and
again, a few pages back, that almost all the matter coming in from
its equatorial regions--even what might be called its tropical
regions--would be intercepted before it could reach the Saturnian
nebula. Likewise, at page 137, when examining Bode's law reversed, we
have seen a limit set to the acceleration of the movement of revolution
in the planets of the system as they approached the centre, because
any acceleration beyond a certain limit, clearly marked out, would of
necessity be within the nebula itself, and the rate of revolution would
be less than that of the sun on its axis at the present day. This may
be used as an argument against the nebular hypothesis, but we think
we have shown in the same Chapter VII. that this is not the case. But
we have still to try to account for the repeated rises and falls in
density in the planets from Neptune to Mercury, or even farther; which
operation causes us to bring forward, first of all, a new idea as to
what the form of the nebula would come to be.
[Illustration: FIG. 2.]
The accompanying rough sketch (Fig. 2), drawn to a scale of one-quarter
inch to 1,000,000,000 miles shows that, supposing the Saturnian nebula
to have been a perfect sphere, and to have abandoned matter till the
velocity of rotation came to be equal in a region corresponding to
the tropical region of the earth, the cylindrical part of it would
present a straight side of more than 1,000,000,000 miles in length;
provided always that the general diameter of the nebula did not
decrease through condensation and contraction during the operation;
but as this could not be the case the length of the cylindrical part
would be considerably less than that. How much less we have no means
of calculating. On the other hand we have seen, when discussing,
in the case of Jupiter, how matter must have been abandoned by any
nebula, that from the time the original nebula began to abandon matter
through centrifugal force, it must have gone on acquiring a constantly
increasing length of straight side as it contracted. Thus the Saturnian
nebula would begin work with the accumulated cylindrical length it had
inherited from Neptune and Uranus, so that the straight side may have
been very much longer than that shown by the sketch; a simple look at
it is enough to make one believe that this would be the case. But this
idea naturally leads us to another digression.
Looking again at Fig. 2, we see that acceleration of rotation in the
nebula would originate where condensation was greatest, that is at
the region of greatest density, and have to be propagated from there
to its periphery so that it would reach the middle of the cylindrical
part sooner than the ends; and as the nebulous matter at the ends of
the cylindrical part could not be abandoned until it had acquired the
centrifugal force necessary to overcome gravitation, it would lag
behind and overhang, as it were, the middle of the cylindrical part;
which means that instead of continuing to be straight, the line of
separation between the nebula and the abandoned matter would come to be
concave; and in this manner the nebula would soon assume the form of a
dumb-bell, gradually becoming more and more pronounced as condensation
proceeded. One can hardly help concluding that this must have been the
way in which the dumb-bell nebula near star 14 Vulpeculæ was formed.
The representations of it given by Chambers, Vol. III., page 92, Figs.
76 and 77, as seen by Smyth and Sir John Herschel are most confirming
of this idea; notwithstanding the changes of appearance shown by Lord
Rosse's reflectors of 3 feet and 6 feet diameter, Figs. 78 and 79,
which are not difficult to account for. It is easy to imagine how
Fig. 78 could be converted into Fig. 79 when observed with a much
more powerful telescope. We can conceive the roundest end of it being
reduced into the sort of compact segmental form on the left hand side
of the figure, and the spread-out part of it into the more diffused
segment on the other side; but the form of the whole figure forces
us into another conception. Mr. Chambers says the general outline
resembles a chemical retort, but to our eyes it is infinitely more like
one half of a dumb-bell broken off from the other. So like it that we
feel inclined to ask what has become of the other half. This again
makes us think of an enormous dumb-bell nebula dividing itself into two
parts, one of which has disappeared or broken up in some manner without
leaving any distinguishable traces of its existence, and the other,
either forming itself into a double star, assuming in the process the
form of a dumb-bell, or actually of one rotating in a direction almost
at right angles to that of the original one; more probably the former
of the two. Perhaps we have allowed our ideas, or fancy, to run on
too far; nevertheless, looking over the forms of nebulæ represented
in Chambers's classical work, and duly considering how inconceivably
strange some of them are, there is nothing impossible in all we have
said.
Returning to the repeated changes of density in the solar planets,
we know that the matter first abandoned by the original nebula,
through centrifugal force, would be at the lowest stage of density,
and that what followed would go on gradually increasing in density
as it contracted to the Saturnian nebula. But, as we have shown that
immense quantities of matter belonging, so to speak, to the sun, though
actually separated from the original nebula, must have fallen in upon
the sheet after being abandoned, it is not difficult to see that the
part of the sheet out of which Neptune and Uranus were made, might be
more dense than the Saturnian nebula, on account of this matter being
added to it; and that, as the greater portion of it must, at the more
advanced stage of the process of condensation, have fallen upon the
Uranian part of the ring, because the space from which it fell would
be higher, the density of that would be greater than the Neptunian
part of the sheet; both of them exceeding the density of the Saturnian
nebula. Again, we have supposed, very naturally we think, that all
extraneous matter coming in from the equatorial direction would be
intercepted by the rings destined for Neptune and Uranus, so that the
density of the ring for Saturn would be only what had been acquired
through condensation, and the planet formed out of it would be less
dense than those made out of matter accumulated in a different way. It
may be argued against this deduction, that density would depend on the
degree of contraction, but it is natural to think that lighter would
take longer time than heavier matter to condense to the same degree;
besides Saturn is of necessity the youngest of the three planets, and
may in due time come to be as dense as either of the other two, but his
diameter will decrease proportionately.
Coming now to the Jovian nebula, whose diameter we have made to be
1,370,000,000 miles, we have seen, at page 115, that--had it been a
perfect sphere--by the time it had contracted one thousand miles in
diameter, it must have had a flat side of more than 1,400,000 miles in
length? then if we add to that length all that the nebula had inherited
from Neptune, Uranus, and Saturn, the cylindrical part of it must
have been many millions of miles in length, and the polar very much
greater than the equatorial diameter of the nebula. In other words
we have to deal with a body having the form of a very long cylinder
terminating in spherical caps. To this we have to add that the density
of the Jovian was more than 111 times greater than that of the original
nebula. Still farther we have to take into account that the whole of
the matter abandoned by that nebula must have been thrown off in less
than one-half of the space in which the ring for even Saturn had been
abandoned, the breadth of the two rings, as shown by us, see Table
III., having been 650,600,000, and 313,400,000 miles respectively. All
these things considered, it is clear that the thickness of the ring for
Jupiter's system must have been very much greater than what we have
given it in the table; which, coupled with its matter being over six
times more dense than that of the preceding ring, is sufficient to
account for the rise in density, the immense size, and mass of Jupiter.
Next, we have the means of accounting for the fact that, the space
occupied by the Asteroids is, and has always been, the least dense
of any portion of space occupied by the solar system. It is easy to
understand that the enormous mass of matter abandoned by the nebula for
the formation of the Jovian ring--more especially towards the end of
the process--would have a very appreciable effect, by its attractive
power, in helping centrifugal force in freeing matter from the power of
gravitation; the consequence of which would be, that the matter thrown
off for the formation of the Asteroidal ring would be considerably less
dense than it would otherwise have been. In this way, then, we have the
decrease of density, as well as the quantity of matter, in that space
very plausibly accounted for.
Then, as the nebula continued to contract, the attractive power of
Jupiter's ring would decrease proportionally to the square of the
distance of the receding mass, ceasing in doing so to lend so great
assistance to centrifugal force in the nebula, and so letting it
subside into its normal state; so that the matter abandoned would
increase in density in comparison to the space over which it was
distributed, thus accounting for the rise in density towards Mars and
the Earth.
With regard to the fall towards Venus and final rise towards Mercury,
we have to take into consideration the anomalies--already taken notice
of--in the dimensions, densities, etc. etc., of the two planets Earth
and Venus; it being, we may confidently say, certain that the whole
of them have arisen from the same causes. Following up the idea of a
dumb-bell nebula--as we might have done in the case of Jupiter also--as
the breadth of space for receiving matter abandoned by the nebula went
on rapidly decreasing, the thickness of the ring left behind would go
on increasing, and the overhanging matter of the dumb-bell would be
deposited always in greater quantity on the outer than the inner part
of the ring as it broadened; we can conceive that the whole extent of
the sheet of matter allotted to the Earth and Venus would be thicker
at the outer than the inner part. Hence, when this part of the sheet
came to be divided into two parts for the formation of two planets,
the outer would naturally be the greater and denser of the two, and
thus occasion the rise in density from Mars to the Earth, and the
fall to Venus. Finally the rise in density to Mercury would be only
the beginning of the gradual, and final, rise to the sun as it is at
present.
