TEXT FLY

WITHIN THE
BOOK ONLY

>

= co

00 p

166218 >m

CONCERNING
THE NATURE OF THINGS

BY THE SAME AUTHOR

THE WORLD OF SOUND

Six Lectures Delivered at the Royal

Institution, Xmas 1919. yd Edition.
Fully Illustrated. Price 6s. net,
G. Bell & Sons, Publishers, London, W.C.

CONCERNING
THE NATURE OF THINGS

Six Lectures delivered

at the Royal Institution

By
SIR WILLIAM BRAGG

K.B.E., D.Sc., F.R.S

LONDON

G. BELL AND SONS LTD.

* 19*5

RO IN GRFAF BKITAIN BY
KD CLAY & SONS, LIMIJED,

BUNC.AY, SUFFOLK.
PREFACE

IT was my endeavour 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 diffi-
culties. The first was the difficulty of under-
standing the minuteness of the scale on which the
action and properties of the atoms must be repre-
sented ; 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

vi PREFACE

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 con-
sideration at the lectures, but are perhaps per-
missible 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.
CONTENTS

LECTURE I

I'AGK

THE ATOMS OF WHICH THINGS ARE MADE . . i

LECTURE II
THE NATURE OF GASES ..... 42

LECTURE III
THE NATURE OF LIQUIDS ..... 83

LECTURE IV
THE NATURE OF CRYSTALS: DIAMOND . .116

LECTURE V
THE NATURE OF CRYSTALS : ICE AND SNOW . 160

LECTURE VI
THE NATURE OF CRYSTALS : METALS . . . 200

LIST OF PLATES

PI ATE To face page

I. (A) MODEL OF BISMUTH CRYSTAL. (&) THE

SHAKING SAND BOX . . .17

II. SHIMIZU-WILSON RAY TRACK APPARATUS . 26

III. ALPHA RA.Y TRACKS .... 28

IV. (A) BAR MAGNETS ON SPIRAL SPRINGS. (B)

MODELS OF ATOMS WITH ELECTRONS . 32

V. (A) FLOATING MAGNETS. (B) CRYSTALS IN

TUBE CONTAINING EMANATION . . 38

VI. (A) TUNING FORK OVER JAR. (B) FOG APPA-

RATUS ...... 56

VII. CIGARETTE SMOKE ..... (>o

VIII. EXPERIMENT SHOWING THE PRESSURE OF

THE ATMOSPHERE .... 65

IX. CAVITATION CAUSING EROSION OF PROPELLER

BLADES ..... 91
X. (A) LARGE DROP OF ORTHOTOLUIDINE. (B)

ONE SOAP BUBBLE INSIDE ANOTHER . 95

XI. (A) CIRCLES CLEARED BY MINUTE DROPS OF

OIL. (B) THE CAMPHOR BOAT . . 104

ix

t LIST OF PLATES

PLATE- To face page

XII. (A) STORMY WATER. (fi) OIL STILLING THE

STORM, (c) GRAPE IN SODA WATER . 106

XIII. CRYSTALLINE FORMS .... 124

XIV. (A) DIAMOND MODEL. (B) PLANE LATTICE IN

THE DESIGN OF A WALL-PAPER . 135

XV. THE CULLINAN DIAMOND . . -145

XVI. (A) LAYERS OF THE GRAPHITE CRYSTAL. (B)

POSSIBLE FORMS OF THE BENZENE
RING 146

XVII. SNOW CRYSTALS OF VARIOUS FORMS . . l6o

xviii. MORF: SNOW CRYSTALS . . . .161

XIX. A HALO AND MOCK SUNS. . . . 163

XX. (A) GLACIER ICE. (B) MODELS OF ICE

STRUCTURE ..... 174

XXI. (A) MODEL OF PENTANE. (B) X-RAY

SPECTRUM OF A HYDROCARBON, (c)

MODEL OF ROCK SALT . . . 186

XXII. TWO PHOTOGRAPHS OF ALUMINIUM . . 202

XXIII. CRYSTAL GRAINS IN A SAMPLE OF STEEL . 202

XXIV. ILLUSTRATING " CLOSE-PACKING " . . 204

XXV. (A) CUBIC PACKING, (fi) HEXAGONAL PACK-

ING . .... 206
LIST OF PLATES xi

PLATE To face page

XXVI. THE YIELDING OF ALUMINIUM UNDER STRAIN 211

XXVII. DAMASCUS BLADES . . . . .226

XXVIII. CEMENT1TE CRYSTALS . . . .226

XXIX. (A) CEMENTITE CRYSTALS BEING BROKEN UP

AND ROUNDED OFF. (B) A NEEDLE
SCRATCH IN A POLISHED PIECE OF

SPECULUM METAL . . . .228

XXX. EFFECT ON SPECULUM METAL OF RUBBING

(WITH FINE EMERY) AND POLISHING
(WITH ROUGED LEATHER) . .228

XXXI. A CONTINUATION OF PLATE XXX. . . 230

XXXII. EXPERIMENT SHOWING EFFECT OF TEMPERA-

TURE ON ELECTRICAL RESISTANCE . 2jO

CONCERNING THE NATURE

OF THINGS

LECTURE 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, individ-
ually 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 him-
self believed to be true. There was a rival set
of views, according to which, however closely

2 THE NATURE OF THINGS

things were looked into, there would be no evi-

dence 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 suffi-
ciently, 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 enquire into the ways of Nature.

Lucretius had no conception, however, of atomic

theories as they stand now. He did not realise
that the atoms can be divided into so many
different kinds, and that all the atoms of one kind

ATOMS OF WHICH THINGS ARE MADE 3

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 indi-
viduals. We should be in despair if we were com-
pelled 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 com-
binations that their importance lies. The atoms
may be compared to the letters of the alphabet,
which can be put together into 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
4 THE NATURE OF THINGS

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 con-

tain, therefore, the essential idea which was neces-
sary for further growth and progress. It withered
away, and the very atom came to be used in a
vague incorrect fashion as meaning merely some-
thing 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

1 See " The Legacy of Rome " (Oxford University Press),

p. 270 an article by Dr. Singer.

ATOMS OF WHICH THINGS ARE MADE 5

are only about ninety sorts of atoms, and of these

a considerable number are only used occasion-
ally. 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 washes, and so the struc-
ture 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

6 THE NATURE OF THINGS

now. We ask ourselves what these atoms are like :

we have been asking the question ever since their
exceeding importance began to be realised 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 realise 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 under-
stand 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 revela-
tions of the truth, lights up the ground over
which we have been travelling 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.

ATOMS OF WHICH THINGS ARE MADE 7

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 theatre 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

8 THE NATURE OF THINGS

in the diamond, because, though heavier individ-

ually, 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 i/io,ooo,oooth
or from the i/io,ooo,oooth to the i/ioo,ooo,oooth
of a centimetre in diameter." 1 Our new methods
tell us that the diameter of the carbon atom in
diamond is 1*54 hundred millionths of a centi-
metre 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. I 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 centimetre, between the centres
of two neighbouring atoms in the pure substance.
For example, the distance between two carbon
atoms in the diamond is 1*54 hundred-millionths
of a centimetre. In the case of oxygen the

1 From a Friday Evening Discourse before the Royal Institu-

tion of Great Britain, March 4th, 1881.

ATOMS OF WHICH THINGS ARE MADE 9

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. i, its
height would be greater than the distance from
the earth to the moon. We need some such com-
Stt-VZR ALUMINIUM COPPER

FIG. i. Sections of some common atoms, in hundrrd-milhonths of a centimetre.

In reference to bismuth see below (p. 12) and Plate I A.

parison as this to make us realise the excessive

smallness of the things of which we are talking.
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 ease with which we all

io THE NATURE OF THINGS

overlook them, and for the difficulty we have in

examining them when at last we have realised
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 arc 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 unim-
portant, 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 com-
bination. 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 arrange-
ments 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

ATOMS OF WHICH THINGS ARE MADE u

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
neighbours, and to say that if one neighbour 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 arrange-

ment 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 suffi-
cient 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 neighbours of the same
kind it is equally distant from them all ; and this

12 THE NATURE OF THINGS

is actually the case. Nevertheless, there are excep-

tions, as in the crystal of pure bismuth, where
each atom has six neighbours 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 them-
selves. 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
ATOMS OF WHICH THINGS ARE MADE 13

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. How-
ever, we need not trouble ourselves about these
matters for the present ; we have merely to
realise that there are forces drawing atoms to-
gether.

