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Title: Concerning the nature of things
Author: William Henry Bragg
Release date: July 21, 2026 [eBook #79146]
Language: English
Original publication: New York: Harper & Brothers, 1925
Other information and formats: www.gutenberg.org/ebooks/79146
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*** START OF THE PROJECT GUTENBERG EBOOK CONCERNING THE NATURE OF THINGS ***
[Illustration]
CONCERNING THE
NATURE OF THINGS
_By_
SIR WILLIAM BRAGG
K. B. E., D.Sc., F. R.S.
_Illustrated with Many
Diagrams and Plates_
[Illustration]
HARPER & BROTHERS, PUBLISHERS
NEW YORK AND LONDON
MCMXXV
CONCERNING THE
NATURE OF THINGS
Copyright, 1925
By Harper & Brothers
Printed in the U. S. A.
CONTENTS
CHAPTER PAGE
Introduction xii
Preface to the English Edition xv
I. The Atoms of which Things are Made 1
II. The Nature of Gases 46
III. The Nature of Liquids 90
IV. The Nature of Crystals: Diamond 126
V. The Nature of Crystals: Ice and Snow 172
VI. The Nature of Crystals: Metals 215
Note 250
LIST OF PLATES
PLATE _Facing page_
I. (A) MODEL OF BISMUTH CRYSTAL.
(B) THE SHAKING SAND BOX 16
II. SHIMIZU-WILSON HAY TRACK APPARATUS 26
III. ALPHA RAY TRACKS 30
IV. (A) BAR MAGNETS ON SPIRAL SPRINGS.
(B) MODELS OF ATOMS WITH
ELECTRONS 34
V. (A) FLOATING MAGNETS. (B) CRYSTALS
IN TUBE CONTAINING
EMANATION 42
VI. (A) TUNING FORK OVER JAR. (B) FOG
APPARATUS 60
VII. CIGARETTE SMOKE 66
VIII. EXPERIMENT SHOWING THE PRESSURE
OF THE ATMOSPHERE 72
IX. CAVITATION CAUSING EROSION OF PROPELLER
BLADES 98
X. (A) LARGE DROP OF ORTHOTOLUIDINE.
(B) ONE SOAP BUBBLE INSIDE
ANOTHER 104
XI. (A) CIRCLES CLEARED BY MINUTE
DROPS OF OIL. (B) THE CAMPHOR
BOAT 112
XII. (A) STORMY WATER, (B) OIL STILLING
THE STORM, (C) GRAPE IN
SODA WATER 118
XIII. CRYSTALLINE FORMS 134
XIV. (A) DIAMOND MODEL, (B) PLANE LATTICE
IN THE DESIGN OF A WALL-PAPER 148
XV. THE CULLINAN DIAMOND 156
XVI. (A) LAYERS OF THE GRAPHITE CRYSTAL.
(B) POSSIBLE FORMS OF
THE BENZENE RING 160
XVII. SNOW CRYSTALS OF VARIOUS FORMS 172
XVIII. MORE SNOW CRYSTALS 174
XIX. A HALO AND MOCK SUNS 176
XX. (A) GLACIER ICE. (B) MODELS OF ICE
STRUCTURE 188
XXI. (A) MODEL OF PENTANE, (B) X-RAY
SPECTRUM OF A HYDROCARBON.
(C) MODEL OF ROCK SALT 206
XXII. TWO PHOTOGRAPHS OF ALUMINIUM 216
XXIII. CRYSTAL GRAINS IN A SAMPLE OF STEEL 218
XXIV. ILLUSTRATING “CLOSE PACKING” 220
XXV. (A) CUBIC PACKING, (B) HEXAGONAL
PACKING 222
XXVI. THE YIELDING OF ALUMINIUM UNDER
STRAIN 230
XXVII. DAMASCUS BLADES 236
XXVIII. CEMENTITE CRYSTALS 238
XXIX. (A) CEMENTITE CRYSTALS BEING
BROKEN UP AND ROUNDED OFF.
(B) A NEEDLE SCRATCH IN A
POLISHED PIECE OF SPECULUM
METAL 240
XXX. EFFECT ON SPECULUM METAL OF RUBBING
(WITH FINE EMERY) AND
POLISHING (WITH ROUGED
LEATHER) 242
XXXI. A CONTINUATION OF PLATE XXX 244
XXXII. EXPERIMENT SHOWING EFFECT OF
TEMPERATURE ON ELECTRICAL
RESISTANCE 246
LIST OF FIGURES
PAGE PAGE PAGE PAGE
Figure 1 10 Figure 1A 18 Figure 2 28 Figure 3 35
Figure 4 57 Figure 5 68 Figure 6 69 Figure 7 70
Figure 8 73 Figure 9 74 Figure 9A 75 Figure 10 78
Figure 11 79 Figure 12 79 Figure 13 93 Figure 14 96
Figure 15 100 Figure 16 101 Figure 17 104 Figure 18 104
Figure 19 106 Figure 20 108 Figure 21 109 Figure 21A 109
Figure 22 117 Figure 23 122 Figure 24 123 Figure 25 124
Figure 26 133 Figure 27 134 Figure 27A 136 Figure 28 139
Figure 29 146 Figure 30 147 Figure 31 148 Figure 32 150
Figure 33 152 Figure 34 159 Figure 35 160 Figure 36 162
Figure 37 162 Figure 38 167 Figure 39 168 Figure 40 170
Figure 41 176 Figure 42 176 Figure 43 179 Figure 44 181
Figure 45 183 Figure 45A 184 Figure 46 189 Figure 47 191
Figure 48 192 Figure 49 196 Figure 50 205 Figure 51 208
Figure 52 209 Figure 53 219 Figure 54 222 Figure 55 225
Figure 56 226 Figure 57 229
INTRODUCTION
IT may be well to explain to American readers for whom this special
edition is published that the Juvenile Lectures of the Royal
Institution were first instituted in 1825. At a general meeting of
the members in December of that year, the Managers reported “that
Mr. Millington had engaged to deliver a set of Lectures on Natural
Philosophy, suited to a Juvenile Auditory, during the Christmas recess,
to be continued and concluded in those of Easter and Whitsuntide.”
For some reason the actual delivery of the course was commenced on
Christmas, 1826, by J. Wallis on “Astronomy.”
In February, 1826, the Managers reported that “they had consulted with
Mr. Faraday on the subject of engaging him to take part in the Juvenile
Lectures proposed to be given during the Christmas and Easter recesses.
The Managers found it would be exceedingly inconvenient to withdraw
Mr. Faraday from his experimental investigations to conduct such
lectures.” Faraday, however, found time in subsequent years to give
no less than nineteen courses of Christmas Lectures. He was extremely
interested in the importance of Science Lectures to young people, and
his Juvenile Lectures were masterpieces of exposition.
Tyndall gave a number of these courses, and others were given by Dewar,
Ball, Fleming, S. P. Thompson, Lodge, Boys, and other well-known
lecturers.
It has become a tradition in the Royal Institution that the lectures
shall be fully illustrated by experiments, and it has generally been
the case that both lectures and experiments have been to some degree
novel, in both the matter and the manner of their exposition. The
audience consists not only of the juveniles for whom the lectures are
primarily intended, but also of seniors who are interested in the
attempts to explain new points or show novel illustrations.
I have written this in the hope that those in America who do me the
honor of reading this book will sympathize in the problem of exposition
which I have tried to solve. The English edition contains a preface
which will be found reproduced in the following pages, and will help
further to explain the immediate purpose of the lectures.
W. B.
London, January, 1925.
PREFACE TO THE ENGLISH EDITION
IT was my endeavor at the Christmas Lectures given at the Royal
Institution in 1923-24 to describe certain features of the recent
discoveries in physical science. Many of the facts that have come to
light might well be the subject of “Lectures adapted to a Juvenile
Auditory,” and would be at the same time interesting and helpful;
interesting because they display a beautiful order in the fundamental
arrangement of Nature, and helpful because they have given us light on
many old questions, and will surely help us with many that are new.
I was aware of two special difficulties. The first was the difficulty
of understanding the minuteness of the scale on which the action and
properties of the atoms must be represented; but, after all, this was
only a difficulty due to unfamiliarity, and would come to a timely end.
The other was the difficulty of grasping arrangements in space. There
are some who think that this difficulty is incurable, and that it is
due to the want of some special capacity, which only a few possess. I
am persuaded that this is not the case: we should have nearly as much
difficulty in grasping events in two dimensions as in three were it
not that we can so easily illustrate our two dimensional thoughts by
pencil and paper. If one can turn over a model in one’s hand, an idea
can be seized in a mere fraction of the time that is required to read
about it, and a still smaller fraction of the time that is required to
prepare the description.
Perhaps some of the readers of this book will be sufficiently
interested to make models of the few crystal structures that are
mentioned in it, and may even go on to other structures that are
described in larger books or in original papers.
I have added somewhat to the lectures as originally given. The
additions are intended to make the treatment of the subject a little
more complete: they were not very suitable for consideration at the
lectures, but are perhaps permissible in the book because the reader
can omit them if he desires or read them more than once, or consider
them with a model in his hand.
At the end of the book there is a short note on the making of models.
CONCERNING THE
NATURE OF THINGS
CONCERNING THE NATURE
OF THINGS
CHAPTER I
_The Atoms of Which Things Are Made_
NEARLY two thousand years ago, Lucretius, the famous Latin poet, wrote
his treatise, _De rerum natura_--concerning the nature of things.
He maintained the view that air and earth and water and everything else
were composed of innumerable small bodies or corpuscles, individually
too small to be seen, and all in rapid motion. He tried to show that
these suppositions were enough to explain the properties of material
things. He was not himself the originator of all the ideas which he
set forth in his poem; he was the writer who would explain the views
which were held by a certain school, and which he himself believed
to be true. There was a rival set of views, according to which,
however closely things were looked into, there would be no evidence
of structure: however the water in a bowl, let us say, was subdivided
into drops and then again into smaller drops and so on and on, the
minutest portion would still be like the original bowl of water in all
its properties. On the view of Lucretius, if subdivision were carried
out sufficiently, one would come at last to the individual corpuscles
or _atoms_, the word atom being taken in its original sense,
something which _cannot be cut_.
There is a mighty difference between the two views. On the one, there
is nothing to be gained by looking into the structure of substances
more closely, for however far we go we come to nothing new. On the
other view, the nature of things as we know them will depend on the
properties of these atoms of which they are composed, and it will be
very interesting and important to find out, if we can, what the atoms
are like. The latter view turns out to be far nearer the truth than the
former; and for that all may be grateful who love to inquire into the
ways of Nature.
Lucretius had no conception, however, of atomic theories as they stand
now. He did not realize that the atoms can be divided into so many
different kinds, and that all the atoms of one kind are alike. That
idea is comparatively new: it was explained with great clearness by
John Dalton at the beginning of the nineteenth century. It has rendered
possible the great advances that chemistry has made in modern times
and all the other sciences which depend on chemistry in any degree.
It is easy to see why the newer idea has made everything so much
simpler. It is because we have to deal with a limited number of sorts
only, not with a vast number of different individuals. We should be
in despair if we were compelled to study a multitude of different
atoms in the composition of a piece of copper, let us say; but when
we discover that there is only one kind of atom in a piece of pure
copper, and in the whole world not many different kinds, we may feel
full of enthusiasm and hope in pressing forward to the study of their
properties, and of the laws of their combinations. For, of course, it
is in their combinations that their importance lies. The atoms may be
compared to the letters of the alphabet, which can be put together in
innumerable ways to form words. So the atoms are combined in equal
variety to form what are called molecules. We may even push the analogy
a little further and say that the association of words into sentences
and passages conveying meanings of every kind is like the combination
of molecules of all kinds and in all proportions to form structures and
materials that have an infinite variety of appearances and properties
and can carry what we speak of as life.
The atomic theory of Lucretius did not contain, therefore, the
essential idea which was necessary for further growth and progress.
It withered away, and the very atom came to be used in a vague,
incorrect fashion as meaning merely something very small: as sometimes
in Shakespeare’s plays, for instance. In another and very different
application of “atomic” theory Lucretius was strangely successful. He
had the idea that disease was disseminated by minute particles. At the
time of the Renaissance Fracastoro was inspired by the atomic theory of
infection as he read it in the poem of Lucretius; but after his day the
secret of bacteriology was again covered up until it was laid bare by
Pasteur.[1]
Let us think of Nature as a builder, making all that we see out of
atoms of a limited number of kinds; just as the builder of a house
constructs it out of so many different kinds of things--bricks, slates,
planks, panes of glass, and so on. There are only about ninety sorts of
atoms, and of these a considerable number are only used occasionally.
It is very wonderful that all the things in the world and in the
universe, as far as we know it, are made of so few elements. The
universe is so rich in its variety, the earth and all that rests on
it and grows on it, the waters of the seas, the air and the clouds,
all living things that move in earth or sea or air, our bodies and
every different part of our bodies, the sun and moon and the stars,
every single thing is made up of these few kinds of atoms. Yes, one
might say, that is so: but if the builder is given bricks and mortar
and iron girders he will build you an infinite variety of buildings,
palaces or cottages or bridges; why may not Nature do something
like that? But one has to think that when a builder sets out to make
a structure he has a plan which has cost thought to devise, and he
gives instructions to his workmen who are to carry out his wishes,
and so the structure grows. We see him walking about with his plans
in his hand. But the plans of the structures of Nature are locked up
in the atoms themselves. They are full of wonder and mystery, because
from them alone and from what they contain grows the infinite variety
of the world. How they came to be such treasure-houses we are not
asking now. We ask ourselves what these atoms are like: we have been
asking the question ever since their exceeding importance began to be
realized more than a hundred years ago. Have they size and form and
other characteristics such as are possessed by bodies with which we are
familiar? We must look into these points.
But first let us realize that in the last twenty-five years or
so we have been given, so to speak, new eyes. The discoveries of
radioactivity and of X-rays have changed the whole situation: which is
indeed the reason for the choice of the subject of these lectures. We
can now understand so many things that were dim before; and we see a
wonderful new world opening out before us, waiting to be explored. I
do not think it is very difficult to reach it or to walk about in it.
In fact, the new knowledge, like all sudden revelations of the truth,
lights up the ground over which we have been traveling and makes things
easy that were difficult before. It is true that the new lines of
advance now open lead the way to fresh difficulties: but therein lies
the whole interest and spirit of research. We will try to take the
first steps into the new country so that we may share in the knowledge
that has already come, and comes in faster every day.
We go back to our questions about the atoms. Before the new period
set in remarkably accurate answers had already been given to some of
them, at least. In this theater of the Royal Institution, Lord Kelvin
gave several addresses which dealt with the properties of atoms, and
especially with their sizes. By several most ingenious and indirect
devices he arrived at conclusions which we are now able to test by
accurate methods; and we find that he was remarkably close to the
truth. It was, of course, far more difficult to say what was the size
of any particular atom than it was to say how much larger one atom was
than another. For instance, the sizes of the atoms of potassium and
carbon could be roughly compared by taking into account the relative
weights of equal volumes of the solid potassium metal and of diamond,
which is a form of pure carbon. Potassium is lighter than water, the
diamond is three and a half times as heavy. We know from chemical
observations that the individual potassium atom is rather more than
three times as heavy as the carbon atom. If we suppose that the packing
of the atoms in the two cases is the same (as a matter of fact, we now
know that it is only approximately so) we must conclude that the atoms
in the metal potassium are much larger than the carbon atoms in the
diamond, because, though heavier individually, they pack so as to make
a lighter material.
To make a reasonable estimate of the actual size of any one atom is a
much more difficult matter, but all the four lines of reasoning which
Kelvin employed led him to very nearly the same result. “The atoms or
molecules of ordinary matter must be something like the 1/10,000,000th
or from the 1/10,000,000th to the 1/100,000,000th of a centimeter in
diameter.”[2] Our new methods tell us that the diameter of the carbon
atom in diamond is 1.54 hundred-millionths of a centimeter, and that of
the atom in the metal potassium is 4.50 hundred-millionths. We see that
Lord Kelvin’s estimate was wonderfully near the truth, considering the
indirect and inexact methods which alone were at his disposal.
In Fig. 1 are shown sections of certain atoms on a scale of fifty
millions to one. The inserted figures give in each case the distance,
in hundred-millionths of a centimeter, between the centers of two
neighboring atoms in the pure substance. For example, the distance
between two carbon atoms in the diamond is 1.54 hundred-millionths of
a centimeter. In the case of oxygen the diameter has been calculated
from the structure of crystals in which oxygen occurs. If the lecture
room of the Royal Institution were magnified as much as the atoms of
Fig. 1, its height would be greater than the distance from the earth to
the moon. We need some such comparison as this to make us realize the
excessive smallness of the things of which we are talking.
[Illustration: Fig. 1.--Sections of some common atoms, in
hundred-millionths of a centimeter. In reference to bismuth see below
(p. 13) and Plate I a.]
At the same time, we must keep in mind that they are not negligible
because they are small: they are the actual elements of construction of
the world and of the universe, and their size has nothing to do with
their importance. But their smallness accounts readily for the case
with which we all overlook them, and for the difficulty we have in
examining them when at last we have realized what they mean to us. The
value of the new methods of which I propose to speak lies in the fact
that they enable us to deal with them, although they are so small.
We have now answered in a way the question as to the size of the atoms;
but when we go further and ask ourselves about the shape we are not so
successful.
The chemist, whose science is immediately concerned with the
combinations of atoms, has rarely found it necessary to discuss their
shapes, and gives them no particular forms in his diagrams. That does
not mean that the shapes are unimportant, but rather that the older
methods could not define them. There is one sense, however, in which
the chemist pays much attention to form. The atoms in a compound
are arranged in some fashion or other which is important to the
combination. If one could see it and sketch it, one would be obliged to
show it in perspective. In the science of organic chemistry especially
it is found to be necessary to imagine such arrangements in space. It
is not enough to represent them on the flat with no perspective at all;
in fact, it is obvious that any flat design must be imperfect in any
sort of chemical picture. We are, unfortunately, compelled to use the
flat for our drawings; solid models in space are costly to make, while
paper and pencil are cheap. It is curious to reflect what a handicap
this technical difficulty puts on the proper development of a very
important matter. Now, when we come to prescribe the arrangements of
the atom to its neighbors, and to say that if one neighbor lies in this
direction, another must lie in that, we are, in effect, giving shape
to our atoms; at any rate, it is all the shaping that can be done for
the present. We cannot do more until we know more about the internal
structure of the atom: what its parts are, and how they are disposed to
one another.
In the newer work, as we shall see, the arrangement of the atoms
is much more closely examined, and for the first time their actual
distances apart are measured. We find it absolutely necessary to make
models because we do not see with sufficient clearness if we are
content to draw on paper. We represent our atoms as round balls, and we
find that we are able to represent most of our discoveries in this way.
This really means that when an atom has several neighbors of the same
kind it is equally distant from them all; and this is actually the
case. Nevertheless, there are exceptions, as in the crystal of pure
bismuth, where each atom has six neighbors and three of them are closer
than the other three. We have to make a ball with three flats on it for
use in constructing the bismuth model (Plate I a).
Let us now ask ourselves what binds the atoms together into the
various combinations and structures. Like our builder, we have got
in our materials--the bricks, slates, beams, and so on; we have our
various kinds of atoms. If we look round for mortar and nails we find
we have none. Nature does not allow the use of any new material as a
cement. The atoms cling together of themselves. The chemist tells us
that they must be presented to one another under proper conditions,
some of which are very odd; but the combination does take place, and
there is something in the atoms themselves which maintains it when the
conditions are satisfied. The whole of chemistry is concerned with the
nature of these conditions and their results.
The atoms seem to cling to one another in some such way as two magnets
do, when opposite poles are presented to each other; or two charges of
electricity of opposite nature. In fact, there is no doubt that both
magnetic and electric attractions are at work. We are not entirely
ignorant of their mode of action, but we know much more about the rules
of combination--that is to say, about the facts of chemistry--than we
do about the details of the attractions. However, we need not trouble
ourselves about these matters for the present; we have merely to
realize that there are forces drawing atoms together.
We may now ask why, if there are such forces, the atoms do not all join
together into one solid mass? Why are there any gases or even liquids?
How is it that there are any atoms at all which do not link up with
their neighbors? What prevents the earth from falling into the sun and
the final solidification of the entire universe?
The earth does not fall into the sun because it is in motion round
the sun, or, to be more correct, because the two bodies are moving
round each other. It is motion that keeps them apart; and when we look
closely into the matter we find that motion plays a part of first
importance in all that we see, because it sets itself against the
binding forces that would join atoms together in one lump. In a gas,
motion has the upper hand; the atoms are moving so fast that they
have no time to enter into any sort of combination with each other:
occasionally atom must meet atom and, so to speak, each hold out vain
hands to the other, but the pace is too great and, in a moment, they
are far away from each other again. Even in a liquid where there is
more combination and atoms are in contact with each other all the time,
the motion is so great that no junction is permanent.
In a solid the relative importance of the attractive forces and the
motion undergoes another change: the former now holds sway, so that
the atoms and the molecules are locked in their places. Even in the
solid, however, the atoms are never perfectly still; at the least
they vibrate and quiver about average positions, just as the parts
of an iron bridge quiver when a train goes over it. It is difficult
to realize that the atoms and molecules of substances which appear
to be perfectly at rest--the table, a piece of paper, the water in a
glass--are all in motion. Yet many of the older philosophers grasped
the fact. For example, Hooke, an English physicist of the seventeenth
century, explains by a clear analogy the difference which he supposed
to exist between the solid and the liquid form: ascribing it to a
movement of the atoms which was greater in the liquid than in the
solid state. “First,” he says, “what is the cause of fluidness? This
I conceive to be nothing else but a very brisk and vehement agitation
of the parts of a body (as I have elsewhere made probable); the parts
of a body are thereby made so loose from one another that they easily
move any way, and become fluid. That I may explain this a little by
a gross similitude, let us suppose a dish of sand set upon some body
that is very much agitated, and shaken with some quick and strong
vibrating motion, as on a millstone turn’d round upon the under stone
very violently whilst it is empty; or on a very stiff drum-head, which
is vehemently or very nimbly beaten with the drumsticks. By this means
the sand in the dish, which before lay like a dull and unactive body,
becomes a perfect fluid; and ye can no sooner make a hole in it with
your finger, but it is immediately filled up again, and the upper
surface of it leveled.
[Illustration: Plate I]
Nor can ye bury a light body, as a piece of cork under it, but it
presently emerges or swims, as ’twere on the top; nor can ye lay a
heavier on the top of it, as a piece of lead, but it is immediately
buried in sand, and (as ’twere) sinks to the bottom. Nor can ye make
a hole in the side of the dish, but the sand shall run out of it to
a level. Not an obvious property of a fluid body, as such, but this
does imitate; and all this merely caused by the vehement agitation of
the containing vessel; for by this means, each sand becomes to have a
vibrative or dancing motion, so as no other heavier body can rest on
it, unless sustein’d by some other on either side: nor will it suffer
any body to be beneath it, unless it be a heavier than itself.”
Hooke’s experiment can be repeated in a somewhat different form. A
cylindrical metal box, ten inches wide and three inches deep, is fixed
upon a platform which is supported on metal balls so that it moves
easily. It is connected through an eccentric joint with a turning
table as shown in Plate I B. When the wheel is turned rapidly,
the box and the sand which it contains are violently agitated as
Hooke prescribes. The details of the mechanism are best understood by
reference to the figure. A heavy metal ball placed on top of the sand
disappears at once, and light objects, such as ping-pong balls, rise
to the surface. A very ludicrous effect is produced if we bury in the
sand some of the celluloid figures which cannot be made to lie down
because they are heavily weighted at the bottom. The figures slowly
rise out of the sand and finally stand erect (Plate I b and
Fig. 1 a).
[Illustration: Fig. 1 a]
We know now that the motion of the atoms of a body is really its heat:
that the faster they move or vibrate the hotter the body becomes.
Whenever we warm our hands by the fire, we allow the energy radiated by
the fire to quicken up the movements of the atoms of which the hands
are composed. When we cool any substance we check those movements. If
we could still them altogether we should lower the temperature to a
point beyond which it would be impossible to go, the absolute zero, as
it is usually called, 273 degrees centigrade below zero.
As I have said already, we have found two new allies, radioactivity and
X-ray, in our attempt to see the very minute atom. They have increased
the fineness of our vision some ten thousand times. The microscope had
done its best for us; but the smallest thing which it could show us
was composed of billions of atoms. No improvement could be made in the
microscope lenses: technique had reached its highest. The difficulty
was really due to the fact that light is a wave motion and light
waves cannot show us the details of objects unless the objects are
much larger in every way than the length of the wave. We wanted a new
light of very short wave length. It came in the form of the X-rays.
At the same time radioactivity came to show us what a single atom
could do by itself if it were given a tremendous speed. We can now see
the single atom, indirectly, no doubt, but quite usefully, and also
observe something which it does: the X-rays help us with the former and
radioactivity with the latter. I hope to explain to you how both these
agents are adding to our knowledge, and I shall take radioactivity
first.
The atom of radium might be roughly represented in size by one of the
larger balls that lie before you. It is one of the heaviest and largest
of the atoms; a number of them together form a substance which is a
metal like iron or gold. It is, of itself, in no obvious way peculiar
as long as it continues to be an atom of radium, but, for some reason,
which no one understands, there comes a moment when it bursts. A small
portion is hurled away like the shot from a gun, and the remainder
recoils like the gun itself. The remainder is not radium any more, it
is a smaller atom, having entirely different properties. The radium has
turned into a new substance. As a matter of fact, the new substance is
a gas, while the projectile turns out to be an atom whose weight is low
down in the series of atomic weights, the lowest but one in fact; it is
called helium. No one knows what brings about the explosion, nor does
anyone know a way of hastening it, or of hindering it. The radium atom
is just as likely to explode at any given moment if it is in a furnace
as if it is immersed in liquid air. Indeed, its independence of its
surroundings in respect to its time of explosion is shown in a much
stronger light by the fact that combination with other atoms makes no
change. Combination, or molecule-forming, is, no doubt, concerned with
the outside arrangements of the atoms, but the bursting of the atom
comes from inside.
The old alchemist tried to find a means of converting one atom into
another, preferably lead into gold. In the action of radium there
is a transmutation, to use an old word, of the kind of which the
alchemist dreamt. But it is not exactly what he strove for, in two
ways. In the first place, it cannot be controlled by human will--which
is extraordinary, because there are not so many things of which this
can be said. Even when an operation is quite beyond our power to
understand, we can often decide whether or no it shall happen. We
cannot understand how a seed germinates, much less make one that will
do so; but we can lock up seeds in a drawer and prevent them from
germinating as long as we like. But the radium explosion does not wait
on anything which we do.
In the second place, the transmutation does not end in gold: it ends
rather in lead. The gas which consists of atoms of radium that have
shot off one atom of helium is very short-lived: the average life of
each of its atoms is a little less than four days, in contrast to the
average life of the radium atom, which is about two thousand years.
The second explosion “transmutes” the gas atom into a new substance
called Radium A, and on the occasion another helium atom is shot away.
There is a further succession of explosions, at very varying average
intervals, and the final product is actually lead, not gold. The gas
was called the “radium emanation” by Rutherford, who discovered it.
The whole operation is very wonderful, but I want to call attention to
what happens to the projectile when it has left the gun. The velocity
with which it starts is so great that one could never have thought any
particle of matter could have possessed it. When Huygens argued with
Newton on the subject of the nature of light, he condemned Newton’s
idea that light consisted of a flight of corpuscles, on the ground that
material particles could not possibly travel as fast as light had just
been found to move. It is curious that we now find atoms moving with
speeds comparable with, a tenth or twentieth of, that which then seemed
impossible. There are even certain particles, called electrons, also
emitted by radioactive substances, which travel, in some cases, very
nearly as fast as light. It is also curious that the second argument of
Huygens was equally unfortunate in view of the observed phenomena of
radioactivity. He said that it would be impossible, on Newton’s theory,
for two people to look into each other’s eyes because the particles
would meet each other and fall to the ground. We shall presently see
that this argument also is set at naught by the facts of radioactivity.
The velocity with which the helium atom begins its flight is something
like 10,000 miles in a second. In less than a minute it could get to
the moon and back again if the speed were maintained, but the curious
thing is that for all the speed and energy with which it starts it
never gets far when it has to pass through anything material. Even if
it is allowed to finish its course in the air, its speed has fallen to
something of quite ordinary value after it has traversed a course of
two or three inches in length. The course is, in general, perfectly
straight, as we shall presently see in an actual experiment, and this
is the very important point which we must consider with particular
care. At first sight one does not realize how remarkable it is that its
path should be straight: one thinks of a bullet fired through a block
of wood, let us say, and making a cylindrical hole, or of the bullet in
its straight course through the air. But the comparison is unfair. The
bullet is a mass of lead enormously heavier than any molecule which it
meets, and it brushes the air aside. But the helium atom is lighter and
smaller than the atoms of nitrogen or oxygen of which the atmosphere is
mainly composed, and we must think of some more truthful comparison.
