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STUDIES IN NATURE AND COUNTRY LIFE

A BOOK FOR CHILDREN AND THEIR PARENTS BY

CATHERINE D. WHETHAM

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W. C. D. WHETHAM, M.A., F.R.S.

FELLOW OF TRINITY COLLEGE, CAMBRIDGE

CAMBRIDGE MACMILLAN & BOWES

BY THE SAME AUTHORS.

A HISTORY OF THE LIFE OF COLONEL NATHANIEL WHETHAM

A FORGOTTEN SOLDIER OF THE CIVIL WARS

LONDON LONGMANS, GREEN & CO.

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Frontispiece

THE RECENT DEVELOPMENT OF PHYSICAL SCIENCE

BY WILLIAM CECIL DAMPIER WHETHAM M.A., F.R.S.

FELLOW OF TRINITY COLLEGE, CAMBRIDGE

LONDON

JOHN MURRAY, ALBEMARLE STREET 1909

First edition, A^lg^l.st 1904 Second edition, September 1904. Third edition , December 1904 Fourth edition, March 1909

CFTHE

UNIVERSITY

OF

PREFACE

IN recent years we have witnessed a great develop- ment of physical science. The different sections into which natural knowledge is, for the sake of convenience, divided, have grown each within its own domain ; and, moreover, have shown increas- ing signs of extending beyond the boundaries arbitrarily traced between them. The methods of physics, in the restricted sense of that word, are being more and more applied to chemical and biological problems, while many questions in physics can only be investigated by those with mathematical or chemical training.

Thus it happens that an acquaintance with the knowledge newly acquired in one department of science is necessary for the study of another ; indeed, the phenomena which need for their inter- pretation the methods of two branches of science have proved often the most fruitful field of inquiry.

For reasons such as these it has been thought possible that a short account of some of the im- portant investigations now being carried on in the physical laboratories of the world might prove useful to students of science in general ;

211697

vi PREFACE

while it is hoped that, by treating the subject as far as possible without technical language, the book may also appeal to those who, with little definite scientific training, are interested in the more important conclusions of scientific thought.

The writer has been fortunate in his surround- ings, where the knowledge and insight of one worker are placed freely and ungrudgingly at the service of another in the day of his need. In the present undertaking he records gratefully the help of several friends who have read the proof sheets of the parts dealing with subjects with which their names are closely associated. Mr. F. H. Neville criticised the chapter on The Philosophical Basis of Physical Science, and that on Fusion and Solidification. Lord Berkeley read the account of The Problems of Solution. Professor J. J. Thomson saw the manuscript of the original article on which is founded the chapters on Conduction of Electricity through Gases and Radio-Activity. Professor Larmor revised the account of Atoms and ^ther, while Mr. H. F. Newall read the chapter on Astro-Physics. For this assistance the writer expresses his cordial gratitude. He wishes especially to thank his wife for continual correction both of the manuscript and of the proof sheets, and his sister for help with the index.

PREFACE vii

The editor of the Quarterly Review has kindly allowed use to be made of the article on Matter and Electricity which appeared in January 1904. Professor George E. Hale was good enough to permit some of his photographs of the sun to be reproduced, while, for other illustrations, acknow- ledgments are due to the Royal Society, to Mr. Heycock and Mr. Neville, to Mr. J. A. Ewing, and to Mr. G. T. Beilby. Lord Kelvin kindly sent a signed portrait, and Professor J. J. Thomson allowed the use of a reproduction of Mr. Arthur Hacker's admirable painting, which now hangs in the Cavendish Laboratory.

In spite of the generous help he has received, the author is sadly conscious of the difficulty of his task. Although the development of physical science is one of the most powerful activities of our time, a knowledge of its aims, methods, and results has not yet been recognised as a necessary part of an English liberal education. To give a popular exposition of results, especially when there is an obvious practical application, is easy ; to enable a non-scientific mind to follow and appreciate the methods by which the results are reached is supremely difficult. But in science methods are usually more important than results, while a superficial acquaintance with results with- out an underlying knowledge of method is useless, or worse than useless.

viii PREFACE

In the possibility of treating the wider and deeper generalisations of natural science as fit subject-matter for current thought and literature, the writer has a profound belief. Whether the failure to secure such treatment has been due to lack of adequate exposition, or to some radical defect in the training of the nation, is a difficult and grave problem ; but, until the point of view has been altered, it is perhaps hopeless to look for a proper understanding of the scientific spirit and of scientific method even among the more educated portion of the community. For the pre- sent, the man of science must perforce occupy a more technical and isolated position than the student of history or the lover of art. From the point of view of the man of science, to break down this isolation would be, at best, but sorry kindness ; but, from a wider point of view, for the good of the nation and of mankind, a more general acceptance of a share in the impersonal open-minded search for truth, which is the essence of science, is ardently to be desired.

With some such thoughts as these, the writer sends forth the following pages.

CAMBRIDGE, June 25, 1904.

PREFACE TO THE SECOND EDITION

THE need for a reprint of this book, coming as it does within a few weeks of publication, must be set down in part to the exceptional interest in the problems with which it deals that has been aroused by Mr. Balfour's Presidential Address to the British Association.

For, when attention has been drawn to the new theory of matter — to "the most far-reach- ing speculation about the physical universe which has ever claimed experimental support " — a state of mind is created that, in thoughtful men, will not rest satisfied without some effort to understand the basis of the speculation, and to weigh the evidence which can be arraigned in its favour. Truly, the new theory is concerned, not " about things remote or abstract, things transcendental or divine, but about what men see and handle, about those l plain matters of fact* among which common-sense daily moves

x PREFACE TO THE SECOND EDITION

with its most confident step and most self-satisfied smile."

The importance of the position now gained for the survey of the material universe lies in the unity of conception it discloses and the resulting simplification of detail. Either instinctively, or as the unconscious result of experience, the mind of man naturally grasps at any plan thus to re- duce and consolidate the questions which beset him in his journeyings through time and space. To the philosophic import of this mental attitude Mr. Balfour has done well to call attention in words that he kindly allows the writer to reproduce : —

" Now whether the main outlines of the world- picture which I have just imperfectly presented to you be destined to survive, or whether in their turn they are to be obliterated by some new drawing on the scientific palimpsest, all will, I think, admit that so bold an attempt to unify physical nature excites feelings of the most acute intellectual gratification. The satisfaction it gives is almost aesthetic in its intensity and quality. We feel the same sort of pleasurable shock as when from the crest of some melancholy pass we first see far below us the sudden glories of plain, river, and mountain. Whether this vehe- ment sentiment in favour of a simple universe

PREFACE TO THE SECOND EDITION xi

has any theoretical justification, I will not venture to pronounce. There is no a priori reason that I know of for expecting that the material world should be a modification of a single medium, rather than a composite structure built out of sixty or seventy elementary substances, eternal and eternally different. Why, then, should we feel content with the first hypothesis and not with the second ? Yet so it is. Men of science have always been restive under the multiplication of entities. They have eagerly noted any sign that the chemical atom was composite, and that the different chemical elements had a common origin. Nor for my part do I think such instincts should be ignored. . . . These obscure intima- tions about the nature of reality deserve, I think, more attention than has yet been given to them. That they exist is certain ; that they modify the indifferent impartiality of pure empiricism can hardly be denied."

The principle of simplicity lies at the base of all our explanations of phenomena, and Mr. Balfour's address will do much to lead to a clearer recog- nition of its importance.

Advantage has been taken of this opportunity to correct a few verbal errors which appeared

xii PREFACE TO THE FOURTH EDITION

in the first edition of the book. The writer's thanks are due to several correspondents, some of them known to him personally and some not, who were good enough to send notes of these errors.

Certain additions, descriptive of work published within the last few months, have been made ; and in places the treatment has been modified in order to make the meaning clearer. In this task the writer acknowledges gratefully the help of his friend, Mr. Stanley Leathes.