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 neighbours ? What pre-
vents 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
one another. 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
handj the atoms are moving so fast that they
have no time to enter into any sort of combina-

i 4 THE NATURE OF THINGS

tion 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 realise that the atoms and mole-
cules 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

ATOMS OF WHICH THINGS ARE MADE 15

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 else-
where 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 simili-
tude, 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 levelled. 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

1 6 THE NATURE OF THINGS

does imitate; and all this merely caused by the

vehement agitation of the conteining vessel;
for by this means, each sand becomes to have a
vibrativc 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 some-

what 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 pre-
scribes. 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. I A.)

ATOMS OF WHICH THINGS ARE MADE 17

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. When-
ever 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

FIG. i, A.

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-rays, in our attempt
to see the very minute atom. They have in-
creased 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 : tech-
nique had reached its highest. The difficulty was

1 8 THE NATURE OF THINGS

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 both 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 will
take radioactivity first.

The atom of radium might be roughly repre-

sented 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

ATOMS OF WHICH THINGS ARE MADE 19

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 any one 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

20 THE NATURE OF THINGS

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 any-
thing 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 dis-
covered 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

ATOMS OF WHICH THINGS ARE MADE 21

never have thought any particle of matter could

have possessed it. When Huyghens 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
Huyghens 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 nought 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

22 THE NATURE OF THINGS

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 realise 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

ATOMS OF WHICH THINGS ARE MADE 23

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 mole-
cules 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

24 THE NATURE OF THINGS

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 straight-

ness 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. However, no other
suggests itself; and, as a matter of fact, it turns

GLASS TOP

S/OES

ATOMS OF WHICH THINGS ARE MADE 25

out that we can explain many other things by its

aid. Consequently, we feel sure that we are on
the right track.
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 experimen-
tal demonstration
if possible, and
convince ourselves
of the reality of
these straight-line
paths. We owe to
Mr. C. T. R. Wil-
son 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

FIG. 2. Section of the expansion chamber

in Mr C. T. K. Wilson's apparatus foi 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 13 suddenly chilled by
expansion and fog settles on the tracks of the
helium atoms shot out by the radium at R.

26 THE NATURE OF THINGS

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
lecture. 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, con-

PLATE II.

N S .2

^-S
(i< -d w>

alS'S

'O- ^

%&*
^po

ATOMS OF WHICH THINGS ARE MADE 27

sequently 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 nega-
tive electricity, and the atom which has lost it is
correspondingly charged with positive electricity.
The electron set free settles on some neighbouring
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, there-
fore, 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

28 THE NATURE OF THINGS

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. 1

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 tjiey 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

1 In the lecture the working of the apparatus was illustrated

by a kinematograph film which had been made for the purpose.
It showed a series of successive expansions, each forming a new
set of lines like those shown in Plate III.

ATOMS OF WHICH THINGS ARE MADE 29

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 defences 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, corre-
sponding to the sun, and round the nucleus there
are to be satellites or planets, which we call elec-
trons. 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 elec-
trons. The electrons are supposed to be in
movement, just as the planets are revolving round
the sun, but the movements are no doubt com-
plicated, and their nature need not for the moment
concern us at all.

30 THE NATURE OF THINGS

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
neighbourhood 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 :

ATOMS OF WHICH THINGS ARE MADE 31

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 hypo-
thesis. 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 towards the
fixed set and is unable to enter in. It seems to
knock at the door at one place after another, but

32 THE NATURE OF THINGS

always recoils. Just so would an electron beat

in vain against the outer defences 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

o / o\<

o y o \*'

O * ,Q O ^

f .' (J

O x->. / , i ,

(*}

(c]

FIG. 3. (),( and (c).

stationary set, the same result would follow.

Here we have a picture representing our atoms,
as we now think of them, beating against each
other and recoiling; each occupies a certain
domain of space and prevents the intrusion of
any other atom.
But if the swinging magnet is drawn sufficiently

PLATE IV.

A. Bar magnets on bpiral springs.

B. Models of atoms with electrons.

ATOMS OF WHICH THINGS ARE MADE 33

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, ). 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 behaviour of the model helps us to antici-

pate 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 each other, 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 deflec-

34 THE NATURE OF THINGS

tion. 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 c. 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
towards 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 further 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 abso-
lutely 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.

ATOMS OF WHICH THINGS ARE MADE 35

These very characteristic pictures are the fruit

of much watching and photographing. Breaks
are found at every expansion, but it may be neces-
sary 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 heUum 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

36 THE NATURE OF THINGS

moisture in the neighbourhood. 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 dis-
covered ; 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 neutralise 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 atten-
dants which they can maintain, and that the
statement of that number describes the atom
completely so far as its attitude towards 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-

ATOMS OF WHICH THINGS ARE MADE 37

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 repre-
sented by a white ball of solid rubber, the
electrons by smaller balls forming the heads of
pins which are stuck into the centre ball. The
pins may be of different lengths (p. 77).

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

38 THE NATURE OF THINGS

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, painte'd 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 to-
gether. The arrangement in which they settle
finally is governed partly by the pull towards the
centre 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 them-
selves 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.

PLATE V.

A. Floating magnets.

When the number of floating magnets is small, they form into a single ring, but
when tl
number is increased, they form concentric rings.
B, Crystals in tube containing emanation.

(From Prof. F. Society's "Interpretation of the Radium" (John Murray), by the

kind permission of author and publisher.)

ATOMS OF WHICH THINGS ARE MADE 39

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 lecture.
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 atten-
dant, 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.
The atom that has lost an electron is now posi-
tively 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

40 THE NATURE OF THINGS

may end this lecture. When the helium atoms

strike certain substances they excite a phosphor-
escent 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 phos-
phorescent sea. The glass vessel (Plate V B) con-
tains 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 imme-
diate descendant of radium itself. When it is
released and is allowed to pass into the tubes
containing the crystals the latter glow in brilliant
colours. 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 com-
pounds, or analyses compounds into elements, he

ATOMS OF WHICH THINGS ARE MADE 41

deals with enormous numbers of atoms in any

operation big enough to see. But in this radio-
active 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 some-
thing 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.

LECTURE 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 posi-
tive 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 arrange-

42

THE NATURE OF GASES 43

ment 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 each others' domains
under ordinary circumstances. Each has an
outer cloak or shell of electrons ; and when two
atoms are brought close together there is a resist-
ing 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 defences may be broken down and
the atoms pass through each other. When this
happens the atoms may afterwards 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 lecture, and
are of importance to us because they make us

44 THE NATURE OF THINGS

realise 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 attrac-
tive 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 each other.
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 pre-
vents us from arriving at a clear understanding.
We have seen how it can happen that when two

THE NATURE OF GASES 45

atoms approach each other at great speeds they

go through one another, 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
neighbourhood, 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.

46 THE NATURE OF THINGS

We are going to consider in this lecture 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 each other. They do not enter
into combination with atoms of other kinds ; in
other words, they do not form chemical com-
pounds. 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

THE NATURE OF GASES 47

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. 1 8, 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 Ib. 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

48 THE NATURE OF THINGS

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 I : 2 : 14/4; the lifting
powers of hydrogen and helium are in the propor-
tion 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

THE NATURE OF GASES 49

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 con-
sequence of Rayleigh's nitrogen experiments.

The ten-electron atom neon, the " new one," is

less common than argon. It has a peculiar pro-"
perty 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

50 THE NATURE OF THINGS

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

ThLE NATUKh Uf UAbfcb 51

temperatures those of a gas. The liquefaction of

hydrogen was accomplished by Sir James Dewar
in the laboratories of this Institution; the
machinery is still here. In the ante-room 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
is giving in this room. The air consists mainly
of a mixture of oxygen and nitrogen molecules.
Other well-known molecules which form gases
under ordinary circumstances are carbon mon-
oxide (CO), carbon dioxide (CO^, methane (CHJ,
and so on. In all these cases when two of these
molecules meet one another 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

52 THE NATURE OF THINGS

table as an illustration, and Messrs. Burroughs

and Watts have very kindly given us one for the
purpose. 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 mo-

tion, once started, lasts
long enough to give
an idea of what must
happen if it were main-
tained indefinitely.