Suppose that a number of billiard balls are lying on a billiard table,
and let them represent air molecules. If they are in movement the
picture will be more correct, but the point does not really matter.
Now let us drive a ball across the table, aiming at a point on the
opposite cushion, and watch what happens as the ball tries to get
through the crowd that lies on the table, which crowd may or may not
be in movement. It hits one of the balls and is turned to one side; it
hits several in succession, and soon loses all trace of its original
direction of movement. Shall we now drive it with all the force we can,
and see whether it keeps any more nearly to the straight path? We try,
and find that there is no improvement at all. The straight path cannot
be obtained by any increase of speed, however great.
This picture or model is much more faithful than that of the moving
bullet, and shows more clearly the remarkable nature of the radium
effect. A helium atom must encounter a very large number of air
molecules if it proceeds on a straight-line path, and if the atoms are
of the size we have supposed them to be. In fact, the molecules lie far
more thickly on the path than we can represent by the billiard-table
model. It is possible to calculate how many air molecules, some oxygen,
some nitrogen, would be pierced by a straight line three inches long
drawn suddenly at any moment in the air, and the result is to be
expressed in hundreds of thousands. How can the helium atom charge
straight through this crowd, every member of which is heavier than
itself? It does so, however, and we have to find some explanation.
Perhaps it might be thought that the straightness of the path is only
apparent, and that if we could look into it in sufficient detail we
should see that it was made up of innumerable zigzags made in going
round the molecules met with. But a moment’s reflection shows that the
idea is absurd: the atom would need to possess the intelligence of a
living being to give it the power of recovering a line once lost. If
there were a cake shop on the opposite side of a crowded street, and if
we gave a boy sixpence and directed him to the shop, he would no doubt
pursue a path which was effectively straight, though it would be broken
up by the need of dodging the various people and vehicles which the boy
met with. But one cannot imagine an atom of helium doing anything of
the sort.
There is only one way of explaining the marvel of the straight path: we
must suppose that the helium atom _goes through_ the molecules it
meets, and that somehow it is enabled to do so by the fact that it is
moving at such an unusual speed. It is a very startling idea.
[Illustration: By courtesy of the Cambridge Scientific Instrument Co.
PLATE II.
Shimizu-Wilson ray track apparatus.
The apparatus which shows the tracks of the helium atom shot out by
radium. The chamber as sketched in Fig. 2 is to be seen on the upper
left of the figure. The disc to the left of it is a screen, in which is
a hole. The light from a lantern--not shown--shines through the hole
and lights up the fog tracks. A second screen revolves, and lets the
radium rays, _i.e._ the helium atom, shine into the chamber just
before the expansion is made. On the right is the driving machinery.]
However, no other suggests itself; and, as a matter of fact, it turns
out that we can explain many other things by its aid. Consequently, we
feel sure that we are on the right track.
[Illustration: Fig. 2.—Section of the expansion chamber in Mr. C. T. R.
Wilson’s apparatus for measuring the track of helium atoms (see also
Plate II).
The piston _PP_ is dropped suddenly from the position indicated by
the dotted lines to the position indicated by the full lines; so that
the air in the chamber is suddenly chilled by expansion and fog settles
on the tracks of the helium atoms shot out by the radium at _R_.]
It is time now that we should see this effect with our own eyes: the
conclusion at which we have arrived is so new and so full of meaning
that we would like to have an experimental demonstration if possible,
and convince ourselves of the reality of these straight-line paths. We
owe to Mr. C. T. R. Wilson a beautiful piece of apparatus which gives
us a vivid picture of what happens, and we will make use of it at once.
The experiment is, in my opinion, one of the most wonderful in the
world of science. We are going to see the actual tracks of separate
helium atoms, each of which begins its course at a speed of ten
thousand miles a second and yet completes it after traversing about
three inches of air. But we must first enter upon some explanation of
how the apparatus works; for there are ingenious devices in it.
There is a cylindrical box of brass, with a glass top and a base which
can be raised or lowered so as to alter the depth of the box. There is
a machinery of wheels, cranks and levers by which the bottom of the box
can be suddenly dropped at convenient intervals. Whenever this happens,
the air or other gas which the box contains is chilled by the sudden
expansion. We shall study effects of this kind more carefully in the
next chapter. At the side of the box, in its interior, a minute speck
of radium is mounted on a suitable holder. Every moment some of its
atoms break up and expel atoms of helium, of which a certain number are
shot straight into the box. The diameter of the box is big enough to
allow the atoms to finish their courses in the air within. The average
life of radium is so long that even if the apparatus held together for
two thousand years, half of the radium speck would still be left. Yet
each second, ten, twenty or a hundred atoms disappear in the expulsion
of the helium atoms. Perhaps in no better way can it be shown how many
atoms are concentrated in a small compass.
The air in the chamber is kept damp, consequently the chill due to
expansion tends to produce a fog. Fog when it has to settle prefers to
deposit itself on a solid nucleus of some sort, rather than to form
independent drops in the air. The small particles of dust, if there are
any, are made use of, which is the reason why fogs so readily form in a
dirty atmosphere. But of all things moisture prefers to settle on those
atoms through which the helium atom has passed. The reason is that
the atom is temporarily damaged by the transit: a small portion has
generally been chipped away. The portion removed is what we now call an
“electron”; it is charged with negative electricity, and the atom which
has lost it is correspondingly charged with positive electricity. The
electron set free settles on some neighboring atom, sooner or later;
and in consequence there are two charged atoms, one positive and one
negative, where previously there were no charged atoms at all. The
charged atoms have a great attraction for moisture, and the fog forms
on them in preference to anything else. If, therefore, a helium atom
has just made its straight road through the gas, and has left behind
it numbers of charged atoms on its track, and if, at that moment,
the sudden expansion causes a chill, fog settles along the track. A
bright light is made to illuminate the chamber, so that the fog tracks
are visible as bright straight lines, showing against the blackened
background of the bottom of the cylindrical chamber. They last a few
seconds and then the fog particles slowly disperse. If the helium atom
completes its track just before the fog is formed, the line is sharp
and clear; because the charged atoms have not had time to wander from
the track. But if the track is made some time before the expansion, the
line of fog is more diffuse. It is to be remembered that the helium
atoms are being shot out all the time, day and night; but it is only
when an expansion is made that tracks are made visible.[3]
[Illustration: PLATE III.]
If we watch the successive expansions, we see that the tracks, though
quite straight over large parts of their course, do undergo at times
sudden sharp deflection, especially when they are nearing the end. This
remarkable effect turns out to be most important, and we must refer to
it presently.
Let us now try to picture to ourselves in what way we must modify our
first conception of the atom so that we can explain the effects we now
see. The atoms must be so constituted that when they meet one another
in the ordinary way, as, for example, when molecules of oxygen collide
in the atmosphere, they behave as if each had a domain of its own into
which no other might enter. Or, when they are pressed together, as in
a solid, they occupy as a whole an amount of space which is sufficient
to make room for them all. But when one atom--the helium atom is our
chief example--is hurled against others with sufficient speed, the one
atom goes through the other, as if the defenses round the domains had
been broken down. We find a satisfactory explanation when we imagine
each atom to be like a solar system in miniature. There is to be a
nucleus, corresponding to the sun, and round the nucleus there are
to be satellites or planets, which we call electrons. The nucleus
is charged with positive electricity; each electron is charged with
negative electricity, and all electrons are alike. The positive charge
on the nucleus is just enough to balance the united negative charges of
the electrons. The electrons are supposed to be in movement, just as
the planets are revolving round the sun, but the movements are no doubt
complicated, and their nature need not for the moment concern us at all.
Instead, therefore, of a round hard ball of a certain size, which was
our first rough picture of an atom, we have something like a solar
system in miniature. We can at once see how one atom of this kind can
pass through another, just as we might imagine one solar system passing
through another, without injury to either provided that no one body of
one system made a direct hit on a body of the other and that the motion
was quick enough. The latter condition is necessary because if one
solar system stayed too long inside or in the neighborhood of another
there would certainly be very serious disturbances of the courses of
the planets.
But then, we may ask, how can an atom, if this be its nature, have the
power of keeping another outside its own domain? How can it appropriate
any portion of space to itself, and prevent the intrusion of another
atom when the speed at which they meet is low? The explanation becomes
clear when we consider the special arrangement of the positive and
negative charges. Every atom is surrounded by a shell or cloak of
electrons; and, when two atoms collide, it is their shells which first
come close together. Since like charges of electricity repel one
another, the two atoms will experience a force which tends to keep
them apart: in other words, they will resist encroachment on their
own domains. This is, no doubt, a very rough picture of what actually
happens, and as a matter of fact it is difficult to explain the
strength of the resisting forces on such a simple hypothesis. Still, it
is on the right lines, no doubt. When the two atoms approach each other
at a high speed, the system of electrons and nucleus of one atom slip
through those of the other. A model will help to illustrate the point.
Plate IV a shows a set of bar magnets mounted on spiral springs and
standing erect. The top of the inside magnet is a north pole, and
the tops of the magnets of the outside ring are south poles. The
model represents roughly the central nucleus surrounded by a ring of
electrons. In the model everything is in one plane; in the atom it is
not so, but the point is not important. A single magnet is suspended
by a long thread from a point vertically over the “nucleus” magnet.
Its lower end is a south pole and the length of the thread is such
that the swinging magnet just clears the fixed magnets. Observe now
that if we pull the swinging magnet to one side (_S_ in Fig. 3,
_a_), but not too far, it moves toward the fixed set and is unable
to enter in. It seems to knock at the door at one place after another,
but always recoils. Just so would any electron beat in vain against
the outer defenses of an atom, if it did not beat hard enough. We can
easily imagine that if the single swinging magnet were replaced by
a system of magnets, like our stationary set, the same result would
follow.
[Illustration: PLATE IV.
=A.= Bar magnets on spiral strings.
=B.= Models of atoms with electrons.]
Here we have a picture representing our atoms, as we now think of them,
beating against one another and recoiling; each occupies a certain
domain of space and prevents the intrusion of any other atom.
[Illustration: Fig. 3 (a), (b), and (c).]
But if the swinging magnet is drawn sufficiently far to one side so
that it acquires a greater speed than before by the time it reaches
the stationary set, its momentum will carry it through. If the speed
is very great, it shows no appreciable change in its motion due to
its passing (Fig. 3, _c_); if the speed is rather less, it often
suffers in going through (Fig. 3, _b_). It comes out less vigorous
than when it went in; often it has changed the direction of motion
also, and it has obviously left energy behind, for the magnets of the
stationary set are left quivering. This happens no matter which pole of
the swinging magnet is the lower, and clearly the same effect would be
shown if the single swinging magnet were replaced by a more complicated
set of nucleus and attendant satellites.
The behavior of the model helps us to anticipate what we should find
when atoms of our new design come across one another. If they approach
at a moderate speed, they may rebound from one another; at a high speed
they go through one another, and the higher the speed, the greater the
chance of a passage without any obvious result. But there is always
the chance that the nucleus of the moving atom may go so near to the
nucleus of the atom through which it is passing that it experiences a
perceptible deflection. The smaller the nuclei are, the less likely it
is that this will happen.
You will have guessed already that you have actually seen such
deflections as these in the kinematograph picture, such as also are
shown in Plate III, a to d. The tracks of the helium atom are quite
straight in the main, but there are decided breaks in the straight
lines, usually not more than one or two in each track. They are found
mainly toward the finish. This is what might be expected, since the
motion will then be slower. Several of them appear in Plate III a; a
very good example of this kind of track is reproduced on a large scale
in Plate III c. The upper track shows a slight but sharp deflection at
a little distance from the end of its course, and a more pronounced
deflection farther on. Nearly every track shows some deviations at the
very end. Thus the new conception of atomic structure explains all the
effects in a satisfactory way.
It is strange to think of an atom as being empty as a solar system;
not a round, hard and absolutely impenetrable body, but a combination
of nucleus and electrons which occupies a certain space somewhat as an
army occupies a country. The bodies of the soldiers do not fill the
country from boundary to boundary; but enemy soldiers may not enter,
nevertheless.
These very characteristic pictures are the fruit of much watching and
photographing. Breaks are found at every expansion, but it may be
necessary to wait for a really good one. A very fine picture is shown
in Plate III d. It is due to Mr. P. Blackett. In this case,
helium was used instead of air. The nucleus of the flying helium atom,
in traversing a helium atom belonging to the gas, has made an almost
direct hit on the nucleus of the stationary atom: it has cannoned
off it, as a billiard player would say. Both atoms now move with not
unequal speeds, and both make fog tracks, as the figure shows. In Plate
III c if we look carefully, we see that there is a minute spur
on the last bend of the track already mentioned, which means that in
this case an atom of oxygen or nitrogen has deflected the helium atom
and has recoiled in consequence. Its track is very short, because it
is much heavier than the atom which struck it, and, therefore, the
velocity given to it has been comparatively small.
There is a certain curious feature to be found in some of the
photographs which may well be explained. In some of the tracks there
are gaps, as if the fog settling had failed. This is indeed the actual
fact: there is no moisture to settle, because a helium atom has gone
that way some very short time before and has used up the moisture in
the neighborhood. In Plate III b several tracks due to radium
emanation are shown. They seem to start from anywhere in the chamber
because the atoms of the emanation have wandered about the chamber
before blowing up.
The next question that arises is as to the number of electron
satellites which each atom possesses. Here we come to a very beautiful
and remarkable feature of the new discoveries. It is not necessary
to explain in full how it was discovered; we will be content with
describing it.
In the atom as we now have it the nucleus is charged with positive
electricity, the amount of the charge being just enough to neutralize
the negative charges on the attendant electrons. All electrons, as we
have already seen, are alike. We find that atoms differ in the number
of attendants which they can maintain, and that the statement of that
number describes the atom completely so far as its attitude toward
other atoms is concerned. For instance, the atom of carbon can hold six
electrons; the positive charge on the nucleus is the counterpart of six
standard negative charges. Every atom which can retain six electrons
is a carbon atom: no other definition of the carbon atom is required.
Just so the “seven-electron” atom is nitrogen, the “eight-electron”
is oxygen, and so on. All numbers are found in nature, with very
few exceptions, from the “one-electron” atom—hydrogen—up to the
“ninety-two-electron” atom—uranium. The missing numbers will probably
be found some day; more or less accidentally, it may well be.
We may use models as a rough illustration of the point. The nucleus
(Plate IV b) is represented by a white ball of solid rubber,
the electrons by smaller balls forming the heads of pins which are
stuck into the center ball. The pins may be of different lengths (p.
84).
It is strange that the immense variety in nature can be resolved into
a series of numbers. It was at one time thought that the various sorts
of atoms owed this variety to something more than that; it is a great
surprise to find such a simple kind of difference between atom and
atom. The unchanging feature of any particular sort of atom is the
positive charge of electricity on the nucleus. It is in consequence of
this that the proper number of electrons gather round. We may expect
that they will arrange themselves in some fashion; we shall see later
that they certainly do so. The sort of arrangement they take in each
case, and the nature of the forces put into it, are very difficult
questions, most of which we may well put to one side for the present,
contenting ourselves with one or two simple aspects of the problem.
In the first place, it is interesting to watch the assembling of
the little vertical magnets floating in the glass tank (Plate V
a). They are buoyed up by ping-pong balls, painted black, and,
so that we may see them easily, they carry white ping-pong balls at
top. The magnets are all the same way up, so that naturally they repel
one another and cluster round the edge of the basin. But there is an
electromagnet underneath the bowl, which, when made active, draws the
small magnets together. The arrangement in which they settle finally
is governed partly by the pull toward the center and partly by the
mutual repulsions. Something of this kind must take place in the atom,
but we must not push the analogy too closely, because the forces may
be quite unlike those which are exerted in the model. We must content
ourselves with observing that when there are only a few magnets afloat
they group themselves in a ring; but when the number is increased they
arrange themselves in concentric rings. A pretty effect is produced by
putting in each additional magnet at the edge of the basin and watching
it float away in a stately fashion to take its proper place.
A similar division into concentric shells or groups is found in the
arrangement of the electrons round the central nucleus of the atom. We
will consider this more carefully in the next chapter. The experiment
does not prove that there ought to be such an arrangement, but
certainly suggests it.
We may now see more clearly what happens when the helium atom injures
the atoms through which it passes and renders them attractive to the
particles of moisture that form the fog. It is possible, in fact, for
an atom to be deprived of one of its attendant electrons. Having lost
one, it resists more strongly the loss of a second, still more of a
third. As the helium atom goes on its way, it strips one atom after
another of an attendant, and the electron set free goes off on a course
of its own. But its separate life is very short-lived: it is soon
attached to another atom.
[Illustration: PLATE V.
=A.= Floating magnets.
When the number of floating magnets is small, they form into a single
ring, but when the number is increased, they form concentric rings.
=B.= Crystals in tube containing emanation.
From Prof. F. Soddy’s “Interpretation of the Radium” (John Murray), by
the kind permission of author and publisher.]
The atom that has lost an electron is now positively charged; the
gainer is negatively charged. The two atoms would make things even
again if they came sufficiently close together, and as they move about
in the gas the negatives and the positives do in the end give and take
electrons, and the whole gas is neutral once more.
There is a beautiful experiment with which we may end this chapter.
When the helium atoms strike certain substances they excite a
phosphorescent glow. It is really, when we look into it closely, a set
of minute flashes due to the impacts of the separate atoms; under a
microscope the effect is as when we drop pebbles into a phosphorescent
sea. The glass vessel (Plate V b) contains crystals that
phosphoresce under the stimulus of the swift-moving helium atoms; one
is kunzite, another zinc sulphide, another willemite. In another tube
is a quantity of radium emanation: the gas which, you will remember,
is the immediate descendant of radium itself. When it is released and
is allowed to pass into the tubes containing the crystals the latter
glow in brilliant colors. In the figure the crystals have been made to
photograph themselves by their own phosphorescence.
The radium action has, we see, given us a remarkable insight into the
structure of the atom, for which there is a general reason to be given.
The student of science has long been familiar with the existence of
various atoms and with their properties; he has never seen one, nor
the effects of one. He has handled atoms in crowds only. When the
chemist causes elements to form compounds, or analyzes compounds into
elements, he deals with enormous numbers of atoms in any operation big
enough to see. But in this radioactive effect we observe the action
of one atom at a time, and here lies the secret of the advance. The
speed of the helium projectile, a hundred thousand times the speed with
which the atoms move ordinarily when they form part of a gas, gives
the individual atom the power of making itself felt. When we look at
the fog tracks, we see the actions of separate atoms; we see something
which would have filled the early defenders of the atomic theory with
astonishment and pleasure. One atom of helium passes through one atom
of oxygen, let us say, and comes out on the other side, and both may
bear evidences of the encounter. Effectively we use such evidence to
help us to determine the nature of the atoms. The helium atom is like a
spy that has gone into a foreign country and has come out again with a
tale to tell.
CHAPTER II
_The Nature of Gases_
WE have seen that all things are made of about ninety kinds of atoms,
and that in them is wrapped up the mystery and the infinite variety
of the material world. In each there is a nucleus which is positively
charged; round the nucleus are electrons which are units of negative
electricity. The positive charge of the nucleus is a multiple of a
certain unit charge, equal to the charge on the electron, but of
opposite sign. The number of electrons which every atom possesses under
normal conditions is an exact balance to the positive charge on the
nucleus, so that the atom as a whole is not charged; its positive and
negative charges balance. Whether or no the electrons are revolving
round the central nucleus like planets round a sun, or whether they
possess other more complicated motions are not matters of importance
to us for the moment. Something is known of these points, but the
whole question is difficult. The only consequences of this strange
arrangement of nucleus and electrons which we must consider can be
drawn without thinking about the possible motions. One consequence is
that the atoms do not encroach on one another’s domains under ordinary
circumstances. Each has an outer cloak or shell of electrons; and when
two atoms are brought close together there is a resisting force which
we may suppose to be due to the mutual repulsion of the two shells.
But when two atoms are hurled at each other with sufficient speed the
outer defenses may be broken down and the atoms pass through each
other. When this happens the atoms may afterward disentangle themselves
and pass on their way as if there had been no encounter at all: one
or both may have suffered the loss of an electron or two, but the
damage is soon made good. It is only when the nucleus of one approaches
sufficiently close to the nucleus of the other that there is a change
of motion like that due to the meeting of two balls. Changes of this
kind are so rare and imply such a closeness of approach that we are
bound to think of the nucleus as very small indeed. These penetrations
of atomic domains are brought to our notice by the actions of radium
and similar substances, as explained in the first chapter, and are of
importance to us because they make us realize the empty nature of the
atom, and its sun and planet structure. They do not occur in the usual
relations of atoms to one another, because the speed is far too small.
The domain which the atom occupies to the exclusion of others is about
a hundred-millionth of an inch across; it is within this minute space
that the nucleus and the electrons perform their relative motions. The
light atoms have smaller domains, and the heavier somewhat larger: a
factor of three or four will take us from the smallest to the largest.
I have said that all atoms are in motion, and that there is a constant
struggle between some form of attractive force which would draw all
the atoms together and this motion which would keep them independent.
The existence of an attractive force which we here take into account
as something very important does not at first seem to be reconcilable
with the atomic structure we have just considered, because in this
we supposed that the outer shells of electrons would prevent the
atoms from coming too close to one another. It is a difficult point,
because both views are certainly correct. It is, no doubt, our present
ignorance of the nature of these forces that prevents us from arriving
at a clear understanding. We have seen how it can happen that when two
atoms approach each other at great speeds they go through each other,
while at moderate speeds they bound off each other like two billiard
balls. We have to go a step further, and see how, at very slow speeds
of approach, they may actually stick together. We have all seen those
swinging gates which, when their swing is considerable, go to and
fro without locking. When the swing has declined, however, the latch
suddenly drops into its place, the gate is held, and after a short
rattle the motion is all over. We have to explain an effect something
like that. When the two atoms meet, the repulsions of their electron
shells usually cause them to recoil; but if the motion is small and the
atoms spend a longer time in each other’s neighborhood, there is time
for something to happen in the internal arrangements of both atoms,
like the drop of the gate-latch into its socket, and the atoms are
held. It all depends on some structure of the atom which causes a want
of uniformity over its surface, so that there is usually a repulsion;
but the repulsion will be turned into attraction if the two atoms are
allowed time to make the necessary arrangements, or even if at the
outset they are presented to each other in the right way. We shall see
later several very interesting examples of this effect.
We are going to consider in this chapter the case when the attractive
forces between the atoms do not act, whether from want of time, or from
feebleness, or from any other reason. A crowd of atoms is, when this is
the case, a gas.
Such cases are very numerous. In particular there are certain atoms
which furnish notable examples; they are Nos. 2, 10, 18, 36, 54, 86:
that is to say, they are those in which the nuclei possess positive
charges whose magnitudes are represented by one or other of these
numbers, and which normally possess negative electrons to match. These
atoms have only the feeblest desire to join up with one another.
They do not enter into combination with atoms of other kinds; in
other words, they do not form chemical compounds. We may call them
the “unsociable” atoms. They take no obvious part in the doings of
the world, and their existence was entirely overlooked until a few
years ago. It was only when the late Lord Rayleigh was making careful
measurements of the weight of nitrogen obtained from various sources,
that he noted a small but unmistakable discrepancy between the density
of nitrogen as prepared from the break-up of a known compound of
nitrogen and the density of what was left of air when every known gas
had been abstracted from it. According to the view held at the time
of his experiment, the residue should have been pure nitrogen. As a
matter of fact, atmospheric air contains a small percentage of one
of these “unsociable” atoms or gases; it is No. 18, that which has
eighteen units of positive electricity in the nucleus. So Rayleigh’s
very careful measurements led to the discovery of the hitherto unknown
substance. It was named argon, the “lazy one.” Perhaps the name does
not express its chief characteristic; for the atom is as quick in its
movements as any other of its own size. The weight of the air in the
lecture room of the Royal Institution is about 15 cwt.; it contains
about 18 lb. of argon. If the gas had had the least tendency to form
any chemical association, such an amount, though relatively small,
would have been easily detected by the delicate analytical methods of
chemistry.
The atom of helium, the smallest of the series, is identical with the
atom expelled by radium and other radioactive substances in the act
of disintegration. It has two electrons normally; though as it flies
through matter when radium has ejected it its complement of electrons
is apt to be torn away for the time. The positive charge on the nucleus
is not affected by the flight, so that when the atom comes to the end
of it, the deficiency in electrons is quickly repaired: there are
always stray electrons to be picked up. Then the atom takes up the
quiet and independent existence which is its characteristic. Perhaps
most of the helium in the world has at some time been fired off, atom
by atom, from radioactive substances. At any rate, it is found in
places where such actions must have occurred. Helium is now collected
in large quantities in America and Canada, where it is found bubbling
up in certain springs. It is used for filling dirigible balloons, for
which purpose its main properties make it most suitable. It is light,
and its lifting power is almost as great as that of hydrogen, the
one-electron atom; the atomic weight increases on the whole with the
number of electrons. The lifting power of a gas, we must remember,
depends not on the density of the gas but on the difference between
the density of the gas and the density of the air. The densities of
hydrogen, helium, and air are in the proportion 1:2:14.4; the lifting
powers of hydrogen and helium are in the proportion 13.4 to 12.4.
But its main virtue is that it is not inflammable. The hydrogen atom
is very sociable, and in particular has a violent desire to become
associated with oxygen: if hydrogen and oxygen are mixed, it needs
but a spark to start the combination, with fire and explosion as the
result. A hydrogen-filled balloon is therefore liable to disaster; but
helium seeks no change, and there is no danger from fire. The name of
the gas is due to its discovery in the sun; a bright line in the sun’s
spectrum could not be identified with lines due to any of the known
elements on the earth. The name “helium,” or “sun-substance,” was
therefore given to the unknown substance to which the line was due. It
was at a later date that helium was found to be a member of the series
of gases which Lord Rayleigh and Sir William Ramsay were led to examine
as the consequence of Rayleigh’s nitrogen experiments.
The ten-electron atom neon, the “new one,” is less common than argon.
It has a peculiar property of glowing easily and brightly under the
stimulus of electric discharge, and is often used in electric-light
bulbs: we have all observed the reddish-orange glow of the neon lamp.
Krypton (36), the “hidden one,” and “xenon” (54), the “stranger,” are
very rare. The last of the series, with eighty-six electrons normally,
is the heavier fragment of the break-up of the radium atom. Like the
rest, it tends to pursue an independent existence, so that radium, when
it breaks up, turns into two gases. In some of the Wilson pictures
(Plate III a, b) of the tracks of the helium atoms we may see a track
that begins in the middle of the chamber: it is due to the break-up, in
its turn, of an atom of this heavy gas, for it also is radioactive. In
fact, its average length of life is only three and a half days.
We must not suppose that these strange atoms cannot be made to
associate together under any circumstances. It is possible to make them
join together as a liquid, but only at extremely low temperatures. At
ordinary temperatures they are all gases. The liquefaction of helium
is one of the achievements of the laboratory of Kamerlingh Onnes at
Leiden, where the production of low temperatures has been carried to a
very great state of efficiency.
There are certain other atoms--hydrogen, nitrogen, oxygen, and
others--which readily form into small companies, or molecules, each
of which is almost as free from any desire to associate itself with
other molecules of the same kind and, in many cases, of other kinds
as the atoms of helium and argon. Two atoms of hydrogen make a very
stable and “unsociable” molecule; so do two atoms of nitrogen, or
of oxygen. In these cases, the properties of the substance are at
ordinary temperatures those of a gas. The liquefaction of hydrogen
was accomplished by Sir James Dewar in the laboratories of the
Royal Institution, London; the machinery is still there. In the
anteroom there is a picture which shows Dewar pouring liquid hydrogen
from one of his vacuum flasks into another during the course of a
lecture which he was giving. The air consists mainly of a mixture
of oxygen and nitrogen molecules. Other well-known molecules which
form gases under ordinary circumstances are carbon monoxide (CO),
carbon dioxide (CO{2}), methane (CH{4}), and so on. In all these
cases when two of these molecules meet each other at speeds which are
proper to ordinary temperatures they recoil from the impact, and so
maintain an independent existence. What we have now to consider are
the consequences we should expect to follow from this condition of
independence.
Let us imagine a closed vessel containing a number of atoms or
molecules moving about within it--containing a gas, as we should say.
They continually meet one another and the walls of the vessel, and
behave as a number of billiard balls set in motion on a table would do
if their motion were frictionless and therefore perpetual. In fact,
it is convenient to use a small billiard table as an illustration,
and Messrs. Burroughs and Watts have very kindly given us one for the
purpose.
[Illustration: Fig. 4.--Diagram of small experimental billiard table,
with balls and loose cushion.
If the balls are in motion they drive the loose cushion before them and
they lose some of their energy. If, on the other hand, the cushion is
suddenly advanced, the energy of the motion of the balls is increased.]
The balls soon come to rest on the table, because the cushions, as well
as the balls, are not perfectly elastic; moreover there are losses
by friction as the balls run over the cloth, smooth though it is.