September 22, 1904.

THIRD EDITION

LITTLE more than verbal changes have been made in transforming the second into the third edition.

November 10, 1904.

FOURTH EDITION

IN the four years which have elapsed since the publication of the third edition of this book, physicists have developed farther the subjects with which it deals, but no striking new branches of knowledge have appeared. Hence it is possible to re-issue the book, with some additions, but with no fundamental changes of plan. January 18, 1909.

CONTENTS

PAGE

INTRODUCTION ....... I

CHAPTER I

THE PHILOSOPHICAL BASIS OF PHYSICAL SCIENCE . II

CHAPTER II

THE LIQUEFACTION OF GASES AND THE ABSOLUTE

ZERO OF TEMPERATURE 45

CHAPTER III

FUSION AND SOLIDIFICATION 78

CHAPTER IV

THE PROBLEMS OF SOLUTION Io8

CHAPTER V

THE CONDUCTION OF ELECTRICITY THROUGH GASES 148

CHAPTER VI

RADIO-ACTIVITY 198

xiii

xiv CONTENTS

CHAPTER VII

PAGE

ATOMS AND AETHER 246

CHAPTER VIII

ASTRO-PHYSICS 295

INDEX 341

LIST OF ILLUSTRATIONS

PORTRAITS

SIR ISAAC NEWTON ....	Frontispiece
LORD KELVIN ....	. To face page 66
J. WILLARD GIBBS ....	• » i, 93
J. H. VAN'T HOFF . . .	. „ „ 112
J. J. THOMSON ....	. ., „ 148
DIAGRAMS FIG. i ......	PAGE 61
FIGS. 2 to 5	to face 83
FIG. 6 . . .	. 87
FIG. 7	. 90
FIG. 8	. . .91
FIG. 9	. 94
FIG. 10	. . . 96
FIGS, ii to 17	to face 99
FIG. 18	. 103
FIGS. 19 to 24	to face 105
FIG. 25	. in
FIG. 26	128

xvi LIST OF ILLUSTRATIONS

PAGE

FIG. 27 , . . , 152

FIG. 28. CONDENSATION OF CLOUD ON GASEOUS

IONS . To face 157

FIG. 29 ......... 168

FIG. 30 169

FIG. 31. DEFLECTION - TUBE FOR CATHODE

RAYS ..... to face 173

FIG. 32 216

FIG. 33 .225

FIG. 34 .... . -233

FIG. 35 . 273

FIG. 36. C LINE IN THE SPECTRUM OF A SUN- SPOT ..... to face 310

FIG. 37. OCTOBER 9, 3ht 30™ • CALCIUM FLOCCULI,

H2 LEVEL .... to face 320

FIG. 38. OCTOBER 9, ih< O4m* HYDROGEN

FLOCCULI .... to face 320

FIG. 39. DIAGRAM TO EXPLAIN THE PHENOMENA OF

COMETS' TAILS . . . to face 332

OF THE

UNIVERSITY

PHYSICAL SCIENCE

" Not clinging to some ancient saw ;

Not mastered by some modern term ; Not swift nor slow to change, but firm : And in its season bring the law."

— TENNYSON.

IN the great advance of recent years, Physical Science has developed chiefly in two directions. Although these movements have been contempo- raneous, it is interesting to note that the methods employed by the two schools of research are, to some extent, the expression of opposite tendencies. On the one hand, we see the growth of the study of the conditions in which all physical and chemical change in a system must cease — the conditions of physical and chemical equilibrium. This growth is due to the thermodynamic methods founded chiefly on the great work of the late Willard Gibbs, of Yale University in the United States. On the other hand, our know- ledge of the mode of the conduction of elec- tricity through gases has been extended, mainly by the efforts of J. J. Thomson, Professor of

A

2 PHYSICAL SCIENCE

Experimental Physics at Cambridge, and of the band of workers trained by him in the Cavendish Laboratory. Of late years students from almost all civilised countries have come to Cambridge as to the centre of this branch of physical research, and many of them are now carrying forward their investigations elsewhere, by methods learnt in the University of Newton, Clerk-Maxwell, and Stokes. As we shall see in the following pages, the work of this school of physicists is undertaken and interpreted by the aid of atomic and molecular conceptions. The theory of the conduction of electricity through liquids, based originally on the work of Faraday, and slowly matured during the last half-century by Hittorf, Kohlrausch, Arrhenius, and many others, had accustomed our minds to the conception of electric con- duction by means of the motion of charged particles, called by Faraday " ions " — the travellers. Each ion consists of an atom, or group of atoms, of the substance in solution, associated with a positive or negative electric charge ; it moves through the liquid under the action of an applied electric force, and gives up its charge to the electrode — that is, the terminal by which the current enters or leaves the liquid. The conduction, instead of being conceived as a river flowing uniformly, must figuratively be represented as taking place

INTRODUCTION 3

by the passage of discrete quantities of electricity ; in much the same way as water is sometimes carried from a lake to a burning house by means of a chain of bucket-bearers.

By the application of similar conceptions, the passage of electricity through gases has received a convincing explanation. Differences appear, but the fundamental ideas are the same in the two branches of the science of electrolytic conduction. It is, however, in the newer side of the subject that the most striking results have been obtained. Electrolysis in liquids had suggested the concep- tion of ultimate units of electricity — atoms of electricity, analogous to the atoms of matter. Gaseous conduction enabled these electric atoms to be isolated, separated from their attendant material atoms, and studied independently.

Great has been the revelation which followed. The isolated atoms of negative electricity — the electrons, as they have been named by Stoney — have been identified by the work of Thomson, Lorentz, and Larmor, with the physical basis of matter, with the corpuscles, or sub-atoms, by means of which, combined in varying numbers and in different arrangements, are composed the chemical atoms, for long taken as ultimate indivisible units.

Farther light has been thrown on these dark

4 PHYSICAL SCIENCE

places by the remarkable series of discoveries through which M. and Mme. Curie and other chemists have given us the radio-active elements such as radium, and the parallel series in which Rutherford has interpreted their properties as due to the disintegration of their atoms, as, one after another, those atoms break down, and are transmuted into other substances.

Throughout these investigations we deal with atomic and molecular conceptions in an extreme form. We look even within the atom, and examine its internal structure ; we trace the cor- puscles or electrons flying round in their orbits, as we watch the planets swinging round the sun.

It is remarkable that, in the other branch of Physical Science in which simultaneous progress has been most striking, the methods chiefly employed have enabled us to dispense altogether with atomic and molecular theories.

At the basis of the theory of physical and chemical equilibrium lies Lord Kelvin's great principle of the dissipation of energy. While the total amount of energy in an isolated system is unchanging and unchangeable, that energy is tending always to become less available for the performance of useful work. The availability of the energy tends continually to become less. It follows that permanent equilibrium can only be

INTRODUCTION 5

attained when the limit has been reached and the availability is a minimum. Such a theorem is independent of molecular hypotheses ; in fact, it expressly disclaims such hypotheses, for, as Maxwell showed, the chance collisions of the individual molecules in a gas will lead to differ- ing molecular velocities, and to a concentration of energy in the fast-moving molecules. If we could follow the motions of the individual mole- cules, and separate the fast from the slow, we could use this energy. The principle of dissipa- tion, therefore, only holds while we are obliged, as of course is always the case in practice, to deal with molecules statistically and in the aggregate.

The principles thus applied to isolated systems have been extended to the visible universe. Predictions have been made that ultimately the energy of the universe will become completely unavailable, and will settle down into the energy of heat, uniformly distributed. But this final sleep of the universe depends on the assumptions that the universe is an isolated system, finite in extent, and that no process of molecular concen- tration of energy, such as was imagined by Maxwell, is going on anywhere throughout the depths of time and space.