It is natural to ask
how the force of
gravity would affect
the movement of the
atoms in our closed
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

O
o
o

o o

o o

1-

LOOSE
"'CUSHION

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 VCSSCl.

of the motion of the balls is increased.

THE NATURE OF GASES 53

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 each other very
often. But at ordinary temperatures their move-
'ments would be so rapid something like 6000 ft.
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
each other more often than the walls. In the
air, the usual length of path between two suc-
cessive 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 be worth while doing so.

54 THE NATURE OF THINGS

If the atoms or molecules of a gas are con-

tinually 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 distension of a balloon is due to the bom-
bardment 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 backwards.
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 pro-
portional 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 tem-
perature.

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 tyre. The converse is
equally true. If the cushion on our table is

THE NATURE OF GASES 55

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 downwards 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. 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.

56 THE NATURE OF THINGS

In the constant movement of the winds it may

happen that some huge volume of damp air ex-
pands into a space where the pressure has been
lowered and becomes so cold that the water
vapour 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 tufye 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 experi-
ment 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

PLATE VI.

Tuning fork over jar.

B. Fog apparatus.
The long glass tube is full of fog.

THE NATURE OF GASES 57

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,

58 THE NATURE OF THINGS

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 oscilla-
tions 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

THE NATURE OF GASES 59

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

60 THE NATURE OF THINGS

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 diffu-
sion of one gas into another is really the same in
character, because the gaps between the 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 con-
vection 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 rises in a waving pencil,
which becomes spread and bent and twisted into
delicate spirals and curved surfaces. As the

PLATE 1 VII.

THE NATURE OF GASES 61

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. 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 each other, 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

62

THE NATURE OF THINGS

to every one ; 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 move-
ment 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. 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

FIG. 5. Reproduced from

Faraday's Chemistry of a
Candle.

THE NATURE OF GASES 63

figure receives a violent knock from the vibrating

prong of the tuning fork.

When Sir James Dewar designed the " vacuum

FIG. 6. Tuning fork and pith ball.

The pith ball is hurled violently from the vibrating fork.

64 THE NATURE OF THINGS

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. No heat could be conveyed to the
liquid air by conduction or by convection. Heat
can also travel by radiation through the ether ;

FIG. 7. Vacuum flask.

Observe the tube at the bottom (now sealed off) through which the air has been
drawn from between the inner and outer glass of each flask.

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 mole-

cules of a gas gives it perfect divisibility. 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
PLATF VffT

Ihe incliarubbcr figure collapses wnen connected to the vacuum pump.

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.

THE NATURE OF GASES 65

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 light-
ness 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

66 THE NATURE OF THINGS

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 aeroplane 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. A piece of paper of any convenient size,

THE NATURE OF GASES 67

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
under side of an inclined plane. 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

FIG. 8. Pieces of paper of various forms fluttering to the ground.

started to move downwards 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 aeroplane when gliding moves in a

68 THE NATURE OF THINGS

steady, stately fashion, and the design of the

wing is in reality anything but simple, as builders
of aeroplanes 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. A bird's wings are used not only
for gliding, but also for flapping, and there is a

FIG. 9. Drawings, after Lihenthal, 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).

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

THE NATURE OF GASES 69

rib of the feather does not always lie in the

centre, 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 louvred window and the
air passes through ; when the wing is forced
down they close, pressing tight against each other.
The two drawings of Fig. 9 A are adapted from

ILp-sbrok*,

Down-siroke,

FIG. gA. Gull in flight. On the down-stroke the gull's wing has turned over
showing the under side, thus giving a shove forward.

Otto LilienthaFs " 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 character-
istics 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

70 THE NATURE OF THINGS

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
those here. 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

THE NATURE OF GASES 71

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 pro-
perly. As the ball moves for- A
ward 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
forwards in the direction of
flight, the right-hand side is
moving the opposite way, so
far as spin goes. The conse-
quence 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.

FIG. to. 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.

72 THE NATURE OF THINGS

This makes the ball tend to rise as it flies. Some-

times 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. 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 a high-speed ball is so
great. We should drive a ball much further if

Ground

FIG. it. Regular flight of golf ball: a pocket of condensed air, shown by the
shading in the drawing, keeps the ball up.

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 the

fast-spinning golf ball, is often curved upwards,
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 forwards
faster than the bottom. This makes the ball

THE NATURE OF GASES

73

duck, so that, though hit very hard, it keeps in

the court after passing the net. 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 marvellous
spectacle. Of
all ways of
studying the
effect, the sim-
plest, perhaps,
is by the use
of toy balloons /
which nowa- /
days are W
toughly made
and will stand

... FIG. 12. Action of stroke of tennis racquet, giving

mUCh. knOCk- spin to the ball and making it drop quickly over the
net (exaggerated).

ing about. It On the right, section of racquet and ball before the
stroke : arrow showing direction of motion of racquet.

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 sorts of swerves and soarings 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

LINE OF NET

74 THE NATURE OF THINGS

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 mole-
cules 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, furnish a ready understanding of their
behaviour.

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 lecture. 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 ques-

TH NATURE OF GASES 75

tions 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, numbers 2, 10, 18, 36, 54, 86.
The first thing that strikes us is that there are
curious connections between these numbers. If
we write down the successive differences we have
2, 8, 8, 1 8, 1 8, 32. The numbers 2, 8, 18, 32
are twice the squares of I, 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.
76 THE NATURE OF THINGS

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 3456789

Alu-

Neon. Sodium. Magnesium, minium. Silicon. Phosphorus. Sulphur. Chlorine.

10 ii 12 13 14 15 16 17

Argon. Potassium. Calcium, and so on.

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 each other in their main property of
unsociability, are in the same column. It then
appears that lithium, sodium and potassium,
which also closely resemble each other in their
properties, are in the next column, and that the
same remarkable classification runs across the
page. The mutual resemblances of the sub-
stances in the same column are manifested in
innumerable ways : they form one of the great

THE NATURE OF GASES 77

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 rela-
tion to any other may well be determine^ 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 present-
ment 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 succeed-
ing 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

78 THE NATURE OF THINGS

electrons taking their place in new groups.

Thus, sodium, like lithium, has one in its outer-
most 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 par-
ticular 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 circum-
stances -to dissolve existing combinations and
form new ones, certain rules appear which are
directly connected with the numbers of the

THE NATURE OF GASES 79

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 behaviour 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

8o THE NATURE OF THINGS

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 dis-
tinguishing 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,
THE NATURE OF GASES 81

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 above), 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 com-
plete 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

82 THE NATURE OF THINGS

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 pro-
perties which we have been considering as the
result of the weakness of tendencies to associate
and the undisputed sway of movement.
LECTURE 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 each other, 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

83

84 THE NATURE OF THINGS

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
jheir 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
for ever, 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
vapour. That may happen before the bowl is
empty ; but if the air in the room is continuously
removed, carrying the water vapour 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

THE NATURE OF LIQUIDS 85

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. In the hot Australian
summer it is usual to see the bag hanging under the
verandah 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.

86

THE NATURE OF THINGS

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, al-
though the upper
bulb has been no-
where 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

FIG. 13. The cryophorus.

The lower bulb, which is empty, is im-
mersed in liquid air. Th? upper bulb
contains water which quickly freezes.

THE NATURE OF LIQUIDS 87

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
88 THE NATURE OF THINGS

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. 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 im-
pressive form. Here is a bent glass tube con-
taining water and no air. The water is made to

THE NATURE OF LIQUIDS 89

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 attach-
ment Of the ^ // ONLY: HO AIR

water mole-
cules to the

FIG. 14.

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 realise the magnitude of the forces that
keep the molecules of solid iron together ; we are

90 THE NATURE OF THINGS

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 mole-
cules 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 one another ; the blow is
felt by the hand that holds the tube. 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 wear-
ing away of the propellers of ships that are driven
by rapidly turning screws. The illustration shows

PLATE IX.