Nevertheless, the motion, once started, lasts long enough to give an
idea of what must happen if it were maintained indefinitely.
It is natural to ask how the force of gravity would affect the movement
of the atoms in our closed vessel. Would it not bring them all to the
bottom? Why should the gas fill the upper as well as the lower parts
of the vessel? The answer is that gravity certainly has its effect in
full, but it is so very small as to be unobservable in our particular
case. If we might imagine that all the heat were taken from the gas,
and its movements therefore ceased, and if the attractive forces could
be ignored, the atoms would, of course, lie about at rest on the bottom
of the vessel. If a very little heat were now given to them, we might
imagine them to begin dancing up and down, like perfectly elastic balls
on a perfectly elastic floor. If the rise were a thousandth of a degree
Fahrenheit, they would bounce to a height of about seven inches. With
enough heat they would begin to hit the top of the vessel as well;
we might suppose them to be so few that they did not hit one another
very often. But at ordinary temperatures their movements would be so
rapid--something like 6,000 feet a second--that gravity would make
little difference in their velocity as they ascended and descended,
and there would be, at any moment, as many at the top as at the bottom
of the vessel. If they were as numerous as the molecules of the air
under ordinary conditions, they would hit one another more often than
the walls. In the air, the usual length of path between two successive
encounters with other molecules is only about four-millionths of an
inch. Since gravity has no obvious effect, the billiard table is all
the better an illustration; we might find an analogy to gravity by
giving it a slight tilt, but it would not to be worth while doing so.
If the atoms or molecules of a gas are continually hitting the walls,
the latter must always experience an outward pressure: we speak, in
fact, of the pressure of a gas upon its envelope. The distention of a
balloon is due to the bombardment of the covering by the molecules. If
we put a loose cushion on our table and make the balls roll about, the
cushion is driven backward. If there were twice as many balls as there
are, there would be twice as much pressure. This is the well-known gas
law that pressure is proportional to density, other things being kept
the same. We increase the pressure on the cushions if we make the balls
move faster; in the same way, the pressure of a gas rises with the
temperature.
Suppose now that I suddenly advance this loose cushion while the balls
are moving and striking it. It is obvious that the motion of the balls
is increased. In the same way, if one of the walls of the gas vessel
is pushed in, as when a piston is forced deeper into a cylinder, the
motion of the atoms is increased. In other words, the temperature is
raised. We all know how hot a bicycle pump becomes when we use it to
force air into a tire. The converse is equally true. If the cushion
on our table is withdrawn as the balls strike it, their motion is
diminished. If we have played cricket, we know that when we want to
catch a ball we must draw our hands back as the ball begins to touch
them: the retreating hands destroy the motion of the ball gradually. If
we hold them in a fixed position, the ball is sure to jump out again.
So also when a lacrosse player catches a ball, he draws his crosse
downward when the ball first enters it, and makes the stopping of the
ball an operation lasting over two or three feet of its path. A tennis
racquet can be used to catch a tennis ball in the same way, but the
action must be well timed, because the racquet face is so stiff. In the
case of the gas, the corresponding effect is its chilling by expansion.
We had an example in the use of Mr. Wilson’s apparatus, where the
sudden enlargement of a space full of moist air caused such a chill
that the moisture settled as a fog on the tracks of the helium atoms.
[Illustration: PLATE VI.
=A.= Tuning fork over jar.
=B.= Fog apparatus.
The long glass tube is full of fog.]
The expansion had to be fairly sudden, because if it had been otherwise
there would have been time for heat to flow in from outside during the
action, and the desired low temperature would not have been reached.
The expansion of great masses of air in the atmosphere is a frequent
source of rain and snow. In the constant movement of the winds it may
happen that some huge volume of damp air expands into a space where
the pressure has been lowered and becomes so cold that the water vapor
begins to condense. It is easy to repeat the experiment on a small
scale. The glass tube which we see on the table (Plate VI b)
contains air which has become charged with moisture which it bubbled
through water on its way to fill the tube. The road by which it came
is now closed by a tap. At the other end of the tube is a second tap,
which at the moment is closed and cuts off the tube from a connection
with a vacuum pump. If this second tap is opened, the air in the tube
expands, and at once a white mist fills the tube. A beam from the
lantern passes down the tube and lights up the mist. We may allow
the air to be drawn off by the vacuum pump: and we can repeat the
experiment as often as we like. Every time that we fill the tube with
damp air which has been filtered from all suspended particles of dirt
and smoke, we get the same sort of white mist that we see sometimes
in the clean country. But if we allow the air from the room to flow
directly into the tube without being filtered, the expansion produces
a dense fog, such as London air is ready to produce at any time, as we
know only too well.
There are other properties of a gas which the billiard table will help
us to understand. Let us mix with the ordinary billiard balls a number
of light ping-pong balls, and set the whole lot in motion. We see at
once that in the general movement the ping-pong balls acquire greater
velocities than the others. Just so if a gas contains two kinds of
atom, one heavy and one light, the latter, in the constant interchange
of motions, acquires a higher average speed than the former. When
hydrogen is mixed with oxygen, the hydrogen molecules actually
move four times as fast as the oxygen molecules on the average. A
calculation, into which we do not enter, tells us that atoms which mix
with one another all possess the same average energy, the lighter
making up for their deficiency in weight by an excess of velocity. Even
if the gases are not mixed, but are contained in separate vessels, the
same rule holds, provided that the gases are at the same temperature.
Although the atoms of the two gases cannot interchange and balance
their energies directly, they do so in effect by way of the various
kinds of matter which reach from one to the other, by the walls of the
vessels, by the table on which perhaps they both stand, and by the
atmosphere. In fact, the average motion of the atom is fixed by the
temperature.
We can easily find an illustration of this effect. Sound is a movement
which is handed on from atom to atom in a gas through which the sound
is passing, just as a chain of workers pass buckets of water to a fire.
The quicker the workers move their hands and arms, the quicker the
water moves. Just so sound travels faster the greater the velocities
of the atoms; or, what comes to the same thing, the lighter the atoms.
An organ pipe blown with coal gas gives a higher note than when it is
blown with air, because the molecules of the lighter gas move more
quickly and the vibrations of the pipe are more frequent. A simple
experiment will help to make this clear. On the table is a glass jar,
into which water has been poured until the air column which is left
responds loudly to the motion of a tuning-fork held over it (Plate VI
a). The air waves pass up and down the jar in exact time with
the oscillations of the fork; the natural period of the jar is the same
as the note of the fork, as I can tell by blowing gently across the top
of the jar and so drawing a whispering note from it. I now introduce
gas into the jar through an india-rubber tube, and the response fades
away. Movements now pass up and down the jar more quickly, and the
natural period of the jar is no longer that of the fork. If I now pour
out some of the water in the jar and begin again with a filling of air,
there is no response to the fork until I put in a certain amount of
gas. Then the note swells out as soon as the mixture is such that the
timing of the gas movement in the jar agrees with the periodicity of
the tuning-fork.
Let us imagine, again, that a very small hole is made in the walls of a
vessel which contains a gas. Every time that an atom, or molecule, as
the case may be, strikes the hole it passes out and never comes back.
It is clear that a light gas will leak away more quickly than a heavy
gas, because its atoms are moving about in the vessel at a greater
rate, and a larger number will strike the hole every second. This
effect is frequently employed to separate two gases, when other means
are ineffective. For example, Rayleigh and Ramsay used it to separate
argon from nitrogen, the mixture of the two being the residue of the
atmospheric air when all other gases had been removed. The mixture
was made to flow along a series of clay tobacco-pipe stems, and the
nitrogen leaked out through the pores of the pipes more quickly than
the argon. The argon atom is forty times as heavy as the hydrogen atom,
and the nitrogen molecule twenty-eight times; the nitrogen therefore
leaks away more quickly through the porous clay walls of the pipe stem,
and the gas that issues from the other end of the pipe system is richer
in argon than the mixture which entered it. The process of diffusion
of one gas into another is really the same in character, because the
gaps between atoms or molecules of one gas are to be compared with the
pores in the clay pipe. Diffusion is a very slow action, in spite of
the fact that the atoms are moving so quickly, the reason being that
encounters are so numerous. One is apt to think that one gas diffuses
into another quickly: on such evidence as that, if a gas tap is left
open, the smell of the gas is quickly perceived all over the room.
This dispersion is, however, due to convection currents rather than
to diffusion, streams of the house gas running in concentrated form
through the air. The effect is beautifully seen in the mounting of
smoke from a cigarette (Plate VII). If the cigarette is laid down on
the ash-tray a fine stream of blue smoke arises in a waving pencil,
which becomes spread and bent and twisted into delicate spirals and
curved surfaces. As the stream mingles finally with the air, it gives
an example of convection. Diffusion between the smoke-laden air stream
and the pure air is taking place also all the time; but the process is
so slow that the edges of the clouds remain sharply defined for a long
time. So also when a room is warmed by hot air, the distribution of
the heat is due to convection currents, streams of hot air percolating
through the cold.
[Illustration: PLATE VII.
Cigarette smoke.
A. The smoke of the cigarette is rising in a straight column. The air
all round is being dragged up with it, though the photograph cannot
show it: there is a rising stream of which the smoke marks the centre.
B. and C. Here the cigarette has been suddenly moved just before the
photograph was taken. The streams of rising air that first met at the
cigarette point and went up side by side are rolling and twisting
over one another, preserving their identity. They do not mix, except
very slowly by means of the diffusion of particles from one stream to
another, though the particles are in motion, otherwise the smoke would
be a sharpless mass. Meeting streams of air become mixed by convection
rather than diffusion.]
It is not due to the molecules of the hot air making their way
individually through the molecules of the cold; that goes on, but its
progress is slow. Convection is more effective than conduction.
Movements of bodies of hot gas in a cold are, of course, governed by
the laws of gravity: the lighter body, if it keeps together, tends to
rise in the heavier. The smoke of the cigarette rises because the air
over the glowing end is warmed and made light; colder currents run in
from all round and, meeting one another, rise together round the thin
sheet of smoke. The thin sheet is their joint boundary; if the air
is still and the currents are steady the upright column grows long;
but a slight movement of the cigarette upsets the even flow, and the
column breaks into beautiful curves. The action of a chimney in the
formation of a draught is, no doubt, known to everyone; but it may be
interesting to look again at an old experiment of Faraday’s. A little
spirit on some tow is lighted and held over the mouth of the shorter
limb of the bent tube in the figure. By blowing for a moment the flame
is made to go down the short limb and up the long one; once started
on the downward direction, it does not change when the blowing stops.
The flues of grates in hospital wards are often built on this plan, the
draught going under the floor. The movement is, of course, due to the
fact that the hot air in the long limb is lighter than a corresponding
volume of the air outside.
[Illustration: Fig. 5.--Reproduced from Faraday’s _Chemistry of a
Candle_.]
The reverse happens sometimes in the house when the chimney is colder
than the air outside, and a down draught brings a sooty smell into the
room.
Something nearer to a conduction process takes place when the gas in
a vessel is heated through the walls. The molecules when they come to
the wall in the course of their movement receive impulses from the
vibrations of the solid material, somewhat in the same way as the ball
in the figure receives a violent knock from the vibrating prong of the
tuning-fork.
When Sir James Dewar designed the “vacuum flask” to hold his liquid
air, he made a double-walled glass vessel and extracted the air from
between the walls. He left no molecules to pick up energy from the
outer wall and carry it to the inner.
[Illustration: Fig. 6.--Tuning-fork and pith ball.
The pith ball is hurled violently from the vibrating fork.]
No heat could be conveyed to the liquid air by conduction or by
convection. Heat can also travel by radiation through the ether; but
this can be stopped by silvering the glass surfaces inside the double
walls. When this is done the isolation of the air is almost perfect.
The entire independence of the atoms or molecules of a gas gives it
perfect divisibility.
[Illustration: Figure 7.--Vacuum flask.
Observe the tube at the bottom (now scaled off) through which the air
has been drawn from between the inner and outer glass of each flask.]
When we cut a solid body with a knife we have to exert a force to
tear the molecules from one another; but such binding forces in a gas
are negligible. If anything is moving through the air it experiences
a resistance only because it is necessary to set some of the air in
motion, and this requires the expenditure of energy. Gases are light,
of course, and the energy required to move them is correspondingly
small. The lightness of the air and the ease with which we pass through
it make it easy to forget both how great is the pressure of the air
at the surface of the earth and how weighty is the air in any large
space such as this room. The air exerts a pressure of about a ton on
every square foot of our bodies; that we do not collapse under it
is due to the fact that any air within our bodies is at practically
the same pressure as the air outside. The little rubber figure in
the illustration (Plate VIII a) collapses utterly if its
air content is withdrawn. The thin tin vessel shown in Plate VIII
b has at first contained some water which has been raised to
the boil so that the steam has driven out all the air. The opening
by which the steam is issuing is closed, and some cold water is then
poured over the vessel. The steam within condenses, and the pressure
falls to almost nothing. The tin vessel then crumples up under the
pressure from outside. Perhaps the magnitude of air pressure is brought
home to us in an even more striking way when we consider that an iron
bar, one square inch in section and nearly five feet long, when resting
erect on the table, exerts of its own weight no more pressure on the
square inch of the table with which it is in contact than the air does.
If we take into sufficient account, therefore, the weight of the air,
it is not surprising that it takes a great force to set it in swift
motion, or that, when moving rapidly, it can exert great pressure
on any body which stands in its road. We all are familiar with the
pressure of the wind, and know what havoc a gale may cause. So also the
revolving airplane screw drives back a mass of air at a high speed, and
the large force of reaction gives the necessary speed to the plane.
Again, when it is on the wing, the plane, like a bird, is continually
tending to fall and to carry with it masses of air beneath and around
it. But it takes force to set such air masses in motion, and the
reaction gives the uplift to the plane. If the plane had no forward
motion it would quickly create a downward movement in the air below it,
and fall with it; but it is always riding on to new masses of air which
have not begun to fall. A simple little experiment illustrates the
point.
[Illustration: PLATE VIII.
A. The india-rubber figure collapses when connected to the vacuum pump.
B. The water in the tin was boiling vigorously when the Bunsen burner
was removed and the stop-cock closed. When cold water was poured over
it, it collapsed.]
A piece of paper of any convenient size, say three inches by one, is
launched as the figure shows; it turns over and over and reaches the
ground along a sloping path. The direction of the turning is related to
that of the sliding, in the same way as that of a ball running down the
tinder side of an inclined plane.
[Illustration: Fig. 8.--Pieces of paper of various forms fluttering to
the ground.]
The explanation is that the leading edge of the paper runs on to new
air which has not begun to fall, whereas the following half of the
paper is on air which has started to move downward because the leading
edge was lately resting on it. So the following half falls and the
leading half does not, which makes the paper turn, as the illustration
shows, until the paper begins to move forward again. But now the edge
which was following becomes the leading edge, and vice versa.
The paper turns over and over, its very simple shape being the cause of
the motion. Now, a bird or an airplane when gliding moves in a steady,
stately fashion, and the design of the wing is in reality anything but
simple, as builders of airplanes have found. The exact form of the
plane--it is not indeed a plane at all--and especially of the leading
edge, is full of subtle importance.
[Illustration: Fig. 9.--Drawings, after Lilienthal, showing feathers
opening to let the air through on the up stroke (upper drawing), and
closed to hold the air on the down stroke (lower drawing).]
A bird’s wings are used not only for gliding, but also for flapping,
and there is a beautiful mechanism which adapts them for their special
purpose. The wing is, in fact, a set of valves, which open when the
wing rises and close when it descends; so that there is less pressure
on the wing in the up stroke than in the down. The action is something
like that of the webbed foot of a duck, which opens out and exerts a
greater pressure on the water as the foot is kicked back than when it
is being drawn forward; but the mode of action is quite different. The
rib of the feather does not always lie in the center, but is often well
to one side, and a row of feathers is so arranged that they overlap and
turn somewhat on their ribs. When the wing is lifted they open like a
louvered window and the air passes through; when the wing is forced
down they close, pressing tight against one another.
[Illustration: Fig. 9a.--Gull in flight.
On the down stroke the gull’s wing has turned over, showing the under
side, thus giving a shove forward.]
The two drawings of Fig. 9 a are adapted from Otto Lilienthal’s
_Birdflight_, p. 101. They are sections of the condor’s wing. As
Lilienthal says, “Every observer of the flight of storks knows that
one is able to periodically see through the wings.” Even the countless
parts of each feather partake in this valve action. It is clear that
with such a mechanism the mere flapping of the wings must give an
uplift apart from all other characteristics of the motion. The forward
thrust is due to the bending of the wing about its stiff leading edge,
as may be seen from the two drawings of the wings of a gull in flight
(_Birdflight_, p. 96). They were made in the sunshine: as the
wing rises, the hinder parts are turned down and show the bright upper
surface; as the wing descends, it twists so as to show the darker
under surface. It must also be true that even if the wings are held
outstretched without motion there will be an uplift if the air is full
of little motions, swirls, and quiverings. The wonderful gliding of
birds that travel for miles without a movement of the wings or any
apparent effort may conceivably be connected with this effect; it is
said that it does not take place when the air is perfectly still.
A very pretty example of the laws of the dynamics of the air is to
be found in the swerve of a spinning ball; it is likely to interest
most of my readers. We see it and make use of it in nearly every
game, though perhaps the golf ball shows it most, because its speed
is greatest. Suppose that the golfer “slices” his ball: instead of
pursuing a straight course in the direction in which it appeared to
be struck, it curls away to the right. The ball is then spinning;
the front of the ball is going from left to right of the golfer as he
gazes after it, the back of the ball is going the other way. It is
clear that he has not hit the ball truly, but has drawn the head of the
club across the ball; perhaps he pulled in his arms at the moment of
striking and did not follow through properly. As the ball moves forward
there is a dense cushion of air in front of it which has not had time
to get away. If the ball is spinning as supposed, the left-hand side
(the golfer being the observer) is spinning forward in the direction of
flight, the right-hand side is moving the opposite way, so far as spin
goes. The consequence is that through friction the air on the left-hand
side is carried forward more than on the right, and the cushion of
air in front of the ball is denser on the left than on the right.
Consequently the ball swerves to the right.
The long carry of a golf ball is always due to spin of the proper kind:
the stroke must be so made that the ball is turning about a horizontal
axis, the lowest part of the ball moving, so far as it is due to the
spin, in the forward direction. This makes the ball tend to rise as it
flies. Sometimes we see it actually take a curved path which is convex
to the ground. If it were not for this action the ball would not go
half the distance that it does.
[Illustration: Fig. 10.--Flight of golf ball with “slice.”
The shading shows where air is piled up by the ball as it spins and
moves forward, and this accumulation makes the ball shear off to the
right.]
If there were no air at all, we may observe, in addition, the carry of
the ball would be two or three times greater than the normal, because
its resistance to high-speed ball is so great. We should drive a ball
much farther if we could avoid the resistance from the air; but as we
cannot do that, we take advantage of what may be done by giving the
ball a spin.
The flight of a Rugby football, like that of fast-spinning golf ball,
is often curved upward, when the kick has gone rather under the ball
and though, of course, it is most obvious when the kick is against
the wind, yet I think it can be seen in still air. In tennis the
player often draws his racquet over the top of the ball, giving it the
opposite kind of spin, the top moving forward faster than the bottom.
This makes the ball duck, so that, though hit very hard, it keeps in
the court after passing the net.
[Illustration: Ground
Fig. 11.--Regular flight of golf ball: a pocket of condensed air, shown
by the shading in the drawing, keeps the ball up.]
[Illustration: Fig. 12.--Action of stroke of tennis racquet, giving
spin to the ball and making it drop quickly over the net (exaggerated).
On the right, section of racquet and ball before the stroke, arrow
showing direction of motion of racquet.]
Heavy balls swerve less than light balls going at the same speed; yet
we all know the swerve that can be given to a cricket ball, and the
swerve that the pitcher can give in baseball, is a marvelous spectacle.
Of all ways of studying the effect, the simplest, perhaps is by the use
of toy balloons which nowadays are toughly made and will stand much
knocking about. It is easy, by striking with the hand, or a racquet if
preferred, to give any sort of spin that is desired and to observe all
sort of swerves and soaring and “dooks.”
The various examples of the properties of gases which we have been
considering are all to be explained, as we have seen, on the hypothesis
that some kinds of atoms have very little tendency to associate with
other atoms, whether of the same or of other kinds: I have spoken of
them as the “unsociable atoms.” Other atoms, again, such as hydrogen or
oxygen, though very sociable individually, tend to form more or less
unsociable molecules. Thus the air consists of a mixture of unsociable
atoms and molecules: there are molecules of oxygen each consisting of
two atoms, and molecules of nitrogen analogously constituted, a few
molecules of carbon dioxide, each consisting of one atom of carbon and
two of oxygen, a certain number of single atoms of argon, and probably
small percentages of other gases. All of them form gases because
of the lack of tendency to associate; the independence which they
possess in consequence, together with their motion, furnishes a ready
understanding of their behavior.
We now ask ourselves whether we see any way of connecting the
properties of these atoms with the general idea of atomic structure
which was put forward in the last chapter. How is the sun and planet
conception to be connected with these tendencies to associate, or
not to associate, with the formation of molecules having similar
tendencies, and so on? To answer these questions fully would be to give
an account of chemistry so far as is known, and that is clearly beyond
our intentions. But there are certain simple rules which, though they
cannot be explained, and though they are often broken in appearance,
provide a most useful thread on which to string our facts. Let us go
back to our unsociable atoms, Nos. 2, 10, 18, 36, 54, 86. The first
thing that strikes is that there are curious connections between these
numbers. If we write down the successive differences we have 2, 8, 8,
18, 18, 32. The numbers 2, 8, 18, 32 are twice the squares of 1, 2, 3,
and 4. We have already seen that the difference between the various
kinds of atoms is simply one of number. I have not attempted to explain
the experimental and theoretical proofs of the numbers of electrons on
the various atoms: they are complicated, while the result is simple
and sufficient for our purpose. Since the number of the electrons on
the atom, or rather the number which expresses the positive charge on
its nucleus, is in itself of such unique importance, we cannot but
think that there must be something underlying the curious numerical
differences we have just observed. The probability is greatly increased
when we consider the question from another point of view.
Chemists have long discovered and pointed out that remarkable analogies
exist between the properties of different kinds of atoms. For our
purpose it will be convenient to express their discoveries in terms of
the numerical relations. We write down some of them in the following
way. We take first the eight atoms, in order of number, which begin
with helium; and put under them the next eight beginning with neon.
We thus have, continuing the arrangement up to No. 20 (see Plate IV
b for rough models):
Helium. Lithium. Beryllium. Boron. Carbon. Nitrogen. Oxygen. Fluorine.
2 3 4 5 6 7 8 9
Neon. Sodium. Magnesium. Aluminium. Silicon. Phosphorus. Sulphur.
10 11 12 13 14 15 16
Chlorine. Argon. Potassium. Calcium; and so on.
17 18 19 20
We have, in fact, written down a portion of the “periodic table.” It
is so set out that the atoms helium, neon, and argon, which so closely
resemble one another in their main property of unsociability, are in
the same column. It then appears that lithium, sodium, and potassium,
which also closely resemble one another in their properties, are in
the next column, and that the same remarkable classification runs
across the page. The mutual resemblances of the substances in the same
column are manifested in innumerable ways: they form one of the great
features of chemistry. The very name “periodic table” was adopted as a
description of the fact.
Now it is reasonable to suppose that the properties of an atom as
manifested by its relation to any other may well be determined by some
arrangement of its electrons, and especially of those which are most on
the surface and are first presented to the other atom. Thus lithium,
sodium, and potassium probably behave alike, because they have all the
same external presentment of electrons; so with carbon and silicon,
with fluorine and chlorine, and so on.
Such considerations have led to the following hypothesis. Let the
two electrons of helium be arranged as a pair symmetrically placed
on either side of the helium nucleus. Let every succeeding atom have
the same arrangement, and, in addition, a further arrangement of
electrons on an outer shell. Thus lithium has two, like helium, and
one as a contribution to a new outside grouping. Beryllium has two in
the outside group, boron three, carbon four, nitrogen five, oxygen
six, and fluorine seven. We will suppose that the list of additions to
this list closes with neon, and that in all atoms of higher number the
inside group of two and the just completed group of eight are retained,
the extra electrons taking their place in new groups. Thus, sodium,
like lithium, has one in its outermost group; magnesium has two, like
beryllium; and so on. Chlorine, like fluorine, has all but completed
an outer shell of eight; while argon, like neon, has completed it.
With potassium still another group begins; calcium has two in this
newest group, and so on. The last group is not complete until it
contains eighteen electrons; so chemical evidence tells us. But we
need not pursue this question further, especially as it becomes more
complicated.
Arguing in this way, we understand why the members of the same columns
should be alike in their properties. We then ask what the particular
properties of an atom have to do with the particular number of
electrons there are in its outer shell, this number being the same
in all members of the same column. To this question also we can find
some sort of answer which we can best state in the following way.
From a general consideration of the vast accumulation of chemical
knowledge regarding the tendencies of atoms to form combinations,
and under proper circumstances to dissolve existing combinations and
form new ones, certain rules appear which are directly connected with
the numbers of the electrons in the outermost groups. In the first
place, there is always a tendency to fill up the vacant places of
an uncompleted group. Thus if chlorine had one more electron in its
external group, that group would be completed in the sense that no more
additions are made to it as we pass from atom to atom in the succeeding
portions of the table. Consequently chlorine is on the search, so to
speak, for the electron which it lacks, and may exert great powers
in dragging it away from other atoms which are not holding on to it
with sufficient energy. It is true that the atom’s electricities thus
become unevenly balanced: the extra electron gives it a negative
charge. But in spite of that there is some force, we do not understand
its origin, which works for the completion of the external shell of
eight electrons. It is, in fact, this power that chlorine possesses of
dragging to itself an electron from other atoms, and upsetting their
combination in order to get it, which makes the substance so actively
poisonous. In the same way, sulphur has two gaps to fill up, and its
behavior is largely governed by that fact.
On the other hand, lithium, sodium, potassium have in each case a group
just in process of formation: there is so far only one electron in it.
The hold upon this electron is feeble, and when a chlorine atom demands
it, the electron changes hands at once. The result of the transfer is
that the external group of each atom is now a completed group: the
chlorine is like argon externally, and, if sodium be the other atom,
it is now like neon. Both the atoms are now charged with electricity:
the chlorine is negative because it has one electron in excess of its
proper number, while the sodium atom is positive because it has one too
few to make the balance between the positive charge on the nucleus and
the negative charges of the electrons that are left. In consequence,
there is an electric attraction between the two atoms: they have now
formed a molecule of ordinary salt. Sodium is a soft white metal. As
we shall see later, the distinguishing characteristic of the metals
is their possession of one or two electrons which can be easily torn
from them. In this combination the white metal and the poisonous gas
have joined to make the transparent crystalline salt. It is a violent
change of character; but it will not surprise us if we remember that
the arrangement of the electrons on the outside of the molecule must be
quite different from the arrangement on either of the atoms before they
become partners, and that the character of the atom or the molecule
depends on this arrangement.
There are innumerable examples of this kind of combination. As one
involving rather more complication we may take calcium fluoride,
which as a crystal goes under the name of fluorspar. Here two atoms
of fluorine, each lacking one electron (see the table p. 82), join
in an attack upon calcium, which has two electrons in its external
group, and each of them takes one electron into its own system. The
molecule therefore contains three atoms. Or, again, in alumina, which
in crystalline form makes ruby or sapphire, we have two atoms of
aluminium, each forced to give up the three electrons in its external
group for the benefit of three oxygen atoms, each of which takes two.
Besides this give-and-take arrangement there is another method by which
atoms seek to complete their external groups: they may share electrons
with one another, each being capable, apparently, of counting them in
its own structure, just as two houses may have the same party wall.
Thus two hydrogen atoms, each contributing one electron, combine so
as to possess a group of two, as helium does, and thus the hydrogen
molecule is formed. Two atoms of oxygen enter into combination, and
form the oxygen molecule in which each oxygen atom is surrounded by
eight electrons, of which four are held in common by both atoms. In
the diamond, as we shall see, each carbon atom is surrounded by four
other carbon atoms, with each of which it shares two electrons. So each
atom is provided with an external shell of eight electrons, none of
which it has entirely to itself. This kind of combination is generally
very strong, and molecules so formed hold together well. Moreover, many
molecules formed in this way are, so to speak, satisfied with their own
company: there is little tendency to associate with other molecules.
They tend to form gases. But on the whole the most permanent gases are
those which have naturally the completed external shell—helium, neon,
argon, and the rest. They show, most fully developed, the gaseous
properties which we have been considering as the result of the weakness
of tendencies to associate and the undisputed sway of movement.