A more restricted, though more fruitful, appli- cation of the dissipation principle enabled Helm-

6 PHYSICAL SCIENCE

holtz, and, in a much more general manner, Willard Gibbs, to place on a firm footing the theory of non-isolated but isothermal systems — systems, that is, maintained at a uniform and con- stant temperature by the gain or loss of external heat. The external work which such a system can perform, by means of a reversible change at con- stant temperature, tends to a minimum, and the system is in permanent equilibrium when, and when only, this available or free energy, as it is called, becomes as small as possible. By this sole principle, Willard Gibbs developed the complete theory of chemical and physical equilibrium ; as Professor Larmor says, his " monumental memoir made a clean sweep of the subject ; and workers in the modern experimental science of physical chemistry have returned to it again and again to find their empirical principles fore- casted in the light of pure theory, and to derive fresh inspiration for new departures."

Simultaneously with the development of ex- perimental research along the two lines we have indicated, has arisen afresh an interest in and inquiry into the philosophic basis on which is built the whole magnificent structure of modern science. How far is that basis secure ? Are the conceptions of science life-like pictures of any fundamental reality behind the phenomena which

INTRODUCTION 7

alone our senses can apprehend ? Such questions have occupied periodically the ablest minds of certain epochs of history, though in the attempts to find answers no such general consensus of opinion has been reached as we see within the building of science itself. Granted the security of the foundations, the edifice seems designed on a consistent plan, for the relations of its parts pre- sent themselves similarly to all minds competent to judge.

The philosophy of science is intimately con- nected with its history ; and interest has been stimulated afresh in the philosophical problems involved in physical conceptions by the publica- tion of Mach's great work on the Science and History of Mechanics. To many that book has put new life into the subject treated in its pages, and has led to a more careful consideration of the fundamental conceptions of natural science in general.

In the following pages an attempt will be made first to consider the philosophic foundations of physics, and then to trace some of the more important developments of the experimental in- vestigations for which the last few years have been remarkable.

The study of physical equilibrium — the equi- librium between different states or phases, solid,

8 PHYSICAL SCIENCE

liquid, and gaseous, of the same substance — • naturally opens with the consideration of the relations between the different states of pure chemical elements and compounds. Here, the most striking recent work is the liquefaction of air and hydrogen, with which the name of Dewar most prominently must be associated.

Next we turn to mixtures, and the fusion and solidification of solutions and alloys claim our attention. The microscopic analysis of metals, when elucidated by the theory of equilibrium, has had far-reaching influence on the applied arts of metallurgy.

Then are considered the problems of solution in general, without restriction to conditions of equilibrium. Now, for the first time, we come in contact with electrical phenomena ; and the theory of ionic conduction throws light, not only on the nature of electrolytic solutions, but on many physiological questions of vital interest.

A natural step leads from the conduction of electricity in liquids to its conduction in gases, and, on our stage, the ion is joined by the cor- puscle or electron. The dream of the old philo- sophers of a common basis for matter is realised by experimental investigation.

Arising from these experiments and their inter- pretation comes the theory of radio-activity, the

INTRODUCTION 9

modern equivalent of the imagined transmutation of the mediaeval alchemist. Though the changes are beyond our control, we see and measure the gradual evolution and disintegration of the chemical elements, and draw on the energy stored within the atoms themselves.

The vibrations of electro-magnetic systems pro- duce the aethereal waves now used in wireless tele- graphy, and the vibrations of atomic systems give rise to light. Thus atoms must be related intimately to the luminiferous aether, and light to electro- magnetic phenomena. Corpuscles or electrons, too, cry aloud for a physical explanation in terms of aethereal conceptions ; and Larmor's idea of an electron as a centre of intrinsic aethereal strain gives us a possible formulation of the subject, and, in some form or other, seems now to hold the field.

Finally, we pass to the bearing of all this new knowledge on cosmical problems. Physics is rapidly annexing the domain of astronomy, as it has already invaded the realms of chemistry and biology. By the aid of the spectroscope we examine the chemical nature of the sun and stars, we measure the rates of their motions and re- volutions, and obtain data from which we may speculate about their origin, development, and decay. From the internal structure of the atom

io PHYSICAL SCIENCE

to the majestic progress of the suns, the investiga- tions of Physical Science are surely and continu- ously gaining new knowledge for mankind.

We scatter the mists that enclose us,

Till the seas are ours and the lands, Till the quivering aether knows us, »

And carries our quick commands. From the blaze of the sun's bright glory

We sift each ray of light, We steal from the stars their story

Across the dark spaces of night.

But beyond the bright search-lights of science,

Out of sight of the windows of sense, Old riddles still bid us defiance,

Old questions of Why and of Whence. There fail all sure means of trial,

There end all the pathways we've trod, Where man, by belief or denial,

Is weaving the purpose of God.

CHAPTER I

THE PHILOSOPHICAL BASIS OF PHYSICAL SCIENCE

" Homo, naturae minister et interpres, tantum facit et intelligit quantum de naturae ordine re vel mente observaverit. . . . Natura enim non nisi parendo vincitur. . . ." — BACON, Novum Organum.

THE mind of man, learning consciously and uncon- sciously lessons of experience, gradually constructs a mental image of its surroundings — as the mariner draws a chart of strange coasts to guide him in future voyages, and to enable those that follow after him to sail the same seas with ease and safety. The chart may be drawn to scale ; it may be consistent with itself and serve its purpose — but it only repre- sents the earth's surface in one limited and con- ventional manner ; it does not give a life - like picture of the original in the same sense as does a photograph or a painting. So it is with the ideas that our minds conceive of the world around us, and with the model of that world which our minds construct. And this analogy may serve to interpret to us our attitude towards the concep- tion that the human race has formed of the world we live in. If the model be consistent, if the various

12 PHYSICAL SCIENCE

parts and aspects of it do not fail to correspond with each other, it serves the double purpose of introducing order into what would otherwise be mental confusion, and of helping us to make systematic use of the resources of Nature.

Confronted with the mystery of the Universe, we are driven to ask if the model our minds have framed at all corresponds with the reality ; if, indeed, there be any reality behind the image. Such a question is a proper study of philosophy, but need not necessarily be answered for the model to be made or used. The whole problem mankind has to face undoubtedly includes this fundamental ques- tion of the ultimate nature of reality, which would enter into a complete explanation of every fact, even of those which we regard as the simplest. This general aspect of the problem is the subject of that branch of philosophy known as Metaphysics. But, if we confine our attention to the phenomena which our senses apprehend, and, thus restricting our inquiry, examine our mental picture of Nature and the relation of its parts to each other, testing their correspondence or want of correspondence, we are studying Natural Science. The limitation indicated has not always been observed, and the name of Natural Philosophy survives to remind us that Natural Science is but one part of the whole of conceivable knowledge.

THE PHILOSOPHICAL BASIS 13

The problem of Metaphysics is of much greater difficulty than that of Natural Science. Hence, Natural Science has only begun to make rapid progress since its separation from Metaphysics. Despite the closest attention of the acutest intellects since the age of Greece, no general consensus of opinion has been reached by metaphysicians. Materialism, Dualism, Idealism, inconsistent views of the nature of reality, are all of them still held by competent philosophers :

" Myself when young did eagerly frequent

Doctor and saint, and heard great argument About it and about : but evermore Came out by the same door where in I went."

The slow and laborious methods of observation and experiment have been pursued from the earliest times for purposes of common life and technical industry. They were first considered philosophi- cally though inadequately by Bacon, and by their help a firm ground has been obtained for the edifice of Natural Science. In contrast with the results of Metaphysics, a general consensus of scientific opinion upon fundamental points has been obtained. No physicist of repute doubts the validity, within narrow limits of error, of Newton's theory of gravity, or of the principle of the conservation of energy.