The right-hand figure shows erosion in a portion of an early propeller blade ot the
" Maiiretani
Notice the small bite m the edge of the blade shown m full in the left-hand figure.

Photograph ot the < auctions foimcd l,j ,i propeller m tk- experimental tank of the
Pardons
Marine Steam lurbinc to. Ihc piopt-llcr is the disc-shajx'd object at the left
rentie of the
photograph. There are three blades on it, and each is leaving a rniU n \\ line of
bubbles m
the water which goes past the blade. We can see where the spuals bi gin at tb< si
tew.

[Reproduced by courtesy of the Manganese Bronze and Brass Co., Ltd.

THE NATURE OF LIQUIDS 91

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 explana-
tion was found in the fact that the steamship was
advancing so fast and the screws were revolving so
rapidly that the water could not fill up entirely
the holes that the blades left behind them. The
illustration shows the cavities as they are formed
in a model tank in the Turbinia Works at New-
castle (Plate IX B). They are arranged in spirals ;
we can trace in the figure the spiral belonging to
each of the propeller blades.

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 labour 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

92 THE NATURE OF THINGS

blade has been improved. A very striking experi-

ment made in the course of these researches is
illustrated in Fig. 15. The strong metal vessel
shown in the centre 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 mo-
mentum 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
afterwards, on account of the pres-
sure 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 audience will be familiar with a

FIG. 15. Parsons'

water hammer.

THE NATURE OF LIQUIDS 93

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

DROPS OP MERCURY ON A TABLE

FIG. 16.

The small drops are almost perfect spheres. The large drops
are flattened out.

breaks up into round drops which run about

as if they were round and hard. 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 wet-
ting means and implies we have yet to consider :
it is a very important part of our subject. Gravi-
tation also interferes with the tendency of a
liquid to gather into spheres. When the drops
of mercury are very small they look perfectly
94 THE NATURE OF THINGS

round, but larger masses are more like thick discs

with rounded edges. If we seek for good examples
of the formation of spheres by the general attrac-
tion of the molecules for one another, we must
contrive to avoid the influences both of wetting
and 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 gravita-
tion 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

PLATE X.

A B

A. A large drop of liquid orthotolwdine 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.

THE NATURE OF LIQUIDS 95

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 circum-
stances 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 wobbling 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

96 THE NATURE OF THINGS

floats in it. If we put clean water into a clean

glass vessel, we see the water heaping itself
against the side. 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

IRON BALL FLOATING ON i i

MERCURY /SECTIONAL] forced down into

I DRAWING J

a dish full of mer-

FIG 17.

cury 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 ex-
planation is simple
and in accordance

x>j ~ ~ _m

GLASS 44- .WA TER w ith the principles

which we have been

FIG. 18. Water heaped up against glass Considering. If the

wall which it wets. t

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

THE NATURE OF LIQUIDS 97

rapidly in pressure if the plate were raised. 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 be-
tween the plate and
the bottom of the
vessel.

Arlrr*T r\f flni/-l FlG - J 9- Glass P la te at bottom of dish

U r UI I1U1U containing mercury. The plate is shown

i slightly hf ted from the bottom, in order to

trieS tO draw illustrate the refusal of the mercury to

. enter the vacuum so made.

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 ex-
posed 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 con-
venient 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

98 THE NATURE OF THINGS

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 unsoci-
able : 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,

THE NATURE OF LIQUIDS 99

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 along-
side. 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 out-
side, of course, and where both kinds of molecules
are present it is the long chain molecules that
form the outside layer. A very simple experi-
ment 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

ioo THE NATURE OF THINGS

stretched across it. In the film floats a ring of

fine cotton 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 touch-
ing 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 fea-

ture of the soap bubble
is its reluctance to join
up with another bub-
ble. If we blow a
bubble on a ring (see

FIG. 20. 6 \

A loop of very fine cotton is floated on Tig. 21), WC Hiay take

the soap film, and the part of the film inside 11111

the loop is touched with a hot needle. a SCCOnd bubble and

Instantly the loop flies into a perfect circle.

(By courtesy of Prof. C.V. Boys.) ^^ fc aga i nst j^e

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. There is no tendency for

THE NATURE OF LIQUIDS

101

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. This is

very clearly seen

in another of the

wonderful

ex-

FIG. 21. Two bubbles in collision.

The two bubbles are pressing one another, and

may be rubbed on one another, 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.)

periments of C.
V. Boys.* A
bubble is blown
on a ring held
in a stand (Fig. 21 A). 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 suit-
able size is released by a skilful
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

* " Soap Bubbles and the Forces which Mould Them,"

C. V. Boys.

FIG. 2 1 A.

102 THE NATURE OF THINGS

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 one another 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 saponins, chain-like formations which
are found in many plants and trees. So also the

THE NATURE OF LIQUIDS ic

foam that gathers on the shore is believed to b

due to the presence of similar molecules forme
in the sea-weeds.

We have learnt much about the form of thes

long-chain molecules within recent years. I
particular we are indebted to the late Lor
Rayleigh, to Devaux in France, to Langmuir i
America, to Hardy and to Adam in England fo
the examination of what happens when oils ar
allowed to spread on water surfaces. We ca
repeat one or two of the experiments in order t
get an idea of the magnitude of the effects c
which we are speaking. We take a clean wate
surface, that is to say, a surface free from an
contamination by oil or grease. It is convenien
to attach a rubber tube to the tap, and let th
free end of the tube lie at the bottom of a basi:
so that the water wells up and overflows th
edges, carrying away any dirt that has settled 01
its surface. We now spread on the water a thii
dusting of talc powder or anything else that i
convenient. Next we take a fine drawn glas
point or needle and dip it into oil olive oil wi]
do and then, after wiping nearly all the oil ofi
dip the point of the slightly greasy needle int(
the water surface. Instantly a circle is cleare<
round the needle (Plate XI A). It appears tha

104 THE NATURE OF THINGS

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 with-
out. 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. 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.

XL

A. Circles cleared by minute drops of oil.

1. The camphor "boat,

A. smq.ll piece of camphor Is fasten?*! at the- stern of a very light boat, ami as
it
dissolves in the water tiw. solution form* a film on the suifact*. It is so eagn-
to

do & that it diivos the bout away $o as to nmlce room for itst4f, If a Mtte oil is
pat
ciii the water and a film H over It, the boat stops, II the oil partly rovers

the water, the stops as as the ruler which is Iield by the operator m tuc

pic two is pashetl so fat forward that tlte oil covers the surface *ft to it.

THE NATURE OF LIQUIDS 105

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 some-
where 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 further. 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

io6 THE NATURE OF THINGS

dissolves, the solution shopts 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 centre 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

PLATE XII.

THE NATURE OF LIQUIDS 107

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 afterwards 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

io8

THE NATURE OF THINGS

the outside their inactive ends, which have very-

little attraction for the water molecules. So
water spilt on a greasy surface gathers into drops,
just as mercury when it is spilt on the table ;
the form of the water is due to the general attrac-
tion 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, per-
haps, is the floating
of a greased wire
sieve (Fig. 22). 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 afterwards be
removed. To show that the pores are quite

FIG. 22. Greased sieve. (By courtesy of

Prof. C. V. Boys.)

THE NATURE OF LIQUIDS 109

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 :

no THE NATURE OF THINGS

washing with soap and water is efficient. No

bubbles form on them and they stay 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 realise 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 each other 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 some-
where 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
THE NATURE OF LIQUIDS in

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

ii2 THE NATURE OF THINGS

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 each other'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 -fa 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

THE NATURE OF LIQUIDS 113

inch of each other, move together, at the end

quite violently. 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

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 5, 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 towards the other.

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, over-
come 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.

H4 THE NATURE OF THINGS

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

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.
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

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 f greater than at

Q'. Thus the balls are forced apart.

forces that are in action. When the vessel con-

taining the water is clean, and the water is heaped
up against the sides, the clean glass balls are
attracted to the side, just as they are attracted

THE NATURE OF LIQUIDS 115

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 towards the edge of the vessel, the clean
balls leave for the middle and the paraffin balls
come to the side and stay there.

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 each other,
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.