CHAPTER III
_The Nature of Liquids_
THE difference between a gas and a liquid is that in the former the
atoms and molecules move to and fro in an independent existence,
whereas in the latter they are always in touch with one another though
they are changing partners continually. In the rivalry between motion
and attractive forces the motion is no longer in complete control: the
attractive forces have now sufficient power to keep the general body
of molecules in touch with one another, or at least so many of them
so that they form a definite volume of liquid, having a surface that
we can see. Yet the control of the attractive forces is not absolute:
there is a continual process which we call evaporation. Suppose a bowl
of water to be placed in an empty room. The molecules of the water are
all in movement--vibrating, turning, shifting, and changing partners
all the time. But their motion is not enough to make them break away
from one another, except at the surface, where the conditions are of a
special nature. In consequence the molecules hold together as a body
having a definite volume, and there are boundaries to that volume.
Only at the surface there are breakaways: in the constant interchange
of motion it will happen that some of the outlying molecules have
impulses given to them which are big enough to break their connection
with the molecules below, and they leave the surface for good. If this
had happened to molecules within the liquid, they would have been
recaptured. Thus the room in which the bowl of water has been placed
will contain a gradually increasing number of water molecules flying
about independently as a gas. If the room is closed, the increase will
not go on forever, because there will come a time when the number of
free water molecules in the room is so great that molecules strike the
surface of the water and re-enter it as fast as others leave it. The
room has become saturated with water vapor. That may happen before the
bowl is empty; but if the air in the room is continuously removed,
carrying the water vapor with it, the water in the bowl will all
evaporate in time.
The molecules that leave the surface will always be those that possess
more than the average amount of energy, part of which they spend in
tearing themselves away from their fellows; the average energy of the
main body will fall steadily as evaporation proceeds. In other words,
the water becomes colder and colder. We all know this effect well. If
we wave our hands when they are wet we feel the chill: we are, in fact,
using somewhat excessively a process which nature employs to cool our
bodies to the proper temperature. Our bodies are called on to make
good the excess of energy which the evaporating molecules have carried
away with them. The rate of chilling may be increased by the use of a
liquid which evaporates more rapidly than water; so, for example, the
surgeon at one time used an ether spray to cause local freezing. In
hot, dry countries drinking-water is cooled by putting it into a bag
made of porous canvas, which is hung so as to be shaded from the sun
but exposed to the wind, and the hotter and drier the wind the better.
[Illustration: Fig. 13.--The cryophorus.
The lower bulb, which is empty, is immersed in liquid air. The upper
bulb contains water which quickly freezes.]
In the hot Australian summer it is usual to see the bag hanging under
the veranda of the house or the roof of the railway station of a
country township. The water leaks through the canvas and is quickly
evaporated by the passing air, so that the water which is left grows
cool.
We can carry out the experiment in a very striking manner on the
lecture-room table. The two bulbs shown in the figure contain water
only, no air. The water is first brought to the upper bulb, and the
lower is then immersed in liquid air; in two or three minutes the water
is frozen, although the upper bulb has been nowhere near the liquid
air. The explanation is that the water molecules which fling themselves
from the surface of the water make their way down the tube and so to
the lower bulb. This would happen whether or no there were any liquid
air round the lower vessel; but then they would come back again, most
of them at least, and return to the water carrying their superabundant
energy with them. Thus the water would be very little cooled. If,
however, the lower bulb is reduced in temperature by the liquid air,
the molecules do not return. Their motion is taken away from them and
they collect first as water and then as ice in the lower bulb. The
water in the upper bulb is rapidly cooled, and soon frozen. The reason
for removing the air from the bulbs is that it is necessary to give the
water molecules a clear road, so that the evaporation may take place
quickly. If the operation were too slow, heat would leak in from the
outside air at such a rate that the freezing would not take place. The
presence of the air does not stop the energetic molecules from leaving
the surface, but it hampers their subsequent movements, reducing the
action to the process of diffusion which we have already considered.
When a liquid boils, the temperature has been raised to such a pitch
that the evaporating molecules are sufficient in number and speed to
lift off the air from the surface of the liquid and push it back _en
masse_. It is no longer the case that the individual molecules have
to thread their way through a crowd. The whole process is so strikingly
different in appearance from that of evaporation that the essential
similarity is apt to be overlooked. The temperature at which a liquid
boils depends on the pressure which the evaporating molecules have to
overcome: at the top of Mount Blanc boiling water is 27° F. cooler than
it is at the base.
The heat that is wanted if a liquid is to be evaporated is a measure
of the energy required to tear the molecules away from one another.
Perhaps that does not impress the mind with a sense of the importance
of these forces, which, though individually minute, are so powerful in
the gross. We may, however, remind ourselves of the heat required to
convert water into steam and of the amount of work that the steam can
do. The forces are manifested to us more directly in every hanging
drop of water or other liquid. The molecules are clinging to one
another like bees in a swarm. The links with which the molecules of the
last layer are attached to the surface from which the drop is hanging
are carrying the whole weight of the drop.
[Illustration: Fig. 14.]
Again the impression of the magnitude and importance of the forces is
not fairly conveyed by this simple effect; but the experiment can be
developed into a more impressive form.
Here is a bent glass tube containing water and no air. The water is
made to fill one limb entirely; if a little bubble of air is to be
found in it, it must be made to pass over into the other by holding
the tube in a suitable position and gently tapping it on the table.
When this has been done, the tube can be held so that the level of
the free end of the water column is far below the level of the other,
where it is clinging to the end of the glass tube. The weight of
the excess column on one side is all borne by the attachment of the
water molecules to the glass tube at the other side, and of other
water molecules to them. In fact, we have a drop of water about a foot
long. We cannot make a drop of this length hang from a finger, for the
reason that the water can break away by changing its shape. If that is
prevented, as it is in the glass tube, the magnitude of these molecular
forces is more obvious. When we try to stretch a bar of iron, the great
difficulty makes us realize the magnitude of the forces that keep the
molecules of solid iron together; we are apt to think that it is easy
to stretch a mass of water, but it is not so. It is easy to make the
water change its shape, but not to pull a layer of molecules directly
away from another with which it is in contact. Water is, in reality,
just as hard to stretch as to compress.
We may here make a little digression from our main line of argument,
because we come across a curious effect while we handle this bent tube.
If the tube is tilted so that the water runs along the tube and is
brought up sharply at one end, the sound of a blow is heard, as of two
hard substances striking each other; the blow is felt by the hand that
holds the tribe. The effect is sometimes described as an example of
water hammer; the explanation is simple enough. There is no air in the
tube, and the water strikes the end of the tube as if it were a rigid
body; and indeed it behaves as such because it is as incompressible. It
is necessary to be very careful in the handling of the tubes, because
it is so easy to knock out an end: it is just as if we struck a glass
vessel with a hammer. A very curious, and as it happens very serious,
example of this effect has manifested itself of recent years in the
wearing away of the propellers of ships that are driven by rapidly
turning screws. The illustration shows the erosion in a propeller blade
of the Mauretania (Plate IX a). The effect first appeared
when the adoption of the Parsons steam turbine increased the rate of
revolution of the screw and boats began to move faster, and it was at
first the cause of great loss, financial and otherwise. The explanation
was found in the fact that the steamship was advancing so fast and the
screws revolving so rapidly that the water could not fill up entirely
the holes that the blades left behind them.
[Illustration: PLATE IX.
A.
The right-hand figure shows erosion in a portion of an early propeller
blade of the “Mauretania.” Notice the small bite in the edge of the
blade shown in full in the left-hand figure.
B. Photograph of the cavitations formed by a propeller in the
experimental tank of the Parsons Marine Steam Turbine Co. The propeller
is the disc-shaped object at the left centre of the photograph. There
are three blades on it, and each is leaving a corkscrew line of bubbles
in the water which goes past the blade. We can see where the spirals
begin at the screw. (_Reproduced by courtesy of the Manganese Bronze
and Brass Co., Ltd._)]
The illustration shows the cavities as they are formed in a model tank
in the Turbinia Works at Newcastle (Plate IX b). They are
arranged in spirals; we can trace in the figure the spiral belonging to
each of the propeller blades.
[Illustration: Fig. 15.--Parsons’ water hammer.]
Now these cavities close up under the pressure of the surrounding
water, and since there is no air in them, the sides of the cavity
strike one another as hard and smartly, when they come together, as the
water in our tube could be made to strike the glass. If part of the
propeller blade forms part of a cavity wall, the blow may be so great
as to tear away pieces of the metal. It has cost much labor to arrive
at the full explanation and to provide a cure; propeller blades are now
made of an alloy specially designed to withstand erosion, and at the
same time the design of the blade has been improved. A very striking
experiment made in the course of these researches is illustrated in
Fig. 15. The strong metal vessel shown in the center of the figure is
filled with water and allowed to fall to the bottom of a tank, also
full of water, where its motion is suddenly stopped. The momentum of
the water in the cone aided by that of the heavy weight _W_ is
sufficient to make the water carry on its motion and leave a cavity
at the top of the cone at _V_. This fills up again immediately
afterward, on account of the pressure of the surrounding water, and as
it does so the water in the cone, increasing its velocity as it rushes
up into the narrowing space, strikes the top of the cavity so hard that
it punches a hole in the brass plate inserted at _P_.
The collapsing of the cavities formed by the screw makes quite a noise
in the water, so that a ship can be heard at great distances by the use
of an underwater receiver of sound.
Many of my readers will be familiar with a less serious example of the
blow that a mass of water can give because of its inelasticity: it
hurts considerably if one dives from any height and does not make a
proper entry into the water!
Since the molecules of a liquid all try to draw together under their
united attractions, they will bunch themselves together into a sphere
if they are allowed to do so, and this happens obviously when mercury
is dropped upon the table and breaks up into round drops which run
about as if they were round and hard.
[Illustration: DROPS OF MERCURY ON A TABLE
Fig. 16.
The small drops are almost perfect spheres. The large drops are
flattened out.]
Water will do the same thing if it does not wet the table: generally it
does wet the solid on which it rests, but we see many exceptions, as,
for example, when it is spilt on a dusty surface. What wetting means
and implies we have yet to consider: it is a very important part of
our subject. Gravitation also interferes with the tendency of a liquid
to gather into spheres. When the drops of mercury are very small they
look perfectly round, but larger masses are more like thick disks with
rounded edges. If we seek for good examples of the formation of spheres
by the general attraction of the molecules for one another, we must
contrive to avoid the influences both of wetting and of gravitation.
The small drops of mercury are a successful illustration. Another is to
be found in the manufacture of lead shot. The molten lead is allowed to
fall in a shower from the top of the shot tower, and gathers into round
drops as it falls, just as the rain does.
Perhaps it seems as if this were inconsistent with what has gone
before: gravitation has not been avoided and is indeed in full action,
yet the drops are formed. But the evil effect of gravitation is
indirect: it is the resistance to gravity which spoils the formation
of spheres. In the case of the large drops of mercury, the flattening
is due, not to gravitation directly, but to the upward pressure of the
table, which is resisting gravitation. When the drops of lead arrive at
the bottom of the tower they fall into water, which freezes them in the
shape they have acquired.
Here is an experiment to illustrate our point. The dark-looking liquid,
ortho-toluidine, does not mix with water, or, in other words, water
does not “wet” it, and its density is such that it floats conveniently
in a layer of pure water riding on a layer of salt water (Plate X
a). It is, even when spherical, supported at all points
by the surrounding water: it is not held up at one point only, as
a mercury drop would have to be were it a sphere resting on a hard
surface. In the circumstances of our experiment neither wetting nor
gravitation has any influence, and a large drop is formed, as we see:
it is perhaps a couple of inches in diameter. If it is pulled about by
a glass rod it sluggishly recovers itself; or, after wabbling heavily
through a variety of strange shapes, may break into smaller spheres.
When the rod is pressed gently against the sphere it makes a depression
or dimple on the surface; the toluidine’s effort to form a spherical
drop is for the moment interfered with, but it adapts itself as well as
possible to the circumstances. So also if we float some solid body--an
iron ball let us say--on the surface of mercury, a dimple is formed;
the surface of the mercury near the ball has the form shown in the
figure. If we look at the form of the mercury surface close to the wall
of the containing vessel, we see the same outline.
It is different when the liquid wets the wall of the vessel which holds
it or of the body which floats in it. If we put clean water into a
clean glass vessel, we see the water heaping itself against the side.
[Illustration: Fig. 17.--Iron ball floating on mercury (sectional
drawing)]
This is a more complicated effect than the other; evidently there are
attractive forces between the glass and the water. If a glass plate is
forced down into a dish full of mercury and made to touch the bottom
so that the mercury is squeezed out and none remains between the plate
and the bottom of the dish, it will stay where it is put, and indeed
great force is required to remove it. The explanation is simple and in
accordance with the principles which we have been considering.
[Illustration: Fig. 18.--Water heaped up against glass wall which it
wets.]
If the plate is to rise, the mercury must be made to get under it
again, otherwise the plate cannot rise far, because if there is not a
vacuum under the plate there is at most only a little air, which would
fall rapidly in pressure if the plate were raised.
[Illustration: PLATE X.
A. A large drop of liquid ortho-toluidine floating in water on a layer
of brine.
B. One bubble rests inside another, but as in Fig. 21 and for the same
reason the two do not coalesce.]
As the pressure on the top of the plate is more than that of the
atmosphere, the downward forces on the plate are greater than those
which try to lift it. At the edge of the plate the form of the mercury
surface is as shown in the figure: the mercury refuses to allow itself
to be drawn out into a thin sheet between the plate and the bottom of
the vessel.
[Illustration: Fig. 19.--Glass plate at bottom of dish containing
mercury. The plate is shown slightly lifted from the bottom, in order
to illustrate the refusal of the mercury to enter the vacuum so made.]
A drop of fluid which tries to draw itself together into a sphere
looks as if it were being held in an elastic bag. The atoms of mercury
in the surface are not quite in the same circumstances as those in
the interior, because they are exposed on one side, but it is only in
this sense that there is a surface film. We use the idea of a surface
film, nevertheless, finding it a convenient term; and we speak of its
tendency to contract and of its tension. Sometimes, however, there is
a real film on the surface which is different in composition from the
liquid of the interior, and then we find many strange and beautiful
consequences. The example most familiar to us is, no doubt, that of
the soap bubble. We put into the water a little soap, and at once we
find it easy to churn the soapy water into a pile of froth or blow it
out into bubbles. What has the soap to do with this effect? The answer
is to be found in the properties of the soap molecule. It is of very
curious shape, many times as long as it is broad; and it is made up
of a chain of carbon atoms fringed along its length with hydrogens,
and ending, at one end, in a little bunch of three hydrogen atoms,
at the other in a little group consisting of oxygen and sodium. The
former of these bunches is very self-contained: its attractions for
other atoms and molecules are small. But the latter is by no means so
unsociable: it is an active group tending to enter into association
with others, and especially it has a strong desire to join up with
molecules of water, for which reason the soap dissolves in the water.
Because, however, it is only one end of the chain which is very active
in this respect--the other end and the sides of the chain behave
differently--the soap molecules are apt to stay on the outer fringe
of the water if they come there in the course of their wanderings.
In this way a real film forms on the surface of the water, consisting
of soap molecules standing on end, so to speak, one end rooted in the
water, and the other exposed to the air. They are packed together side
by side like the corn in a field, or the pile on a piece of velvet.
They are not as free, however, as the hairs of the pile: they are
tied together side by side, because there is some force of attraction
between them when so laid alongside. We find that effect displayed
under other circumstances, as we shall see later. Thus they form a sort
of chain mail over the surface of the water--a real envelope. The sheet
can be stretched in the sense that if it has to be extended other long
molecules will come out of the body of the liquid and take their place
with the rest.
The soap bubble is a thin-walled sphere of solution bounded within
and without by the soap films; it holds together so well because the
films are there. It shrinks if the air within it is allowed to escape:
evidently the long molecules would gather together with the water
molecules as closely as possible. But there must be an outside, of
course, and where both kinds of molecules are present it is the long
chain molecules that form the outside layer. A very simple experiment
will illustrate still further the tendency to shrink. A wire ring is
dipped into some soap solution, and when lifted out carries a soap film
stretched across it.
[Illustration: Fig. 20.--A loop of very fine cotton is floated on the
soap film, and the part of the film inside the loop is touched with
a hot needle. Instantly the loop flies into a perfect circle. (By
courtesy of Prof. C. V. Boys.)]
In the film floats a ring of fine cotton shows. It is clear that which
was attached to the wire ring before the latter was put into the
solution. If the film inside the cotton loop is burst by touching it
with a hot needle, the loop flies instantly into the form of a perfect
circle, as the figure shows. It is clear that the whole film is under
tension and is trying to contract.
A very curious feature of the soap bubble is its reluctance to join up
with another bubble. If we blow a bubble on a ring (see Fig. 21), we
may take a second bubble and knock it against the first with force,
one would think, enough to break them. But the bubbles bounce from
one another like india-rubber balloons. Perhaps the explanation lies
in the fact that in both cases the outer layer consists of those ends
of the molecules which, as we saw before, have very little tendency to
associate with other molecules or parts of molecules.
[Illustration: Fig. 21.--Two bubbles in collision.
The two bubbles are pressing each other, and may be rubbed on each
other, but do not coalesce, because their liquids do not mix; it is
only the inactive ends of chain molecules that come into contact. (By
courtesy of Prof. C. V. Boys.)]
There is no tendency for the one bubble to coalesce with the other when
the two are pressed together, because the parts that come first into
contact do not attract each other.
[Illustration: Fig. 21A.]
This is very clearly seen in another of the wonderful experiments
of C. V. Boys.[4] A bubble is blown on a ring held in a stand (Fig.
21a).
A small ring carrying a tiny weight is attached to the under part of
the bubble as shown. A glass pipe is charged with solution and pushed
through the top of the bubble; when blown, a second bubble appears
within the first, and when it has attained a suitable size is released
by a skillful twist of the pipe. The inner bubble falls gently to rest
on the lower part of the outer, which it touches along a ring, not at
the bottom point. This is intentional, and was the purpose for which
the weight was attached to the outer bubble. The two do not tend to
coalesce, although in contact all along a line, no doubt because they
are presenting to each other surfaces composed of the inactive or
unsociable ends of the chains. If the outer bubble had not been pulled
out of shape, the inner and outer would have touched each other at
their lowest points. Now there is generally a drop of solution at the
lowest point of the inner bubble. When this comes into contact with the
outer, the bubbles generally coalesce. The drop of solution in some way
forms a bridge between the two. If the glass pipe be pushed through the
outer and made to touch the bottom point of the inner, and so drain it,
the weight hanging from the outer may be peeled off, and now the two
can touch each other at this lowest point without disaster (Plate X
b.)
The frothing of liquids is often caused by the presence of molecules
which have the same property of forming a skin over the surface. When
the foam gathers on a brook it is due to the presence of such molecules
as those of the various saponines, chain-like formations which are
found in many plants and trees. So also the foam that gathers on the
shore is believed to be due to the presence of similar molecules formed
in the seaweeds.
We have learned much about the form of these long-chain molecules
within recent years. In particular we are indebted to the late Lord
Rayleigh, to Devaux in France, to Langmuir in America, to Hardy and
to Adam in England for the examination of what happens when oils are
allowed to spread on water surfaces. We can repeat one or two of the
experiments in order to get an idea of the magnitude of the effects of
which we are speaking. We take a clean water surface, that is to say, a
surface free from any contamination by oil or grease. It is convenient
to attach a rubber tube to the tap and let the free end of the tube
lie at the bottom of a basin so that the water wells up and overflows
the edges, carrying away any dirt that has settled on its surface. We
now spread on the water a thin dusting of talc powder or anything else
that is convenient. Next we take a fine-drawn glass point or needle
and dip it into oil--olive oil will do--and then, after wiping nearly
all the oil off, dip the point of the slightly greasy needle into the
water surface. Instantly a circle is cleared round the needle (Plate
XI a). It appears that the long molecules range themselves
side by side on the surface as before; to the soap bubble they came
from within, now we apply them from without. Each molecule hastens to
root itself in the water by its active end, and stands upright, as if
it were a water plant rooted and growing in the water. In the end all
the molecules are successful, and a thin sheet, one molecule thick,
covers the surface of the water; its thickness is of the order of a
ten-millionth of an inch. By measuring the weight of the oil that has
been placed on the water—a difficult task, since it is so small—and the
area covered, it is possible to find a measure of the thickness of the
film.
[Illustration: PLATE XI.
A. Circles cleared by minute drops of oil.
B. The camphor boat.
A small piece of camphor is fastened at the stern of a very light
boat, and as it dissolves in the water the solution forms a him on the
surface. It is so eager to do so that it drives the boat away so as to
make room for itself If a little oil is put on the water and makes a
film all over it, the boat stops. If the oil partly covers the water,
the boat stops as soon as the ruler which is held by the operator in
the picture is pushed so far forward that the oil covers the surface
left to it.]
This is, in fact, the method that has been followed by the workers
mentioned. More recently it has been possible to apply a new method,
based on the use of X-rays, to the exact measurement of the same
quantity, and I hope to show you presently how this is done. On
the results of the earlier work it was possible to assert that the
thickness of the layer was such as would be expected if it were one
molecule thick; and the argument was greatly strengthened by the fact
that when different substances, known by chemists to be chain molecules
of different length, were placed upon the water, the thickness varied
with the length, as it ought to do.
If the drop of oil is small enough, and the dust is finely scattered,
the cleared spot is exactly circular. If we prick the water surface
somewhere else, another circle is formed. Each circle is totally
unaffected by the presence of others. This was relied on by Devaux to
show that the action of each drop was concerned only with the surface
round it over which the oil was spread: it was not a general effect on
the body of the liquid. It was just what one would expect if the drop
of oil had spread out until it was drawn down to a certain thickness
and could then spread no farther. By putting on a larger drop, we can
see that larger spaces are cleared. We may, for example, pour a few
drops into a large bath, and clear the whole surface. When the dust
layer on the surface of the water is broken up into little patches by
several applications of minute drops, in different places, and when
the surface is not covered all over with the oil film, we can observe
the quickness of the spreading by touching the surface with the oiled
needle at some little distance from a floating patch, and watching
how suddenly the patch is hurried away from the spot. The impulses
that are given in this way are the cause of the lively movements of
camphor fragments when they are dropped on the surface of the water,
an old experiment. As the camphor dissolves, the solution shoots
over the surface in a film, and the camphor itself recoils like a
gun when it is fired, or a rocket when the heated gases stream from
its tail. Sometimes the fragments dart to and fro and sometimes spin
round merrily. A tiny boat can be made to sail about on the water by
fastening a little piece of camphor on its stern in such a way as to
touch the water (Plate XI b). When a number of camphor boats
and pieces of camphor are all on the move, it is quaint to see how
suddenly it all goes dead when a little oil is poured on the water. The
oil film has covered the water in an instant, and the dissolved camphor
no longer spreads over the surface.
We have all heard of the stilling of the waves by pouring oil upon the
sea. We can watch the effect by making a series of waves run along the
long tank which Lord Rayleigh once used here for the same purpose; a
vacuum cleaner serves to provide the wind, and you see there is quite a
heavy storm on the water (Plate XII a, b). It is magically stilled if a
few drops of oil are allowed to fall in the center of the storm; after
a few moments the oil sheet is blown to the end of the tank and the
waves rise once more. We can repeat the experiment again and again. We
must suppose in this case that the wind has no “bite” on the water. The
latter is covered, as we know, with a film of oil, the top surface of
which is formed of the inactive ends of the long-chain molecules; and
it may well be that the molecules of the air when they strike it recoil
as from a smooth surface. A rough surface would be driven forward by
the impacts of the air molecules--rough, that is to say, in the sense
that the spaces between the exposed molecules are of the same size as
the molecules that strike. But if the surface of the oil film is very
smooth and has little tendency to hold on to any molecules that strike
it, the air cannot push it and make it rise in little waves which
afterward grow to great ones. So the oil stills the waves by stopping
the action of the wind, and the motion of the waves dies out in their
own friction.
We now come to the problem of the “wetting” of a surface. We know, for
example, that a clean glass surface is wetted by water, but not when it
is smeared with grease, even if the film is almost invisible. The water
molecules clearly refuse to associate with the molecules of the grease.
That is not surprising, perhaps, because we have seen that in some
cases at least the long molecules that make the fats and oils present
to the outside their inactive ends, which have very little attraction
for the water molecules. So water spilled on a greasy surface gathers
into drops, just as mercury when it is spilled on the table; the form
of the water is due to the general attraction of its molecules for one
another. An oiled needle can be gently laid on water without sinking
more than to make a depression in the surface, just as if there were
a skin on the water which gave slightly under the weight. Still more
striking, perhaps, is the floating of a greased wire sieve. (Fig. 22).
[Illustration: Fig. 22.--Greased sieve. (By courtesy of Prof. C. V.
Boys.)]
The sieve is dipped in melted paraffin wax, shaken so as to clear the
pores, and allowed to dry; it is well not to touch it with the fingers.
It will float readily and carry quite a lot of cargo, as Boys showed at
the Christmas lectures many years ago. Or it may be filled with water;
but the water must not be poured in roughly; it must be allowed to
flow in gently on to a piece of paper which can afterward be removed.
To show that the pores are quite open we can give the sieve a sharp
movement, when the water film gives way and the water falls in a heavy
shower on the floor.
When soda water is poured out into a clean, smooth tumbler, very few
bubbles come to the surface; but if the surface of the tumbler is at
all dirty or rough we may see streams of bubbles rising. There is a
beautiful old experiment which illustrates this effect, that of “the
grape and champagne.” We must use soda water instead of champagne. A
grape is not wetted by water, and so when it is put into the tumbler it
sinks to the bottom of the soda water, where it collects bubbles at a
great rate (Plate XII c). Soon it is covered over with a sheet
of bubbles that look like seed pearls, and these bring it by their
buoyancy to the surface. The grape is not much heavier than the water,
and does not require much to lift it. At the surface the grape parts
with some of its bubbles, which burst into the open air, and this goes
on until it sinks again, only to collect a few more bubbles and once
more be made buoyant. The process will repeat itself continually for
many minutes until the soda water is “dead.”
It is interesting to put in two glass beads instead of the grape. They
have been cleaned: washing with soap and water is efficient. No bubbles
form on them and they stay at the bottom.
[Illustration: PLATE XII.
A. Stormy water.
B. Oil stilling the storm.
C. Grape in soda water.
A and B. The blower raises a storm and the waves run along the tank.
A drop of oil stills the waves at once, and the water surface becomes
level. Notice the blank space in B. After a while, the oil is blown to
the end of the tank, and then the waves rise again. The photographs
have been retouched so as to bring out the reflection of the light by
the waves.
C. The grape and the greasy glass sinker are carried to the top by
bubbles; the clean glass sinker has no bubbles and stays at the
bottom.]
We take one of them out, rub it over with a greasy finger, and now it
behaves like the grape, collecting bubbles, rising, parting with some
of them, falling, and so on.
We must realize that when a bubble of carbonic-acid gas forms in the
soda water the particles of the gas have to collect and push back the
water all round. Now the water molecules are holding on to one another
tightly, and resist being torn asunder. For this reason we do not see
the bubbles forming in the middle of the water. At the edge, when the
glass is clean, the water wets the glass, or, in other words, the water
molecules are clinging to the glass even harder than they cling to one
another. Bubbles cannot under those circumstances form here, either,
for they would have to tear away the molecules from the glass. But it
is different if the surface is greasy and the molecules are not really
holding on to the glass--merely pressed against it by the pressure
of the rest of the water which is behind them. In that case the gas
bubbles find somewhere to grow, and quickly increase in size. It is
easier to push back the surrounding water when the bubbles have grown
somewhat. One of the most beautiful ways of showing that is by another
of Boys’ soap-bubble experiments. Two bubbles of different sizes are
blown on the two ends of the same tube; when they are allowed, through
the opening of a tap, to communicate with one another, the little bulb
blows out the big one and disappears. Of the mass of bubbles in the
soda water which lie side by side on the wall or the grape, the larger
ones tend to take up the smaller, and all of them to amalgamate.
The little streams of bubbles that we sometimes see rising from
definite points on the surface of the tumbler are due to some
irregularity in the glass--a tiny protuberance, perhaps--on which, if a
bubble tends to form, it already is past the earliest stages of small
diameters.
This tendency of bodies under water to collect bubbles and rise to the
surface has of recent years become the basis of a great metallurgical
industry. Various metal ores when crushed into powder form a mixture of
particles of rock material, such as quartz and various silicates, and
of metallic sulphides. It is found possible to treat the mixture so
as to cover the particles containing metal with a thin oil film, which
is not wetted by water, while at the same time the particles of rock
are still clean and the water wets them. The mass is then churned up
into a froth. All the metal-bearing particles are made buoyant by the
adherence of bubbles and rise to the top in a thick frothy scum; the
rest of the ore stays at the bottom of the vat, and the two parts are
easily separated.