If the idea of a nebula in the form of a cylinder with hemispherical
ends is admitted as possible, or somewhat like a dumb-bell, the
extreme diameters of the 9 successive nebulæ we have dealt with would
be considerably different in their equatorial directions to what we
have given them, although their polar diameters might continue to be
not far from the same; but that would have very little effect on the
operations we have gone through, seeing we have shown that there could
be no actual divisions between them such as we have adopted; and that
the division of the sheet of matter abandoned into separate rings
must have been brought about by some means which we cannot explain; a
process, nevertheless, which has been subject to some law, or laws,
operating evidently in a regular and steady manner throughout the whole
time, during which the matter was being abandoned, as is proved by the
general uniformity, or harmony, in the distances of the planets from
the sun. Should anyone come to be able to account for the division of
this sheet of matter into distinct and separate rings, he will also be
able to account for the acceleration of rate of revolution from one
planet to another, and for the anomalous rates in the cases of the
Earth and Venus.
In a former part of our work we have followed up, at different
stages, the condensation of the original nebula until it attained the
dimensions, appearance, and some of the features of the sun as it is,
but we have still something to add as to how the condensation could
produce a body so strictly spherical as the sun is represented to be.
All the other bodies of the solar system, as far as astronomers have
been able to measure them, are spheroids more or less oblate, and it
seems strange that the principal should be the only one that does
not conform to the general figure. It is rather hard on the notion
that the original nebula gradually assumed the form of a lens, for
it would require a special mode of manipulation of a very mechanical
kind, rather than the steady, imperceptible self-action of the law
of attraction, to transform a lens into even an oblate spheroid; to
transform it into a perfect sphere would be absolutely impossible.
For, if at the end of the process it was found that there was too
much material to form a sphere, it would be hard to get rid of the
superabundance, unless it was converted into meteorites--evidently
another hand process. On the other hand, should a hole remain to be
filled up, the material would have to be lugged in somehow from some of
the errant masses, or lambeaux, which impact-theorists find it so easy
to have at hand when required. Let us then think of why and how it came
to pass that the sun is an almost perfect sphere.
If we suppose that, when cosmic matter ceased to be thrown off by
it, the form of the nebula was that of a cylinder terminating in
semi-spherical caps at the ends, it requires no great stretch of
imagination to conceive that, between attraction and centrifugal force,
the whole mass should be converted through time, first into a prolate
spheroid, and then into a perfect sphere. And very possibly time only
is required for the sun to become an oblate spheroid, the same as his
dependent planets.
Should this form of nebula not be admissible--and we can see no
mechanical reason why it should not--and we are thrown back on a
lens-shaped nebula, the only resource left us is to suppose that
through continued action of attraction, and of centrifugal force,
or rather revolution constantly increasing, the latter gaining the
victory over attraction, finally converted the lens into an actual
ring, something of the nature of the ring in Lyra; and that that ring,
no longer increasing in revolution, would have to yield to the law of
attraction, and would condense and contract and close up into an oblate
spheroid, and then into a sphere. It is a roundabout, rather fanciful,
process, but any other way of converting a lens-shaped nebula into a
sphere, under the law of attraction, is absolutely impossible.
CHAPTER XVII.
PAGE
301 Former compromises taken up and begun to be fulfilled.
302 Estimates of the heat-power of the sun made only from
gravitation hitherto.
303 Contraction and condensation of a nebula solid to the centre.
Heat produced from attraction as well as by gravitation.
304 What quantity of heat is produced by a stone falling upon
the earth.
305 Showing again that there is a difference between attraction
and gravitation.
305 Contraction and condensation of a hollow-sphere nebula, in the
same manner as the solid one.
306 Differences of rotation would be greater in a hollow nebula;
because a great deal of the matter would be almost motionless
in a solid sphere.
307 In neither case could matter be brought to rest, but only
retarded in motion. Different periods of rotation
accounted for.
309 Table of different rates explained.
310 Heat produced by gravitation, attraction, and churning,
not all constituents of the heat-power of the sun.
311 There can be no matter in the sun so dense as water.
312 The hollow part of the sun acting as a reservoir of gases,
heat and pressure.
313 The behaviour of heat produced in the nebula, and its power.
314 How sun-spots are produced.
315 Cyclonic motions observed in sun-spots. Why not all in certain
directions, and why only observed in a very few.
316 Cyclonic motions in prominences treated of.
317 Many other things might be explained, on some of which we
do not dare to venture. Concluding observations.
At the end of Chapter VII., when making some remarks on the heat of
the sun produced by gravitation, we said that according to the areolar
law the condensation produced thereby would originate difference of
rates of rotation in the nebula--provided it did rotate as Laplace
assumed--depending on its degree of contraction and consequent density
increasing as the centre was approached; and that these differences
of velocity of rotation would give rise to a churning action in its
interior which, owing to the friction caused thereby amongst the
particles of its matter, would produce heat over and above what was
produced by gravitation alone. Again, at the end of Chapter XII., we
said it would not be difficult to show what tremendous commotions
throughout the whole nebula would be produced by these differences
of rotation; but that this could not be properly done until we had
reconstructed the original nebula, and had shown how from it the solar
system might be constructed. Now, therefore, that we have set forth, as
fully as we can, our ideas of the formation of a hollow nebula and the
construction from it of the solar system, we shall proceed to show how
heat was, and must still be, produced by the churning action, over and
above the definite quantity that could possibly be produced by simple
gravitation. And also to show how our notions of the interior of the
nebula first, and afterwards of the sun, are simplified and made more
natural by looking upon it as a hollow sphere.
We will begin by considering, first, what would take place during
the contraction and condensation of a rotating nebula solid to the
centre--i.e. filled with cosmic matter to the centre--as that is the
condition under which such a body has been studied hitherto--as far as
we know at least....
Not to weary humanity--our own included--by repeating, what almost
every one knows, who the parties were and how they came to the
conclusion, that by far the greatest part--almost the whole--of the
heat expended by the sun, ever since it had any to expend, has been
produced by condensation caused by gravitation; we shall for the
time being accept this as the general, almost universal, opinion at
the present day. If any proof of this being the case is considered
necessary, we have only to appeal to Sir William Thomson's lecture,
delivered at the Royal Institution on January 21, 1877, in which he
showed how a cone of matter, similar to that of which the sun is
made, with base at the surface and apex near the centre, falling into
a similar hollow cone excavated in his body, would, in descending
a certain distance, generate as much heat as would maintain a
proportional part of his expenditure for a year; and in which, beyond
stating that a very small part might be produced by the fall of
meteoric matter on his surface, he makes no mention whatever of any
heat-producing power except gravitation pure and simple. The weight
of the cone falling into the conical pit alone, produced almost the
whole of the desired supply. That this manner of calculation is one
of those modes which, as we have said from the very beginning of our
work, could never have been adopted had a little more thought been
expended on them, can be easily demonstrated even in the case we are
now considering. This we say with all due deference to so great an
authority; more especially as we know how difficult it is, how seeming
unnecessarily laborious, to examine everything to the very bottom;
and how pleasant and satisfying it is to feel contented, when we have
obtained what suits our purpose.
When we began to consider, in Chapter XV., what would be the interior
construction of the nebula, we supposed, at page 269, that it had
assumed a somewhat globular form when its diameter came to be three
times that of the orbit of Neptune, which would be 16,764,000,000
miles; and we will return to that supposition to set forth our
conception of how heat would be produced in a nebula of that diameter
solid to the centre--that is full to the centre of cosmic matter. In
that case a particle of matter starting from the surface, under the
power of gravitation, would have to travel 8,382,000,000 miles before
it reached the centre, and would carry with it a constantly increasing
power of producing heat, derived solely from the action of gravitation.
Next, we have to consider what would stop it when it reached the
centre and enable it to give out its heat--for until it was stopped it
could give out no heat at all--and the most easily conceived means of
stoppage would be to suppose that an equal and similar particle coming
in from exactly the opposite side of the nebula met it there. If it
was not that it would be something equivalent and much more difficult
to describe, while the result would be the same. The result would be
that, as each particle came in with equal power of producing heat,
the the amount produced when the two met and stopped each other would
be just double what each of them brought with it; that is our way of
looking at it at least, considering that the velocity with which they
met would be just double what each brought with it, and the force of
the shock would be double what it would have been had only one of them
been stopped in some other way; that other way would have had to give
or furnish its half of the shock, and would therefore be able to give
out as much heat as the stopped particle. Whether two of Sir William
Thomson's cones meeting at the bottom of his pit, from exactly opposite
sides of the sun, would have the same effect as we have found for the
two particles, may perhaps give rise to the discussion; but we do not
see why the result should be in any way different. When a stone falls
from a height upon the earth it gives out, in the form of heat, all
the heat-producing power it had accumulated in its fall, but we are
apt to forget, perhaps have never thought at all of, the why and the
how it gives it out, especially of the latter. The why is because it
is stopped, and the how is by the earth coming to meet it, and these
two ways have an inseparable relation to each other. And if the earth
comes to meet it, which it most undoubtedly does, though we cannot
measure how far it travels, it must bring along with it an amount of
heat-producing power equal to that possessed by the stone, when it
in its turn is stopped by the stone; thus the amount of heat arising
from the fall of a stone to the earth is, apparently, just double what
it is usually estimated to be. This fact comes under the category of
splitting hairs or, more truly speaking, of negligible quantities; but
the whole mass of the sun falling to the centre cannot enter into that
category, and whether we will or no we have to take it all into account.