But observation and experiment can be directed

14 PHYSICAL SCIENCE

only to the examination of our conceptions. In this way we gain materials for the construction and examination of the mind's model of reality ; we do not touch reality itself. If this be doubted, we must reflect that we can apprehend the results of experiment through our senses alone. Though, for instance, the galvanometer seems at first to supply us with a new electrical sense, on further thought we see that it merely translates the unknown into a language our sense of sight can appreciate, as a spot of light moves over a scale. It is possible that Philosophy may take into account knowledge which reaches us by means other than the senses. Intuitions, fundamental assumptions, mental pro- cesses generally, doubtless have an external aspect, and may be studied by the science of Psycho- physics, but they may have also another aspect in their internal relations to consciousness. Here they can be examined by Metaphysics. But we can only study Nature through our senses — that is, we can only study the model of Nature that our senses enable our minds to construct; we cannot decide whether that model, consistent though it be, represents truly the real structure of Nature; whether, indeed, there be any Nature as an ultimate reality behind its phenomena.

In emphasising the essential distinction between Natural Science and Metaphysics, we must not sup-

THE PHILOSOPHICAL BASIS 15

pose that the results of Natural Science have no metaphysical import. The possibility of putting to- gether a consistent mental model of phenomena is a valid metaphysical argument in favour of the view that a consistent reality underlies those phenomena, and that the reality is represented with more or less faithfulness by the mental picture we have pieced together. Such an argument must carry great weight, and may, perhaps, be considered conclusive; but it is a metaphysical argument, not one with which Natural Science is concerned directly. In framing and attempting to answer her own deeper questions, Metaphysics uses the results of Natural Science, as indeed of all other branches of inquiry. But this does not make Natural Science a branch of Metaphysics, or remove the essential difference between the subjects of the two studies.

The object of Natural Science, then, is to fit together a consistent and harmonious model which shall represent to our minds the phenomena which act on our senses. We need not fear that this limitation will lower the dignity or circumscribe unduly the extent of our inquiries. Whether we look inwards or outwards, the complexity of the phenomena seems boundless :

" Boundless inward in the atom ; boundless outward in the whole."

16 PHYSICAL SCIENCE

The more we learn, the more various and intricate are the new avenues of research which open before us. As has been well said, the larger grows the sphere of knowledge, the greater becomes its area of contact with the unknown.

So complex would be an entire mental picture of phenomena, that divisions of Natural Science have arisen, each of them tending more and more to demand the exclusive attention of the specialist. These divisions are purely arbitrary ; they have arisen partly from differences in methods of in- quiry, partly from historical reasons. Moreover, they are variable, and are shifted from time to time according to the needs of each department and the prevalent direction of inquiry, while new divisions may spring into existence.

The different sciences are not even parts of a whole ; they are but different aspects of a whole, which essentially has nothing in it corresponding to the divisions we make ; they are, so to speak, sections of our model of Nature in certain arbitrary planes, cut in directions to suit our convenience. Thus a nerve-impulse may be considered in a psy- chological aspect, a physiological aspect, or a physical aspect. Even these divisions may be sub- divided ; the physics of the nerve impulse may be studied first from the electrical side by investigat- ing the electric currents that accompany it, and

THE PHILOSOPHICAL BASIS 17

then from the mechanical side, by correlating the electrical currents with the movements of matter that simultaneously occur. No one of these aspects of the phenomenon is essentially more fundamental than any other, and the conviction at one time pre- valent, and even now by no means uncommon, that a complete mechanical explanation of every phenomenon is possible and fundamental, seems merely an unphilosophical fallacy. Its origin is to be sought in the historical fact that the section known as mechanics was the earliest of the physical sciences, and that its methods and conclusions are fairly intelligible to the ordinary man, and, in their elements, essential to his daily life. The science of mechanics has been more fully developed from its experimental basis by the methods of mathematical deduction than any other branch of Natural Know- ledge, and mankind has hence come to believe that it is essentially simpler and nearer reality. But in truth it is no more fundamental than elec- tricity, and, as we shall see in the following pages, there is a growing tendency in modern thought to conceive matter itself as an electrical manifestation. Again, it is sometimes argued that mechanics is the fundamental science because its extension is universal, while that of physiology, for example, is not. The contraction of a muscle has clearly a mechanical aspect, while the fall of a stone to the

i8 PHYSICAL SCIENCE

earth has nothing to do with physiology. Even a thought, from one side purely a psychological phenomenon, may have a mechanical aspect if we could trace the physical changes in the brain which accompany it, whereas, it may be said, the expansion of steam in an engine has no psychological sig- nificance. Such considerations certainly indicate that the arbitrary plane cut through our solid model of the universe by mechanical science is cut in such a place that it traverses a large part of the model — a larger part, perhaps, than any other section which has yet been cut. It does not follow, how- ever, that it cuts through the whole ; still less that a plane section can represent fully a solid model. Thus the argument that, because of its wide ex- tension, mechanics has some fundamental signifi- cance is seen to be a fallacy. It may be prima inter pares of the natural sciences, but nothing more. To go even further than this, as has some- times been done, and to suppose that the ultimate nature of reality is the same essentially as our idea of a single arbitrary section, cut through an imaginary model of it, seems only to need stating in these terms to be disbelieved.

The study of physics enables us to examine nature from a broader standpoint than that used by mechanics. But here again other aspects must be ignored. As Mach has well said, " Physical

THE PHILOSOPHICAL BASIS 19

Science does not pretend to be a complete view of the world ; it simply claims that it is working towards such a complete view in the future. The highest philosophy of the scientific investigator is precisely this toleration of an incomplete concep- tion of the world and the preference for it rather than for an apparently perfect but inadequate conception."

When the experimental study of nature was new, when man first caught a glimpse of order in the multiplicity of phenomena, such a view of the all-comprehending character of physical science seemed just. Let us again listen to Mach : —

"The French encyclopaedists of the eighteenth century imagined they were not far from a final explanation of the world by physical and mechani- cal principles ; Laplace even conceived a mind competent to foretell the progress of nature for all eternity, if but the masses, their positions, and initial velocities were given. In the eighteenth century, this joyful over-estimation of the scope of the new physico-mechamcal ideas is pardonable. Indeed, it is a refreshing, noble, and elevating spectacle ; and we can deeply sympathise with this expression of intellectual joy, so unique in history. But now, after a century has elapsed, after our judgment has grown more sober, the world-con- ception of the encyclopaedists appears to us as a

20 PHYSICAL SCIENCE

mechanical mythology in contrast with the animistic mythology of the old religions. Both views contain undue and fantastical exaggerations of an incom- plete perception. Careful physical inquiry will lead, however," to a more complete philosophy. "The direction in which this enlightenment is to be looked for, as the result of long and painstaking research, can of course only be surmised. To anticipate the result, or even to attempt to intro- duce it into any scientific investigation of to-day, would be mythology, not science.'

Physical Science, then, the subject of the present work, is merely one aspect from which we may agree to look at the model of Nature that our minds construct. It ignores the biological standpoint, from which phenomena are regarded in their bear- ing on life ; it ignores the psychological standpoint, from which they are studied in relation to mind. With these limitations, let us see what kind of model of Nature we are led to build.

The ideas of length and time may be regarded as primary — length as the simplest form of space con- ception, time as a recognition of sequence in our states of consciousness. One of the earliest ad- vances in exact science was the power of counting and the resultant method of expressing quantities as numbers. In spite of its essential nature, the

THE PHILOSOPHICAL BASIS 21

capacity for so doing is by no means innate ; nor is it even yet properly developed among all the races inhabiting this globe. In order to measure quantities, it is necessary to choose or invent some unit, and then to count the number of times that unit is comprised in the quantity to be measured. In civilised countries the unit of length is taken as the length between two marks on a certain standard metallic bar. In England there is a standard yard, and in France a standard metre. In fact, both these units are arbitrarily selected for their convenience, though the original idea of the metre was derived from a connection with the supposed dimensions of the earth.