There is one other experiment which will help to illustrate these
principles. We know that water heaps itself up against the side of a
clean glass vessel which contains it. The molecules cling to the glass,
and as it were climb up the wall on one another’s shoulders in their
eagerness to affix themselves thereto. If we dip two glass plates side
by side in the water, the water rises higher to the space between them
than it does outside. Those that are climbing one wall now help those
that are climbing the other. The effect is spoken of as being due to
“capillary action,” the name being given to it because it is so marked
in the case of a fine or “capillary” tube. The water in the fine bore
is lifted up to a great height, one inch in the case of a tube of
one-twentieth-inch diameter. If we float a small hollow glass ball on
the surface of the water, the water rises up the sides of the ball. If
two floating balls are made to approach each other, they will, when
within a short distance--perhaps half an inch--of each other, move
together, at the end quite violently.
[Illustration: Fig. 23.--Two hollow glass balls floating in mercury.
The pressure at _Q_ is less than the pressure at _R_ because it is at a
higher level in the water. The pressure at _R_ is the same as at _S_,
because _R_ and _S_ are on the same level. The pressure at _S_ is that
of the atmosphere, which is the same as the pressure at _P_. Hence the
pressure at _P_ is greater than the pressure at _Q_, and the one glass
ball is forced toward the other.]
We shall understand that if we consider the diagram in Fig. 23. Two
glass balls are floating in the water. The pressure at _Q_ is less
than the pressure at the level of the dotted line, because _Q_ is
at a higher level in the water. The pressure at the level of the dotted
line is the pressure of the atmosphere, because the line continues the
level of the water without. So the two pressures marked _P_, both
sensibly equal to the pressure of the atmosphere, overcome the two
pressures marked _Q_ and drive the balls together.
If we float on the water two balls made of paraffin, or two glass balls
coated with paraffin, the two attract each other as the clean glass
balls did, though the action is somewhat different.
[Illustration: Fig. 24.--Two greased glass balls floating on water.
The pressure at _P_ is greater than that of the atmosphere and
therefore than that of _Q_, and the balls are forced together.]
As the figure shows, the balls combine in making a dimple in the
water, and again if we study the forces acting on the balls we find
that the pressures are such as to force the balls together. But the
clean glass balls avoid the paraffin balls. This action is a little
more complicated, but it can be followed from the figure, which shows
the forces that are in action. When the vessel containing the water is
clean, and the water is heaped up against the side, the clean glass
balls are attracted to the side, just as they are attracted by each
other. On the other hand, the paraffin balls avoid the side of the
vessel. If now we carefully fill up the vessel with water until it
tends to brim over, so that the edge of the water no longer curls up
against the side, but curls down toward the edge of the vessel, the
clean balls leave for the middle and the paraffin balls come to the
side and stay there.
[Illustration: Fig. 25.
The left-hand ball is wetted by the water; the right hand ball is
greased and is not wetted. The pressure at _P_ is greater than
that at _Q_, and at _P_' greater than at _Q_'. Thus the
balls are forced apart.]
All these facts which we have been considering are illustrations of
the one principle on which the formation of a liquid depends, namely,
the strength of the attractions between the atoms and the molecules
which are strong enough to keep them in constant association with one
another, though they are not so strong as to bind them together into
a rigid, solid body. And it is important to remember that molecule
attaches itself to molecule at special points; one part of a molecule
may be able to exert a strong hold on a special part of another.
Presented differently to each other, there may be little or no tendency
for the two to join together.
CHAPTER IV
_The Nature of Crystals: Diamond_
WE have seen that when the effects of movement overcome the forces
of mutual attraction, the atoms and molecules have an independent
existence and form a gas; and, further, that when the attractive forces
are somewhat stronger or the effects of movement are somewhat less,
the molecules may cling together and form a liquid. In this state we
suppose that the connections between the molecules are loose enough
to allow a molecule to change its position and its partners with
ease. We have now to consider a final state in which the attractive
forces have quite the upper hand. The bonds between the molecules
are more numerous, and it may be stronger: each molecule is tied to
its neighbors at more than one point of its structure, so that it is
riveted into its place, and in this way the _solid_ is formed.
Molecules differ very much from one another in their form and in the
forces which they exert on one another. When the forces are strong,
much movement is required to prevent them from binding the molecules
into the solid: in other words, the melting point is comparatively
high. Substances like diamond or tungsten, of which the filaments of
electric lamps are made, are so tightly bound together that they must
be raised to temperatures of several thousands of degrees centigrade
before the molecules are forced to release their hold. Such substances
as butter or naphthalene barely remain solid at ordinary temperatures;
others, again, like carbon dioxide, still more oxygen or hydrogen, must
be greatly reduced in temperature before solidification takes place.
It is all a matter of the balance between the two opposing agencies,
motion and mutual attraction, and it is easy to realize that the
melting points of substances may differ very widely from one another.
Furthermore, a molecule is not to be thought of as a body of vague
and uncertain form exerting a loosely directed attraction on its
neighbors. When two molecules are brought together they may or may
not draw tightly together: everything will depend on the way they
are presented to each other. Each molecule has a definite shape or
outline, we may say; though in using these words we must remember that
their meaning will require careful consideration when we look more
closely into the matter. The molecules join together as if there were
definite points of attachment on each, and the junction implied that
the proper points were brought together. The action between them is not
usually to be compared to the general attraction between two oppositely
electrified bodies, but rather to the riveting together of two parts of
a mechanical structure, such as two parts of an iron bridge. Just as
in the latter case the parts must be brought into the proper relative
positions so that the rivets can be dropped into their places, so we
find two molecules of a solid substance tend to arrange themselves so
that certain parts of one are fastened with considerable rigidity to
the proper corresponding parts of the other. There may be more than one
way in which molecules can be joined up, and in consequence different
structures may be formed out of the same molecules; for example, there
are different forms of sulphur, of quartz, and of many other things.
It often happens that one mode of arrangement is adopted at one
temperature, and a different mode at another temperature.
The consequence is that when the molecule contains many atoms, and is,
therefore, probably of complicated structure and curious form, the
solid that is formed by their union is of a lace-like formation in
space. We may compare it to a bridge formed of iron struts and stays;
which is a very empty structure, because each member is peculiar in
form, generally long and narrow, and is attached to the neighboring
members at definite points. Most organic substances, like naphthalene,
or one of the solid paraffins, have such a complicated character, and
the emptiness of the structure makes for a low density. Few organic
substances are much heavier than water. When the molecules are less
complicated, less irregular in outline, they may pack together more
closely; if the molecule contains one or two atoms only, like the
molecule of ruby, or iron pyrites, still more if it contains but one
atom, atom and molecule being then equivalent terms, as in the case of
gold or iron, then the packing may be very close and we have relatively
heavy substance.
The infinite variety in the properties of the solid materials we find
in the world is really the expression of the infinite variety of
the ways in which the atoms and molecules can be tied together, and
of the strength of those ties. We shall never thoroughly understand
the materials that we put to use every day, nor grasp their design,
until we have found out at least the arrangement of the atoms and
molecules in the solid, and are able to test the strength and other
characteristics of the forces that hold them together.
Now, within the last few years the discovery of the X-rays has provided
means by which we can look far down into the structure of solid bodies,
and observe in detail the design of their composition. We have advanced
a whole stage toward our ideal purpose--that is to say, toward the
position from which we can see why a material composed of such and such
atoms has such and such characteristics, density, strength, elasticity,
conductivity for heat or electricity, and so on; or, in other words,
reacts in such and such ways to electricity or magnetism, or mechanical
forces, or light or heat. How far our new powers will carry us, we do
not yet know; but it is certain that they will take us far and give us
a new insight into all the ways in which material things or structures
are handled, consciously or unconsciously, it may be in some industrial
process, or it may be in some action of a living organism.
The new process is especially applicable to the solid, and I hope to
describe it in this and the following chapters, which deal especially
with the solid state. It depends on the combined use of crystals and
X-rays, and we must give a little consideration to each of these
subjects. Let us take the crystal first.
Imagine a slowly cooling liquid to reach the stage of which I have
already spoken, when the heat motions have decayed so far that the
molecules or atoms begin to attach themselves rigidly together. They
will lay themselves side by side, so arranged that the attractions
of various points on the one for various points on the other are
satisfied as far as possible. We can imagine two molecules, already
tied together at one point, to swing about each other with diminishing
movements until at last a second tie is made, quite suddenly, perhaps.
Then it may be that a third tie is quickly made in the case of each
molecule, linking it to the other of the two, or to a third; and so it
becomes locked into position. Thus, as the liquid cools, molecule after
molecule will take its place with others already locked together, and
the solid grows.
Or it may be that a solid substance forms out of a solution in which
it has been dissolved. The solution evaporates and the molecules meet
one another more often, so that their association is encouraged. When
the liquid has entirely disappeared, the substance is all solid. If
the evaporation has been slow, the molecules as they wander on their
way through the solution come to places where already a few molecules
have tied themselves together, and join up with them, quietly and
deliberately arranging themselves before they finally settle down, or
refusing to take their places before they are presented to one another
in the right way.
We can well imagine that under such circumstances a regularity in the
arrangement will ensue. Suppose that a flat body, shaped like A, had
four centers of attraction, two positive and two negative, arranged as
shown. If we had to lay a number of such bodies on a flat surface, and
so join them together that a positive and a negative center lay always
close to each other, we might arrive at some such arrangement as is
shown in Fig. 26.
[Illustration: Fig. 26.]
Whatever arrangement we adopted we should naturally find in the result
a certain regularity, as in the figure. And apparently nature works
in some such way: the molecules lie side by side in an ordered array.
The point is of fundamental importance. Order and regularity are the
consequence of the complete fulfillment of the attractions which the
atoms or molecules exert on one another. When the structure has grown
to a size which renders it visible in the microscope, or even to the
naked eye, the regularity is manifest in the form of the solid body: it
is what we call a crystal. It is bounded by a number of plane faces,
often highly polished in appearance, so that the crystal has a certain
charm due partly to glitter and sparkle, partly to perfect regularity
of outline. We feel that some mystery and beauty must underlie the
characteristics that please us, and indeed that is the case.
[Illustration: Fig. 27.--Models illustrating screw structure.
A. One sort of peg: _i. e._, every peg is like every other, and all
point the same way. B_1 and B_2. In each of these there are two sorts
of peg: _i. e._, one lot of pegs pointing to the right and one to the
left. Two varieties of arrangement. C_1 and C_2. Three sorts of peg:
pointing in three different directions. The two arrangements C_1 and
C_2 give a right-handed and a left-handed screw, respectively.]
Nature is telling us how she arranges the molecules when given full
opportunity. There are but two or three in her unit of pattern, and
when the unit is complete it contains every property of the whole
crystal, because there is nothing to follow but the repetition of the
first design. Through the crystal, therefore, we look down into the
first structures of nature, though our eyes cannot read what is there
without the use, so to speak, of strong spectacles, which are the X-ray
methods. A few crystal forms are shown in Plate XIII.
[Illustration: PLATE XIII.
Crystalline forms.
A. Sulphur trioxide crystals which have grown from vapour in a glass
vessel. B. Erythritol crystal, grown from solution. C. Ammonium
chloride: ideal and distorted cubical crystals from solution containing
urea. Crystal forms: Quercite: Cocosite. E. Crystal forms: Alizarin;
Rubidium alum; Sodium chloride: Ammonium cobalt sulphate; Phthalic
acid. F. Ammonium chloride: fern-leaf crystals (octahedral) and cubical
crystals from solution containing urea.]
There are three stages in the arrangements of matter: the single atom
as we find it in helium gas; the molecule as it is studied by the
chemist; and the crystal unit which we now examine by X-ray analysis.
To take an example, there are the _atoms_ of silicon or of oxygen.
The _molecule_ of silicon dioxide contains one unit of silicon
and two units of oxygen, arranged, no doubt, in some special way.
Lastly, there is the substance quartz, of which the _crystal unit_
consists of three molecules of silicon dioxide, arranged, again, in a
special fashion which we now know has a certain screw-like character.
The quartz crystal contains an innumerable multiplication of these
units. Each of the units has all the properties of quartz, and, in
fact, is quartz; but a separate molecule of silicon dioxide is not
quartz. For example, one of the best-known properties of quartz is its
power of rotating the plane of polarization of light, and this property
is associated with the screw which is to be found in the crystal
unit. It takes three molecules to make the screw. If we insert pegs
into a round stick as in the figure, and make all the pegs the same
in every particular--that is to say, if our unit of pattern contains
one peg only--we may form an arrangement like _A_. With two pegs
to the unit of pattern we can make an arrangement like _B{1}_ or
_B{2}_. With three pegs to the unit of pattern we may make one
as in _C_, which may twist either of two ways, _C{1}_ or
_C{2}_, or, as it is generally said, may be either right-handed or
left-handed.
[Illustration: Fig. 27a.]
The X-rays actually tell us that the quartz unit contains three
molecules, and that they are arranged in a screw-like form, with which
facts the form of the quartz crystal is in complete agreement, because
there are two varieties in the form, as shown in Fig. 27 a. In
one there is a sequence in the faces x, s, r', which screw off to the
right, while in the other they go to the left. Such a dual arrangement
may be expected to be a consequence of the existence of the two kinds
of screw, though we do not yet know enough to enable us to guess why
these particular faces are prominent. Quartz or “rock crystal” was
called “Krystallos” by the Greeks; the name was given to ice also,
because the two substances were confused with each other. It is
appropriate, therefore, that we should use quartz as an illustration of
what is meant by crystal structure and the crystal unit.
We may now ask ourselves why, if the natural arrangement of molecules
is regular, we do not find all bodies in crystalline form. To this
we must answer that in the first place a large perfect crystal must
grow from a single nucleus. It is difficult to say what first arrests
the relative motion of two or three molecules of the cooling liquid,
joining them together and making a beginning to which other molecules
become attached. Perhaps it is a mere accident of their meeting;
perhaps some minute particle of foreign matter is present which
serves as a base, or some irregularity on the wall of the containing
vessel. If there are very many nuclei present in the liquid, very many
crystals will grow; and since they are not likely to be oriented to
one another when they meet, they will finally form an indefinite mass
of small crystals, not a single crystal. They may be so small that
to the eye the whole appears as a solid mass without any regularity
of form. In order that a large perfect crystal should be formed, the
arrangements must be such that the molecules find few centers on which
to grow. And they must grow, usually, very slowly and quietly, so
that each molecule has time to settle itself correctly in its proper
place. The molecules must have enough movement to permit of this
adjustment. These conditions are well shown in the methods which the
crystallographer employs for the growth of crystals. If, for example,
he is growing a large crystal of salt from a solution of brine, he will
suspend a minute, well-formed crystal in the brine, and he will keep
the temperature of the latter so carefully adjusted that the atoms of
sodium and chlorine are only tempted to give up their freedom when
they meet an assemblage of atoms already in perfect array--that is to
say, when they come across the suspended crystal. If the solution is
too hot, the suspended crystal will be dissolved in the unsaturated
solution; if it is too cold, crystals will begin to grow at many
points. Sometimes the liquid is kept in gentle movement so that various
parts of it are brought to the suspended crystal in due turn.
[Illustration: Fig. 28.--The thermostat.
The temperature of the bath in which stand the bottles containing the
growing crystals must be free from sudden and irregular variations, and
must be slowly lowered day by day. The temperature is maintained by an
electric heater: if it rises too high the current is turned off through
the expansion of the liquids in the large thermometer which also stands
in the bath. The rise of the mercury closes a circuit containing
an electromagnet which pulls the switch. The clock is all the time
lowering--very slowly--a wire to meet the mercury in the thermometer,
so that the temperature at which the heating coil is turned off is
being steadily diminished. The heater is at the bottom of the bath, and
a stirrer is just above it.]
The principal conditions are time and quiet, a solution of the salt
just ready to precipitate its contents, temperature and strength of
solution being properly adjusted for the purpose, the presence of a
small perfect crystal and the gentle movement of the solution past
it. We do not, of course, quite understand how these or some such
conditions come to be realized during the growth of a diamond or a
ruby; but we find them to be necessary in the laboratory when we
attempt to grow crystals ourselves.
When the conditions are fulfilled in part only, we may get a mass of
minute crystals in disarray; we may even find a totally irregular
structure--an amorphous substance, to employ the usual phrase. This
alone would account for the seeming rarity of crystals, and we
have also to bear in mind that many bodies are highly composite in
character, consisting of many substances each of which has its own
natural form. The X-rays show us that the crystal is not so rare as
we have been inclined to think; that even in cases where there is no
obvious crystallization. Nature has been attempting to produce regular
arrangements, and that we have missed them hitherto because our means
of detecting them have been inefficient. The regularity of Nature’s
arrangement is manifested in the visible crystal, but is also to be
discovered elsewhere. It is this regularity which we shall see to be
one of the foundation elements of the success of the new methods of
analysis.
Let us now turn to the consideration of the X-rays. The reason of their
ability to help us at this stage may first be given in general terms.
The X-rays are a form of light, from which they differ in wave length
only. The light waves which are sent out by the sun or an electric
light or a candle and are perceived by our eyes have a narrow range
of magnitude. The length of the longest is about a thirty-thousandth
of an inch, and of the shortest about half as much. These sizes are
well suited to the purpose for which we employ them. Let us remember
that when we see an object we do so by observing the alterations which
the object makes in the light coming from the source and reaching our
eyes by way of the object. Our eyes and brains have attained by long
practice a marvelous skill in detecting and interpreting such changes.
We may be unsuccessful, however, if the object is too small; and this
is not only because a small object necessarily makes a small change in
the light. There is a second and more subtle reason: the _nature_
of the effect is changed when the dimensions of the object are about
the same as the length of the wave, or are still less. Let us imagine
ourselves to be walking on the seashore watching the incoming waves.
We come in the course of our walk to a place where the strength of the
waves is less, and when we look for the reason we observe a reef out
to sea which is sheltering the beach. We have a parallel to an optical
shadow: the distant storm which has raised the waves may be compared
to the sun, the shore on which the waves beat is like the illuminated
earth, and the reef is like a cloud which casts a shadow. The optical
shadow enables us to detect the presence of the cloud, and the silence
on the shore makes us suspect the presence of the reef. Now the
dimensions of the reef are probably much greater than the length of the
wave. If for the reef were substituted a pole planted in the bottom of
the sea and standing out of the surface, the effect would be too small
to observe. This is, of course, obvious. Even, however, if a very large
number of poles were so planted in the sea, so that the effect mounted
up and was as great as that of the reef, the resulting shadow would
tell us nothing about each individual pole. The diameter of the pole is
too small compared with the length of the wave to impress any permanent
characteristic on it; the wave sweeps by and closes up again and there
is an end of it. If, however, the sea were smooth except for a tiny
ripple caused by a breath of wind, each pole could cast a shadow which
would persist for at least a short distance to the lee of the pole. The
width of the ripple is less than the diameter of the pole, and there is
therefore a shadow to each pole.
Just so light waves sweeping over molecules much smaller than
themselves receive no impressions which can be carried to the eye and
brain so as to be perceived as the separate effects of the molecules.
And it is no use trying to overcome our difficulty by any instrumental
aids. The microscope increases our power of perceiving small things:
with its help we may, perhaps, detect objects thousands of times
smaller than we could perceive with the naked eye. But it fails when
we try to see things which are of the same size as the wave length of
light, and no increase in skill of manufacture will carry us further.
But the X-rays are some ten thousand times finer than ordinary light,
and, provided suitable and sensitive substitutes can be found for the
eyes, may enable us to go ten thousand times deeper into the minuteness
of structure. This brings us comfortably to the region of atoms and
molecules, which have dimensions in the various directions of the order
of a hundred-millionth of an inch, and this is also the order of the
wave lengths of X-rays. Broadly speaking, the discovery of X-rays has
increased the keenness of our vision ten thousand times, and we can now
“see” the individual atoms and molecules.
We must now connect the X-rays with the crystal, and again we may first
state the point in a broad way. Although the single molecule can now
affect the X-rays just as in our analogy the single pole can cast a
shadow of the fine ripples, yet the single effect is too minute. In the
crystal, however, there is an enormous number of molecules in regular
array, and it may happen that when a train of X-rays falls upon the
crystal the effects on the various molecules are combined and so become
sensible. Again, we may make use of an analogy. If a single soldier
made some movement with his rifle and bayonet, it might happen that a
flash in the sunlight, caused by the motion, was unobserved a mile away
on account of its small magnitude. But if the soldier was one of a body
of men marching in the same direction in close order, who all did the
same thing at the same time, the combined effect might be easily seen.
The fineness of X-rays makes it possible for each atom or molecule to
have some effect, and the regular arrangement of the crystal adds all
the effects together.
We may now consider more in detail the way in which the properties of
X-rays and crystals are combined in the new method of analysis. The
explanation is, perhaps, a little difficult, and I am trying to state
both what precedes and what follows the explanation in such a manner
that the explanation can be omitted by those who wish to leave it for
a time. It must, however, be mastered sooner or later by everyone who
wishes to make use of the new methods.
We have seen that the atoms and molecules of a crystal are in regular
array, and have even found reasons for expecting them to be so.
Suppose that we stand before the papered wall of a room and consider
the pattern upon it. It is a repetition of some unit (Plate XIV
b). Mark one particular point of the pattern whenever it
occurs; if a real marking is disallowed, a mental marking must suffice.
[Illustration: Fig. 29.--Space lattice.]
It will be found that the marks lie on a diamond- or rhombus-shaped
lattice, and that this lattice has the same form no matter what point
of the pattern has been chosen for the marking. The rhombus will
have different sizes and shapes in different wall-papers, though the
four sides will always be equal or, it may be, the rhombus will be
a rectangle, because no one could endure a wall-paper in which this
was not the case. The whole pattern of marked points may be called a
“lattice.” Each rhombus contains the substance of one whole unit of
pattern with all its details, and no more.
The arrangement in space of the units of the crystal is like the
arrangement on the wall of the unit of the wall-paper design, except
that the plane lattice is replaced by a “space lattice” (Fig. 29).
[Illustration: Fig. 30.--Size and dimensions of the unit cell of the
quartz crystal in hundred-millionths of a centimeter.]
Each little cell of the lattice is bounded by six faces, which are
parallel in pairs. The cell can have any lenghts of side and any
angles; its simplest and most regular form is that of a cube. Each cell
contains a full unit of pattern with all its details, and no more: it
is the crystal unit, which possesses all the qualities of the crystal,
however large the latter may be. In the case of quartz, for example, it
has the special shape that is shown in Fig. 30, and it contains three
molecules of silicon dioxide. This fact is readily determined by X-ray
methods, and also the size and dimensions of the cell, as we shall see;
but it is a far more difficult matter to discover the arrangement of
the atoms and molecules within the cell.
[Illustration: Fig. 31.--An atom group is associated with each point of
a lattice.]
Suppose that we were able to look into a crystal along one of the cell
edges of Fig. 29, and found ourselves able to represent what we saw
in some such way as is shown in Fig. 31. There is a grouping of atoms
associated with each point on the lattice, which grouping we represent
by the entirely imaginary set of circles in the figure. The form of the
grouping is of no account, nor its contents; it may contain any number
of atoms and molecules, but the essential point is that an exactly
similar group is associated with each point on the lattice, as in the
design of the wall-paper. Suppose a train of X-ray waves to strike the
crystal; in Fig. 32, A, they are represented by the line _WW_ and
the parallels to _WW_.
[Illustration: PLATE XIV.
A. Diamond model.
The model shows only the arrangement, and says nothing about the size
or shape of the carbon atom.
B. Wall-paper.
The unit cell is outlined in two ways: (a) by thick lines, (b) by
thin lines. The shape and content of the cell are exactly the same
in the two cases, although the corners of the two cells are chosen
differently.]
When these waves strike the series of groupings strung along
_AA_--each grouping is now represented by a single dot--a new set
of similar waves will start from every grouping, though the wave as a
whole sweeps on, just as a row of posts planted in the sea would each
become the center of a disturbance when a wave passed by.
[Illustration: Fig. 32.--Reflection of X-rays.]
At a little distance from the row _AA_ these minor disturbances
link themselves together in a connected set of waves, represented by
the parallel lines _aa_. The effect is analogous to the reflection
of sound by a row of palings, or by a stretched piece of muslin. In all
cases the bulk of the wave goes on, but there is a reflected wave which
makes with the reflecting layer the same angle as the original waves.
The reflected waves form a simple train, the same as the original as to
wave length, but far weaker, of course: it might be thought that the
reflection would simply be a confused mass of ripples, but it is not
so. Quite close to the groupings there is some apparent confusion, but
a little farther along the track of the reflection the wavelets melt
into the steadily moving train _aa_, etc.
Behind the row of groupings strung along _AA_ there is another,
exactly like the first, which is strung along _BB_ (Fig. 32, B). The
original waves, which experiment shows to be very little impaired by
their passage over _AA_, sweep over _BB_ in turn, and again there is a
reflection represented by the group of parallel lines _bb_. Behind that
there is a row _CC_ forming a _cc_ train, a row _DD_ forming a _dd_
train, and so on.
As a rule the lines _aa_, _bb_, _cc_, do not coincide with one another.
But if the wave length of the rays, the distance between _AA_ and
_BB_ (which are really planes seen edgeways), and the angle at which
the waves meet _AA_, _BB_, are correctly adjusted to each other, then
the lines _aa_, _bb_, etc., do coincide with one another. In actual
practice thousands of reflecting planes come into play, and when the
reflections all fit together in this way exactly, the whole reflection
is strong. If the adjustment is incorrect as it is drawn in the
diagram, the reflections do not add together into a sensible effect;
some throw their crests, or what corresponds to the crests on a water
wave, into the hollows of other waves, and there is mutual interference
and annulment. The adjustment has to be exceedingly exact, because
there are so many reflecting planes, one behind the other. It is easy
to find a formula which expresses the condition for correctness of
adjustment, and therefore for reflection. The line _A'B'B_ must be
longer than _AB_ by a whole number of wave lengths. If λ is the wave
length, _d_ the distance between planes, or spacing, as it is usually
called, and θ the angle shown, then
_n_λ = A'B'B - AB = A'D - AB = DN = 2_d_sinθ,
where _n_ is any whole number.
It is not necessary, as I have stated already, for the reader to go
through the calculation just given, from which the fundamental equation
of the subject is derived.
The essential point is that if the direction of the original rays is
gradually altered with respect to the planes _AA_, _BB_,
etc., there will be _no_ observable reflection until the proper
inclination is reached; when this happens there is a sudden flash of
reflection. The angle of inclination is observed; and when, as is
always the case in crystal analysis, the wave length of the rays is
known, it becomes possible to measure the spacing.
[Illustration: Fig. 33.--The law of reflection of X-rays.]
The reflected rays cannot, of course, be detected by the eye, but they
can make their mark on a photographic plate and be observed in other
ways which need not be considered here. The instrument constructed
for the purpose of the experiment is called an X-ray spectrometer. It
measures the angles at which reflection occurs; and its observations
are used to determine spacings in the first instance, and in the second
the angles between the various planes of the crystal. For instance,
it gives not only the spacings between _AA_, _BB_, but also
between _PP_, _QQ_, (see Fig. 32, B) and the angle between
_AA_ and _PP_. It gives, in fact, the dimensions and form of
the unit cell.
It is, in general, a simple matter to find by experiment the density of
the crystal, and then we can find the weight of the matter contained
in the cell. Since we always know the weight of the molecule, it is
easy to find how many molecules go to the unit; as already stated, it
is always a very small number. Moreover, the observations of the X-ray
spectrometer give us some knowledge of the relative positions of the
molecules that make up the unit of pattern. They would tell us far
more than this if only we knew how to interpret them, but we are too
inexperienced as yet. We have found our Rosetta Stone, but are as yet
only learners of the new language.
The most important point to bear in mind is that the X-rays give us
the distance between any sheet on which the atom groups are spread,
and the next sheet, which is exactly the same as the first, on which,
therefore, another lot of atom groups is spread. This spacing is the
same thing as the distance between two opposite faces of the unit
cell. We can draw the cell in many ways by joining up different corners
of the space lattice. There are not only three spacings to be measured
in the crystal, but in reality any number of them; usually we are
content to determine a few of them.
In a few cases the crystal analysis has already been carried so far
that we know where every atom has its place in the unit of pattern.
To get so far we have made use not only of our X-ray analysis, but
of many facts of chemistry and physics. I shall not describe these
further details in any case; the general explanation I have given above
will serve as a sufficient indication of the methods that have been
followed. But I think we shall be interested in some of the results.
First of all let us take the diamond, which is a prince among crystals.
It is not only a beautiful and valuable gem, but in its structure
it teaches us many things concerning the most fundamental truths of
chemistry, particularly organic chemistry. Only one atom, that of
carbon, goes to the building of the diamond; but that atom is of
vital interest to us. It is a fundamental constituent of foods and
fuels, dyes and explosives, of our own bodies and many other things.
The structure of the diamond is remarkably simple, though, like all
constructions in space, it is difficult to comprehend quickly. We are
so accustomed to drawings on the flat, paper and pencil are so handy,
that our minds easily grasp the details of a plane design. But we
cannot draw in space; we can only construct models at much cost of time
and energy, and so our power of conceiving arrangements in space is
feeble from want of practice. A few have the natural gift, and some,
being crystallographers, have trained themselves to think in three
dimensions. Most of us find a great difficulty in our first efforts to
realize the arrangements of the atoms and molecules of the crystal.