LECTURE IV

THE NATURE OF CRYSTALS : DIAMOND

WE have seen that when the effects of move-

ment 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 con-
nections 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 neighbours
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

116

THE NATURE OF CRYSTALS 117

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 solidi-
fication takes place. It is all a matter of the
balance between the two opposing agencies,
motion and mutual attraction, and it is easy to
realise that the melting points of substances may
differ very widely from each other.

Furthermore, a molecule is not to be thought

of as a body of vague and uncertain form exerting
a loosely directed attraction on its neighbours.
When two molecules are brought together they
may or may not draw tightly together : every-
thing 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

n8 THE NATURE OF THINGS

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 corre-
sponding parts of the other. There may be
more than one way in which molecules can be
joined up, and in consequence different struc-
tures 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

THE NATURE OF CRYSTALS 119

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 neighbouring 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 substances.

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
120 THE NATURE OF THINGS

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
towards our ideal purpose that is to say, towards
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 uncon-
sciously, 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

THE NATURE OF CRYSTALS 121

solid, and I hope to describe it in this and the

following lectures, 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 mole-
cules 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 move-
ments 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 each

122 THE NATURE OF THINGS

other more often, so that their association is

encouraged. When the liquid has entirely dis-
appeared, 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 ar-
ranging themselves before
they finally settle down,
or refusing to take their
places before they are

FIG. 26. r '

presented to each other

in the right way.

We can well imagine that under such circum-

stances a regularity in the arrangement will
ensue. Suppose that a flat body, shaped like A,
had four centres 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 centre lay always close to one another,
we might arrive at some such arrangement as
is shown in Fig. 26.

Whatever arrangement we adopted we should

naturally find in the result a certain regularity,

THE NATURE OF CRYSTALS 123

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 con-
sequence of the complete fulfilment 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 mani-
fest 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. 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

I2 4

THE NATURE OF THINGS

methods. A few crystal forms are shown in

Plate XIII.

There are three stages in the arrangements of

matter : the single atom as we find it in helium

gas ; the mole-

cule as it is
studied by the
chemist; and
the crystal unit
which we now
examine by X-
ray analysis. To
take an exam-
ple, there are
the atoms of
silicon or of
oxygen. The
molecule of sili-
con dioxide con-
tains 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 con-

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.

BI and B t . In each of these there are tuo sorts of

peg : i.e. one lot of pegs pointing to the right and one
to the left. Two varieties of arrangement.

Cj and C,. Three sorts of peg : pointing in three

different directions. The two arrangements C t and C a
give a right-handed and a left-handed screw respectively.

XIII

A. Sulphur trioxide crystals which have grown from vapour in a. glass vessel 15.
Erythntol
crystal, grown from solution. C. Ammonium chloride : ideal and distorted cubital
crystals
from solution containing urea. D. Crystal forms: Quetcite: Cocositc. H. Crystal
forms:
Alizarin, Rubidium alum; Sodium chloride; Ammonium cobalt sulphate; Phthahc acid.
F. Ammonium chloride: fern-leaf crystals (octahedral) arid cubical crystals from
solution
containing urea.

THE NATURE OF CRYSTALS 125

tains 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
polarisation of light, and this property is associ-
ated 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 l 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 l or C 2 , or, as it is generally said,
may be either right-handed or left-handed. 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. 2/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.

126

THE NATURE OF THINGS

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 sub-
stances were
confused with
each other.
It is appro-
priate, there-
fore, 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
FIG. 27A.

THE NATURE OF CRYSTALS 127

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 orientated to each other
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 centres 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 tem-
perature of the latter so carefully adjusted that
the atoms of sodium and chlorine are only tempted

128

THE NATURE OF THINGS

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 sus-
pended crystal. If the solution is too hot, the

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 NATURE OF CRYSTALS 129

suspended crystal will be dissolved in the unsatur-

ated 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. The principal conditions are time and
quiet, a solution of the salt just ready to pre-
cipitate its contents, temperature and strength
of solution being properly adjusted for the pur-
pose, 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 realised 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

K

ijo THE NATURE OF THINGS

there is , no obvious crystallisation Nature has

been attempting to produce regular arrange-
ments, and that we have missed them hitherto
because our means of detecting them have been
inefficient. The regularity of Nature's arrange-
ment 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 marvellous skill in detecting and

THE NATURE OF CRYSTALS 131

interpreting such changes. We may be unsuc-

cessful, 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 com-
pared 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 dimen-
sions 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

132 THE NATURE OF THINGS

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 impres-
sions 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 over-
come 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

THE NATURE OF CRYSTALS 133

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 keen-
ness 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
134 THE NATURE OF THINGS

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, how-
ever, 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

A. Diamond model.

The modc'l 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) bv thick lines, (b) by thin lines. The

THE NATURE OF CRYSTALS 135

occurs ; if a real marking is disallowed, a mental
marking must suffice. 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

/ ,/^TT " LST I J^

^^^>

FIG. 29. Space lattice.

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

i 3 6

THE NATURE OF THINGS

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). Each little cell of the lattice is
bounded by six faces, which are parallel in pairs.
The cell can have any lengths 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,

u. ? JT '

^ has the special shape that

j g ^^ ^ ^ ^ ^ ^

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.

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

4-8*
FIG 30. Sizf* and dimen-

millionths of a centimetre.

THE NATURE OF CRYSTALS

137

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 cry- o o
stal ; in Fig.
32, A, they are
represented by the line W W and the parallels to
W W. 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 centre of a disturbance when a wave
passed by. At a little distance from the row AA
these minor disturbances link themselves together
in a connected set of waves, represented by the
FIG. 31. An atom group is associated with each
point of a lattice.

138 THE NATURE OF THINGS

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 further 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 each other. But if the wave length of the
rays, the distance between AA and BB (which
are really planes seen edgeways), and the angle

THE NATURE x OF CRYSTALS 139

at which the waves meet AA, BB are correctly

adjusted to each other, then the lines aa, bb, etc.,
do coincide with each other. 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 re-
flections 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 adjust-
ment 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

PQ
FIG. 32. Reflection of X-rays.

140 THE NATURE OF THINGS

therefore for reflection. The line A'B'B must

be longer than AB by a whole number of wave
lengths. If I is the wave length, d the distance
between planes, or spacing, as it is usually called,
and 6 the angle shown, then :

nl = A'B'B - AB = A'D-AB = DN = 2</sin0,

where n is any whole number.

FIG. 33. The law of reflection of X-rays.

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

THE NATURE OF CRYSTALS 141

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. 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

H2 THE NATURE OF THINGS

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.

THE NATURE OF CRYSTALS 143

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 chemis-
try. 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 con-
stituent 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 dimen-
sions. Most of us find a great difficulty in our
first efforts to realise 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.

144 THE NATURE OF THINGS

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 centre 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 centres of two neighbouring carbons is
1*54 Angstrom Units; this unit is the hundred-
millionth of a centimetre. It does not seem
surprising that this particular plane should be
[ISy courtesy of Joseph Archer & 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 NATURE OF CRYSTALS 145

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. 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 labour
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 the.se rings
out from the model, it has the appearance of

146 THE NATURE OF THINGS

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 NATURE OF CRYSTALS 147

the case. These substances are called the

" paraffins " (see the latter part of the next
lecture) ; 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 pre- H H H H H H

paration are preserved as H c c c c c c H

i i i i i i
an historical treasure in H H H H H H

the Royal Institution. FIG. 34 .-Hexane.

The molecule of this

substance contains six carbon atoms 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 chemi-
cally 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 Kekule, who sug-
gested 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

148 THE NATURE OF THINGS

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.

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

H \ / H substances. The ring is the

n~c^ ^c H basis of many thousands of

H _ _ H known molecules, including

H/ ^ c \ H dyes and explosives, drugs

H H such as quinine and sac-

F IG . 35-Hexahydrobenzene.

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 neigh-
bours 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
THE NATURE OF CRYSTALS 149

molecule can exist contentedly enough without

them. 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. The new mole-
cule has the structure shown in
Fig. 36, and is known as toluene, ^
a very important substance, a i

liquid at ordinary temperatures.

A second hydrogen can be re- j

moved from the ring molecule H

FIG. 36. Toluene.