Like the unit of length, the unit of time is arbi- trary, and ultimately rests on a measure of our sequence of consciousness. Again we have to choose some arbitrary unit, which, in this case, should always contain, under similar conditions, a similar amount of human consciousness. For purposes of the convenience of daily life the ob- vious unit to select is the day, while the sequence of the seasons suggests another equally arbitrary unit — the year. The exact relation between these two units can only be determined by careful astrono- mical observation. Wrong determination and con- sequent re -determination have led from time to time to necessary changes of calendar ; while the

22 PHYSICAL SCIENCE

partial adoption of these changes has resulted in the inconvenient differences of date in vogue among the various nations. That the units of time cannot be regarded as essentially fixed and unalterable is clear when we remember that any friction on the earth, such as that of the tides, is slowly prolonging the day, while resistance to the bodily motion of the earth round the sun would gradually alter the length of the year. Such changes may become appreciable only after the lapse of thousands or millions of years ; but the possibility of their oc- currence shows that our time-units are as purely arbitrary as are those of length.

From the conceptions of length and time, and the arbitrary units chosen to measure them, may be derived the more complex ideas required for a description of motion, and the derived units needed to investigate it quantitatively. Thus velocity is measured by the ratio of the number of units of length to the number of units of time, while acceleration, or the rate of change of velocity, is measured by the number of units of velocity gained or lost per unit of time. These relations are ex- pressed by saying that the dimensions of the unit of velocity are L/T, while those of the unit of acceleration are v/T or L/T2.

With metaphysical theories of matter, Physical Science has no direct concern ; and mechanics, at

THE PHILOSOPHICAL BASIS 23

any rate, deals only with matter as that concep- tion, which, in our mental image of phenomena, is always associated with another and more definite conception, that of mass. We need not ask whether matter has any objective existence, or whether our conception of mass corresponds with any actual property possessed by a real thing-in-itself. Such inquiries are of great interest and importance j but they are metaphysical inquiries, not those which the physicist, as physicist, must answer.

The conception of mass, as distinct from that of weight, may arise from the results of our daily experience. Let us suppose, for instance, that two fly-wheels of the same size, one of wood and the other of iron, were mounted on axles, and were free to revolve. When the wheels are set spinning, the weights do not come into play, for neither wheel is raised or lowered as a whole. Nevertheless, a great difference will be felt if we try to set the two wheels in motion suddenly. It takes either a much harder push or a much longer time to produce a certain velocity of rotation in the iron wheel than in the one made of wood, and, on the other hand, once moving, the iron wheel is much more difficult to stop. It is these results which lead us to say that the mass of the iron wheel is the greater.

The idea of mass first arises from the sense- perception of force ; but, to examine mass quanti-

24 PHYSICAL SCIENCE

tatively, more definite observation is necessary. The mutual action of two bodies, as examined by experiment, is such that our description of their relative motion becomes greatly simplified by assigning to each of them a certain relative number to express a quantity which we may term its relative mass. Let us make the two bodies, when free to move, act on each other in any way, excluding the possibility of rotation, for the sake of simplicity. Let us, for instance, connect them by means of a long, stretched elastic cord, and allow them to move each other. After the action has begun, we shall find that one body is, in general, moving faster than the other, and that the ratio of their accelerations is constant. The inverse ratio of these accelerations is the measure of the ratio between the masses of the two bodies ; the body with the smaller mass is moved faster by the mutual action than is the body with the greater mass.

We now need only to choose some mass as our unit with which to compare other masses, and to prove experimentally that the mass of a body as thus defined is a constant quantity, to complete our preparations for using the conception of mass in our physical description of observed phenomena.

Experience shows us that we can generalise the result of our experiment on the motion of the two bodies connected with each other by means of

THE PHILOSOPHICAL BASIS 25

a string. We can assert that no body has an acceleration unless another body is acting on it. Thus, we cannot form a complete picture of the motion unless we consider both bodies. But it is often necessary to concentrate our attention on one of them, and it is then convenient to find some quantity which measures correctly the effect of the other body on the first. This quantity is not the acceleration, for that depends on the mass of the moving body, but it is the product of the mass and the acceleration, and is independent of both. This product records completely the mechanical effect of the second body ; it measures the force, and instead of saying that one body is acted on by another, we may, if more convenient, say that it is acted on by a force. If a force moves its point of application, work is done, and the quantity of work is measured by the product of the force and the displacement in the direction of the force. The capacity for doing work is known as energy. A clear distinction is to be made between the ideas of force and energy.

Together with the conceptions of length, time, and mass, the conception of force also was employed by Newton in his development of mechanical theory. A simultaneous and parallel development of the science was led by Huygens, who used the conception which we now call

26 PHYSICAL SCIENCE

work or energy as a means of co-ordinating the phenomena, instead of stating them in terms of force as Newton did. Although it gave a more in- timate insight into mechanical processes, Newton's method was perhaps less general than that of Huygens, which often enables us to pass directly from a knowledge of the initial to a prediction of the final state of a system, and to avoid the diffi- culties of tracing its intermediate operations. In the history of mechanical science, now one method and now the other has proved the more useful ; and, in the wider field of physics, the two schools are still represented, on the one hand, by those who seek to trace the intimate processes of change by means of molecular theories, and, on the other, by those who rely on a more general presentment, which avoids such hypotheses by the use of the principles of thermodynamics.

By simple experiments, such as those described above, the relative masses of two reacting bodies may be measured by the constant inverse ratio of their accelerations. It follows that the product of the mass and the acceleration is the same for the two bodies. Thus the force which the first body exerts on the second is the same as the force which the second exerts on the first; or, as Newton expressed it, action and reaction are equal and opposite.

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In the ways we have now considered, mass and force may be defined in a manner free from all metaphysical subtleties, and in these senses alone should they be used in physical science. A defini- tion of matter is not needed : an inquiry into the so-called properties of matter being, from the physical point of view, an investigation into the phenomena which are associated with mass.

The conception of mass, in the present sense of the word, we owe to Newton : before his day no clear distinction was made between mass and weight. We cannot predict whether mass, as defined above, has any relation to weight ; any discovery of a connection between them must be a matter of experiment.

Weight is the force between the earth and the body considered, the product of the mass and acceleration being the same for the earth as for the body. If the forces were equal, the accele- rations towards the earth of two bodies would, by our definition of mass, be inversely propor- tional to their masses. By experiments on the acceleration, then, the forces may be determined. Now it was shown by Galileo that, if the resistance of the air be eliminated, bodies fall at the same rate to the earth ; that is, that the accelerations of all bodies to the earth are the same. It follows

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that the forces, that is, the weights of the bodies, must be proportional to the masses. Masses can thus be compared by weighing, and this method is much the most convenient in practice. Nevertheless, it must always be remembered clearly that the proportionality between mass and weight, and the consequent possibility of comparing masses by means of the balance, is not a relation which could be predicted a priori, but one which has been established as the result of carefui experi- mental investigation.

When we turn from mechanics to the other branches of physics, it is necessary, in the present state of knowledge, to use certain new funda- mental conceptions, such as temperature and quantity of electricity, though it is probable that ultimately these quantities will be connected with the mechanical units. Again, in this place it should be remarked that such a connection would not show that mechanics is necessarily the more fundamental science : it would be quite as correct, when the connection is established, to express mechanical quantities in terms of electricity or temperature.

This example leads us to state in a general form the immediate object of Physical Science. The physicist seeks to discover the relations between different phenomena, considered in one limited

THE PHILOSOPHICAL BASIS 29

aspect, and to express those relations in a definite quantitative way. Our minds, led by the analogy with their own volitions, usually think of one of the related phenomena as the cause, and of the other as the effect. The physical equation which expresses the dependence of A on B, or, in symbols, A = f(B), may equally well be written in the inverse form, by which B is asserted to be a function of A. In such cases, there is probably no philosophical distinction between cause and effect ; it is no more right to say that an increase of pressure produces a decrease of volume in a gas than to say that a decrease of volume produces an increase of pres- sure. The student merely discovers by experiment that the two phenomena accompany each other in every case investigated, and sums up the re- sults of experience in conceptual language and in a short-hand form, in order to save the detailed investigation of each future individual case.