We have conducted two particles of matter from exactly opposite points
of the surface of the nebula to its centre, and shown that by simple
gravitation a certain amount of heat would be produced by them when
they met there and stopped each other; now, we propose to conduct two
particles, not far from each other, from one side only of the nebula to
the centre, and point out what would happen to them on their voyage
thither. The road is long, as we have seen, and during their voyage
there would be time enough for a good many things to happen, but we
shall only take notice of two for the present, namely, gravitation--of
which we have already almost disposed--and attraction; for as far
as their journey is concerned there is a very marked difference in
the meaning of the two words. Gravitation--that is, the action of a
ponderable body falling--acts only in a straight line from any point
to a centre of attraction, while attraction acts in every possible or
imaginable direction. We have already seen what happened to the first
particle despatched to the centre under the power of gravitation alone,
and have only to say, that the same would happen, under that power, to
the two we have now in hand; but attraction--actually the father or
mother of gravitation--would have a good deal to do with their journey.
From the moment they started--very likely they were practising before
they left--they would rush at and continue to bombard each other during
the whole voyage. At each encounter or collision, however caused, a
certain amount of heat would be produced in each of them which they
would carry along with them, and would augment the gravitational
quantity they would have to give out when stopped in their fall, in the
way we have pointed out would be the only one that could bring them
to rest. It may be said that that heat would be left behind in space
on the way but space cannot absorb heat unless it contains something
to hold it in, and that something could only be similar particles
of matter on the same voyage, also creating heat and having as much
to dispose of, no doubt, as the two we are conducting. This lateral
attraction, so to speak, is really what instituted rotary motion in
the nebula, and produced the differences of rotation and the churning
action in it with which we shall have to deal presently.
Having passed under examination the quantity of heat produced by the
contraction and condensation of the solar nebula into a globe solid
to the centre, we have now to do the same for the case of its being a
hollow sphere, and we may say that our work has already almost come
to an end; for we have only to vary to a small extent what we have
just set forth. Beginning then as before, with one particle of matter
falling, or rather being attracted, from the surface of a hollow-sphere
nebula, we find that it would not reach the centre at all, but would
be stopped by another drawn out from the centre by its own attraction,
which would meet it--say for brevity--half-way between the starting
points of the two, each bringing along with it its own heat-producing
power and giving it out to its opponent, there being nothing else to
give it to; so that if each brought with it _x_ heat-power they would
have 2_x_ heat-power between them, just as we have said would happen
in the first case, and the heat of each one of them would consequently
be doubled. In this case we have to observe, though it is really
unnecessary, that as yet we have spoken of attraction as acting in one
direction only, that is, in doing only the work of gravitation; so we
have still to consider the voyage of two particles of matter proceeding
from the surface and meeting two coming from the centre, and have only
to say that their mutual collisions caused by lateral attraction on the
way, would enable them to bring along with them certain quantities of
heat produced by these collisions, which would be over and above what
they acquired in their straight-line imaginary voyage.
If any one doubts that additional heat would be produced by this
lateral attraction and bombarding, let him take two hammers and
strike the one against the other as rapidly as he can for some time,
and he will be able, by touch, to convince himself that heat can be
produced by this lateral attraction as well as by the _attraction of
gravitation_; and, if he could measure it afterwards, he would find
that if he dropped the hammers on the ground, they would not give out
any of that heat but only what they had derived from gravitation in
falling from his hands to the ground, unless the ground was colder
than they, and if the ground was not colder, the heat it had would be
augmented from this source also.
If the heat produced in both of the cases we have been examining
caused differences of rotation in the nebula--as we have said on a
former occasion--increasing in velocity as the region was approached
where the stopping process came into action, it is clear that these
differences would be greater near that region in a hollow-sphere
nebula than near the centre of a solid sphere; for the reason that
the particles of matter would there have more freedom, that is, more
room to act in. We have shown that in the solid sphere the particles
would come to be more or less inert, in proportion as they approached
the centre; and also that in a hollow-sphere nebula no particle could
ever come to be near to a state of rest, but that each could be freely
driven by the collisions produced by lateral, angular, universal
attraction over every part of the hollow shell--an effect that could by
no means be produced in a nebula solid to the centre. We, therefore,
think that there would be more life-power in a hollow-sphere sun than
in the kind of sun from which all calculations of length of life have
hitherto been made--at least, as far as we know.
It will be understood that we have spoken of particles of matter being
stopped, or stopping each other, before they could give out their heat,
only for facility of explanation; for no particle of matter can ever
be brought to absolute rest, until all its heat and heat-producing
power, _i.e._ motion, could be taken out of it, and that can only be
when it is reduced to absolute zero of temperature. Cosmic matter could
be reduced to the state of rock or steel, but its particles would not
be at rest then, or else our ideas of the nature and construction of
rock and steel are very erroneous; but it must be acknowledged that
it would be much more easily reduced to the state of rock in a body
solid to the centre than in the shell of a hollow sphere. In fact it
is difficult to conceive how matter could exist at the centre of the
sun at the present day without being as solid as rock, considering
the enormous pressure it must be subjected to there, if its whole
mass is condensing to the centre. But although the particles of the
nebula could not be absolutely stopped, they might be so far retarded
in their velocities derived from attraction that they would give out
heat to each other, and wherever a collision took place there heat
would be made evident, and condensation might take place. Particles
of matter would not have to fall to a centre, but only to a a meeting
place, in order to condense and create heat, and might form layers of
condensation anywhere between the centre and the surface, either in
a solid or hollow sphere, which would ultimately, even in the former
case, form a hollow shell, as we have supposed, at page 274, might be
the case. For even a small sphere formed around the centre in that way
would be hollow, and would be undone when the different concentric
layers approached each other, under proportionate forces of attraction,
and formed into one hollow sphere. Thus we again come to the conclusion
that the formation out of cosmic matter acted upon by the law of
attraction, of a sphere full of that matter to the centre would be a
mechanical impossibility. In either case the total quantity of heat
produced by the contraction and condensation of the nebula would
include, not only what has hitherto been looked upon as belonging to
gravitation alone, but that other part derived from attraction in all
other directions. So the age and duration of the sun still remain to be
estimated.
We have not said, but we have not forgotten that it may be said that,
if in Lord Kelvin's estimate of the sun's heat, a cone of matter
falling in from one side of it was stopped by a similar cone falling in
from the exactly opposite side, one half of the sun's mass stopping the
other could only produce the amount of heat calculated by him. Neither
do we deny that the same may be said of the two half-volumes of the sun
meeting at the region of greatest density in a hollow sphere, and that
the amount of heat produced by gravitation alone would be the same in
both cases. All that we have wanted to show is that, in addition to the
quantity so produced, the quantity produced by lateral attraction, so
to speak, has to be taken into account, in order to estimate the total
quantity ever possessed by the sun.
Referring now to what we have said towards the end of Chapter XV., of
rotary motion being instituted at the region of greatest density of the
nebula, and being propagated from there to all parts both outwards and
inwards, we can at once account for the different periods of rotation
observed on different parts of the surface of the sun; and not only
that, we can assert that these differences of rotation must exist
throughout the whole volume and mass of its body up to the present day.
We have no need to appeal for producing them to showers of meteors
falling on its equatorial regions; neither do we pretend to say that
such showers have no part in producing them; but we do say that the
part they play in the affair, and the depth to which they can penetrate
into the sun's body, must be altogether insignificant compared to what
we have pointed out as the true and indisputable cause.
We may now proceed to consider what would result from the commotions
produced by these differences of rotation in the interior of the sun,
and we shall begin by observing that an enormous amount of heat would
be produced thereby. The churning action, as we have called it, must
be of a very formidable character, for, supposing the whole of the
interior to be in a gaseous or gasiform state, it must be effected
under a pressure of not less than 28 atmospheres at the surface, and at
what pressures as the centre is approached no one can tell; and if the
matter in the interior is in a viscous condition, the friction caused
by the churning will only be the greater. But let us try to form an
idea of what the force, or rather violence, of that churning action
must be in the sun if constructed in the manner we are advocating;
for which purpose we have to form some definite notion of what is
the difference of velocity of rotation at different parts of its
circumference, which can hardly be better shown than by Table X., in as
far as these rotations have been approximately measured.
The first thing to be observed in the table is that the rate of
rotation at the equator is 75·10 miles per minute, and that at Lat. 45°
it is only 48·23 miles, giving a difference of 26·87 miles per minute
in one-fourth part of the sun's circumference, which is a velocity 27
times greater than our fastest express trains. And the next is to note,
in the last column, how these 26·87 miles of difference, when divided
over spaces of 5° each, show decreases in velocity of from 0·39 at Lat.
5° to 5·06 miles between degrees 40 and 45.