Nevertheless, the diamond structure shown in Plate XIV a will
become clear at the cost of a little consideration. The black balls
represent carbon atoms, in respect to position only, not in any way as
to size and form, of which we know very little. Every carbon atom is
at the center of gravity of four others; these four lie at the corners
of a four-cornered pyramid, or tetrahedron, and the first carbon
atom is, of course, at the same distance from each of them. We have
reason to believe that the ties between the atoms are very strong, and
there is only one form of tie throughout the whole structure. In its
uniform simplicity and regularity we can surely see the reason why the
diamond is placed in the highest class on the scale of hardness. If
it is pressed against any other crystal it is the atoms of the latter
that must give way, not the atoms of the diamond. The diamond has a
cleavage plane. In the figure it is parallel to the plane of the table
on which the model stands; there are four such planes, one parallel to
each face of the four-faced pyramid. The model can be turned over so
as to rest on any one of the four faces, and looks exactly the same
in each position. The distance between the centers of two neighboring
carbons is 1.54 Ångstrom units; this unit is the hundred-millionth of
a centimeter. It does not seem surprising that this particular plane
should be the cleavage plane, because it cuts straight across the
vertical connections between the horizontal layers that appear in the
figure. Each of the layers may be described as a puckered hexagonal
network.
[Illustration: PLATE XV.
(_By courtesy of Joseph Asscher & Cie._)
A. The Cullinan diamond split into three pieces.
It was originally as large as a small fist.
(_By courtesy of Joseph Asscher & Cie._)
B. The table and tools used for splitting the diamond.]
The crystal may, of course, be considered as an arrangement of layers
parallel to any one of the four faces of the tetrahedron, not merely
the face on which the model happens to stand.
The existence of this cleavage is well known to diamond cutters, who
save themselves much labor by taking advantage of it. In the Tower of
London are shown the tools wherewith the great Cullinan diamond was
split during its “cutting.” Plate XV a shows the diamond in
three pieces; and XV b the tools used in splitting it. It is
possible to cleave a diamond in yet another plane, which contains any
one edge of the tetrahedron and is perpendicular to the other edge; but
the operation is difficult and rarely used.
When we consider the diamond construction we cannot but notice the
striking appearance, in every part of the model, of an arrangement of
the carbon atoms in a ring of hexagonal--or six-sided--form. If we take
one of these rings out from the model, it has the appearance of Plate
XVI b, 2: a perfect hexagon when viewed from above, but not a
flat ring.
Now the ring of six carbon atoms has already a famous place in
chemistry. No one has ever seen the ring: it is too small. But the
chemist has inferred its existence by arguments which are most
ingenious and most interesting. Even those of us who are not chemists
may find no great difficulty in acquiring some understanding of them.
For instance, it was well known in the middle of last century that
certain molecules could be formed in which the fundamental structure
consisted of carbon atoms in a row or chain, and that hydrogen atoms
could be attached to the various carbon atoms in such a way that every
carbon atom had four other atoms attached to it. That was known because
the molecule could not be made to take on any more hydrogens: it was
full, or, as the chemists say, “saturated,” because a single carbon
atom is “saturated” when it has four other atoms attached to it, as,
for example, in marsh gas or methane (CH{4}). The relative
number of carbons and hydrogens was exactly what would be expected
on this hypothesis. With six carbon atoms there ought to be fourteen
hydrogen atoms, as the diagram shows, and this is found by experiment
to be the case. These substances are called the “paraffins” (see the
latter part of the next chapter), the various members of the series
having different numbers of carbons in the chain. The particular
substance shown in the figure is called hexane.
Now in 1825 Faraday isolated a certain substance from the residue found
in gas retorts, which he called bicarburet of hydrogen; it is now known
as benzene. A few drops of Faraday’s first preparation are preserved as
an historical treasure in the Royal Institution.
[Illustration: Fig. 34.--Hexane.]
The molecule of this substance contains six carbon like hexane, and
six hydrogen atoms. It can be made to take on six more hydrogen
atoms, twelve in all, but no more, and the new molecule then behaves
chemically like hexane in respect to most of its properties. But it
cannot have the same structure as hexane, because it has two hydrogen
atoms less. The riddle was solved in 1867 by Kekulé, who suggested that
the framework of benzene is a ring, not a chain, of six carbon atoms;
we may think of it as derived from the chain of Fig. 34 by the removal
of the two hydrogen atoms at the ends and a bending of the chain round
until the two ends meet and are joined up. We then have the structure
shown in Fig. 35. Its chemical name is hexahydrobenzene. Benzene
itself has only one hydrogen at each corner of the hexagon.
[Illustration: Fig. 35.--Hexahydrobenzene.]
The carbon chain and the carbon ring are the foundations of the two
great divisions of organic chemistry. Chain molecules are found not
only in the paraffins, but in fats, oils, soaps, and many other
important groups of substances. The ring is the basis of many thousands
of known molecules, including dyes and explosives, drugs such as
quinine and saccharine, and so on.
The conception of the closed hexagonal ring leads at once to a
simple and beautiful explanation of a number of remarkable chemical
observations, of which we will consider one example. The benzene
molecule consists of the hexagonal ring of carbon atoms, with one
hydrogen at each corner. Each carbon atom has only three neighbors in
this molecule: it can take on a fourth, so that on the whole there
is room for six more atoms or groups of atoms, to be tied on at the
corners, and these can be added. But the benzene molecule can exist
contentedly enough without them.
[Illustration: PLATE XVI.
A. The layers of the graphite crystal.
(_a_) and (_c_) are similar in all respects, but (_b_)
is like (_a_) when turned round through two right angles in its
own plane about any such vertical line as is drawn in the figure.
B. Possible forms of the benzene ring (see p. 164).
No hydrogens are shown.]
Taking the benzene molecule as it is, chemists find that they have
the power to alter its constitution, pulling off one or more of the
hydrogen atoms, and substituting other atoms or groups of atoms. In
a well-known and important case, a single hydrogen is removed and
replaced by a group consisting of one carbon and three hydrogen atoms,
known as the methyl group.
[Illustration: Fig. 36.--Toluene.]
The new molecule has the structure shown in Fig. 36, and is known as
toluene, a very important substance, a liquid at ordinary temperature.
A second hydrogen can be removed from the ring molecule and replaced,
let us say, by an atom of bromine; the new substance is known as
bromotoluene. It is very remarkable that when this has been done three
different substances are obtained, all having the same composition,
_viz._, the six carbon atoms, four hydrogen atoms, one bromine
atom, and one methyl group which we will presume remains intact. How
are we to explain the existence of these three, endowed with different
properties, yet all having the same constitution? The ring hypothesis
gives an immediate answer. There are three ways and no more of making
the substitutions, which are shown in the figure. The bromine atom may
be next to the methyl group, or next but one, or next but two.
[Illustration: Fig. 37.--Bromotoluene.]
The three molecules have different shapes, and therefore may be
expected to have different properties; and there is no doubt that
there are actually the three different substances. Chemists have even
been able to tell which is which. Many other similar examples could be
given, but this one will suffice as an illustration of the significance
of position as well as of composition, the three molecules differing
only in the relative positions of the two things substituted. The
methods of X-ray analysis are peculiarly fitted to deal with such
differences as these, because they measure the dimensions of the unit
of pattern into which two or more molecules are packed, and can detect
the effects of altering the _shape_ of the molecule. A little work
of this kind has already been done.
It is very interesting to observe that in the case of chain molecules
the number of carbon atoms is found to vary within wide limits;
butyric acid, the substance characteristic of rancid butter, contains
four carbon atoms, while palmitic acid, found in palm oil and other
places, contains sixteen (see the latter part of the next chapter).
On the other hand, the ring molecule of six carbon atoms occurs far
more frequently than any other. It must be the easiest to form and the
strongest in construction. Now the diamond, the only crystal, except
graphite, which consists of carbon atoms only, is full of hexagonal
rings. It is natural to suppose that the reason for the ring of six is
to be found in the diamond structure. But the basis of the latter is
simply the principle according to which each carbon atom is surrounded
by four others symmetrically arranged round about it. The two lines
which join a carbon atom to two of its neighbors are inclined to each
other at an angle readily calculated to be 109° 28'. If in certain
circumstances it is the rule that the junction of two carbon atoms with
a third must always be made so as to show this angle, see Fig. 50, then
the shortest ring that will close up contains six carbon atoms. (A
model may be made to illustrate the point. Wooden balls of sufficiently
regular form can be obtained in large numbers, being used in the
manufacture of large buttons. Four holes are drilled at the proper
places on each ball, and gramophone needles are used as connections.
Models of diamond, and many forms of ring and chain molecules, can
then be put together.) Five carbon atoms in one plane nearly make a
ring, because the angle of a pentagon is 108°. But if the angle is to
be 109° 28' it is necessary to take six, and to arrange them in the
puckered form of Fig. XVI b, 2. Whether the benzene ring is
actually puckered under all circumstances, or is sometimes flat, in
which case the angle is 120° (Plate XVI b, 1), or even has the
shape shown in Plate XVI b, 3, which is another form based
on the tetrahedral angle, we find it difficult at present to say with
any certainty. Experimental evidence is accumulating, but is not yet
decisive as to this particular point; perhaps all three forms occur.
Meanwhile, many facts emerge in the course of the work which are
definite and very interesting.
The remarkable substance graphite is, like diamond, composed of carbon
atoms only. It is much lighter, its density being 2.30 nearly; the
density of diamond is 3.52. Clearly, some rearrangement of the atoms
has taken place in which the spacings between the atoms have on the
average materially increased. The X-rays show that the increase has
taken place entirely in one direction. There are layers in graphite as
in the diamond structure (Plate XVI a). To one looking down
on a layer from above it presents the same appearance of a hexagonal
network; and moreover the side of the hexagon is almost exactly the
same in length. But the distance between layer and layer has been
greatly increased, and it is this change which has made the substance
so much lighter. Recent experiments seem to show that the layers have
been flattened out, so that each carbon is now surrounded by three
atoms in its own plane. If the ties between the atoms in each layer
have altered at all, they have at least not lost in strength; on the
other hand, the ties between layer and layer are greatly weakened. For
these reasons the layers slide over one another very easily, and at the
same time each layer is tough in itself. It is the existence of these
two conditions that makes graphite so good a lubricant; not only is the
readiness to slip of importance, but also the fact that the layer does
not easily break up into powder. When one slips on the black-leaded
hearthstone, some of the layers are clinging to the stone and some to
the sole of one’s boot; it is these layers that slide on one another.
It is very curious that a single change--whose real nature is, however,
a mystery--should convert the substance which is chosen as the type of
hardness into one of the most efficient lubricators we possess.
Another set of facts which also supports the idea that the ring is a
real thing, having dimensions which can be measured and allowed for,
is to be found in the comparison of two crystals, naphthalene and
anthracene. These substances are of the greatest importance in the
dye industry, the former being used in the manufacture of artificial
indigo, the latter in the manufacture of alizarin, which is the active
constituent of madder.
[Illustration: Fig. 38.--Naphthalene and anthracene.]
Naphthalene is a common substance; to most of us it is no doubt
familiar in the form of the white, strongly smelling balls which we
put into drawers to keep the moth away. If naphthalene is dissolved
in ether, and the solution allowed to dry off gradually, the crystals
are readily formed. In general appearance they resemble the crystals
illustrated in Plate XIII d.
The chemist finds that naphthalene consist of a double benzene ring
which we draw as in Fig. 38, A; anthracene is based on a treble ring,
Fig. 38, B. When crystals of the two substances are subjected to X-ray
analysis, it is found that the unit of pattern contains two molecules
and that the shape of the cell which contains the unit is as shown in
Fig. 39. The dimensions of the cells are given below the figures. If
the two cells are compared with each other, it is noteworthy that along
two of the edges the cells are very nearly the same size, but that
there is a great difference in respect to the third.
[Illustration: Fig. 39.--Unit cells of naphthalene and anthracene,
drawn to the same scale. Figures in Ångstrom units: see p. 156.
OA OB OC
Naphthalene 8.34 6.05 8.69
Anthracene 8.58 6.02 11.18]
The natural inference is that the double and treble ring molecules
lie parallel to _OC_ in the two cases, and that the difference
between 11.18 and 8.69 is to be ascribed to the extra length of the
molecule. The anthracene contains one more ring than diamond, which
gives it the extra length, 2.49. Now if we measure the width of the
ring as it occurs in diamond, it is found to be 2.50. Thus we again
find support for the view that the ring has a definite form, and
nearly constant dimensions; so that we have something to guide us in
trying to discover the structure of a crystal of which the ring forms
part. The X-rays tell us the size and form of the unit cell, and how
many molecules it contains, as well as certain information about the
relative positions of the molecules. If we know the size, more or less
accurately, of the ring or rings which form part of the molecule, we
can set out on the investigation of the structure, knowing that bodies
of definite dimensions have to be fitted into cells of definite shape.
Work of this kind is extraordinarily interesting, since it gives us new
knowledge of the arrangements of the atoms in the organic molecules
and of the forces that bind the atoms in the molecule and the molecule
in the crystal. It is a new field of inquiry, in which some results
are definite and clear, others more obscure and difficult to interpret
until greater experience has been obtained.
The organic molecule appears to us so far as a light rigid framework,
in itself tightly held together, but weakly joined to its neighbors in
the crystal. Organic substances are nearly always light, not very much
heavier than water. The fact that the density of naphthalene is only
1.15 shows the emptiness of its structure. Even the diamond is full
of holes, like a sponge. If the holes were filled up by other carbon
atoms, the density of the diamond would be doubled, for each hole is
just large enough to take one more carbon atom, and there are as many
holes as there are atoms.
[Illustration: Fig. 40.--Showing mutual relations of three naphthalene
molecules and parts of others.]
The weakness of the bonds that join molecule to molecule is the cause
of the softness of the organic crystal and of the ease with which
it can be melted. For the same reason naphthalene “sublimes”: it
evaporates while in the solid state. Whole molecules are flung off
from the solid, and form a vapor which may crystallize again in a
cooler part of the containing vessel.
Naphthalene and anthracene are flaky in structure: they have, as it is
said, a well-developed cleavage. The dotted lines show the cleavage
plane; clearly the molecules break away from one another more easily at
the ends than at the sides. In each flake the molecules stand nearly
upright, like corn leaning over in the wind.
The general conclusion to which we are led by these considerations is
that the “benzene ring” is a real material object of definite form
and dimension, which is built into crystalline structures with little
alteration of form. We must now go on to consider the “chain” molecule:
the basis of as great a section of organic chemistry as that which
rests on the ring. As this chapter is already long enough, we can
consider the chain in our next chapter, in addition to the ice crystal,
which will be our main subject.
CHAPTER V
_The Nature of Crystals: Ice and Snow_
WHEN we look round to see what crystals we shall examine by our new
X-ray analysis, the crystals of ice and snow at once strike our
imagination. Water is one of the most obvious substances in the world:
it affects our lives in numberless ways and we are interested in all
the forms which it can assume. And again, from a scientific point of
view we should like to discover the structure built with so simple a
molecule, one oxygen and two hydrogens, and we might find that it was
within our power to do so. But there is one very compelling reason
in the beauty of the snow crystal, with its tracery so delicate and
finished, and of the frost crystals on the windowpane, so quaint and
charming in their outline. It is true that the blocks of ice that come
from the freezing works are not remarkable for grace of outline, though
there is a fascination in watching them slither across the pavement at
the end of the ice-man’s pincers.
[Illustration: PLATE XVII.
(By courtesy of the Chief of the U.S.A. Weather Bureau.)
Snow crystals of various forms.
(From Monthly Weather Review, U.S.A.)]
The manufacture of commercial ice is too rapid to bring out the ice
design: the crystalline structure is there, but the mass contains a
multitude of tiny invisible crystals oriented in all directions, and is
full of bubbles and sheets of air.
If we are to see what Nature will do if left to work out her design
in peace, we must examine the snowflakes that fall in a hard northern
winter. In England, we do not see the best crystals: it is not cold
enough. Observers in other countries such as Sweden and America have
many exquisite drawings, which are to be found scattered through
physical and meteorological publications. Some of them are reproduced
in Plates XVII and XVIII.
We can imagine the way in which the snowflakes grow. One or two
molecules of water become associated in the upper air; molecule after
molecule adds itself to the growing, falling crystal, filling out the
details of the pattern until at last the six-pointed snowflake rests
gently on the ground. If the weather is cold the flake may continue to
grow in the same way, and the crystals develop perfect little facets,
which glitter like diamonds in the sunshine. When the snow crystal
first forms, it is very often feathery; the six arms grow outward
and other little arms grow out from each of them to right and left,
and from these yet smaller arms, and so on, all the arms joining one
another at the angle of 60°, so that the whole is like a six-pointed
star of fine lace. These feathery forms are peculiar to the early stage
of crystallization, and seem to be the consequence of sudden and rapid
freezing. The arms stretch out from the center because they have used
up the nearer molecules that are ready to join up into the structure,
and they must stretch out into new fields. This effect is often found
in other cases of rapid crystallization; a notable example is the
formation of skeleton crystals of iron in the crucible of molten and
cooling metal. If they are to be preserved, the rest of the liquid must
be poured off before the crystal has had time to fill up vacant spaces.
They are called “dendrites,” because they look something like trees,
with trunks, big branches, small branches, and so on, but the angle at
which two branches of an iron crystal join together is a right angle,
not 60°, and the form is far from being as graceful as that of ice.
[Illustration: PLATE XVIII.
(By courtesy of the Dept. of Scientific Research of the Admiralty.)
A. Snow crystals. (From the Monthly Weather Bureau. U.S.A.)
B. Ice flowers growing on the ice floes. C. Bundle of irregular prisms.
(From “The British Antarctic Expedition, 1910-1913.”)]
When the snow crystal has had time to grow, and there is an available
supply of molecules, the gaps fill up, and the crystal becomes a
hexagonal plate (Plate XVII b).
[Illustration: Fig. 41.
The hexagon represents a magnified section of an ice prism. _ABCD_
is a ray passing through it.]
Sometimes, it is supposed, the plates grow in that form from the
beginning. Strange to say, these plates are often connected in pairs
by a hexagonal prism; one plate is generally larger than the other,
and the whole is like a fairy tea-table (Plate XVIII a). The
prism appears also in the curious formations of Plate XVIII c,
which is taken from Wright and Priestley’s _Glaciology_, British
Antarctic Expedition, 1910-1913.
The prisms and plates and “tea-tables” are believed to be the cause of
the mock suns and halos that are observed in high latitudes (Plate XIX).
Suppose that the hexagon in Fig. 41 represents a section of one of
these prisms or plates, and let _ABCD_ be the path of a ray of
light going through it. It is refracted at the points _B_ and
_C_; the ray is on the whole bent through an angle of at least
21° 50', which is, in the language of physics, the angle of minimum
deviation.
[Illustration: Fig. 42.--Shows how the ice halo is formed. For a
description see the text.]
If in Fig. 42 _S_ be a source of light and _E_ the eye, a ray from _S_
is bent in going through _P_, and will enter the eye if _F_ is properly
placed. In the figure the prism is placed symmetrically, in which case
it is known that the deviation _SPE_ has its minimum value. Any prism
lying between _SPE_ and _SP'E_, such as _P{0}_, will bend the ray from
_S_ in such a direction that it cannot possibly get to the eye, no
matter how the prism is placed. The eye cannot receive a refracted ray
from any such prism.
[Illustration: PLATE XIX.
The first picture is due to Mr. G. A. Clarke, and is taken from Mr. F.
J. Whipple’s article on Meteorological Optics in the “Dictionary of
Applied Physics,” Vol. III., p. 529 (by courtesy of Messrs. Macmillan
& Co.). It shows a halo and mock suns. The second picture is from an
interesting original sketch in the possession of the Royal Institution:
it shows the halo and the “sun-pillar.”]
A prism _P{1}_ may send light to the eye, if it has an
unsymmetrical position, as the figure shows; the angle of deviation
has to be more than the minimum, and that is why the prism must be
crookedly placed, as in the figure. If, therefore, an observer at
_E_ stands facing the sun at _S_, light will be seen to come
from the directions _PE_ and _P'E_, and also other directions
outside; but the latter will be relatively feeble, because most of
the deviations are not far from the minimum value--the farther they
are from it, the fewer they are, in accordance with a known law of
maximum or minimum values. Also there is no light at all from within
_PEP'_, and the consequence is that the strong light of the
minimum deviations is the more sharply defined.
This applies to rays coming from all directions round the sun; and so,
on the whole, the observer must see a ring round the sun, sharp on
the inside, rather more diffuse on the outer. For red light the angle
_PEP'_ is rather smaller than for blue, so that the halo is not
quite white, but is colored, red on the inside, blue on the outside.
The halo is observed if there are enough ice prisms in the air, just
as a rainbow is seen if there is a sufficiently large number of drops
of rain. When a ray of light goes into a raindrop and out again it is
bent through an angle of more than two right angles, so that to see a
rainbow one must have the sun at one’s back.
A little model may help to make this explanation clearer. The arc-lamp
at _S_ in the figure is the source, the eye is at _E_. Between _S_ and
_E_ is a stand on which an arm is mounted; the latter carries a glass
prism. The dimensions of the model are so adjusted that a ray of light
refracted by the prism falls on _E_. If the arm swings round _J_, the
eye continues to be illuminated. If there were prisms all around the
circle, the eye would see a circle of light round the central spot.
If for any reason the prisms tended to set themselves in certain
positions only, the halo would be incomplete. Something of this kind
actually happens. When a long prism falls through the air, the axis
tends to set itself horizontally. If, however, it has the tables at
the ends, as shown in Plate XVIII a, or if it is simply a
hexagonal table which may be considered as a very short prism, its
axis tends to become vertical, or, in other words, the table itself to
become horizontal.
[Illustration: Fig. 43.--Model showing the formation of the ice halo.
_S_, _J_, _E_ should be in the same straight line.]
This rather strange effect is in accordance with a well-known rule
concerning the movement of bodies through gases or liquids. They tend
to set themselves so as to offer as much opposition to the motion as
possible. If we make a packet of two or three letters or postcards, and
drop them from a height, holding them horizontally and taking the hand
quickly from underneath, they remain level throughout the fall. But if
we let them fall edge first, they subsequently turn over and over. When
we drop a white plate into the water, we see it swaying from side to
side, but always tending to the horizontal position. The consequence is
that the falling shower of ice crystals contains an undue proportion
of vertical and horizontal crystals. Those parts of the halo which lie
at the ends of the horizontal and vertical diameters are emphasized,
and are like bright spots on the ring; they are often spoken of as mock
suns.
It is easy to show the tendency of the “tea-table” forms to become
vertical as they fall. We make a number of models of ebonite and allow
them to fall in a tall jar full of water. A very tall jar is the
best, but even if the depth is not more than eighteen inches or so the
tendency is quite obvious.
[Illustration: Fig. 44.--Flat disks, and prisms some of which end in
disks falling through water in a tall jar.]
Curiously enough, some of the bodies tend to fall with the plate
leading the way, and some with the plate in the rear. The point was
examined mathematically by Besson, who showed that when the diameter
of the plate is small compared with the length of the prism, the plate
tends to go first, and vice versa. We can prove this by experiment; it
is best to hold the axis horizontally under the surface of the water
and then let go.
The whole of the vertical line through the center of the halo is often
illuminated also, but this is due to a different reason altogether; it
is caused by reflection at the flat surfaces of the snow crystals and
plates. Consequently the observer receives reflections of the sun from
snowflakes at all altitudes, but they must all lie in a vertical plane
through the sun. The bright vertical line is called a “sun-pillar.”
Ice when it forms quietly on a water surface exposed to the sky
crystallizes in a form analogous to that of the snow crystal, all the
six-sided figures being horizontal. That it does so is not generally
very obvious, though in books of Arctic exploration pictures are to be
found of table ice breaking up into six-sided vertical columns, like
the basalt columns of the Giant’s Causeway. It is also said that when
the ice on a lake breaks up, it first divides into vertical columns,
which for a time hold one another up; when, however, the ice begins to
move, the collapse is rapid and the lake clears quickly.
In the accounts given by Antarctic explorers, it is especially
mentioned that the ice on fresh-water lakes was found to be divided
into six-sided prisms, all standing upright on the surface. The planes
of separation were marked by lines of air bubbles. On the sea ice the
formation of the crystals led to an expulsion of the salt which was
deposited in the spaces between the crystals, and sometimes squeezed
out above the top surface. The prisms were nearly free from salt
inside, and fairly fresh water could be obtained if the outside layers
were first melted off. They were clear crystals, through which an
observer might look at the rocks underneath as through tubes.
There is a very beautiful way of observing the crystalline structure of
ice, which is described by Tyndall in his book on _Heat_.
[Illustration: Fig. 45.]
A slab of clear ice is placed in the rays from an arc-lamp and is
focused on the screen, as in Fig. 45. The heat of the lantern begins to
“undo” the crystals, which come to pieces in the order inverse to that
in which they were put together. Little six-rayed cavities appear and
grow, looking like flowers of six petals, and other cavities having a
fern-like form in which the fronds are inclined to the stem at an angle
of 60°. Soon the whole screen is covered with these “flowers of ice,”
as they are called; it looks like a beautiful carving in low relief.
[Illustration: Fig. 45 a.--This illustration of the “flowers
of ice” is taken from the original sketch in Tyndall’s _Heat_.
It represents a certain stage in the growth of the flowers; at a
later stage the whole screen is covered with interlacing figures.]
The ordinary commercial ice does not show the effect; there is a
specially prepared “plate ice” which is fairly satisfactory. But the
natural ice that is formed in the open at nighttime is far better than
anything frozen under the usual conditions of ice manufacture. Many
disappointing trials were made to prepare a satisfactory experiment.
After all, there was a kindly frost one night, and the next day a young
enthusiast rode out on his bicycle and collected from a pond a number
of pieces which showed the effect splendidly. It is clearly essential
that the ice should grow quietly; probably it is also a condition that
the water should lose heat quietly at one face, as the water of a pond
does on a still, frosty night.
A little black spot often appears in the center of the ice flower.
Tyndall was greatly interested in it, and explained its occurrence.
When the ice melts within the block and a cavity is formed, the water
due to the melting occupies less volume than the ice from which it
came. Perhaps it holds together at first in a highly strained condition
and fills as water the space it filled as ice. But if so the strain
must be very great; it breaks away from the ice and shrinks to its
natural volume. A vacuum is left, which acts as a tiny lens and
diffuses the light that crosses it. Hence the black spot, which implies
the absence of light going straight through the cavity.
The ice flowers can be seen in glacier ice, where they are produced
by the heat of the sun. When a glacier is formed by the contributions
of ice from tributary glaciers or from blocks that have fallen in on
the sides, the mass may consist of a pile of ice masses all frozen
together, each of them showing ice flowers. The orientation of the
flowers shows in each case the original lie of the block, for they
are always formed in planes which were once horizontal. In the figure
(Plate XX a), taken from an old volume by Agassiz, a section
of glacier ice shows well the various positions of the cavities--some
in full view, some on edge, and some in intermediate position.
Let us now turn to the analysis of the structure of the ice crystal
which X-rays have made possible. We must hope to find in it some
explanation for its form and other physical properties which we have
been considering. It turns out that the structure is something like
that of diamond: there is the same symmetrical arrangement of four
neighbors of like kind round every atom. In this case, it is the oxygen
atom that stands at the center of a tetrahedron, four other oxygen
atoms lying at the four corners. There are, however, certain minor
differences of structure. In the first place, in diamond the carbon
atoms join on to one another. In ice there are the hydrogens to be
placed. If we put one hydrogen between each pair of oxygens we shall
have a symmetrical arrangement in which the atoms are in the proper
numerical proportion. Every oxygen has four hydrogen neighbors, and
every hydrogen has two oxygen neighbors, which implies that there are
twice as many hydrogens as oxygens. A model showing the arrangement
under these conditions is illustrated in Plate XX b, c. The large balls
represent oxygen, the small represent hydrogen. It must be clearly
understood that the X-ray methods do not measure the size of the oxygen
atom, or of the hydrogen. All that they do is to find the distance
between the center of one oxygen and the center of an oxygen neighbor,
a distance which is the sum of the diameters of oxygen and hydrogen.
The oxygen atom may take ah the room, and the hydrogen none, because
the hydrogen atom is supposed to hand over its electrons to the oxygen
and be left a bare nucleus. No one can say how its size should then be
represented. In making a model we must adopt some sizes for the balls
which represent the atoms, and the model must be interpreted with the
corresponding reservation.
There is a second point of difference between diamond and ice which is
subtler and more difficult to realize; but it is worth while trying to
understand it. If the reader finds it too difficult to grasp, he may
leave it out without any fear of losing the thread of the story.
Suppose that we are looking down on the diamond model from above, and
we see a single puckered layer, as in Fig. 46, A. The carbon atoms are
marked as 1, if they lie directly on the base of the crystal, and as
1' if they are atoms which are somewhat raised above their neighbors
in the layer. Take another layer exactly like the first, and write 2
everywhere instead of 1, and place it on the first, so that each 2
comes over a 1'--that is to say, an atom in the lower level of the
second layer comes over an atom in the higher level of the first.