In these examples, the needlessness of the ideas of cause and effect will be fairly clear, whatever may be thought about their metaphysical import- ance. It is where the element of time is in- volved that the idea of causation is most vivid. When one of the two related phenomena follows the other, the mind instinctively identifies post hoc with propter hoc. And, even if such a distinc- tion is philosophically unnecessary, as a matter

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of convenience in language it is perhaps justified, When carefully examined, however, the difficulty of isolating the lt cause " of any particular "effect" will be found to be insuperable. A long train of circumstances has preceded the phenomenon considered, and the phenomenon would not have appeared had any one of those circumstances been absent. Each or all of them might equally well have been called the " cause." Whether the idea of cause and effect represents a real distinction in the hypothetical world which our conceptions represent, remains, like the nature and existence of that world itself, an inquiry for the philosopher.

Physical Science, then, seeks to establish general rules which describe the sequence of phenomena in all cases. Underlying all such attempts is the belief that such an orderly sequence is invariably present, could it only be traced. This belief, which is the result of constant experience, is known as the principle of the Uniformity of Nature. In its absence no organised knowledge could be obtained, and any attempt to investigate phenomena would be perfectly useless. Unless, to use the conventional language justified above as a matter of convenience, like causes always produce like effects in like circumstances, science, and indeed all organised knowledge, would be impossible.

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When fitted into our mental picture, a generalised result of experience is known as a physical law, or, to change the form of a word and the size of two letters, as a Law of Nature. Many brave things have been written, and many capital letters expended in describing the Reign of Law. The laws of Nature, however, when the mode of their discovery is analysed, are seen to be merely the most convenient way of stating the results of experience in a form suitable for future reference. The word " law " used in this connection has had an unfortunate effect. It has imparted a kind of idea of moral obligation, which bids the phenomena " obey the law," and leads to the notion that, when we have traced a law, we have discovered the ulti- mate cause of a series of phenomena. Newton and Ohm did not first promulgate and then enforce the regulations which are associated with their names, though it is not only elementary students who may be heard saying that a stone falls to the ground " because of the law of gravitation." We must still ask why each particle of one body attracts each particle of another, even when we know that the force between them is proportional to the product of the masses divided by the square of the distance. We do not necessarily know why the electric current through a conductor varies as the applied electro-motive force, when

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we have discovered how these two quantities are connected.

The great change in the rate of progress of Natural Science has occurred since men learned to concentrate their immediate attention on the question of how phenomena are related, and to cease, for the time at any rate, to ask why they appear. Before Galileo's day men sought to ex- plain the fall of bodies to the earth by saying that " every body sought its natural place" — the place of heavy bodies being below, and that of light ones above. Galileo, exercising the true scientific spirit of restraint, set himself to de- termine by experiment how bodies fell. He thus discovered that the speed was proportional to the time of fall, and, by dropping bodies from the leaning tower of Pisa, showed that, contrary to the received doctrine of tendency to seek their natural place, heavy bodies fell no faster than light ones.

The natural laws of falling bodies were thus established, and the method of their discovery shows how such steps in knowledge are always made. In the first stage new phenomena are observed, or old phenomena are brought under accurate and quantitative measurement, probably by the light of tentative hypotheses. Here the virtues of patience, accuracy, incredulity, and con- scientious elimination of personal bias are of chief

THE PHILOSOPHICAL BASIS 33

account. The classical example is Kepler's life-study of the motions of the planets — a study which led to the establishment of general laws, such as that the planets move in ellipses having the sun in one focus.

But such laws alone are insufficient to satisfy our minds, which inevitably return to the question why such relations hold. The relations are misinter- preted and re-interpreted, until some Newton with the touch of genius which often accompanies sober scientific insight and imagination — some one who is able to brush aside for a time the non-essential, and to rise above the confusion of detail — is inspired with a conception of order in the multiplicity of the phenomena : order to be seen when some simple principle is borne in mind, and is expressed in a formula, which, in terms of our conceptual short- hand, enables us to remember and to predict the sequence of phenomena. If the formula is expressed in terms of simple conceptions, already known and often used in other branches of knowledge, the mind at once looks on it as an "explanation" of the phenomena, though it is evident on further thought that the phenomena are no more fully understood than are the funda- mental conceptions — mass, force, whatever they be — in which the " explanation " is expressed.

The next step consists in deducing new conse- quences of the hypothesis ; and here the methods

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of mathematical analysis are usefully applied. The science of mathematics as such has nothing to do with natural phenomena. Like physical science it is concerned with ideal conceptions ; but neither does it seek to gain those conceptions from an examination of Nature, nor to check their correspondence by the methods of experiment. Mathematics may borrow subject-matter from observational science, or may acquire by pure mental processes subject-matter, such as the geometry of four dimensional space, which has no counterpart in Nature as we know it. In either case, mathematics deals with the concep- tions as such, and traces their results and the relations between them by the methods of logic, with no necessary intention of elucidating the phenomena of Nature. Except when inventing new methods, the mathematician is a calculating machine. His conclusions are, or ought to be, contained implicitly in the premises he uses. He develops the premises, discovers their full meaning, and elaborates their consequences, in a way quite beyond the unaided power of thought, which, without the guiding rules and generalisations of mathematical analysis, would be lost in the maze of complications. But the mathematician lives in a purely conceptual sphere, and mathematics is but the higher development of symbolic logic.

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Taking, then, a new-born hypothesis, its con- sequences are deduced by logical common-sense reasoning ; and, where such reasoning cannot see its way unaided, by the help of mathematical analysis. The results thus obtained are then used by the observer or experimenter, who tests by the use of old, or the determination of new data, the truth of the formula by every possible means. Its relations to other ascertained prin- ciples, its power of correlating hitherto uncon- nected phenomena, are examined in turn. From consideration of its significance, we gain sug- gestions for further observation, if possible for future experiment. Such experiments, undertaken with the express purpose in view, are probably better adapted to test the formula than the observations previously accumulated. If the con- cordance is complete as far as the accuracy of experiment can go, the formula becomes, in the then state of knowledge, an accepted theory. Whatever this means, such a generalisation will, at all events, prove a useful working hypothesis, by the light of which research may be guided into promising paths. As the range of observation widens, and as the accuracy of the old observations is in- creased, the fate of the new theory hangs in the balance. The formula may, perhaps, still be confirmed, it may require modification, or it may

36 PHYSICAL SCIENCE

have to be abandoned as a theory which has played a useful and honourable part in its day, but has become inadequate to express the de- veloping knowledge of a later time. If so, it ceases to be cited as an accepted theory. Not that Nature has changed, but rather our attitude towards her, and our conceptual model of her phenomena. Thus new theories replace the old ones.

Some years ago the constancy of the chemical elements was, in the then state of knowledge, an accepted theory. Latterly, the phenomena of radio- activity have forced us to believe that radium is passing continuously and spontaneously into helium — that true transmutations of matter occur. The obvious transmutation of one kind of matter leads to the possibility, nay, the probability, of the gradual transmutation of all ; since as yet no property of matter has been noted which is the exclusive possession of one substance alone. New pheno- mena, or rather phenomena for the first time appreciated, are continually coming to light, and evidence is accumulating from which the pro- fitable construction of theories — for a time in abeyance — may again be pursued. Nothing must be ruled out of court because contrary to re- ceived views ; when a primd facie case has been made out, everything must be examined by ex- periment, induction, deduction, and again experi-

THE PHILOSOPHICAL BASIS 37

ment. This is the only sure road to the under- standing of Nature ; and, in times to come, it may lead us into regions now unknown, or considered to be closed to the investigations of science. The evolution and disintegration of matter, the problems of hypnotism and of direct thought transference, are questions which seem to be coming rapidly within the range of scientific inquiry. It is possible that an advance has already been made towards clearing away part of the mystery, so attractive to some, so repellent to others, that surrounds these phenomena. At any rate, in several of the great -schools of psycho-medicine, notably in France and America, materials are being accumulated, their trust- worthiness examined, and the results systemati- cally collated. It may be that these investigations, so beset with evident difficulties, are indeed in- definitely complicated in their issues by questions of racial predisposition, of individual temperament and mental condition, both of observed and ob- servers. Whether any or all of these problems will prove amenable to the methods of dispas- sionate observation and experiment is a matter which the years to come alone can show.