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

ISO THE NATURE OF THINGS

hypothesis gives an immediate answer. There

are three ways and no more of making the sub-
stitutions, which are shown in the figure. The
bromine atom may be next to the methyl group,
or next but one, or next but two.

The three molecules have different shapes, and

therefore may be expected to have different
properties ; und there is no doubt that there are

i i i

H C H H C H H C H

"Y
H H Br

(1) (2) (3)

FIG. 37. Bromo toluene.

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

THE NATURE OF CRYSTALS 151

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 o 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 lecture).
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 neighbours are inclined to one another
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

152 THE NATURE OF THINGS

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 Plate
XVI B 2. Whether the benzene ring is actually
puckered under all circumstances, or is sometimes
flat, in which case the angle is 1 20 (Plate XVI B i ),
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 accumu-
lating, 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

THE NATURE OF CRYSTALS 153

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
each other 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
154 THE NATURE OF THINGS

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 sub-
stance 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 dimen-
sions 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.

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.

THE NATURE OF CRYSTALS 155

In general appearance they resemble the crystals

illustrated in Plate XIII D.

The chemist finds that naphthalene consists 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

H H

X-ray analysis, it I I

is found that the H\ x xC \ x xC \ ^-H

unit of pattern A III

contains two mole- H X ' CN ^ C X X( '\ /^H

cules and that the | |

shape of the cell H H

1-1 i H H H

which contains the | I |

unit is as shown H\ rX x c \ r x xC \ r / c \^^H

in Fig. 39. The

dimensions of the H X

cells are given be- | j J

low the figures. H H H

FIG. 38. Naphthalene and anthracene.

If the two cells

are compared with each other, it is note-

worthy 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. The
natural inference is that the double and treble
ring molecules lie parallel to OC in the two
cases, and that the difference between iri8 and

i S 6

THE NATURE OF THINGS

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

NAPHTHALENE

ANTHRACENE

FIG. 39. Unit cells of naphthalene and anthracene, drawn to the same scale.

OA OB OC
Naphthalene. 8-34 6-05 8-69 Figures in Angstrflra

Anthracene. 8-58 6-02 11-18 Units: see p. 144.

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

THE NATURE OF CRYSTALS 157

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 to-
gether, but weakly joined to its neighbours 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.

The weakness of the bonds that join molecule

to molecule is the cause of the softness of the

I S 8

THE NATURE OF THINGS

organic crystal and of the ease with which it can be

melted. For the same reason naphthalene " sub-
limes " : it evaporates while in the solid state.
Whole molecules are flung off from the solid,
and form a vapour which may crystallise again
in a cooler part of the containing vessel.

^-'Cleavage

FIG. 40. Showing mutual relations of three naphthalene molecules and parts o

others.

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 each other 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 NATURE OF CRYSTALS 159

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 lecture is already long enough, we
can consider the chain in our next lecture, in
addition to the ice crystal, which will be our
main subject.

LECTURE 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 imagin-
ation. Water is one of the most obvious sub-
stances 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 window-pane, so quaint and charming in
their outline. It is true that the blocks of ice
that come from the freezing works are not remark-
able 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.

1 60

PLATE XVII.

[13 y courtesy of the Chief of the U.S.A. Weather Bureau.

Snow crystals of various forms.
(From Monthly Weather Review, U.S.A.)

PLATE XVIII.

[Ily courtesy of the Defit of Scientific Research oj tin.

staK (1 mm the iU<>ath1> U < itfu r 15ur< an, I'.S.A.)
111^" ihc^liiitish Aiitantic i:\pt clitiuii, 1910-1913.")

THE NATURE OF CRYSTALS 161

The manufacture of commercial ice is too rapid

to bring out the ice design : the crystalline
structure is there, but the mass contains a multi-
tude 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 snow-

flakes 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 outwards and other little arms

M

162 THE NATURE OF THINGS

grow 'out from each of them to right and left,

and from these yet smaller arms, and so on ; all
the arms joining each other 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 crystallisation, and seem to be the
consequence of sudden and rapid freezing. The
arms stretch out from the centre 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 crystallisation ; 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.

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). Sometimes, it is supposed,

PLATE XIX,

The first picture 1 is due to Mr (i. A. Clarke, and is taken from Mr. F. J.
Whipple's article on
MetomKnal Optus m tlir "IMdionarv of Applied I'hvsics," Yol HI, p. ^9 (by courtesy
of

MrsMs M.inmll.in \ C<> } It Mum--, i lul> \\\<\ \\\n< \, sinis I'hr KM ond |m t HIT
is from an interesting
tlic iKiss-ssioiKil the Kn\al liiMiliilinii it s|,d\\> the h.ilu and the " sun-
pillar."

THE NATURE OF CRYSTALS 163

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 Priest-
ley's " Glaciology," British Antarctic Expedition,
1910-1913.

The prisms and

plates and " tea-
tables " are believed

tO be the CaUSe Of the The hexagon repress a magnified

. 111 section of an ice prism. ABCD is a ray

mock suns and nalos passing through a.

that are observed in high latitudes (Plate XIX).
Suppose that the hexagon in Fig. 41 repre-
sents 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 2i5o / , which is, in the language of
physics, the angle of minimum deviation. 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 P is properly placed. In the
figure the prism is placed symmetrically, in which
case it is known that the deviation SPE has its

164

THE NATURE OF THINGS

minimum value. Any prism lying between SPE

and SP'E, such as P , 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. A prism P x may send light to the eye,
FIG. 42. Shows how the ice halo is formed. For a description see the text.

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

THE NATURE OF CRYSTALS 165

minimum value the further 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 con-
sequence 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 coloured,
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 explan-

ation 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

w
5?
TfifS

THE NATURE OF CRYSTALS 167

round J, the eye continues to be illuminated. If

there were prisms all round 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. 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 post-
cards, 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
Vinrirnntal nnsitinn. The ronsennenre is that

i68

THE NATURE OF THINGS

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 emphasised, 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 be-
come 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. Curiously
enough, some of the bodies tend
to fall with the plate leading the
4 I0 ^ F J^ way, a *d som e with the plate in
Tnfthr^wltlrfna the Te^T. The point was examined
mathematically by Besson, who
showed that when the diameter of the plate is
small compared to 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

THE NATURE OF CRYSTALS 169

axis horizontally under the surface of the water

and then let go.

The whole of the vertical line through the

centre 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 crystallises 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 explor-
ation pictures are to be found of table ice breaking
up into six-sided vertical columns, like the basalt
columns of the Giants' 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 each other 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-

1 70 THE NATURE OF THINGS

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

LAIN TERN ->

FIG. 45.

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."

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 NATURE OF CRYSTALS 171

FIG. 45A. This illustration of the " flowers of ice " is taken from the original
sketch in TyndalTs " Heat." It represents a certain stage in the growth of the
flowers : at a later stage the whole screen is covered with interlacing figures.

1/2 THE NATURE OF THINGS

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. 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 night-time is far better than
anything frozen under the usual conditions of
ice manufacture. Many disappointing trials were
made to prepare a satisfactory experiment for
these Christmas Lectures. After all, there was a
kindly frost on the night before, and 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 centre

of the ice flower. Tyndall was greatly interested
in it, and explained its occurrence. When the

THE NATURE OF CRYSTALS 173

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 positions.

Let us now turn to the analysis of the structure

of the ice crystal which X-rays have made possible.

1/4 THE NATURE OF THINGS

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 neighbours of like kind round every atom.
In this case, it is the oxygen atom that stands at
the centre 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 each other. In ice there are the hydro-
gens 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 neighbours, and every hydrogen has
two oxygen neighbours, 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 re-
present 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 centre of one oxygen and
the centre of an oxygen neighbour, a distance which

PLATE XX.

ill-

o r ^ +3
-f= T=! ._ K

a -So

THE NATURE OF CRYSTALS 175

is the sum of the diameters of oxygen and hydro-

gen. The oxygen atom may take all 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 realise ; but it is worth while trying to under-
stand 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 I, if they lie directly on the
base of the crystal, and as i' if they are the atoms
which are somewhat raised above their neighbours
in the layer. Take another layer exactly like
the first, and write 2 everywhere instead of I,
and place it on the first, so that each 2 comes
over a i' that is to say, an atom in the lower
level of the second layer comes over an atom

THE NATURE OF THINGS

in the higher level of the first. This is what

happens in diamond. The combination is shown
in Fig. 46, B, where i'z means that the atom 2 lies
over the atom i'. Now take a third layer, which

(I) w () 05

C D
(13)

^/-N^^N^/T5N^/-X ^

fo fo fa (ft

<<r

FIG. 46. Arrangement of atoms in ice structure.

we may denote by using 3*8, 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 I 2 3 I 2 3, we get
the diamond structure.