[Illustration: PLATE XX.
A. This is due to Agassiz. It shows that the mass of glacier ice is an
agglomeration of smaller blocks in which, when first laid down, the
ice flowers would be in a horizontal plane. The blocks have now been
heaved into various positions, and the flowers are seen some edgeways,
some in full face, and in various other positions. B. The model is made
of balls of two colours, the white representing oxygens and the black
hydrogens. C. A smaller section of the ice model, showing the grouping
of the oxygens and hydrogens.]
[Illustration: Fig. 46.--Arrangement of atoms in ice structure.]
This is what happens in diamond. The combination is shown in Fig. 46,
B, where 1'2 means that the atom 2 lies over the atom 1'. Now take a
third layer, which we may denote by using 3's, and lay this so that 3
comes over 2'. We then get the arrangement of Fig. 46, C, and when this
is repeated over and over again, in the same order 1 2 3 1 2 3, we get
the diamond structure.
If now we begin again with a layer of 1's, but take as the arrangement
of a layer of 2's that which is shown in Fig. 46, D--which, it must
be carefully observed, is not the same as before; the layer of 2's
has been turned round in its own plane through 180°--we then repeat
the first layer, and alternately have 1 and 2. This gives us the
arrangement of the oxygens in ice. The structure is complete when we
place a hydrogen between each pair of oxygens.
If we look at the picture of the ice model shown in Plate XX
b, we may be able to realize the arrangement. Why one crystal
should repeat continually a series of three layers, and the other of
only two, we cannot imagine.
If we now look at the model of the ice structure we can see in it
many interesting features which help to explain what we know of the
properties of ice. The hexagonal structure is there, of course, and
the emptiness of the model is surely connected with the lightness of
ice and the featheriness of snow. Ice floats on water; we can see that
the molecules of water when they join up in the crystal structure must
take up more room than before. We could obviously crush the model
together into a smaller space, and that is, no doubt, what happens
when ice melts under pressure. There is a well-known experiment which
illustrates the point. A block of ice is supported at its ends, and a
fine wire carrying heavy weights is slung over it, as shown in Fig. 47.
[Illustration: Fig. 47.--Wire cutting through ice (from Tyndall).]
The wire proceeds to sink slowly into the ice, but as it does so the
ice closes up behind it, and when, finally, the wire makes its way
right through the block and drops, with the weights, on the floor,
the block is still whole. It would seem that the pressure of the wire
on the block breaks down the structure of the ice, and some of the
molecules are set free. In other words, a certain quantity of ice is
melted under pressure and becomes water, which is squeezed out from
under the wire and slips round to the vacant space above it. There
it joins up again with the ice on either side. We can imagine the
molecules as settling into their places, because on either side there
is crystalline ice holding out hands to them.
[Illustration: Fig. 48.--Ice molds and the making of a cup (from
Tyndall).]
Crushed ice can be molded under great pressure into various shapes. We
may, for instance, make a crystal cup: we need two or three boxwood
molds of the proper shape. In one we can form the upper portion of the
cup, in another the stem, and in yet another the foot; then we join
them together into one piece by holding them into position for a few
moments. The molds we use in making the cup shown in Fig. 48 were once
used by Tyndall for the same purpose.
When Tyndall showed these experiments he was proposing a theory of
the movement of glaciers, and employed them as an illustration of
his arguments. Tyndall, we may remember, devoted a great deal of
time to the measurement of glacier movements: he was interested in
them both from the scientific point of view and from his devotion to
mountaineering.
Glaciers descend from the snow-covered mountains, glide along the
valleys, and pour out into the plains almost as if they were fluid:
a very viscous, treacly fluid, because the motion is so slow--a few
inches a day or even less in some cases, many feet a day in others.
That which has always excited wonder and interest is the stateliness
of the motion, and the strange way in which a substance so brittle
and crystalline can flow like a river, can move round the corners of
a valley, or fall over a cliff and yet remain whole. In Tyndall’s
time much consideration was given to a theory which supposed that the
glacier melted internally in places where the strain was great, and
that the water thus formed slipped away, relieving the pressure. It
would freeze again, it was said, if it made its way into empty cracks
or spaces where there was no longer the pressure required to keep it
molten. Thus the glacier would, in a way, contract where compressed and
expand elsewhere, and so accommodate itself to its bed. The explanation
seems to offer difficulties when we think of the glaciers in the Arctic
or Antarctic which also flow, though the temperature is so low that no
conceivable pressure would bring about any melting.
It is possible that when we look a little more closely into the
behavior of a crystalline structure we shall find another way of
conceiving how the motion takes place: not so very different in reality
from the view that Tyndall maintained, but not so open to criticism.
There are many substances that can be made to flow like a glacier:
metals can be squirted through holes; wires can be drawn; plates can
be rolled. Even the surface of glass, or of a perfect crystal such as
Iceland spar, can be made to “flow,” as Sir George Beilby has shown.
Now all these things are crystalline; if we did not know it before,
the X-rays have emphasized the fact for us. And they are just as
crystalline after the flow as before. We shall see some examples when
we come to speak of the metals. The substance accommodates itself
to pressure, changing its shape as it does so. Whole layers of atoms
or molecules are momentarily uprooted from their places, ride over
the tops--so to speak--of the atoms on which they lie, and settle
down into a new position, or perhaps are kept on the move for some
time. When they settle down again for a moment the crystal is perfect
once more, and when they are uprooted, the bonds are broken as if
the substance was going to melt. This must be especially the case
when, as in ice, the substance contracts on melting, when the bonds,
breaking under pressure, let the atoms and molecules take up positions
in which less space is occupied than before. When a piece of metal is
bent or squeezed into a new form, the crystals of which it is made,
whether few or many, are “sheared”--that is to say, one part slides
on another part; and we can understand how many successive “shears”
can bring about any change of shape. So it may be in the case of ice:
both shearing and melting may be called into play during the change of
shape. The “shearing” of ice has often been observed. A block of ice
is cut from the ice that has formed naturally on the surface of the
water. If such a block is supported at its ends, and lies in the same
position which it had when it grew, it bends under a weight, just as a
beam would (Fig. 49, A).
[Illustration: Fig. 49.--A set of planks arranged as in A would bend
under a weight. Set up on edge as in B, they would bend far less. If
arranged as in C, stuck together by some very viscous substance, they
would yield gradually and continuously.]
If it is turned on its edge and placed so that the layers which were
horizontal are now vertical, and their plane is parallel to the line
joining the supports (Fig. 49, B), then the block yields very little
indeed. If the planes that were horizontal are perpendicular to the
line joining the support, they slide one on another, and the ice block
is altered in shape (Fig. 49, C). If under pressure and local melting a
few molecules are set sufficiently free to move as a liquid into a new
place, they will, as in the case of the wire, readily join on to the
ice structure on either side, simply because a place is always waiting
for them. But we can look on the effect in the general sense as due to
the movement of the planes over one another.
It is curious to see with what readiness pieces of ice join together.
If we rest one fairly flat piece on another for a few moments, we can,
keeping hold of the latter piece, turn the pair upside down, and the
added piece does not fall. When two pieces of ice are held together
under water, even warm water, they join together.
We may now go back to the consideration of the peculiar chain molecules
of carbon atoms which we referred to in the previous chapter. When
we considered the structure of the diamond, we saw that there was a
certain arrangement of the carbon atoms which was found everywhere
within it. It was an arrangement of six atoms in the form of a ring.
We saw that a similar arrangement formed the basis of the so-called
benzene ring, which is a molecule formed by fringing the six-sided
carbon ring with six hydrogen atoms; and that a very large number
of other important molecules were founded on the same arrangement,
the hydrogen atoms being replaced by various other atoms or groups of
atoms. The study of these molecules is the purpose of one of the great
branches of organic chemistry. The molecules form substances which are
called “aromatic,” because many of them have a fragrant smell.
There is a second great branch of organic chemistry, which deals with
substances of a different kind. They are called “aliphatic,” the word
implying that they are well represented by oils and fats. The chemist
has been able to prove that in this case the molecule is formed of a
chain of carbon atoms, to which various atoms, particularly hydrogens,
may be attached along its length and its end. The ring was obvious in
the diamond structure. It seems, from recent experiments, that we may
find the chain also in the diamond; so that the diamond contains the
essentials of both the great branches.
We considered a few examples of the ring in the last chapter, but left
the chain until now. The chain is formed of any number of links,
each of which, in general, is made out of one atom of carbon and
two atoms of hydrogen; and the ends are formed of various groups of
atoms, of which some are very common and give to the chain well-known
characteristics. In the simplest case the ends are formed of hydrogen
atoms, and we have then the hydrocarbon or paraffin molecule. The
symbol of pentane, for example, is written by the chemist as follows:
[Illustration]
Pentane is an inflammable liquid used in standard lamps--that is to
say, lamps which serve as a standard of comparison for other lamps,
because they burn with a steady and constant flame. The diagram is
intended to represent the way in which the various atoms are attached
to one another. Each carbon is joined to four other atoms. The carbon
atom cannot link up closely to more than four, so that the molecule
cannot be added to without first breaking it somewhere. It is said to
be saturated. In the diagram it is represented as lying altogether in
one plane, partly because of convenience of drawing, partly because
so little is known of its actual arrangement. One of the objects of
the X-ray analysis is to determine the relative positions of the atoms
in a molecule more accurately than has been possible hitherto, and
to measure the linear dimensions. In the case of these long-chain
molecules, the X-rays have recently had an unexpected success. In
order to express this additional knowledge, we really need a model or
a sketch in perspective; a model of the probable form of the pentane
molecule is shown in Plate XXI a.
Many members of the paraffin series are found mixed together in
petroleum wells. They are inflammable, because they readily break up
under the proper stimulus in the presence of oxygen, and the atoms
rush into fresh combinations, developing great heat in doing so. The
shortest member of the series contains only one link. It is a gas,
called methane or marsh gas, represented thus:
[Illustration]
It bubbles up from stagnant water containing vegetable matter in
decay. As the chain grows longer, the substance holds together better.
Pentane, with five links, is a liquid at ordinary temperatures and
boils at 36° C.; pentadecane, with fifteen links, boils at 257° C.,
while pentacosane, with twenty-five links, is solid at ordinary
temperatures and melts at 54° C. The long molecules are supposed to
have a tendency to lie side by side, like matches in a box; we shall
see that this view is strongly supported by the X-ray results. It may,
therefore, be expected that the longer they are, the greater the forces
required to tear them apart; so that for this reason alone the longer
the chain the higher its boiling point and melting point. As a class
they have no strong hold on one another: the boiling and melting points
are low. The cloak of hydrogens with which they are covered seems to
hinder their association with other molecules such as those of acids.
In fact, the word paraffin is derived from two Latin words meaning
“little” and “affinity.” But, as I have already said, they join up very
readily with oxygen under the proper circumstances.
The behavior of these chains is greatly altered if we take off an end
group and put on a different one. By substituting for one of the end
hydrogens a certain group, containing a carbon, two oxygens, and a
hydrogen, we get another highly important series of compounds called
the “fatty acids.” The group is known as the carboxyl group. Here again
the chain may be of any length.
[Illustration]
When there is only one carbon in it, the chemist represents it thus:
meaning that of the four bonds which carbon can exert, drawing four
other atoms to itself, one goes to a hydrogen, another to an oxygen
which carries a hydrogen, and two go to a separate oxygen, binding it
very tightly. This substance is formic acid, which is secreted by ants,
and has a very irritating action on the skin, as we all know. When
a fresh link is added to the chain, we have acetic acid, which gives
acidity to vinegar; in fact, the name is derived from the Latin word
for vinegar. The formula is now:
[Illustration]
Butyric acid has four carbons; it is the substance that gives to
rancid butter its peculiar taste and smell. Lauric acid has twelve
carbons, and is found in laurel oil and cocoanut oil. Myristic acid has
fourteen, and is found in the butters of mace and nutmeg. All these are
liquids. Palmitic acid, found in palm oil, has sixteen, and stearic has
eighteen. The last two are solids at ordinary temperatures. They are
used in the manufacture of stearine candles, and, slightly modified,
are the most important constituents of animal fat.
The alcohols constitute another of these chain series. They are formed
from the paraffins by taking off a hydrogen from one end and replacing
it by an oxygen and a hydrogen in combination. Thus, is the ordinary
alcohol.
[Illustration]
And so we may go on describing an immense number of substances, all
consisting of links of CH{2}, with varying terminations.
Sometimes one or more hydrogens are taken off the side of the chain and
replaced by other atoms or atom groups; sometimes there are further
complications. There is a fascination in the simplicity of the general
principle and in the wonderful variety and influence of detail. Why
should different plants or different animals, or different members of
the same plant or animal, contain these carbon chains of different
lengths, on which their own growth and properties and characteristics
greatly depend? Of course, the whole effect rests, in the first place,
on the properties of the carbon atom, and it is that which gives a
peculiar interest to the crystal forms of carbon, diamond, and graphite.
We may look again at the diamond model and ask ourselves whether we can
see any skeleton form of the chain, just as we saw the skeleton of the
ring. The model (Plate XIV a) shows that it can be cut into
chains of any length and of this form, in which the angle that recurs
at every bend can be calculated to be 109° 28'.
[Illustration: Fig. 50.--Chain from diamond.]
We might suppose this to be a simple form of the chain. We are only
speculating, of course, trying to imagine possible solutions of our
problems, which we may put to the test of experiment, and even when we
seem to have a success, not counting too much upon it. If this were
the chain, two hydrogens would naturally be attached to each carbon
at points which, with the two points of attachment of its carbon
neighbors, would make four points symmetrically arranged, like the four
points at which each carbon atom is attached to its four neighbors
in the diamond, as in Plate XXI a. This picture goes more
into details than the form of illustration generally employed by the
chemist; the latter is merely a representation on the flat, our new
figure is in three dimensions. And no doubt the true figure is in three
dimensions. The chemist has not drawn it so hitherto, because he has
had no direct evidence as to how he ought to do it. We are trying to go
one stage further, with some hesitation, because we are not perfect in
the interpretation of our new methods, though very hopeful as to their
value to us in the end.
In the last year or two we have been able to make accurate measurements
of the lengths of the chain molecules by means of the X-rays. The
discovery of the method arose from a curious accident. A certain
crystal was under examination by X-rays, and because it was liable to
suffer rapid deterioration from the moisture of the air, it was covered
over with a thin layer of the solid paraffin, which is generally used
in laboratories as an electric insulator. Certain reflections of the
X-rays were found which could not be reconciled with what was known.
[Illustration: PLATE XXI.
A. Model of a hydrogen chain, pentane, containing five carbon atoms.
The larger balls represent carbon atoms, the smaller hydrogens.
B. An X-ray spectrum of the hydrocarbon containing 18 carbons obtained
by the method shown in Fig. 52. (Müller.)
C. The model shows the arrangement of the sodium and chlorine atoms in
rock-salt: the dark balls represent sodium, the white chlorine, or vice
versa. Only _arrangement_ is shown: there is no attempt to show
the size or shape of the atom.]
It was found that they were due to the paraffin. The commercial
paraffin is a mixture of several of the fatty acid chains, and is
not suitable for accurate experiment. It happened, however, that a
certain enthusiastic student of organic chemistry, Doctor Le Sueur, had
prepared a great number of these chain substances in a pure state, and
these were fortunately available. Those and many others have now been
examined, with very interesting and, on the whole, simple results.
[Illustration: Fig. 51.--Diagrammatic arrangement of the molecules in
the layers of a substance like stearic acid, or a hydrocarbon such as
pentane.]
The particular method is a good example of the way in which the X-rays
can be used. A little of the solid substance is put on a piece of glass
and pressed flat: we will consider the significance of the pressing in
a moment. The substance is now, as it turns out, in layers parallel to
the glass. The molecules in each layer are more or less perpendicular
to it, and are linked together side by side. They may be represented
as in Fig. 51, in which three layers are drawn. Each layer is perhaps
a fifty-millionth of an inch thick, and the thickness is proportional
to the length of the molecule. When a beam of X-rays is passed through
such a sheet, composed of layers, a little is reflected by each layer,
just as would happen in the case of a beam of light passing through
a pile of glass plates. The principle of the experiment has already
been described on p. 152. Suppose _S_ is the source of X-rays, and
_P{1}_P{1}_ is the glass plate with its layers upon it. When the X-ray
beam along _SC_ falls on the plate at the proper angle, the reflection
from the different layers are all in step and the reflection is strong.
We may imagine the reflected ray going off on the line _CR{1}_, and
making its mark at _R{1}_ on the photographic plate _DD_. If the plate
is then turned round about the vertical line through _C_--the figure
shows the experiment in plan--reflection as a whole ceases, because
the separate reflections from the various layers get out of step and
destroy one another. But when the plate has been turned sufficiently,
another general reflection appears, because the reflections from
the different layers have got into step again. The first general
reflection comes when the particular reflection from one layer is
_one_ wave-length behind or in advance of the reflection from the
layers on either side of it; the next when there is a difference of two
wave-lengths, and so on. Consequently the photographic plate when it
is developed shows a whole series of such general reflections. Usually
the plate is turned so as to throw reflections both above and below the
line (Fig. 52).
[Illustration: Fig. 52.--The method of making the X-ray spectrum of
a hydrocarbon. The X-rays from _X_ pass through a limiting slit at
_S_, and if the layer, which has been pressed flat on the glass plate
_P{1}P{1}_ is at the proper angle for reflection, there is a reflection
pencil, _CR{1}_, which makes an impression on the photographic plate
at _R{1}_. If the plate is turned sufficiently there is another
reflection, _R{2}_, when the plate occupies the position _P{2}P{2}_ and
so on.]
A central mark _M_ is due to the direct action of the X-rays--this
part of the plate is usually shielded, so that the direct action is
not too strong--and all the different orders of reflection appear on
either side. An actual example showing the reflection of a paraffin
of eighteen carbons is shown in Plate XXI b. It was obtained
by Doctor Müller. It will be seen that the reflections are very well
marked. It is possible to measure their distance apart with accuracy,
and from this we calculate the thickness of one of the layers in the
reflecting material. We cannot be quite sure that the molecules stand
upright and perpendicular to the layer, but we have good grounds for
supposing so, which we need not enter into here. We find that the
length of the chain increases with perfect regularity as carbon links
are added to it. We actually find that many of them have exactly the
length we should expect if they were as represented in Fig. 50.
The whole series of experiments of this kind bears out the idea
that the chemist has formed as to the shape of these molecules: his
representation has been wonderfully correct. The X-rays have given
precision to the idea, suggesting also that the molecule must be drawn
in three dimensions, and at the same time measuring the length. I may
add that the sideways dimensions can be measured also.
We may now go back to the curious point that we get much better X-ray
reflections if the material is pressed on to the glass plate. It seems
likely that it naturally forms flakes, and in each flake the molecules
are perpendicular to the flake. They join together side by side, as
I have already said, and hold together much better in this union than
one flake holds to another. This last linking is affected by the ties
at the ends of the molecules, and these are much weaker. It is exactly
the same effect as we found in graphite, where flakes held together
strongly as flakes, but slid easily on one another. It is this that
gives the greasy, slippery feeling both to the greases and fats and
to graphite. When pressure is applied to the material, the layers
are squeezed flat, just as when graphite is rubbed on a surface, and
the X-ray reflections are good because the layers are made to lie
regularly. When the material is melted and cooled again, the layers
are broken up, and though, no doubt, they are formed again, they lie
irregularly; the X-ray reflection is then poor. We find the same effect
in the case of gold leaf, as we shall see in the next chapter.
There is another curious property of the long-chain molecules which
is worth our consideration. The paraffin chain has hydrogens at both
ends. Each flake is one molecule thick. But in the case of the fatty
acids (p. 202), the X-rays show that there are two molecules in the
layer, end to end. This is, indeed, to be expected, because it is known
that a carboxyl group has a tendency to join up with another of its
own kind. Consequently the chains attach themselves together in pairs,
forming a chain of double length, the ends of which are hydrogen; the
two carboxyl groups are in the center. This result is obtained from the
X-ray measurements. Here again the X-rays confirm a chemical conclusion
and throw a fresh light upon it.
There is a type of crystal structure which, differing entirely from
those that we have considered already, is of such great importance that
we must not pass it by. The crystals of ordinary salt are good examples.
Sometimes, as we have already seen, a molecule is formed from two
atoms, of which one, being greedy for an additional electron, has
satisfied itself at the expense of the other atom. The latter, before
the transference, has held one electron in a loose binding. For
example, chlorine has seventeen electrons: two in an innermost shell
or coating, and eight in the next shell. In the outer shell there are
seven, and the chlorine atom exerts a great force, tending to complete
the shell, which when full contains eight. It will then present the
external appearance of argon. Sodium has eleven electrons normally:
two in the innermost shell, and eight in the next, but only one in the
outer shell instead of the seven in chlorine. The sodium atom has no
tight hold on this odd electron, so the chlorine takes it. The sodium
atom then has the external appearance of a neon atom (p. 82).
The two atoms are now charged electrically; the chlorine is negative,
because it has one negative charge over and above its proper number,
and the sodium is positive, because it has one too few. The governing
principle in the growth of the crystal is the attempt on the part of
the atoms to satisfy as fully as possible the mutual attraction of the
positive sodiums and the negative chlorines. The system of packing
which nature adopts is that in which each chlorine is surrounded by
six sodiums, and _vice versa_. It is shown in Plate XXI c. It is
very simple--a cubic arrangement in which each of the lines of atoms
that are parallel to the edges consists of sodium and chlorine atoms
alternately. The white balls may represent chlorine and the black
sodium, or _vice versa_. It is because of this arrangement that salt
crystallizes from brine in cubic form. The crystals are not necessarily
cubes, but are rectangular blocks, all faces of which are of the same
type. The frequent differences between their sizes and appearances are
merely accidents of growth.
Very many crystals are built on this principle: in particular all the
salts of the metals, in which the metal has lost one or more electrons,
and the remainder of the molecules, as a group, has gained them. The
resulting structure is not always so simple as that of salt, because,
for instance, the group may be more irregular in outline than the
single chlorine. In calcite, the metal atom calcium loses two electrons
to the group CO{2}, and the result is the rhomb of Iceland
spar. It is still true that each metal atom is surrounded by six
negatively charged bodies, and each of the latter by six metal atoms;
the crystal is no longer rectangular, because the CO{2} group
is not round.
CHAPTER VI
_The Nature of Crystals: Metals_
THE use of metals has been one of the great factors in the development
of the activities of the human race. The beginning of the story is
so far back in the ages that we can only make guesses as to how men
first made metal tools and weapons. Perhaps copper was picked up in
its native state, and its weight suggested its usefulness in a fight.
Copper is too soft to take a cutting edge, and it may not have been
very long before it was found that there was an alloy of copper and tin
which was far harder and more serviceable than copper alone. Perhaps
there was tin in the stones of which the copper smelting furnace was
built, perhaps copper and tin occurred together in the same mineral.
And so the age of bronze set in. Iron came later, of course. From that
time to this there have been workers of metal--important members of the
human community. We have but to think of the magnitude of the metal
industry in this country alone, to realize how great a part the metals
play in the life of the world.
In all these thousands of years a vast body of experience has been
gained. Some of it is in books, some of it is still a tradition handed
down by the skilled workman to the apprentice. There is even a sense of
the nature, or condition, or property of a metal which cannot be put
into words, and is only taught by example to such as have the power
to understand. Nor is this any trifling matter: the whole movement of
trade and the welfare of a nation may rest upon it.
On the other hand, the properties of the metals must depend, in the
first place, on the properties of the individual atoms, and, in the
second place, on the atomic arrangement, which is in effect the state
of crystallization. In the very centers of the metal industries it has
been realized of recent years that the scientific observer with his
microscope can bring some system into the mass of disordered knowledge,
and can improve the quality of the manufacture and the certainty of its
production.
[Illustration: PLATE XXII.
Two photographs of aluminium: the surface has been prepared so as to
show the different crystals. The crystals scatter the incident light
differently because they are set in different ways, and the surfaces
exposed by treatment are therefore different in nature, in one figure
the scale has been reduced somewhat from the natural size, in the other
considerably enlarged.
(From a paper by Carpenter and Elam, read before the Institute of
Metals, Sept. 1920.)]
Yet, as I have said already, the microscope can only go to a certain
length: it stops far short of the point which we must reach if we
are to understand how the atoms are acting so as to give the various
materials their specific properties. It can show the existence of the
separate crystals in the metal, but not the arrangement of the atoms
in the crystals (Pls. XXII, XXIII). In the X-rays we find a new hope;
indeed, it is more than a hope. We may be sure that the intimate
knowledge which they give us will in the end throw a flood of light
upon the inner meaning and purpose of all the complex properties of
metals. It may be a long time before the new movement will become great
and obvious. The experience of thousands of years has to be caught
up with and explained. It is quite otherwise with such a subject as
electrical engineering, or wireless telephony, which is a branch of it.
Here the whole process is rooted in the work of the physics laboratory,
and development has been directed by knowledge and anticipation. The
worker in metals has been guided through the ages by trial and error,
by experiment with little knowledge to guide it. It is a very slow
process; but it has been going on a long time, and its findings
command respect. They must be studied very carefully in the new light
which the X-rays give us.
Already we begin to find explanations, as we may call them, of some
of the properties of the metals. They depend upon the crystalline
structure, as we might have expected. Sometimes the crystals are to be
seen by the naked eye; sometimes they become obvious when the surface
is properly prepared and placed under the microscope. But the easiest
and most complete way of discovering them is by means of the X-rays,
with their fineness of vision.
The structures of almost all the metal crystals have been determined
by the X-rays, and it appears that they are usually very simple.
For instance, the atoms of gold, silver, copper, and aluminium are
put together like the piles of round shot that used to stand beside
the guns of a hundred years ago. It is worth while to look a little
carefully into this arrangement, although we are really repeating the
comparison (p. 189) between the structures of ice and diamond.
[Illustration: PLATE XXIII.
(By courtesy of the University of London Press, Ltd.)
The photograph shows the irregular outline of the crystal grains in a
sample of steel, and, in addition, a cross-crossing of lines within
each grain, known as “Widmanstätten lines.” These last are due to the
fact that the polishing tool has rut across the “atom layers,” in much
the same way as polishing cuts across layers of mother of pearl.
(From Belaiew’s “Crystallisation of Metals.”)]
Suppose we put together a number of balls into the triangular
arrangement of Fig. 53, and surround them by a triangular guard, as
shown, just as balls are packed together for playing pool on the
billiard table.
[Illustration: Fig. 53.--A close-packed arrangement of balls in one
layer.]
We lay on these another layer, forming a triangle a little smaller
than the first, and again other layers until the triangular pyramid is
finished (Plate XXIV b). Obviously there can be no closer method of
packing round balls together. Now if we look into the arrangement of
the layers one above the other, we find that the balls in any layer are
exactly over the balls in the next layer but _two_. In the absence of a
model this effect may be realized by the help of Fig. 54. The crosses
represent the centers of the balls in a certain layer, the circles
the centers in the next layer, and the black spots the centers in the
third. The centers in the fourth will be over the crosses, in the fifth
over the circles, and in the sixth over the spots, and so on.
When balls are arranged in this way, it is possible to cut cubes out of
the assembly, as in Plate XXV a. It is always a surprise when
this fact is first realized, but it is well to understand the cause of
it, because so many crystals are made up of atoms piled together in
this way, and they so often grow as cubes or in some way show their
close connection with the cubic form.
Now if, when we have laid down two layers and come to the arrangement
of the third, we place it so that each ball is exactly over a ball in
the first layer, which arrangement is the only alternative to the one
we chose before, we have another way of packing the balls which is as
compact as the other. In this case, the balls in any layer are exactly
over the balls in the _next layer but one_, and Fig. 54 a will be
replaced by Fig. 54 b, and the arrangement of Plate XXV a by that of
XXV b. This arrangement will not stand up now without containing walls,
if we are to have a reasonable number of balls in the model; we must
pin them together in some way. When we look down on this model from
above, we see six-sided tunnels running through it, and we do not sec
any arrangement of this kind when we look in any other direction.
[Illustration: PLATE XXIV.
A. Small groups of shot are in close packing, and there are irregular
gaps between the groups.
B. A pyramid, built by the super-position of layers like that of Fig.
53.]
[Illustration: Fig. 54.--In A is shown the arrangement of the layers as
seen by an observer looking along a diagonal of the cube of Plate XXV
a. The black spot represents the ball at the corner. The small
circles represent the six balls in the next layer, and the crosses
the fifteen in the next layer. In B the arrangement is as seen by an
observer looking down on Plate XXV b from above. The nineteen
black spots represent the balls in the top layer, and the twelve small
circles the balls in the next layer. The third layer is like the first,
the fourth like the second, and so on. The repetition is after every
second layer; in A it is after every third.]
The model has a single axis in the vertical direction, and round that
axis the arrangement is such that a crystal built on this plan would
naturally form hexagonal columns.