A little thought bestowed on these two points will show what
commotions must be produced at the surface by this enormous variation
of rotation and make us speculate on how much greater it must be near
the poles than at the half distance from the equator. Then, if we look
upon the sun as a hollow sphere we have to consider that, according to
the theory that the condensation of a nebula increases its rotation in
proportion to its approach to the region of greatest density, of the
velocities of all the rotations expressed in the table, the greatest
must be at that region, the others diminishing from there outwards to
those of the surface, and inwards to almost nothing at the centre; for
we have seen that there must be gases enclosed in the hollow, and that
motion must be communicated to them, through friction, down to the very
centre. Taking all these things into consideration, it is certain that
the churning must be very much greater than anything we have thought of
up to the present moment, the commotions created more tumultuous, and
the heat produced by friction incalculable.
TABLE X.--SHOWING THE DIFFERENCES IN VELOCITY OF ROTATION
OF THE SURFACE OF THE SUN, AT DISTANCES OF 5° FROM
EACH OTHER, FROM THE EQUATOR TO 45° OF LATITUDE.
-------+----------+--------+--------+--------+--------+------------+
|Circumfr. | | | | |Retardation |
Lati- |at each 5°|Time of |Rotation|Rotation|Rotation|in Miles per|
tude |Latitude |Rotation|per Day |per Hour|per Min.| Minute for |
Degrees| from | (Days) | (Miles)| (Miles)| (Miles)| each |
|0° to 45°.| | | | | 5 degrees. |
-------+----------+--------+--------+--------+--------+------------+
| | | | | | |
0 | 2,723,767| 25·187 | 108,142| 4506 | 75·10 | ... |
| | | | | | |
5 | 2,713,367| 25·222 | 107,581| 4483 | 74·71 | 0·39 |
| | | | | | |
10 | 2,682,387| 25·327 | 105,910| 4413 | 73·55 | 1·16 |
| | | | | | |
15 | 2,631,058| 25·500 | 103,170| 4299 | 71·65 | 1·90 |
| | | | | | |
20 | 2,559,504| 25·737 | 99,441| 4143 | 69·06 | 2·59 |
| | | | | | |
25 | 2,468,572| 26·040 | 94,799| 3950 | 65·83 | 3·23 |
| | | | | | |
30 | 2,358,852| 26·398 | 89,357| 3723 | 62·05 | 3·78 |
| | | | | | |
35 | 2,231,179| 26·804 | 83,242| 3468 | 57·81 | 4·24 |
| | | | | | |
40 | 2,086,526| 27·252 | 76,564| 3190 | 53·17 | 4·64 |
| | | | | | |
45 | 1,925,994| 27·730 | 69,455| 2894 | 48·23 | 5·06 |
-------+----------+--------+--------+--------+--------+------------+
NOTE.--The times of rotation are taken from
Messrs. Newcomb and Holden's "Astronomy," p. 290.
Lest we should have been misunderstood in what we have said a few pages
back, and it be thought we consider that all the heat produced by this
churning action ought to be added to that produced by gravitation
alone, when attempts have been made to compute the total quantity
ever possibly possessed by the sun, we have to insist that the idea
of gravitation in itself--that is, of matter falling to a centre--is
altogether erroneous in connection with the construction of the sun
from a nebula, and that it is in truth utterly misleading. We know
perfectly well that in the construction of the sun, heat could only be
produced, in the main, by bodies colliding with, or rubbing against,
each other, and that a large part of that produced by universal
attraction must have been expended in producing rotary motion; but we
also know that in its construction no particle of matter can ever,
as yet, have been brought to the state of rest of solid matter even,
that it has still the power of colliding with its neighbours and of
producing heat, and that it will continue to preserve that power
until it is bound up into a solid state along with its neighbours.
Even then it will not be absolutely at rest, but will have lost its
heat-producing power, and will begin to lose the quantity it then
possesses when it gets permission from its neighbours. It is a fallacy,
therefore, to suppose that the matter of which the sun is composed
has no other heat-producing power than what is derived from its fall,
through gravitation alone, from the potential position it held to the
centre of the incipient nebula. The only end to heat-producing power is
fixed position.
If science chooses to fix that position at the centre of the sun, or
as near to it as successive particles can reach, there must be any
quantity of it in a solid state even now in that neighbourhood, if
due consideration is given to the pressure it must be subjected to
there. If it chooses to entertain the idea of the sun's being a hollow
sphere, somewhat in the form we have described, there can be nothing
in its whole body so dense as even water up to the present time. In
the first case it has to remember what we have done our best to prove:
That _gravitation_ ceases to act when a body falls to a fixed centre
or position and can fall no farther. From there it cannot rise except
through upper or exterior attraction, and in that case it would leave
a hollow space in the place it had occupied. It is altogether illusory
to dream of convection currents where no means or force of any other
kind than attraction could give rise to them, in which case we should
have attraction and gravitation working against each other, two things
that have been confounded into one turning out to be antagonistic, as
no doubt they sometimes actually are--as we have shown when treating
of the discovery of Neptune--but when they are so, they never can
produce convection currents. In the second case in which, as we have
seen, there can be no matter at all near to the solid state or fixed
position up to the present day, we can conclude that the life of the
sun, measured by heat-producing power, must be very much longer than in
the first case, in which a very large part of the matter of which it is
composed must have lost that power ages ago.
We have still to bring to mind what we have said in Chapter XV. of
the region of greatest density of the nebula being the region of
greatest activity and greatest heat; and to add now, that the whole
space between that region and the centre must have been acting as
a reservoir--partly material, partly gasiform--of heat, ever since
the nebula began to contract and condense, quite independently of
its carrying before it the minus or plus sign. From that time that
region would be the regulator of the radiation of heat into space, or
to wherever it was radiated; because no heat produced on the inner
side could escape into space without passing through and acquiring
the temperature of that region, or first giving out to the outer side
any greater heat that it might have produced and accumulated; facts
which involve the necessity of the whole of the interior space, or
volume being heated up or lowered down to the same degree before any
of it could be transmitted outwards. Thus, in addition to all we have
said of the means of lengthening the sun's life, we have to take
into consideration that all heat radiated from the surface must be
conducted, or carried somehow, through a distance somewhere between
about 2,000,000 and 90,000 miles, before it could escape into space
or elsewhere, according to when it began to be radiated at all. And
we have also to take into consideration the probability that the heat
produced and accumulated in the inner half of the volume would, by
its repulsive force, retard the condensation of the nebula, and thus
prolong its heat-giving life.
Looking back on our description of the construction of the sun, how
rotary motion was established in it, and how that motion has produced
the different velocities of rotation, not only on the surface where
they have been observed and measured, but which must penetrate to the
very centre; we may now proceed at the expense of some repetition--in
which we have already somewhat indulged--to show how our mode of
construction and development enables us to understand a great many
things that have been observed in it, much better than we have been
able to do from any explanations that have hitherto been available. It
gives the most satisfactory reason possible for the sun-spots occupying
principally two zones at marked distances from the equator. There is
one belt round the equator of 16° to 20° wide on which we know, from
Table X., that the differences of velocity of its edges and of those
of the contiguous zones, one on either side, hardly exceed 1 mile per
minute. Towards the poles there are two segments measuring from 80° to
90° broad, at the borders of which the rotary velocity is slower by
26·37 miles per minute than it is at the equator, and 5·06 miles per
minute slower than at 5° less latitude, as also shown by the table.
And between the central belt and these segments there are two belts or
zones, each 30° to 35° wide, in which sun-spots are almost only to be
found. In these two zones the churning of the interior would be in all
its vigour, most probably more active at their centres than where they
meet the central belt and the polar segments; where our knowledge of
the diminished velocity ceases, but where we have no reason to suppose
that it actually stops.
Were the period of rotation the same throughout the whole body of the
sun--with the exception of what has hitherto been considered to be a
mere surface difference produced by external causes--we could conceive
that the heat produced solely by condensation would find its way to
the surface equally in all directions, even bubble up all round like
steam rising from the surface of the water in a boiler, in this way
forming what is called the sierra; and that there would be neither
sun-spots nor eruptive prominences, hardly any of the violent movements
recorded in works on astronomy. But the churning action we have been
exhibiting, extending to the deepest recesses of the sun, must produce
commotions quite adequate to give birth to the most violent phenomena
that have been recorded. Viscous gases and vapours, gasiform vapours,
ground against each other at depths of hundreds of thousands of miles,
under pressures of hundreds, much more likely of many thousands, of
atmospheres, and confined by superincumbent strata, so to speak, would
acquire a dynamitical explosive force that could be conceived to be
powerful enough to rend the sun into fragments, were it composed of
anything comparable to solid matter. On the other hand, the friction
of the solar matter operated under the pressure of 28 atmospheres at
the surface, and up to the unknowable number at the greatest depth,
converted into heat, would have explosive energy enough to give rise
to all the phenomena that have been observed; from the veiled spot to
Professor Young's prominence, which was thrown up to the height of
350,000 miles above the photosphere.
A veiled spot seems to be one that has broken through the photosphere,
perhaps not even entirely, but not through the light or white clouds
which float immediately over it; which, in consequence, goes a long
way to prove that sun-spots have their origin in up-rushes of heated
vapours from beneath; for a downfall of cooled metallic or other
vapours would break through the light clouds first of all; and which
is confirmed, as far as anything in solar physics can be confirmed,
by what we are exposing. That there is a down-rush also, goes without
saying, because there is no other way of giving account of what becomes
of the vapours of metals and other elementary substances brought up by
the outpours of heat, after they are cooled in the solar atmosphere.