THE NATURE OF CRYSTALS 177

If now we begin again with a layer of i'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 9 s has been turned round in its own
plane through 180 we then repeat the first
layer, and alternately have I 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 realise 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

1 78 THE NATURE OF THINGS

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. The wire pro-
ceeds to sink slowly into the ice, but as it does so
the ice closes up behind it, and when, finally, the

FIG. 47. Wire cutting through ice (from Tyndall).

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

THE NATURE OF CRYSTALS 179

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.

Crushed ice can be moulded under great

pressure into various shapes. We may, for
instance, make a crystal cup : we need two or

FIG 48. Ice moulds and the making of a cup (from Tyndall).

three boxwood moulds 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 moulds 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,

i8o THE NATURE OF THINGS

and employed them as an illustration of his argu-

ments. 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
TyndalFs 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

THE NATURE OF CRYSTALS 181

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 behaviour 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
emphasised 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

1 82 THE NATURE OF THINGS

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). If it is turned on its
edge and placed so that the layers which were hori-
zontal 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

THE NATURE OF CRYSTALS

183

were horizontal are perpendicular to the line

joining the support they slide on one 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

rfiove 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 FIG. 49. A set of planks'arranged as in A

* J would bend under a weight. Set up on edge

together. If We reSt as in B ' they would bend far less. If arranged

one fairly flat piece -^tani'VyTouTd y^Su^

B
184 THE NATURE OF THINGS

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,
from want of time, we were obliged to leave over
from the last lecture. 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 arrange-
ment 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

THE NATURE OF CRYSTALS 185

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 at 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 lecture, but left the chain until to-day. 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 :

H H H H H

I I I I I
H C C C C C H

I I I I I
H H H H H

Pentane is an inflammable liquid used in standard

1 86 THE NATURE OF THINGS

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 arrange-
ment. 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

PLATE XXI.

ing five tarbou atoms. The larger

halls represent carbon atoms, the smaller I^ch.^ciib.

B. An X-ray spectrum of the hy dioi arbuii containing 18 carbons obtained by

the method shown 1.1 Fig. 52. (Muller )

C. The model shows the arrangement of the sodium and chlorine atoms in rock-salt :
the dark balls repr

is shown : there is i

present sodium, the white chlorine, or vice versa. Only arrangewen

s no attempt to show the size or shape of the atom.

THE NATURE OF CRYSTALS 187

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 :

H C H

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 penta-
cosane, 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

1 88 THE NATURE OF THINGS

hold on each other : 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 behaviour 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. When
there is only one carbon in it, the chemist repre-
sents it thus :

H-C<

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

THE NATURE OF CRYSTALS 189

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 :

f^ (~^<y

v^~~~*^/\

I o

H X H

Butyric acid has four carbons ; it is the substance

that gives to rancid butter its peculiar taste and
smell. Laurie 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

190 THE NATURE OF THINGS

it by an oxygen and a hydrogen in combination.

Thus :

H H

H C C O H

is the ordinary alcohol.

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

THE NATURE OF CRYSTALS 191

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 :

109 2tf

AAAA

FIG. 50. Chain from diamond.

in which the angle that recurs at every bend can

be calculated to be 109 28'. 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 neighbours, would make four points
symmetrically arranged, like the four points at
which each carbon atom is attached to its four
neighbours 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

192 THE NATURE OF THINGS

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 examin-
ation 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. 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,
Dr. Le Sueur, had prepared a great number of
these chain substances in a pure state, and these
were fortunately available. Those and many

THE NATURE OF CRYSTALS

193
others have now been examined, with very-
interesting and, on the whole, simple results.

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-mil-
lionth 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 though a pile of glass plates. The
principle of the experiment has already been
described on p. 140. Suppose S is the source of
the X-rays, and P^ 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

FIG. 51 Diagram-
matic arrangement of
the molecules m the
layers of a substance
like stearic acid, or a
hydrocarbon such as
pentane.

194 THE NATURE OF THINGS

and the reflection is strong. We may imagine

the reflected ray going off on the line CR^ and
making its mark at R x 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 each other. But
when the plate has been
turned sufficiently, another
P2

FIG. 52. The method of making the X-ray spectrum of a

hydrocarbon. The X-rays from X pass through a limit-
ing 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 reflected pencil, CR lt which makes an
impression on the photographic plate at R t . If the plate
is turned sufficiently there is another reflection, R,, when
the plate occupies the position P,P g , and so on.

general reflection appears, because the reflec-

tions 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 photo-

THE NATURE OF CRYSTALS 195

graphic 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). 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 18 carbons is shown in Plate XXI B.
It was obtained by Dr. Miiller. 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
196 THE NATURE OF THINGS

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 regu-
larly. 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

THE NATURE OF CRYSTALS 197

same effect in the case of gold leaf, as we shall see

in the next lecture.

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. 188), 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
hydrogens ; the two carboxyl groups are in the
centre. 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 con-
sidered 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

198 THE NATURE OF THINGS

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 inner-
most 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. (See p. 76.)

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

THE NATURE OF CRYSTALS 199

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 crystallises
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 molecule, 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 3 , 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 3 group is not round.

LECTURE VI

THE NATURE OF CRYSTALS I 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 useful-
ness 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 magni-
tude of the metal industry in this country alone,

200

THE NATURE OF CRYSTALS 201

to realise 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 crystallisation. In the very centres
of the metal industries it has been realised 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 produc-
tion. 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.

202 THE NATURE OF THINGS

It can show the existence of the separate crystals in

the metal, but not the arrangement of the atoms
in the crystals (Plates 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 know-
ledge 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 develop-
ment has been directed by knowledge and antici-
pation. 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

PLATE XXIT.

T\vo photographs of aluminium the sin! i< < has hern prep, in <1 so as to ^ho\\ the
diffcieiit
crystals. The crystals statU r the incident li^ht dnferently heiaii < tln-\ an- set
m dilleient
ways, and the sutfacos e\pos ( d h> In cUnient .in Iherefoie dnfeteii! m natuie In
one ligure
the Sc.de Ins heen lediux-tl soni< \\ iiat liom t IK n.it m. lUi /e, in theotlu i <
<>iiM(U'i.ihl> ( n l.u^ed.

(From a paper b> (. aip.-ntcT and Llam, u ad l Ion (hi Institute ot .Metalb, S -pt.
ly^u.)

ily of L&ndun !*;>>'< JU</,

The pbtni?r-ph sinws U* iwpuUr ontluw of tiw crystal grains n a Mnf*- ot *lw .
atwt, t
addition, a -ri*U rowing cf lim-s uilhiri writ raiu, ko.wti as- " \\ KliH.iuMaUon
uiw." ilww
Usr aro <hc to tho f;tf! that the puli^hiitg tool has nit armss the " atom 1,i>\
( in HUH* tho

' way as polifthinp, nits a*"Jxws layers ot rudhor ol ^,ca

THE NATURE OF CRYSTALS

203

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 tlie X-rays, with
their fineness of vision.

The structures of almost all the metal crystals

have been determin-
ed 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 arrange-
ment, although we are really repeating the com-
parison (p. 176) between the structures of ice
and diamond. Suppose we put together a
number of balls into the triangular arrange-
ment of Fig. 53, and surround them by a tri-
angular guard, as shown, just as balls are packed
together for playing snooker on the billiard table.

FIG. 53. A close-packed arrangement of

balls in one layer.