In the case of the cube there are four ways of thinking of the
arrangement of the layers; there is a layer perpendicular to each
diagonal of the cube, and, as a cube has four diagonals, there are four
sets of layers. This does not mean that the atoms in any one layer are
specially tied together in that layer; merely that one can sort out the
atoms of the crystal into this kind of layer in four different ways.
Now it turns out that these layers are of very great importance
in respect to the properties of the metal crystals built on the
close-packed cubic plan. Gold, silver, copper, aluminium, and other
metals like them can be drawn into wires, rolled into sheets, and
beaten into various shapes. They are, as we say, ductile, and their
ductility is one of the characteristics that make them so useful. They
can be bent and pulled into all sorts of convenient forms. It seems
possible to make a metal flow like treacle. Gold can be hammered into
leaves so thin that the metal in a sovereign will cover a large field;
the others can be beaten nearly as thin.
[Illustration: PLATE XXV.
A. Cubic packing. B. Hexagonal packing.
(From Pope’s “Modern Aspects of the Molecular Theory.”)
A shows how balls are packed together to form a cube. It is exactly the
same packing as in Plate XXIX B. The close-packed layers of Fig. 53
are horizontal in Plate XXIV B, and in A they are perpendicular to a
diagonal of the cube.
B shows the other form of close packing. Each horizontal layer is a
close-packed layer of Fig. 53.]
Cups and vessels of all sorts, chains and ornaments, and innumerable
useful things are made by taking advantage of this singular property of
ductility. The first thing that we should like the X-ray to explain for
us more clearly, if we can make them do so, is that feature in their
structure which accounts for this most valuable property. We should
also like to understand the inner meaning of the hardening and other
changes that are due to “cold-working,” as it is called--that is to
say, to hammering or straining the metal when it is cold. And what is
annealing, the softening and relief from strain that heat brings about?
Why are all these things so obvious in the case of a metal, while they
do not appear in, for instance, diamond or rock salt or quartz?
Already we begin to see some little way into these difficult questions;
and in particular we have found out something about the way in which
the metal yields to a pull or any other strain, and have learned that
it has to do with the layers of which I have spoken.
A metal is rarely one whole crystal: it is, in general, an assemblage
of crystals, pointing in all directions. Sometimes these crystals can
be seen easily; sometimes the microscope is required to show them. Very
often they are too small even for the microscope, and the X-rays alone
can make them clear.
If we put a number of shot on a tray and let them all run together by
tilting the tray slightly (Plate XXIV a), we observe that
there is a tendency for the shot to arrange themselves like the balls
in Fig. 53. It will not often happen that all the shot will form one
arrangement: there will be groups, each properly arranged in itself,
but not correctly aligned with its neighbors. In just the same way
there will be local arrangements among the atoms of a metal--in other
words, there will be crystallization in groups, larger or smaller, the
connection between the groups being somewhat irregular. We may observe
at once that the connection between group and group is not necessarily
any weaker than the connection between the atoms in any one group. Why
this is so, it is difficult to say. We need not be surprised at it,
because the ties between atoms are complicated things, imperfectly
known to us, and we cannot predict accurately what will happen in every
case.
[Illustration: Fig. 55.--The two blocks are stuck together, but can
slide over each other. When pulled they change in relative position
from (_a_) to (_b_).]
It is said that when gold is at a high temperature a fracture cuts
through the crystals, but when the gold is cold it goes round them; and
this will illustrate the complexity of the effect.
A block of one of these metals may reasonably be expected, therefore,
to consist of a mass of crystals, large and small; and this is exactly
what the X-rays show to be the case, even when the microscope fails
because the crystals are too small for it to see.
Now when we take a single crystal and try to bend it or distort it, we
find always that it gives finally through a slip along a plane: all
that is on one side of the plane slipping with respect to all that is
on the other. These planes are the planes we spoke of before--those
that contain atoms arranged as in Fig. 53. A single metal crystal does
not give way exactly in the direction in which it is pulled. If we had
two blocks of glass, let us say, held together by grease as in Fig. 55,
and pulled them, they would give along the plane between them.
[Illustration: Fig. 56.--This figure represents in the form of a
diagram the slipping on one another of the layers of the aluminium
crystal.]
Naturally they will slide over one another on this plane rather than
themselves be torn to pieces. In the case of a metal there is not
merely one plane, but many planes, and many of them will be planes of
sliding either together or one after another. We might represent the
crystal by a set of lines as in Fig. 56 (_a_), which, if pulled
in the direction of the arrows, would yield as in Fig. 56 (_b_).
Often when a single metallic crystal has been stretched, we can see the
marks on its surface which show the lines along which slip has taken
place.
Professor Carpenter and Miss Elam have shown recently some beautiful
examples of this kind of effect in the case of large crystals of
aluminium. An ordinary piece of the metal consists of a multitude of
crystals pointing in all ways, as we have already understood to be the
case. By a somewhat complicated process of heating and stretching, the
many small crystals can all be made to line up and form a small number
of large crystals, just as we might imagine that by shaking or tapping
the tray of shot shown in Plate XXIV a in some way, to be
found out by experience, we could get all the minor regular groupings
merged into one large one.
The pieces chosen for experiment were of a form often used for pieces
to be tested for their resistance to pull; the form is shown in Plate
XXVI; the original length of each piece is eight inches. The broad
ends are intended to be gripped by the jaws of the machine that is to
stretch the piece; the narrower part is that which is to give way, and
to show by the way in which it does so, and the pull that is exerted,
the capacity of the metal to resist the forces that would strain it.
When one of the test pieces so treated is put into the testing machine
and pulled, it gives way in a curious fashion, which differs for
different specimens (Plate XXVI, 1 to 4). Sometimes the width of the
piece remains the same, and it thins out gradually as the test piece
lengthens under the pull: it may grow longer by several inches before
it gives way. Sometimes the thickness remains the same, and the piece
shrinks sideways, developing a waist which finally is the place of
breaking. At other times, again, there are more curious changes still.
These pieces have been examined by the X-rays, and it turns out that
the nature of the yield depends entirely on the way in which the large
crystals are set toward the line of pull. The metal gives way along the
plane of slip. If, for example, the crystal is so set--and there is no
telling during the heat and strain treatment how the forming crystal
will lie--that the layers of which we have spoken are as in Fig. 56,
then stretching will make the piece draw in sideways.
Sometimes the direction in which the crystal gives way depends on a
more complicated use of two sets of slip planes alternately. When the
crystal might slip on more than one set of planes, it is apt to choose
the one which is more nearly perpendicular to the line of pull. We can
imagine that this is so because a slip means a riding of one set of
atoms over another, and the motion would be helped by a force tending
to pull one layer away from the other. If we had a solid body made up
of a row of balls like the top layer in Fig. 57, and it rested on a
similar row like the bottom layer, it might be easier to drag the top
layer over the bottom if the line of pull were along _P_ rather
than along _Q_.
[Illustration: Fig. 57.--The top layer, as a unit, might be more easily
pulled through from position _A_, through _B_, to _C_, if the pull were
along _P_, than if it were along _Q_.]
Since (see Fig. 55) the pull always tends to bring the plane of slip
more nearly into its own line, there arises a sort of seesaw action:
the crystal slips along one set of planes until the set comes too
nearly into line with the pull, and then along another. In the end
the line of pull bisects the angle between the two sets. The balance
is often shown in the shape of the broken ends; in Plate XXVI, 3, for
example, there is a kind of knife-edge at the point of rupture. The
two sides of the edge are parallel to two different sets of slip
planes, and are equally inclined to the line of the pull which finally
tore the metal in two.
In the case of the aluminium, the yield is so easy that a sheet of some
thickness, when composed of a single crystal, can be bent quite easily
by one’s fingers. An ordinary piece of aluminium sheet is quite stiff,
however, and the explanation of the difference is that, when there are
crystals pointing in all directions, there are some ready to take and
bear the strain, no matter from what direction it comes. The strength
of a chain is that of its weakest link, and the weak part of a crystal
is its slip plane. This is a point of extraordinary importance in the
manufacture of metal, though it is often linked up with so many others
that its special effect is difficult to sort out from the rest. Many
factors go to the design of steel, let us say, for some given purpose;
but one of them is certainly the degree of fineness of the crystal
grains of which it is composed. Fineness and uniformity of size both
contribute to the toughness of steel and its quality generally.
[Illustration: PLATE XXVI.
These photographs an due to Professor Carpenter and Miss Elam
(_Proceedings of the Royal Society, A._, 100, p. 346). They show
the yielding of aluminium under strain, the part finally giving way
being a single large crystal in the narrower portion of the test piece.
In (1) and (2) the slip planes are disposed--to the observer--like the
layers of Fig. 56. The test piece has contracted sideways, and finally
developed a waist, as the picture shows. There is no thinning from back
to front. In (3) and (4) the reverse has taken place before the break:
the width has remained the same, but the material has grown thinner
(this cannot be seen in the photograph).]
When the single crystal of aluminium gives way along a layer, we may
suppose there is a moment when the one set of atoms is riding over
the other, followed by a drop into place again: _A_ goes through
_B_ into _C_ (Fig. 57). When the latter case is reached, the
close-packed arrangement is resumed. The metal is still a crystal. Now,
as we know, the regular crystalline arrangement is the natural one, and
so the substance slips easily from one natural arrangement to another,
adjusting itself to the pull or other strain by doing so. No doubt this
is one of the causes, and a very important cause, of ductility.
But why does the metal often become harder when it is beaten? And what
happens to it when it is annealed? Perhaps we are guided toward an
answer by considering what happens to gold when it is beaten into leaf
and subsequently heated. Gold leaf is very thin, as we have seen. It
is even transparent, but it absorbs part of the spectrum of light that
passes through it, allowing a greenish light to filter through. It is
yellow when viewed by reflected light, as we know. It is very curious
that when it has been heated to a dull red heat it becomes permanently
transparent, and white by reflected light. Faraday was very interested
in this fact; he suggested as a partial explanation that the thin
layer of gold broke up, the metal gathering itself together in little
heaps, and that the light went through the holes that were left. Sir
George Beilby has made many experiments, and added considerably to
the information we have in regard to the behavior of this and other
substances when heated in the same way. If there are holes in the
heated leaf, they are exceedingly small, he says, beyond the power of
the microscope to see. Now the X-rays have something to say on this
point. When gold leaf is examined by their aid, it is found that it
consists of masses of cubic crystals of gold all lying with faces
parallel to the leaf. They are not necessarily cubes, of course. They
consist, like ordinary salt, which is cubic, of rectangular blocks of
all sizes. They must be exceedingly thin blocks, and no doubt their
thickness is far less than their width or length. When the leaf has
been heated, the blocks are piled up anyhow, perhaps gathered together
to some extent in heaps, as Faraday supposed, even if they are too
small to be seen by the microscope; and perhaps this is the reason
why gold and silver leaf become transparent when heated. Why gold
should be green when looked through is a mystery. But we do see that
the beating of the gold has spread out the crystal blocks so that they
all lie with one face in the leaf surface, and that heat has destroyed
this amount of regularity of arrangement. When the heated gold leaf is
pressed with a body having a smooth, hard surface, such as an agate,
it goes back to the other condition, as we might expect, since the
pressure would force the blocks once more into the flat. In both cases
the metal is crystalline, but there is more arrangement in the usual
than in the annealed form of the gold leaf. The same effect is found
with silver. To show it in the case of copper it would be necessary to
carry out the experiment under such circumstances that the air could
not act on the metal. When copper is heated in the open, a film of
copper oxide quickly forms all over it, an action which also can be
followed by the X-rays. We often see this tarnish form slowly on copper
even when no heat is applied. But it is easy to show by X-rays that
in copper foil there is the same arrangement of the crystal block as
in the case of the gold leaf. On the other hand, a block of ordinary
copper shows no such arrangement; the crystals are arranged anyhow.
The hardening of these metals by cold working is, therefore, due in
some way to the fact that they are put into a state of strain by the
rearrangement of the crystals which the X-rays show; annealing is the
release of this strain and the destruction of the arrangement. As to
why this is so, we are still very ignorant: we can simply be satisfied
that we have made one step forward.
It is worth noting that, in general, when a metal has been thrown into
a state of strain in this way, it is more readily subject to the action
of chemicals, as we might expect. It is not so well settled into what
we may call a comfortable condition.
We ought now to go on to the consideration of other peculiarities
possessed by metals, since we may expect them all to be due to more or
less the same causes and we must study them all together. Two of their
most remarkable properties lie in their powers of conducting heat and
electricity. We all know how quickly heat spreads through a metal:
we might be inclined to say that a metal could be identified by its
possession of that property. We all know, too, how metals, especially
copper, are used as conductors of electric current.
Going back to our first consideration of the nature of the atoms,
and of the differences between the various atoms, we find at once a
feature which on the whole seems capable of giving us a satisfactory
explanation of their conducting powers; no doubt, too, it has much to
do with their crystalline structure and their ductility. The atoms of
the metals always have one or more electrons which are lightly held.
For instance, sodium has eleven electrons; two of these are very close
to the nucleus, eight more form a very strongly held system round the
first two. The odd electron belongs to an outer system altogether,
which becomes filled up as we go from sodium to magnesium with two
in the outermost system, aluminium with three, and so on. This odd
electron is not held tightly. When it is stripped off for any reason,
the atom is outwardly reduced to the form of the unsociable atom
“neon,” except that as a whole it carries a positive electric charge
due to the want of balance on loss of an electron. An aluminium
crystal is an assemblage of spheres like neon, all in close packing,
as explained, and all the odd electrons are more or less free to move
about in the structure. It must be said, however, that this picture
is doubtless much too crude to be the whole truth; there must be much
more in the design of which as yet we know nothing. Yet it must be
right to a certain extent. We see at once why metals are conductors
of electricity: it is because the electrons, the fundamental charges
of negative electricity, can move about so easily. When a current of
electricity runs along a metal wire, it is the electrons that make the
flowing stream. It is curious that they must move, being negatively
charged, in the opposite direction to that in which the so-called
current of electricity is always imagined to flow. It was always a
matter of words, this talk of a flowing current of electricity. It is
quite a new discovery that anything moves at all, and we need not be
surprised that the real direction of flow is opposite to that which had
been supposed.
So we must think of the battery or the dynamo, not as manufacturing
electricity, but as sending round a circuit a stream of the electrons
that are already there and are more or less free to move.
[Illustration: PLATE XXVII.
(By courtesy of the University of London Press, Ltd.)
Damascus blades.
(From Belaiew’s “Crystallisation of Metals.”)]
Just so the engine in a factory makes a leather belt continually travel
round a certain circuit; but the engine does not manufacture leather.
When a metal is heated, the contained electrons dance more quickly
to and fro, and may break away into the open. Electrons are pouring
in a continuous stream from the hot wire in the “valve” of wireless
telephony, and the outpouring is necessary to the action of the valve.
The electrons do not move so easily in a metal when it is hot as when
it is cold. Here again it is easy to imagine how this may be. We can
see that the electrons will have more difficulty in threading their way
among the atoms of the metal if through heat the latter are moving to
and fro and getting in their road. It is much more difficult to explain
the strange fact, discovered at Leiden by Kamerlingh Onnes, that
some substances when their temperature has been lowered to a certain
very low point--a point which differs for different metals--offer
no resistance at all to the movement of the electrons, so that a
current once started will keep on running for days before it finally
fades away, the metal being kept continuously at this extremely low
temperature.
The electrons must to some extent contribute to the capacity of a metal
for conveying heat as well as electricity, because the electrons at the
hot end of a metal bar must pass on some of their excessive energy to
the electrons at the cold.
Thus the presence of electrons in the metal, able to move with some
freedom among the atoms of the structure, gives a very good reason why
the metal conducts both heat and electricity. Of course it is only a
rough picture that we have drawn; many details require to be filled in,
and no doubt many really important facts have been left out altogether
because of our ignorance.
Let us turn back to the question of the ductility of metals, and
consider whether the presence of the electrons helps us here also.
We now see our atoms as spheres, all of them charged with positive
electricity and packed closely; and we may perhaps be right in thinking
that the electrons hold them together like a cement.
[Illustration: PLATE XXVIII.
(By courtesy of the University of London Press, Ltd.)
The long needle-shaped bodies are cementite crystals forming part
of the general mass of steel. (From Belaiew’s “Crystallisation of
Metals.”)]
But the most important point is that the atoms are not tied together by
sharing electrons as in the diamond: they must rather repel one another
than otherwise, being all charged with positive electricity. They are
free to roll or slide over one another, because they are not attached
to one another at definite points, as often occurs in other crystals.
These things seem helpful when we consider the slipping of one plane
over another.
So far we have been considering the crystalline structure and
properties of a few of the metals in the pure state. Now in practice
we meet with alloys far more often than with pure metals, and that
for the reason that alloys have properties of their own of the
greatest value. Alloys are, in fact, extraordinarily interesting in
their immense variety and in the wide range of their usefulness. New
forms are constantly being discovered. No matter what peculiar virtue
may be required for some special purpose, an alloy of some sort is
forthcoming, which satisfies the demand more or less completely. We
must try to see some reason for these things, if we can, in what we
have recently discovered. Of course, we know so little as yet, and
there is so much to explain, that in a few years’ time we may think
very little of our present attempts, but we must make a beginning.
It very often happens that the addition to a metal of quite a small
quantity of a second metal, or even a non-metal, causes a notable
improvement in hardness. Pure metals are generally very soft, because
their slip planes are so ready to give. The first of all the great
alloys was bronze, a mixture of copper and tin, which is far harder
than either metal alone. The mixture of copper and zinc produces the
serviceable brass, of which there are varying qualities, depending
on the proportions of the mixture. Steel is formed by the addition
of a small percentage of carbon to pure iron. There are alloys of
copper and aluminium, which are very tough and do not corrode, but are
difficult to work in the shaping machine. There is an alloy of copper
and nickel, which does not corrode and is easily molded; it is used
for the coverings of bullets. German silver is a white, ductile alloy,
non-corroding, which is used in the manufacture of such articles as
spoons and forks, which are afterward coated with silver in the process
known as electroplating. An alloy of nickel with chromium stands very
great heat, and is used for the wiring of electric furnaces.
[Illustration: PLATE XXIX.
(By courtesy of the University of London Press, Ltd.)
(By courtesy of Sir George Beilby.)
A. Section magnified a thousand times and showing the cementite needles
in process of being broken up and rounded off.
(From Belaiew’s “Crystallisation of Metals.”)
B. The dark band is a scratch made by a very fine needle in a polished
piece of speculum (mirror) metal, highly magnified. The fine vertical
scratches are made by emery powder in polishing. Many small particles
have been torn up and deposited in the trough made by the needle.
(From Beilby’s “Aggregation and Flow of Solids.”)]
Chromium, cobalt, and tungsten combined in definite proportions make
stellite, an extraordinarily hard, non-corroding substance; some of the
standard weights at the National Physical Laboratory are being made of
it. There are alloys for the making of bells, very soft alloys for type
metal, and a great variety of solders. There is the aluminium bronze,
which is used for cheap jewelry and consists of aluminium with a small
percentage of copper. And so on to a long list, if it were necessary to
make one.
Let us take one of the simpler cases--for example, that in which
the addition of a small quantity of aluminium to copper produces an
increase in hardness. The X-rays show that the structure of the copper
crystals remains the same, except that here and there an aluminium
atom takes the place of a copper atom. Now the weakness of the crystal
lies, as we have seen, in the fact that one part slides on another
part along a certain plane. This plane is now no longer even: there
is a scattering of aluminium atoms in it, and we can readily suppose
that the slipping has become more difficult, and that we have here
the cause of hardening.[5] There is a remarkable effect which makes us
think we are right in supposing so. The atoms of aluminium must strain
the structure of the copper crystal, because the copper will not take
up more than a certain number. If an alloy is made containing more than
about 10 per cent of aluminium, the X-rays tell us that the copper
crystals are broken up altogether, and a new structure is formed.[6]
The aluminium atoms must be distorting the copper crystal, and this
fits in very well with the fact that it hardens the copper. On the
other hand, when nickel is added to copper the atoms of the former
replace the atoms of the latter to any extent: evidently they can
slip into the places of the copper atoms without straining the copper
crystals at all. And in this case there is no hardening effect, which
is just what we should expect. It is only when we push in atoms which
really strain the copper crystal and make its planes uneven that the
hardening is brought about. We have jammed the sliding planes.
[Illustration: PLATE XXX.
In A a piece of speculum metal, after being rubbed with fine emery, has
been polished with rouged leather. The metal has been dragged over the
emery scratches; there is a reminiscence of butter spread on bread.
In B the polishing with rouge has been carried further; the emery
scratches have disappeared, but the outlines of the grains in the metal
begin to appear.
(From Sir George Beilby’s “Aggregation and Flow of Solids,” by courtesy
of the author.)]
In the case of steel the action is of the same kind, but here the
carbon atoms that are the cause of the hardening do not replace the
iron atoms, but are forced into the empty spaces between them. We
can easily see that this may distort the iron crystal, and as before
prevent the movement along a plane of slip. Once again there is a limit
to the amount of the alloying substance: only a small percentage of
carbon can be introduced into the iron without breaking up its ordinary
simple structure.
The problems of iron and steel contain, however, many more
complications than this. We have only to ask what happens when more
carbon is put in than the iron structure can carry, and we find we have
a new problem. Among other things, a new crystal appears, formed of
molecules, each containing three atoms of iron and one of carbon; it
is known as cementite. The new crystals are very hard and unyielding,
and in form are like needles (Plate XXVIII). Their presence hardens the
iron very greatly and makes it difficult to work. A beautiful example
of its effect on steel is to be found in the old swords that once made
their way from India through Damascus into Europe. Damascus steel was
greatly valued for the excellence of its qualities. Fine specimens are
to be seen in the Wallace Collection; they show the characteristic
wavy pattern (Plate XXVII) which has always been looked on as evidence
of genuineness. When examined under the microscope the lines of the
pattern are seen to consist of multitudes of dots, forming a sort of
Milky Way in the steel. These dots are the tiny crystals of cementite.
As Colonel Belaiew tells us, the steel when it was first made was most
difficult to work. The smith, with his little furnace, would heat the
steel red hot, but after he had struck but a few blows and made a
slight impression on the steel, the momentary softening had gone. The
hardness due to the cementite crystals had only been removed for an
instant. More heating, a few more blows, and slowly the steel became
less rigid. In fact, the cementite crystals were changing their form.
They were becoming less like needles, gathering themselves together
into more rounded shapes, and as they did so the steel became more
pliable (Plate XXIX a). At last the fine Damascus steel was
reached, so strong and yet so elastic.
[Illustration: PLATE XXXI.
In A the metal has been etched with acid: the “flowed” parts have been
readily attacked and removed, the grains now show up very clearly. In B
polishing has begun again.
(From Sir George Beilby’s “Aggregation and Flow of Solids,” by courtesy
of the author.)]
It is very likely that much of the keen edge that these swords would
take was due to the presence of the very hard particles embodied and
held in the softer iron. The edge would be like a saw with extremely
fine teeth. In the trial of skill between Saladin and King Richard
which Walter Scott describes in _The Talisman_, the former threw
a gossamer veil into the air and severed it by drawing his scimitar
across it, a fine test of keenness and of skill. Richard, on the other
hand, used his sword like an ax, and clove in two an iron bar, the mace
of one of his knights. This also was a test requiring great qualities
in the steel, but on the part of the man the skill lay more in the
power to strike a terrific blow than in delicacy of touch.
Grinding, sharpening, and polishing are really very interesting
operations. When we put a knife on the grindstone we let the hard
crystals in the stone cut minute furrows in the steel, actually
removing the material. This is one stage of the sharpening process.
But the polishing on the oil stone or the strop is a different thing
altogether. Here we actually make the steel to flow, smoothing down the
furrow; sometimes, as Sir George Beilby has shown, actually drawing
a skin of metal over the deeper hollows. The metal seems to remain
crystalline all the time; the X-rays show readily the crystals in a
razor blade. Probably the action is the same as that which took place
in the gold leaves when they were heated. The oil that we use helps
in the smoothing process. The metal is strained by the flow; in time
the strain tends to come undone, and heat especially can take away the
keenness of the edge (Plates XXIX b, XXX, XXXI).
An alloy is generally a much worse conductor of electricity than a pure
metal. It may well be that when the stranger atoms are forced into the
structure of the pure metal, and the planes of atoms are made uneven,
the electrons are more hampered in their passage through the metal.
More energy is required to force them along, and the metal becomes
hotter through the passage of the current than if it were pure. In the
case of a pure metal, as I have already said, the resistance to the
movement of the electrons becomes greater if the temperature is raised.
We can imagine that the electrons find it harder to get past the atoms
when the latter are more active: heat makes them move to and fro more
quickly about their proper positions.
[Illustration: PLATE XXXII.
A. The resistance of the pure metal coil in the same circuit as the
shining lamp has been reduced by surrounding it with a freezing mixture.
B. The iron wire is stretched by a hanging weight; its expansion and
contraction are magnified by the lever arrangement. The wire is heated
by passing an electric current along it.]
But heat does not make so much difference in the case of alloys,
because the passage of the electrons is already so difficult that heat
does not make much change. We can show this by a simple experiment:
A battery sends a current round a circuit which has two branches, as
in the figure (Plate XXXII a). One of them contains a coil
of copper wire, M, and a lamp, L{1}, the other a coil of an
alloy such as German silver, for example, and a lamp, L{2}.
The coils are so adjusted in respect to the resistance which they offer
to the passage of the electric current through them that the lamps
both burn dimly. A vessel containing liquid air is brought up so as
to include the coil, M, and the lamp, L{1}, at once burns
brightly. The cooling of the copper wire has lowered its resistance to
the passage of electrons, and more current flows through the lamp. But
when the alloy is, in its turn, immersed in liquid air, no change is
made.
Sometimes metals crystallize in more than one way. Iron furnishes one
of the simplest and most striking examples. At ordinary temperatures
the iron atoms are arranged so that each atom has eight neighbors. The
latter are at the corners of a tiny cube, of which the former atom
occupies the center. This is not the closest form of packing, as will
readily be found on trial. The packing of the pile of shot of which
I spoke before gives the closest packing, and in that each shot has
twelve neighbors, six touching it round an equator, and three more
round a line of latitude in each hemisphere: or, as we may put it,
six in its own layer and three in each of the next layers. It is the
packing of gold, silver, copper, and aluminium. It is very curious that
when iron is heated to a cherry red the atoms change their arrangement
and pack in the tightest form, that of the pile of shot. The effect
is easiest to see when an iron wire is heated beyond this point and
allowed to cool. When it comes to the critical temperature, the atoms
suddenly adopt the looser packing and the wire stretches a little: the
increase of length is easily observed by the use of some magnifying
device. It is very curious, too, that when the old form changes to the
new, some energy is set free and the iron suddenly brightens up again.
The stretching and brightening have long been matters of observation,
but it is only quite recently that we have discovered that the packing
of the atoms into two different crystalline forms is at the bottom of
what we have seen (Plate XXXII b).
These very few instances of the relation between the properties of a
metal and its crystal structure are drawn from an immense subject,
most of it still waiting exploration with our new helpers, the X-rays.
We cannot say beforehand what will be found out. We can be very sure,
however, that the better we understand our materials the better use we
can make of them.
FOOTNOTES:
[Footnote 1: See “The Legacy of Rome” (Oxford University Press), p.
270--an article by Dr. Singer.]
[Footnote 2: From a Friday Evening Discourse before the Royal
Institution of Great Britain, March 4th, 1881.]
[Footnote 3: For lecture purposes the working of the apparatus is
illustrated by a kinematograph film which has been made for the
purpose. It shows a series of successive expansions, each forming a new
set of lines like those shown in Plate III.]
[Footnote 4: C. V. Boys, “Soap Bubbles and the Forces Which Mold Them.”]
[Footnote 5: Rosenhain, “The Inner Structure of Alloys,” Institute of
Metals, May 2, 1923.]
[Footnote 6: Jette. Phragmen, and Westgren, Institute of Metals, March,
1921.]
NOTE
AFTER trials of many ways of making models of atomic structure and of
many substances I find that two have real merits:--
Balls representing the atoms may be made of hard dentists’ wax, which
softens in boiling water and can then be pressed into proper shape in
metal molds made for the purpose, just as we used to remake our golf
balls in the old days. The spherical mold is made in two halves; and
it is convenient to mount them in the lathe, one on the head and one
on the back center. Small balls harden at once, and can be made very
quickly: larger balls must be left a little while in the mold. The hard
wax can be drilled without becoming softened and deformed by the heat
generated in drilling. The models made of the wax are very finished in
appearance, and will stand all ordinary temperatures. The wax is rather
costly.
Gramophone needles make good connectors, the balls, wax or wood, being
drilled to receive them. The holes should be drilled true and in
correct position. Convenient little contrivances can be made to be used
for this purpose on the lathe.
THE END
=TRANSCRIBER’S NOTES=
A list of figures has been included to enhance readability.
Parentheses were applied to chemical compounds to prevent confusion
with italicized text in the transcribed version.
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