That they should fall down into the same opening they had made in
rising up, is the most natural supposition that can be made; for,
otherwise, they would have to be carried beyond, or outside of, the
spot before falling. Moreover, a sun-spot is said to be generally
surrounded by prominences which bring up vapours of elementary
substances, that we must believe to be much heavier than those from
eruptions of sun-spots, because they issue much more violently,
showing that they must have been expelled by much greater force,
which must form a sort of wall all round the spot through which the
matter, thrown out by it, would have to be carried before it could be
deposited; and outside these walls there are no visible signs of where
it falls, so that we are forced to believe that all the substances,
those from prominences as well as those from sun-spots, fall into the
same general receptacle. Surely it could not be argued that there can
be no eruptions from a sun-spot, seeing that the force required to
drive matter through it must be less than when it is expelled from
depths very much greater than the depths of the spots. Thus we have
both up-rush and down-rush in sun-spots accounted for very plainly; and
they are always large enough for both operations being carried on at
the same time. Besides, they have been credited by eminent astronomers
with the faculty of sucking in the cooled vapours from the surrounding
prominences into the common pit.
In some sun-spots, said to be about 3 per cent. of those observed,
cyclonic motions have been observed in the umbræ and penumbræ, which
under the churning process might be expected to be universal in all of
them, but it is not necessarily so; even leaving out the consideration
of the difficulty of detecting them. We see in a deep smooth-flowing
river eddies revolving in all directions, caused by currents of
different velocities approaching each other, quite independent of the
form of the banks of the river or obstructions in the places where we
see them, but without doubt derived from sources of that kind higher up
in the river; and so it may be with cyclonic motions in the sun-spots.
The velocity and direction might be given to the vaporous matter by
the churning action before issuing into the spot, which would cause
eddies in it in all directions, the same as those in the water of the
river. It would be absurd to think that in a space so immense as the
bottom of a sun-spot, there should be only one orifice of emission of
vaporous matter: there might be any number; consequently, there may
be times when the out-flowing currents annul each other and none at
all are seen, or when there are partial currents in any direction;
others when they may be all so uniform as to produce a cyclonic motion
all round a spot, or nearly all round it, or two or more in opposite
directions, all as has been recorded on more than one occasion. Neither
could it be supposed that any cyclonic motion, caused by the churning,
could depend on which side of the equator the spot was formed in. There
must be little churning going on under the surface at the equatorial
belt, hence the paucity of spots there; but between the surface and
the centre there must be some point of meeting of the motions that are
produced on each side of the equator which, even were there no special
reason for it, would destroy all chance of uniformity, or distinctive
direction, in the upheaved matter when it arrived at the surface, let
it reach that place on whichever side of the equator it might. The
original salient motion at the bottom of a sun-spot might be to right
or left, or according as the material from which it proceeded had been
tumbled about, and the issuing motion might also be controlled greatly
by the form and position of the orifice, or rather tunnel, through
which it escaped. Common churning, we know, could not drive all the
milk in one direction, even were the paddles of the churn solid; and
in our case, the paddles have to be looked upon as even more divided,
magnitude for magnitude, than they are in an ordinary churn, for the
matter itself forms the paddles.
The cyclonic motions observed in prominences must come from the same
causes, and ought to be more general in them, seeing that they must
proceed from apertures much fewer in number than in the sun-spots, and
very probably from one orifice in the case of jet prominences. One
would expect also that these cyclonic motions would be more regular
in the prominences, from being generated deeper down in the interior
than those of the sun-spots, and less affected by the motions they
encountered on their way out, owing to the great original energy
required to force them through the superincumbent mass of matter,
and might even have--in jet prominences especially--the motion to be
expected according to the hemisphere from which they proceeded. But we
have already said that, deep in the interior, the churning motion may
be in any direction whatever. It is natural to suppose that the highest
prominences are ejected from the greatest depths, because they require
the greatest ejective force to throw them to such immense heights,
and because the greatest ejective force must be where the heat and
pressure are greatest, that is, at the densest and most active depths.
And probably the reason why prominences generally surround sun-spots
is that they have had their exits facilitated by the relief from
pressure, brought about by the discharge of churned matter into them
(the sun-spots), and thus, as it were, attracting the eruptions of the
prominences towards them.
We had almost omitted to say that the churning theory would very well
account for almost every sun-spot having more or less proper motion of
its own independent of all others, and for all of them drifting towards
the central belt, or towards the polar segments when they begin to
dissolve and disappear.
There are many other things in connection with the sun that could
be explained through our mode of construction, some of which are so
evident that they will occur to anyone, and others that lead into
depths too profound for us to enter.
To conclude. The construction of the sun we have set forth would be of
great service towards the completion of either of what Professor A.
C. Young calls the competing theories of M. Faye and Fr. Secchi, in
which the former would find the origin of the solar storms, to which
he appeals for producing sun-spots in particular zones, and a better
way of accounting for the differences in velocity of rotation between
the equator and the poles than in the depths of the strata between
these regions; and the latter the means of forming the dense clouds of
eruption which he assumes to form sun-spots by settling down into the
photosphere. But theorists seem to be partially right by a divination,
and to have only failed through their not having found out the sources
of the powers they called into existence, in order to have some
foundation to build their theories upon.
CHAPTER XVIII.
PAGE
319 Return to the peaks abandoned by the original nebula.
An idea of their number.
320 Example of their dimensions. What was made out of them.
321 What could be made from one of them.
322 How it could be divided into comets and meteor swarms.
323 An example given. How a comet may rotate on its axis.
And what might be explained thereby.
Orbits and periods of revolution.
324 Not ejected from planets. Their true origin.
326 Study of the velocities in orbit of comets, and results thereof.
327 How far comets may wander from the sun and return again.
328 No reason why comets should wander from one sun to another.
Confirmatory of the description, in Chapter XV. of
the sun's domains.
329 Of the eternal evolution and involution of matter.
The atmosphere and corona of the sun.
331 Partial analogy between it and the earth's atmosphere.
332 The density of it near the sun's surface cannot be normally
less than 28 atmospheres, but might be so partially
and accidentally.
332 Probable causes of the enormous height of its atmosphere.
334 The mass taken into account, but cannot be valued.
335 Most probably no matter in the sun exceeds half the density
of water. The unknown line in the spectrum of the corona
belongs to the ether.
When we were attempting to describe in some measure the region of space
from which the sun obtained the nebulous matter out of which it was
formed, we found that it would produce a nebula somewhat resembling a
most gigantic starfish, with arms or legs stretching out from it in
every direction, which might be likened to mountain-peaks rising from
a tableland or range of mountains; and when we began to condense the
nebula we concluded that these peaks would very soon, comparatively,
be left behind the main condensation, owing to their being more under
the influence of the attraction of surrounding suns. And we might then
have added less under the attraction of the main body, on account of
its gradually increasing distance arising from its greater rapidity
of contraction. Now, we propose to return to these portions of the
sun's property so long left out in the cold, to think of what in all
probability became of them, seeing that they must all have had somehow
a part of some kind to take in the formation of the solar system.
First of all, we have to form some idea, however vague, of their
number, which may be divined to a very limited extent from the
following considerations: We see, from Table VIII., that the sun's
sphere of attraction extends to more than 4000 Neptune distances in
the direction of [Greek: a] Centauri, the star nearest to the earth,
which corresponds to 11 billions of miles. Then, although we have said,
in Chapter XV., that instead of there being a peak on the nebula in
that direction there would be a deep hollow in it, we shall proceed
to find out what might be the diameter of the base of a peak at that
distance supposing it to be somewhat in the form of a cone. We know
that the moon does more than eclipse the sun, which is 867,000 miles
in diameter; so, for facility of calculation, we may suppose that it
eclipses a portion of space at its distance of 1,000,000 miles in
diameter. Consequently, the base of a peak such as we are measuring
would be eclipsed were it 129,000 millions of miles in diameter, and
then only. Moreover, we have deduced the diameter of the base of such a
peak from _one_ diameter of the moon; so that wherever we see two stars
only one breadth of the moon from each other, there we have room for
at least one peak with a base of the above diameter. Last of all, when
we come to think that there are as many as six to seven thousand stars
visible to the naked eye, and of the intervening spaces between them,
we have to conclude that the number of peaks surrounding the original
nebula before they began to be left behind, or cut off, must have been
almost beyond our conception; more especially if we look at Table VII.,
where we see that the star Canopus is 25 times farther from the sun
than [Greek: a] Centauri. We are accustomed to look with wonder on the
volcanic peaks of the moon, but they can do nothing more than give us
an exceedingly faint representation of the original nebula seen from
an appropriate distance outside, when it had begun to contract more
rapidly than the peaks could follow it; seeing that we are comparing a
diameter of 2,160 miles with one really almost infinitely greater.