We must thus look on natural laws merely as convenient shorthand statements of the organised

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information that at present is at our disposal. But when Physical Law, as understood in the eighteenth century, has been dethroned from a place that was never rightly its own, let us not think that its use- fulness has been diminished or its dignity unduly lowered. Without the possibility of discovering such laws, and framing theories of their meaning, mankind would be lost hopelessly in a wilderness of phenomena ; no continuous progress could be made; no consistent idea of the world around could ever be attained. Each individual phenomenon, as it appeared time after time, might still be investigated; but, with his limited mind and short life, no one man could ever secure a basis for adequate know- ledge. Without some general way of stating his experiences, he could hand on neither his guesses after truth nor his hard-won information : mankind would never have emerged from barbarism.

The fundamental conceptions of length, time, and mass from which, as we have seen, the other mechanical units can be derived, enable us to con- struct a mechanical model of Nature. It is incom- plete ; for even the simplest mechanical fact, such as the fall of a body to the ground, inevitably has other aspects. Heat may be developed, electrical mani- festations appear, and, if the body be a living one, physiological and psychological changes take place.

THE PHILOSOPHICAL BASIS 39

Neglecting these aspects, however, a complete mechanical account of the phenomenon can be given in terms of the three fundamental concep- tions. As we have seen, new ideas, which may be derived from the primary ones, become necessary in the course of the investigation. The body falls with a certain acceleration, and, at any instant, is moving with a definite velocity. As it falls, it acquires energy of motion and loses energy of posi- tion.

During the fall we find that we can successfully describe what happens by assuming that the quantity which we call the mass of the body keeps constant, and that the sum of the two kinds of energy keeps constant also. If we include in our view the complete physical and chemical aspects of the phenomena, we may greatly extend these results. When the body reaches the earth, it is possible that processes of decay set in, which eventually result in most of its substance disappearing in gases or other products. The energy of motion acquired by the body during its fall also seems to disappear, with no corresponding gain of energy of position. Chemistry, however, generalising from many ex- perimental results, tells us that, if we could trace all the forms of matter into which the body is resolved, we should find that there was no loss. Every particle of the original body still exists in one of its

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products. Physics, on the other hand, teaches us in the same way that the sum of all the forms of energy, heat, sound, &c., which appear as a con- sequence of the impact on the ground, could they all be taken into account, would be exactly equi- valent to the energy of motion possessed by the body at the instant before contact. These great principles of the conservation of mass and the con- servation of energy are two of the most important generalisations ever reached by Physical Science.

While fully recognising the importance of these generalisations from the physical point of view, we must be careful how we give them any metaphysical significance. Under certain limiting conditions, other physical quantities besides mass and energy may be conserved. Thus in pure mechanics we recognise the conservation of momentum — a name for the mathematical quantity obtained by multi- plying together the measures of mass and velocity. Again, in reversible systems, where physical or chemical changes may occur in either direction with equal freedom, thermodynamics indicates the conservation of another quantity, named by Clausius, entropy. Momentum and entropy are only conserved under restricted conditions ; in physical systems the momentum of visible masses is often destroyed, while in irreversible processes entropy always tends to increase.

THE PHILOSOPHICAL BASIS 41

Mass and energy may seem to be conserved in the conditions known to us, and we are justified in extending the principle of their con- servation to all cases where those conditions apply. It does not follow, however, that conditions un- known to us may not exist, in which mass and energy might disappear or come into existence. The persistence of matter, for instance, might con- ceivably be an apparent persistence. A wave, travel- ling over the surface of the sea, seems to persist. It keeps its form unchanged, and the quantity of water in it remains unaltered. We might talk about the conservation of waves, and, perhaps, in so doing, be as near the truth as when we talk of the persistence of the ultimate particles of matter. But the persis- tence of the wave is an apparent phenomenon. The form of the wave indeed truly persists, but the matter in it is always changing — changing in such a way that successive portions of matter take, one after the other, an identical form. Indications are not wanting that only in some such sense as this is mass persistent. The conservation of mass and energy under all known conditions is a valid meta- physical argument in favour of the view that our ideas of them correspond with ultimate realities, but it is no more than an argument ; it deserves due weight, but it is not conclusive evidence.

Even if we assume that some reality underlies

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phenomena, it is clear that the reality must be very different from the mental picture which common- sense frames, when unaided by the inductions of science. Our first conception of a wooden stick involves the ideas of a certain long-shaped form, of hardness, of weight, of a colour more or less brown, perhaps of some amount of elasticity. Examination with a microscope reveals many appearances in- visible with the unaided eye, and we find that the stick has a structure much more detailed than we imagined. From the results of observation and experiment, physics teaches us that the properties of the stick can only satisfactorily be represented by the hypothesis that the substance of it is divisible, but not infinitely divisible; that it consists of discon- tinuous particles or molecules. Again, chemistry assures us that the molecules of the stick are made up of still smaller parts or atoms, which separate from each other when chemical action occurs, when, for instance, the stick is burnt, and can afterwards re-arrange themselves into new molecules.

When we pursue our inquiries into the nature of these chemical atoms, we find that recent research has resolved them, as we shall see later, into much smaller particles or corpuscles, and we are asked to imagine that these are in constant motion within the atom, somewhat as the planets move within the solar system. Intimate relations exist between

THE PHILOSOPHICAL BASIS 43

the properties of these corpuscles and the pheno- mena of electricity, and it seems probable that a corpuscle may be regarded as an isolated electric charge, or electron, as it is called, the mass of the corpuscle being an apparent effect due to electricity in motion.

Thus we have " explained " electricity in terms of corpuscles, and mass itself in terms of electricity. At present adventurous pioneers are striving to escape from the circle and to reach more ultimate conceptions by resolving the corpuscle or electron into a centre of intrinsic strain in the luminiferous aether. Whatever fate may await their efforts, we have already travelled far in attempting to con- struct a complete mental image of the wooden stick and all its known properties. We have reached ideas very different from those of the hard, continuous substance from which we started.

The other properties of the stick can be analysed into physical conceptions in much the same way. Thus the colour is found to be due to a sorting action which the particles of the wood exert on the complex system of aethereal waves, making up white light. Some of these waves have their energy more freely absorbed by the molecules of the wood than have others ; the balance of light is upset, and the reflected beam produces the sensation of colour. Here, again, the most fundamental conceptions

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into which modern science enables us to resolve our primitive ideas are very different from those in which they took their origin.

While Natural Science is not committed to any particular philosophical system, while in its essence it is independent of all such systems, the language it uses habitually is based on the common-sense realism, which is the philosophic creed of most men of science — indeed, of the great bulk of man- kind, or at all events, of that part of mankind belonging to the races of Western Europe. The mass and energy with which we deal in physical experiments, and in the mathematical reasoning based on inductions from the experiments, are purely conceptual quantities, introduced to bring order and simplicity into our perceptions of pheno- mena. But science talks of matter and energy as though it knew of the existence of realities corre- sponding with the mental images to which alone these names strictly apply. In the laboratory, as in practical life, there is neither room nor time for philosophic doubt In periods of reflection, how- ever, when considering the theoretical bearing of the results of our experiments, it is sometimes well to remember the limitation of our present certain knowledge, and the purely conceptual nature of our scheme of Natural Science when based merely on its own inductions.