204 THE NATURE OF THINGS

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 another, 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 realised by the help of Fig. 54. The crosses
represent the centres of the balls in a certain layer,
the circles the centres in the next layer, and the
blaclj spots the centres in the third. The centres
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 realised,
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

PLATE XXIV.
A. Small groups of shot are in close packing, and there are irregular gaps between
I B. A pyramid, built by the super-position of layers like that of Fig. 53-

X X X X X

O O O

X X X X

O O

X X

0000

o o o

BOO

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 bl^ck spots repre-
sent 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.

205

206 "THE NATURE OF THINGS

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 com-
pact 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 reason-
able 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 see any arrange-
ment of this kind when we look in any other
direction. The model has a single axis in the
vertical direction, and round that axis the arrange-
ment 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.

PLATK 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 m Plate XXIV 13. The close-packed layers of Fig. 53 are hon/.ontal in
Plate XXIV B, and iti A they are perpendicular to a diagonal of the cube.

B shows the other form of close packing. Kach horizontal layer is a close-packed
layer of Fig. 53-

THE NATURE OF CRYSTALS 207

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. 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-rays 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

208 THE NATURE OF THINGS

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 learnt 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 into a single layer 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 v;Ill
be groups, each properly arranged in itself, but
not correctly aligned with its neighbours. In
just the same way there will be local arrangements
among the atoms of a metal in other words,
there will be crystallisation in groups, larger or

THE NATURE OF CRYSTALS 209

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. It is said that when gold is at N 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

Betid 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

210

THE NATURE OF THINGS

(a)

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 to-

gether by grease as in Fig.
55, and pulled them, they
would give along the plane
between them. 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 ().
f Often when a single metallic

IP/ crystal has been stretchiJ,

^\ //A we can S ee the marks on its

surface which show the lines

along which slip has taken

FIG. 56. This figure repre-

sents in the form of a diagram place.

the slipping on one another of Jt

ttoujm oi the aluminium p ro fessor Carpenter and

FIG. 55. The two blocks are

stuck together, but can slide over
one another. When pulled they
change in relative position from (a)
to (b).

PLATE XXVI.

These photographs are d

se pliotographs are due to 1'ioft -M>I I .ni"' 1111 ' 1

, p .ufi) they show the jioldiig <>f .ihiiuuui
singlt- l.\ij;e crystal in the uanusvrr portion of the U
to the obbt'ivor like the layers of Fig. 56. Tl
developed a waist, as the picture shows. There .
the reverse has taken place before the break : the
grown thinner (this cannot be seen in the photograph),

id Miss I Inn [/'mn./f/jo <>f lite Royal Society, A.,

i mull t --tuin, the ji.irt mully giving way being a
incn' In (i) aud(:) the slip planes are disposed
u><t I'K-i'c has contracted sideways, and finally
mi thinning from back to front. In (3) and (4)
idth has remained the same, but the material has
THE NATURE OF CRYSTALS 211

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 resist-
ance to pull ; the form is shown in Plate XXVI ;
the original length of each piece is 8 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
how by the way in which it does so, and the pull
tliat 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, I to 4). Sometimes the

212 THE NATURE OF THINGS

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, develop-
ing 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 towards 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

THE NATURE OF CRYSTALS

213

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. Since (see Fig. 5 5)
the pull always tends to bring the plane of slip

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.

more nearly into its own line, there arises a sort

o see-saw 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,

214 THE NATURE OF THINGS

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 in-
clined 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 extra-
ordinary 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.

When the single crystal of aluminium gives way

along a layer, we may suppose there is a moment

THE NATURE OF CRYSTALS 215

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 f And what happens to it when
it is annealed ? Perhaps we are guided towards
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,

216 THE NATURE OF THINGS

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 behaviour
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 ha? spread out
the crystal blocks so that they all lie with one face
in the leaf surface, and that heat has destroyed

THE NATURE OF CRYSTALS 217

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 crystal-
line, 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
ai*ranged 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 rearrange-
ment of the crystals which the X-rays show;
annealing is the release of this strain and the

218 THE NATURE OF THINGS

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 con-
ductors 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 satis-
factory explanation of their conducting powers ;
no doubt, too, it has much to do with their crystal-

THE NATURE OF CRYSTALS 219

line 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
b 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

220 THE NATURE OF THINGS

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.
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
aw&y 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

THE NATURE OF CRYSTALS 221

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 sub-
stances 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 con-
tinuously 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 end.

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
mtal 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

222 THE NATURE OF THINGS

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. But the most
important point is that the atoms are not tied
together by sharing electrons as in the diamond :
they must rather repel each other than otherwise,
being all charged with positive electricity. They
are free to roll or slide over each other, because
they are not attached to each other 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 mote or

THE NATURE OF CRYSTALS 223

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 improve-
ment 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 moulded ;
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

224 THE NATURE OF THINGS

as spoons and forks, which are afterwards 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. Chromium, cobalt and tungsten com-
bined 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 jewellery 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 nc
longer even : there is a scattering of aluminium
atQms in it, and we can readily suppose that the

THE NATURE OF CRYSTALS 225

dipping has become more difficult, and that we

have here the cause of hardening. 1 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. 2
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
'places uneven that the hardening is brought
about. We have jammed the sliding planes.

1 Rosenhain, " The Inner Structure of Alloys," Institute of

Metals, May 2, 1923.

2 Jette, Phragmen and Westgren, Institute of Metals,

March 1921.

226 THE NATURE OF THINGS

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. Amongst 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

PLATE XXVII.

[By courtesy of the University of London Press, Ltd.

Damascus blades.
(From Belaiew's " Crystallisation of Metals.")

PLATE XXVIII,

[By courtesy oj lite rmct'W/j* of London Press, Ltd.

The long needle-shaped bodies are ci-mentite crystals forming part of the general
mass of steel.
(1'Yuin Bc-laiew's " Crystallisation of Metals.)

THE NATURE OF CRYSTALS 227

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 micro-
scope 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 tbgether 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.
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
228 THE NATURE OF THINGS

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 axe, 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

PLATE XXIX.

'' i W** V m 3 i * y 6 " ** * * -^ J

MT.^fe^o**^"*^

"" - *fer ' *>f ^ftf^^ I/ %ii , * *? *P* *, **

^$M$^

^^j^U^^ ' > %-- J "

A. Secti

d ti
. agnified a t

ocess of being Virnkt-n up arid rounded off.

(From BeUtiew's " Crystallisation of Metals.")

K. The dark band is a scratch made by a very fine needle in a polibhed 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 de-
posited in the trough made by the needle.

(From Beilby's " Aggregation and Flow of Solids.")

PLATE XXX.

In A .i piece of speculum metal, after being rubbed with fine emery, has been
polished with rouged leather. The metal has be n dr.igged over tl;c emery
scratches;
there is. a reminiscence of butter spread on bread In B the p.>ii^hiii "with rouge
ha 1 -? been carried further; the emery scratches h.i\< <li>app< .IK <!, but the:
outlines
of the grams in the metal begin to appear.

(From Sir George Beilby's " Aggregation and Flow of Solids," by courtesy of
the author.)

THE NATURE OF CRYSTALS 229

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 resist-
ance 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. 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

230 THE NATURE OF THINGS

lamp L 13 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 Lj 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 crystallise 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 neighbours. The latter are at the corners
of a tiny cube, of which the former atom occupies
the centre. This is not the closest form of pack-
ing, 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 neighbours, 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

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.)

PLATE XXXII.
metal coil in

een reduced by surrounding it with a f

B. The iron wire is stretched b

magnified by the le
along it.

the same circuit as the shining lamp has

_ :ing mixture.

LLCI.WIJCU oy a hanging weight; its expansion and contraction are

arrangement. The wire is heated by passing an electric current

THE NATURE OF CRYSTALS 231

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.
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
m^tal moulds made for the purpose, just as we
usfed to remake our golf-balls in the old days.
The spherical mould is made in two halves ; and
it is convenient to mount them in the lathe, one
on the head and one on the back centre. Small
balls harden at once, and can be made very quickly :
larger balls must be left a little while in the mould.
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.

Wooden balls can be obtained much more

cheaply than wax. I have bought them from
Messrs. Maxime, Ltd., 6 Featherstone St., City
Road, E.G. 2. They can only be obtained in
certain sizes, but these are reasonably convenient :
moreover, they are not so truly spherical as the
wax balls. But they are good enough for practical
purposes.

Gramophone needles made 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.