Finding ourselves, then, with an innumerable host of peaks, or cones,
of cosmic matter on our hands, we have to think of what can be done
with them, and we begin by saying that the use to be made of them was
suggested to us when we discovered the jagged nature of the domains
of the sun. Some of them have been most probably swallowed up in the
formation of the sun, and could we believe in the plenum of meteorites
in all space, that has been fancied to exist by some physicists, we
might derive its origin from a part of these peaks; but if there can be
such a plenum in space, its origin might be much more naturally derived
from a suggestion made in a former chapter, at page 258, to which we
shall refer presently. In the meantime, looking upon the multitude
of comets, meteor-swarms, etc., which revolve around the sun, or are
supposed to exist somehow in its neighbourhood, it is very natural to
entertain the belief that they have been made out of some of the most
important peaks--or the refuse from them--that must have formed part
of the original nebula. To deal with all of them when we cannot number
them, or even with the six of Table VIII., about which we actually know
something, is out of the question, so we shall only try to show what
could be made out of one of them.
Confining ourselves, then, to the peak of [Greek: a] Geminorum, whose
collecting ground had originally reached to 24,000 Neptune distances,
or 67 billions of miles--this being the point of space where the
attractions of the sun and that star balance each other--if we suppose
it to have been contracted till its base was of the same diameter, and
its distance the same from the sun, as that of the base of the peak we
measured not many minutes ago, 129,000 million miles, and 11 billions
of miles, respectively, we can easily conceive that its height may have
been 10 times as great as the diameter of the base, or more than 1-1/4
billions of miles. Here then we have in the direction of only one
star a mass of cosmic matter out of which something more than a comet,
even of the grandest known to modern astronomy, could be made. Of its
tenuity, all that we have any necessity to think is, that it would be
much less--i.e. more dense--than that of the original nebula.
Beginning then with the dimensions we have just stated, we know that
the attraction of the nebula would draw the matter of the base-end
of the peak more rapidly towards itself than that of the apex-end;
we know also that there would be different rates of contraction
going on in different parts of the length of the peak--for the same
reason we have given for the peaks being cut off from the nebula; so
that the condensation throughout its whole height, or length, would
be proceeding at different rates at different places, which would
certainly divide the peak into several parts, perhaps into many. If now
we suppose that the leading part of it--the one nearest to the nebula
or sun--or even the whole of it, formed itself into a comet, it is not
difficult to see that it might have a tail infinitely longer than any
comet the length of whose tail has been measured.
There can be no doubt that in the whole length of the peak the action
of attraction would be exactly the same as we have found it to be in
the nebula itself; that is to say there is no reason why it should not
come to be a hollow cone--comets are reported to be hollow in most
cases--condensed into layers, and to revolve on their axes throughout
a great part at least of where their diameters are greatest. This mode
of formation seems to throw light on some of the phenomena that have
been observed in comets. We have just said that our peak would be
divided into several parts, so if we suppose the leading part of it to
have been made into a comet, we can see why its tail should have the
appearance of a hollow cylinder; and there might be no reason why the
second division, or even the third, should not become a comet also.
Then for further divisions, where the diameter came to be too small to
make a comet, its matter might have formed itself into a meteor-swarm,
and account for the fact of some comets and meteor-swarms revolving
round the sun in the same orbits; perhaps even for some of the observed
meteor-swarms being denser at one part than another, owing to two or
more of the sections of the peak following each other at some distance.
We have to notice, after what we have just said, that it is quite
possible that if the different sections of our peak did come to revolve
round the sun, their perihelion distances might be so different that it
would be impossible to trace any connection between them and the peak
from which they were derived. But if we were to attempt to set forth
all the explanations of the phenomena of comets and meteor-swarms that
have occurred to us, there would be no end to our labour.
Passing now from one to the whole host of peaks, we have seen that at
one time they projected from all sides of the nebula; it is clear,
therefore, that the bodies formed from them must have fallen in
towards the sun from all directions, which is exactly what they have
been found to do. Then, if we think of the multitude of them there
would be, we have also to think that there would most certainly be
collisions among them, which would smash them to atoms, and thus
help to make the plenum, or host of independent meteorites that are
supposed to exist, or would be swallowed up by the sun in mouthfuls.
Others might coalesce, which they could only do through coming in from
slightly different directions and with nearly similar velocities; and
they would thus account to us for comets with a plurality of tails.
Again, looking back to what we have just said of the form that might
be assumed by the leading end of the peak [Greek: a] Geminorum, which
was suggested by Donati's comet, we could imagine another, the same in
almost all respects, coalescing with it, and between the two showing
us how Coggia's comet was formed. Furthermore, with respect to one of
the gigantic comets with endless tails: If we suppose it to rotate on
its axis, and to be not so smooth on its outside as a cone formed in a
turning lathe, we could account for the light from the sun reflected
from it having an appearance of flickering; and, were the outside very
rough, for the reflected light flashing from millions of miles of its
length in a few seconds.
All this about nebular peaks, comets, etc. formed from them, will, far
more than likely, be looked upon as imagination or speculation run
mad; but if it is looked into properly, it will be found that no part
of it is based on assumption; farther than that, the universe has been
formed out of cosmic matter of some kind. There is no step in the whole
process, from cosmic matter to the sun--even myriads of suns--that does
not conform to what are generally called the laws of nature; whereas
it is not difficult to show that some other speculations on the same
subject have never been carried beyond the stage of conception.
When thinking of how comets might be formed, we could not help
thinking of their orbits and periods of revolution. It was easy to
see that their orbits depended on where, and how far, they came from;
that the where might be from any and every direction, and that the
how far would be the principal element in their greater or lesser
ellipticity, which could only be determined by measurement; but their
periods of revolution, as far as we can see, could only be determined
by observation, which would involve the study of several revolutions.
On these points the data we have been able to collect are not very
satisfying, neither are they given to us as very reliable, except
as to those whose orbits have been often observed and measured; and
even among these the orbits are said to vary, and some of the comets
to disappear altogether. Again, some of them are said to have a
disposition to become associated with particular planets; and yet
again, some people have gone the length of supposing that they have
been ejected from some of the planets. To us it seems much more
rational to suppose that the known periodical comets have been made out
of part of the multitude of peaks which must have surrounded the nebula
at one time, if the sun was formed out of nebulous matter, subject to
the attraction of similar matter surrounding it on all sides. It seems
to be only a way of getting out of a difficulty to suppose that matter
ejected from, say the earth, with a velocity of 7 miles per second
would be freed from its attraction, that it would be involved somehow
in the sun's attraction, and that it would revolve thenceforth round
the sun like any other wanderer; because we cannot see what would stop
its progress upwards, so to speak, from the earth after getting beyond
its control, or communicate to it at the right height and time, the
exact velocity required to make it revolve for ever afterwards round
the sun; nor, supposing the sun would have nothing to do with it, where
it would go. When it left the earth, it might have a direct motion
of near one-third of a mile per second derived from its rotation,
and also one of 18 miles per second due to the revolution of the
earth round the sun. It might also be ejected in a direction exactly
away from, or directly towards the sun; so we should have two very
different cases to reconcile in order to set up the theory of ejection
of comets from planets, and of their being involved somehow in the
sun's attraction. It presents us with a very strong case for calling
for either the immediate intervention of some power other than what we
conceive attraction to be, and of which we know nothing physically, or
we have to trust in _man_ipulation of which we have no very exalted
idea. We prefer to look upon the formation of all comets as derived
from the peaks we have been treating of, or, if that is inadmissible,
from shreds and patches of the original nebula; where no immediate
intervention, or instant application, of supernatural power is
required, but only the even and tranquil operation of original design.
For comets larger, and which travel to greater distances, than those
alluded to above, it is very difficult to get data on which we can
form satisfactory calculations of the lengths of their orbits and mean
velocities of revolution, for there is almost always awanting some
one or more of their elements, or totally different statements given
of their value; but we think we have found a few from which we can
collect data sufficiently accurate to enable us to show that there is
no necessity for going beyond the domains of the sun, as described by
us in a former chapter, to account for any one of the comets which have
been taken notice of in astronomical history; and still less necessity
to suppose that any of them have wandered, or been shot forth, from
some neighbouring star into the solar system.
From the data we have been able to collect it would appear that when
a comet comes to have a period of over 70 years, it is either too
far removed from the sun at its aphelion passage, or its mass is too
great for it to be perturbed by the attraction of any of the planets.
For instance, we have Halley's comet, which has been observed for
not far from 2000 years, whose period has averaged very close upon
77 years during the whole of that time, showing that it has not
been perturbed to any appreciable extent when near its perihelion
passage. No doubt 2000 years is a very small period of time to judge
from, and its aphelion distance being only 3,258,000,000 miles, it
might be influenced to some extent by some planet, so we can hardly
count upon its being permanently exempt from perturbation. Indeed,
Halley himself supposed that its velocity of revolution had been
considerably increased when it was in the neighbourhood of Jupiter in
the interval between 1607 and 1682; but if it was so, there must be
some counter-perturbation which restores the balance so as to make
the average period of 77 years. Looking over the register of its
appearances, we find that in its re-appearances of the years 66 and
1758, the period was about 75 years, and that in those of 451 and 1066
it was 79 years; so that if there are perturbations, we must claim
that there are also compensations. Seeing, then, that we can find no
evidence to the contrary, we may suppose that when the periods of
comets, and, perhaps more especially, when their aphelion distances
reach to beyond--and the farther the more so--the orbit of the most
distant planet, they may be looked upon as not being liable to be
seriously perturbed by any of the members of the solar system, until
something to the contrary had been proved. Following this idea, then,
it occurs to us that something may be learnt from their mean velocities
in their orbits, as will be seen from the following very small list
of those we have been able to submit to calculation, which form the
accompanying
TABLE XI.--SHOWING THE MEAN VELOCITIES IN ORBIT OF SEVERAL COMETS.
----------------------+-----------------+----------+---------------+
| | Period of| Mean Velocity |
Designation of Comet. |Aphelion Distance|Revolution| in Orbit. |
| (Miles) | (Years) | (Miles/Sec) |
----------------------+-----------------+----------+---------------+
Halley's comet | 3,258,000,000 | 77 | 4·18 |
| | | |
Comet of 1532 & 1661 | 4,464,000,000 | 129 | 3·45 |
| | | |
Donati's comet | 13,873,280,000 | 2,000 | 0·69 |
| | | |
Comet of 1811 | 40,000,000,000 | 3,065 | 1·3 |
| | | |
Comet of 1680 | 78,468,852,000 | 15,864 | 0·49 |
----------------------+-----------------+----------+---------------+
These orbital mean velocities per second have been calculated from
aphelion distances as diameters and from circular orbits, which
probably give results rather lower than would be derived from
elliptical orbits--were they known--but on the other hand, the
perihelion distances have not been taken into account in fixing the
diameters--because they were unknown--so the error will be so far
compensated, if not altogether.
We know that the mean velocities in orbit of the planets decrease as
their distances from the sun increase, and our table, as far as it
goes, leads us to believe that the same holds good with comets whose
aphelion distances are comparable to those of the planets, in being
measured by hundreds of years or less of revolution; but with those
whose periods are measured by thousands of years, the same rule seems
to fail. One thing, however, that we seem entitled to believe is that,
generally speaking, the greater the period of revolution of a comet
is, the less will be its mean velocity per second in its orbit. It
will be observed that the average mean velocity of the three remote
comets in the table is only 0·83 mile per second, and it is by no means
unreasonable to suppose that the average mean velocity per second of
any number of comets whose aphelion distances are greater than the
highest of those in the table, is not likely to be so great as the
average of the three; on this understanding, then, let us take, or
suppose, one whose mean velocity in orbit per second is only one mile,
and look into what may be learnt from it.
Going back to the peak of [Greek: a] Geminorum which we supposed, at
page 321, to be condensed to 129,000 million miles in diameter of base,
its height 1-1/4 billion miles, and distance from the sun 11 billion
miles, we may take a comet formed from it as an example. If, then, we
suppose the leading part of it to have been formed into a comet with
that aphelion distance--11 billion miles--and other dimensions suitable
to its new condition; taking its mean velocity in orbit at 1 mile per
second, we find that its period of revolution might be 1,200,000 years,
or three times greater than that of the comet of 1882, namely 400,000
years, mentioned by Mr. Chambers as being not very reliable, probably
because its angles in orbit could not be measured with sufficient
accuracy. Then, when we think that the sphere of the sun's attraction
in that direction--of [Greek: a] Geminorum--extends to 67 billions of
miles, and that there are stars more than 6 times farther off, e.g.
Canopus, see Table VII., we see that a supposed comet might have an
aphelion distance equal to that; and were we further to consider that
were its major axis 67 billion miles long, including aphelion and
perihelion distances, and that it went straight from the one end of
it to the other and back again, its period of revolution, if it could
be so called, would be 8,500,000 years; that is 20 times greater than
Mr. Chambers's doubtful 400,000 years for the comet of 1882. There
seems, therefore, to be no necessity for the solar system sending its
cometary produce to a foreign market; and our mechanical imagination is
not sufficiently vivid to allow us to conceive what kind of potential
energy even Jupiter can have to give an impetus to a comet, great
enough to send it flying to so great a distance. What velocity would
it have when it left the sun? And what would remain in it to carry it
over the debatable land between the sun and a distant neighbour? Or
are we to believe that all the solar system's produce of that kind
is only sent over the channel, as it were, to our nearest neighbour,
[Greek: a] Centauri? Conceptions of that kind are too elevated for
us, and we must leave them alone. Mr. Chambers expresses doubts as to
the determination of whether the orbit of a comet is elliptical or
parabolic when its period of revolution is measured by hundreds of
thousands of years, and we think we are safe in following him until
actual proofs are presented. If the comet of 1882 never comes back, we
may then believe it has gone elsewhere.
Having used up all the nebulous matter in the sun's domains, as
described at the beginning of Chapter XV., or at least shown how it
may have been, or may yet be, used up, we have now only to make a few
remarks to prove that our description of the said domains is not by any
means fanciful. It matters very little whether the solar system was
begun to be brought into existence at the same time as the surrounding
systems or before or after them. What is certain is that the sun's
sphere of attraction among its neighbours is bounded, at the present
time, just in the way we have taken to describe its domains. How they
were filled with cosmic matter may be disputed, but filled they must
have been somehow, if the solar system was formed out of a nebula; and
the way adopted by us was the only one that occurred to us when we
began to reconstruct the original nebula. Since then we have had time
to reflect on our work, and to see how it points out the simplest way
that can be conceived, which may be expressed in the few following
words. We may suppose that the ether was the primitive matter, as we
have done at page 258, and that the whole material universe has been
formed from it and through it. This idea will assist physicists in
forming their theory of a plenum of meteorites or meteoric matter, if
such they choose to call it. It will also enable us to complete the
circle of our notions with respect to matter. We believe that we can
neither destroy nor produce the smallest portion of it, although we can
change its form. Thus, looking upon the ether as primitive matter, we
can understand how the solar system could be elaborated from it; and
how, after having accomplished the purposes for which it was brought
into existence, it may again be resolved into the primitive element out
of which it was made, ready to take its part in the evolution of some
other system with, perhaps, a new earth "without form and void."
We have now to direct our thoughts, as far as we can, to the mass,
which furnishes the really effective power of the sun as the ruler of
the system; and, first of all, we have to think of what are the real
active elements which form that mass. Hitherto we have looked upon
them as all included within a diameter of 867,000 miles, but now we
have to take notice of the clouds of meteoric matter which have been
supposed by some astronomers and physicists to be revolving round the
sun and continually raining into it; and of the enormous atmosphere
which surrounds it. With regard to the former of these two elements,
we shall compound our ignorance by looking upon it as a merchant does
on his account of Bills Receivable, as not being available in the
case of a sudden demand for cash, and therefore as not forming a part
of the mass, any more than as the attraction of the earth aids the
sun in its management of the planet Neptune; the same as the bills
receivable strengthen the credit of the merchant. But with regard to
the second element of the two, we must recognise that it forms part of
the mass and power over the whole of the system, and from all that is
known about it we are not authorised to look upon it as a negligible
quantity. It so happens that the only thing we have to which we can
compare it is the atmosphere of the earth, and we immediately find
that there is absolutely nothing to be learnt from such a comparison.
We know that one-half of the weight or mass of the earth's atmosphere
is contained in a belt of 3-1/2 miles high above its surface, so that
double the volume of that belt estimated at atmospheric pressure gives
us the true measure of its mass. This mass, when reduced to the density
of water, and compared to that of the earth as we have dealt with it
all along, turns out to be about 1/824,000th part of it; and were
we now to add that to the earth's mass we have been using, its mean
density would be 5·66065 instead 5·66 times that of water.
Now, let us suppose the sun to have an atmosphere of the same kind
as the earth's: Seeing that the force of gravity at its surface is
about 28 times greater than it is at the surface of the earth, a belt
around it which would contain one-half of its mass would be 28 × 3-1/2
= 98 miles, or say 100 miles thick. Dealing then with this dimension
in the same manner as we have done in the case of the earth, we find
that its supposed atmosphere would be 1/836,000th part of its mass,
which, if added to the mass we have used for it, would make its mean
density 1·413016 instead of 1·413 times that of water. Then again, if
we suppose the earth's atmosphere to extend to 100 or 200 miles above
its surface, the supposed atmosphere of the sun would extend to 2800 or
5600 miles above its surface, according to which of the above heights
on the earth is adopted; whereas the highest of our authorities say
that the corona, or apparent atmosphere, extends to at least 350,000
miles from its surface.
It would appear then that there is no analogy whatever between the
atmospheres of the sun and the earth; but there must be some analogy,
because the law of attraction cannot be suppressed at the surface of
the sun; neither can any vaporous matter near it cease to be attracted
in the same proportion as it is at the surface. Our atmosphere causes
a pressure of 29-1/2 inches of mercury at the earth's surface, and
the attraction of the sun at its surface must cause a pressure equal
to nearly 28 times that without fail, i.e. 420 lb. per square inch
instead of the 15 lb. of the earth. We know that some spectroscopists
believe that the pressure at the surface of the sun is sometimes as
low as it is at the surface of the earth, even lower; but we require
an explanation of why it is so. At the surface of the sun one second
of arc corresponds to a height of 450 miles above its surface, and
Mr. Proctor states in his "Sun," page 295, that if even "two or three
hundred miles separated the lower limit of chromatosphere from the
photosphere, no telescopes we possess could suffice (when supplied with
suitable spectroscopic appliances) to reveal any trace of this space.
A width of two hundred miles at the sun's distance subtends an arc of
less than half a second; and telescopists, who know the difficulty of
separating a double star whose components lie so close as this, will
readily understand that a corresponding arc upon the sun would be
altogether unrecognisable." We can understand this, and perhaps find an
explanation for ourselves.
According to our supposition that the sun may have an atmosphere
similar to the earth's, at one hundred miles in height it would be
reduced in pressure to 14 atmospheres, and, extending the analogy, at
2800 miles high the pressure would still be equal to one-eighth of 28
atmospheres, or equal to something less than 2 lb. per square inch at
the surface of the earth; so that if spectroscopists have measured the
sun's atmosphere at the disk, and found it to be lower than the earth's
at its surface, their results must have been caused by some fortuitous
circumstance which they did not notice at the time; because the force
of attraction at the surface of the sun can never be overcome except by
some counteracting force, which, if in the form of a vapour, or what
we call a gas, issuing from its interior, would increase rather than
diminish the pressure. We know that in the heart of a cyclone on the
earth there is sometimes a vacuum sufficient to explode (pull out the
walls of) houses near which it passes; and, at the same time, we know,
more or less, what heat the sun sheds upon the outer atmosphere of the
earth, and also the rate of rotation of the earth in the regions where
the fiercest of these cyclones occur, the only two causes which can
produce them. Now, if we compare these causes in the two bodies, that
is, the earth's rotation of about 16 miles per minute and the sun's of,
say, 60 to 75 miles per minute, and the temperatures of the sun and the
earth at their respective surfaces, we can imagine that in the heart of
a cyclone on the sun there may be a vacuum much nearer absolute zero
than there can be in any one on the surface of the earth. If then the
spectroscopists, without knowing it, have caught the spectra of the
hearts of cyclones, we can conceive them to be right, otherwise no.
Again, we know that when big guns are fired off partial vacuums are
formed near them, sufficient to cause disaster to windows, doors, and
even walls of houses too near them, but whatever we may have said of
force sufficient to produce explosions in the sun, we have never
believed that matter is ejected from the sun by explosions. We have
supposed the sierra, or chromosphere, to have oozed out through its
pores, sometimes to less, sometimes to greater heights, like steam
from an open boiler, and the prominences to be eruptive, neither of
which modes could produce anything approaching to vacua in their
neighbourhoods. There can be no resemblance between the ejection of
matter or gas from the sun and from a cannon, but there is between
the ejection of vapours and the escape of steam from the safety-valve
of a closed steam boiler; both of them continue to pour out their
vapours till the pressure within falls down till it is equal to the
resistance to their escape; there is no explosion, therefore no vacuum,
appreciable at least, in the neighbourhood. There may be surrounding
matter drawn up by the velocity of the outward current, but that is all.
Notwithstanding all this, we see no reason why the sun should not have
an atmosphere of exactly the same kind as the earth's, composed of
exactly the same kinds of gases, including vapour of water in some part
of it, though, perhaps, far removed from the photosphere. Every other
element found on the earth can be found in the sun, and so it is not
unreasonable to suppose that the same kind of atmosphere may exist upon
it; we have only to acknowledge that its conditions must be somewhat
varied, all the difference being that the atmosphere of the sun must
be heated up to the temperature of the photosphere where it comes in
contact with it, while that of the earth is only of the temperature of
the earth at its surface. In the case of the earth, if this were at
a white heat, one-half of the weight of its atmosphere would not be
comprehended in a belt around it of 3-1/2 miles thick. That balance of
mass might take place at a height of even hundreds of miles--we have no
means of calculating how high--and still its pressure at the surface
would be the same as now, as long as the earth's attraction remained
the same; so must it be with the sun. Instead of limiting its height
to 5600 miles at the utmost as we have done above, it would be no
stretch of imagination to suppose that it might extend to ten, twenty,
or more times that height. In addition to this we have to take into
consideration that the sun's atmosphere must be swept up to something
far beyond 5800 miles high by the whirlwinds created by the velocity
of rotation at its surface, the same as we saw the earth's might be
when we were explaining how an aurora could be made to glow at heights
far beyond what we were accustomed to believe its atmosphere could
reach. Adding, then, together these two motive forces for elevating
the atmosphere of the sun, it would be a bold assertion to say that
it cannot have one exactly similar to the earth's, reaching up to the
height of 350,000 miles mentioned a few pages back. And now, having got
this length, we may venture to assert that the corona of the sun is
made up of this atmosphere, and of the vapours of the elements thrown
out from its interior, somewhat in the manner we have described in last
chapter; to which we have only to add that the bubbling up of vapours
all around the sun, which produces the sierra or chromosphere, would
not be interfered with in any way by the tremendous commotions which we
have shown must be produced between the surfaces of the sun-spot zones
and the centre; and that the projection of the high prominences would
assist in elevating the aeriform atmosphere.
If then the sun has a compound atmosphere of this kind, it must be
considerably more dense, proportionately, than that of the earth, and
will consequently form a greater addition to its mass than we have
found would be made by its airlike atmosphere. But, whatever density
has to be added to it on that account has to be subtracted from the
interior having been ejected from thence; because, in whatever manner
its mass has been calculated in respect of the other members of the
system, the total amount must turn out to be always the same. We have
always estimated its mass from a diameter of 867,000 miles, which gave
us a volume of 341,237,638^{9} cubic miles, so that if we now include
in the diameter the 350,000 miles height of the atmosphere, we get a
volume of 2,053,500^{12} cubic miles, which is as near as possible six
times the volume in which we had to distribute the volume of the sun.
How to do this, we know not. We cannot fix the region of greatest
density in the same manner we have done at page 221, but we know that
it must be considerably nearer to the surface of the photosphere than
we have there placed it; and of one thing we are sure, and that is,
that the densities we have named for that region and the outer and
inner surfaces of the shell, at page 223, must be less than those there
expressed; how much we cannot calculate, but we have certainly found
that the limits must be lower, and that most probably there is no
matter in the sun exceeding the half of the density of water.
Whatever the composition of the sun's atmosphere, or corona if
that name be preferred, may be, spectroscopists have found in it a
_spectral_ line derived from some substance totally unknown to science.
Now, looking back on our work from almost the very beginning, it seems
to have been gradually borne in upon us that this unknown substance
is the ether. That it is a material substance we were hardly ever in
doubt, and our studies of it have substantiated and confirmed our
belief. In our analysis of the Nebular Hypothesis in Chapter VI.,
after combating the notion that the light of nebulæ is occasioned by
incandescent gas, we showed, by the example of an air furnace, that an
incandescent gas is composed of two elements, one consisting of solid
matter which takes up and gives out heat and has all the properties of
a heated solid or liquid substance, and the other of gaseous matter
which, being the element that fills up the empty spaces between the
solid atoms of a gas or vapour, only performs the office of carrying
the solid part into the furnace. This forced upon us the idea of the
gaseous part being a carrying agent, and very naturally to think of its
being really the ether, that being the only acknowledged agent for the
carriage of light, heat, and electricity, two of which are easily seen
and felt, and the third cannot be awanting, in an air furnace. Again,
when treating in Chapter VII. of what effect the ether might have on
the density of the original nebula, we concluded that its density must
be much lower than what we then knew it had been estimated to be, and
also that its temperature in space must be lower than -225°; which two
circumstances combined showed us that if it is a gaseous substance it
must be very different to any gas that had been liquefied up to that
time. This we repeated in great part in Chapter XII., calling attention
to the peculiarity of its being able to carry a higher temperature than
its own--to all appearance--into a "hot box." Then we have dedicated
two Chapters, XIII. and XIV., almost exclusively to the study of the
ether, and have been led from one stage to another to look upon it as
the only substance that agrees with the definition of a gas as given
by science; true gas there is; as the primitive and sole element in
the formation of all matter and in the evolution of the universe; and
what is something more than an unfounded guess, as the mysterious and
incomprehensible agent attraction, unfortunately almost universally
spoken of as gravitation. And now to conclude: From what we have been
able to learn, very slight differences have been found in various
spectra of the position of the line representing the unknown substance,
but this can cause very little doubt of its always being the same, as
spectra often contain several lines of hydrogen, owing most probably to
combinations with other substances; and if the ether is the primitive
chemical element, there may be slight differences in the position of
its line, as shown in all the phases in which we seem to have found it,
but they must be slight as compared with the hydrogen lines, because
even these must be in some measure, perhaps even great, influenced by
the unfailing and inevitable mixture of the ether in their composition.
LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
Transcriber Note
Several tables were reformatted to fit a maximum 75-column width.
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