CHAPTER II

THE LIQUEFACTION OF GASES AND THE ABSOLUTE ZERO OF TEMPERATURE

"Scientia et potentia humana in idem coincidunt, quia ignoratio causse destituit effectum." — BACON, Novum Organum.

MATTER is known to us in three states — as solid, as liquid, and as gas. The relations between these three states have been the subject of investigation throughout the history of Physical Science, and, indeed, almost throughout the history of the human race. The solidification of water in a frost, and its evaporation by the sun or a fire, have been familiar to mankind from the earliest times. But water shows these changes of state under too favourable an aspect to be taken as a general example. It has by no means always been clear that such transformations were possible to all kinds of matter, and it has been necessary to exhaust the resources of modern civilisation to liquefy the more permanent gases.

Ice, when heat is supplied, begins to melt at a definite temperature, which is called o° on the

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Centigrade scale, and 32° on the scale devised by Fahrenheit. While any ice remains, no change of temperature occurs in the mixture of ice and water. Heat is still absorbed, but its energy is used to effect a change of state, not to raise the temperature. The pure substance ice has a con- stant melting-point. Similarly, if water be cooled at constant pressure, it begins and finishes to freeze at the same temperature. It has a constant freez- ing-point, identical with the melting-point.

When water boils, a still larger quantity of heat is absorbed, but the temperature again remains unaltered during the whole process. When the barometer stands at 760 millimetres, or just under 30 inches, of mercury, the temperature of the boil- ing-point is taken as the second fixed point on our thermometers, and called 100° or 212° according as we use the Centigrade or the Fahrenheit scale. If the barometer stands higher or lower than the standard height, the boiling-point of water is found to be above or below 100° C., rising or falling through i° C. for a change of 27 millimetres in the barometer. The freezing-point also depends on the pressure ; but the change is much smaller than in the case of the boiling-point, and delicate experiments are necessary to determine it.

The variation with pressure of the points of transition from one state of matter to another are

THE LIQUEFACTION OF GASES 47

connected with the changes of volume which simul- taneously occur. Water expands on freezing, for ice floats on the surface of a lake, and pipes burst in a frost. If this increase in volume be resisted by an external pressure, as by putting the water into a strong closed vessel, the act of freezing involves the performance of external work in forcing outwards the walls of the vessel to give room for the ice to form. It is therefore more difficult to produce ice under pressure, and a greater lowering of temperature is necessary. Thus an increase of pressure must lower the melting or freezing-point. On evaporation, the increase in volume occurs with the change from liquid to vapour ; an increase of external pressure there- fore makes evaporation more difficult, and con- sequently produces a rise in the boiling-point. If the change in volume and the amount of heat required to produce the change in state are known, the principles of thermodynamics enable us to calculate the exact amount of alteration in the freezing or boiling-points.

There is reason to suppose that the three states of solid, liquid, and gas, assumed within a mode- rate range of temperature and pressure by the familiar substance water, could be obtained with all bodies if we could command temperatures and

48 PHYSICAL SCIENCE

pressures high enough and low enough. Metals melt and volatilise at high temperatures, while even gases such as air and hydrogen have now been liquefied.

Several gases, previously unknown in any other form, were liquefied by Faraday. His method consisted in evolving the gas by heating chemical re-agents in one limb of a bent glass tube, and cooling the other limb in cold water or a freezing mixture. As the gas is evolved, the pressure rises, and either the gas is liquefied in the cold limb, or the tube bursts. By this simple means chlorine, sulphur dioxide, ammonia, and a few other gases may be liquefied.

The conditions necessary for liquefaction were not fully understood till Andrews, in 1863, showed that carbonic acid gas could not be liquefied unless its temperature was reduced below a definite fixed point, which he called the critical point. The critical point of carbonic acid is fairly high, about 30° on the Centigrade scale ; but for other gases, such as air or hydrogen, it is much lower, many degrees below the freezing-point of water. How- ever low it be, unless a gas is cooled to its critical point, no pressure, whatever be its intensity, can produce liquefaction. Below their critical points, gases may be considered as vapours, and will liquefy if the pressure applied is high enough.

THE LIQUEFACTION OF GASES 49

The problem of the liquefaction of a refractory gas is thus solved if we can produce cold suffi- ciently intense to reduce it below its critical point. Three methods have been used, either singly or in conjunction, to cool gases below their critical points. The first method depends on the heat which it is necessary to supply in order to evaporate a liquid. A liquid boils when the pressure of its vapour is equal to the pressure of the atmosphere acting upon its surface, and, if we reduce this external pressure, the boiling-point is lowered. Thus, by pumping away the vapour as fast as it is formed, and so keeping the pressure low, a liquid can be boiled at a temperature much below its normal boiling-point. By this method, for example, it is possible to make water boil with no outside supply of heat. The heat necessary for evaporation is then taken from the water itself, which in this way is gradually cooled. If the air- pump is efficient, and if very little heat is allowed to leak in, the cooling may go so far that the re- maining water is frozen. Beginning at the normal boiling-point of water, we should then have cooled the system by means of evaporation through 100°. If, instead of water, we had taken some liquid of low boiling-point, such as liquefied sulphur dioxide, or, better still, liquefied carbonic acid, the same

process of cooling under exhaustion would have

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50 PHYSICAL SCIENCE

taken place ; but the final temperature reached would have been much lower.

Starting then with some substance like sulphur dioxide, which is easily liquefied by pressure alone at ordinary temperatures, we can boil it away under exhaustion, and so produce a low tempera- ture. By making a more refractory gas, such as carbonic acid, circulate through a tube surrounded with the cold sulphur dioxide, this new agent is cooled below its critical point, and liquefied. In its turn the liquid carbonic acid is boiled away under low pressure, and used as a refrigerating agent to cool the gas — oxygen, let us say — which we are attempting to conquer. This, sometimes called the cascade method of cooling, was the plan adopted by the Swiss physicist, Pictet of Geneva, in the experiments which, simultaneously with those of his French contemporary Cailletet, first liquefied oxygen. With one of those curious coincideaces which the broad wave of advancing knowledge sometimes produces, both these results were an- nounced at a memorable meeting of the French Academy, held on the 24th of December 1877.

Even when the gas was thus cooled, however, Pictet's process was not entirely effective. In order to pass the last few degrees and reach the critical point, a second method of cooling had to be brought into play. To explain this second method

THE LIQUEFACTION OF GASES 51

other principles must be taken into account. When a certain mass of gas, forced into a closed vessel till the pressure rises to several atmospheres, is let out suddenly, its volume is, of course, greatly increased by the sudden expansion. Room has to be made for the increase of volume, and this process re- quires the expenditure of work, for the atmosphere is pressing on the gas on all sides, and has to be forced back when the expansion occurs. Moreover, if the particles of the gas attract each other, work must be done in the separation necessary for the increase of volume. Thus internal as well as external work may be performed during the expansion. Unless heat is supplied from without, the energy needed to perform all this work must come from the heat supply of the gas itself, which becomes cooled in the process. If the expansion is sudden and therefore rapid, there is no time for heat to enter the gas, and the cooling represents the full effect of the work done. By this means, Pictet finally liquefied his oxygen. The highly compressed gas, which had been cooled in liquid carbonic acid boiling under low pressure, was allowed suddenly to escape into the atmosphere. A large amount of external work was thus done, intense cooling resulted, and liquid oxygen was seen as spray in the issuing jet of gas. It was by a still more sudden expansion that Cailletet liquefied oxygen,

52 PHYSICAL SCIENCE

using preliminary cooling only to 30° below the Centigrade zero.

In modern forms of apparatus for the liquefaction of gases it is found advisable to sacrifice the cooling gained by the performance of external work, and to rely on that due to the internal work alone. By this means it is possible to construct much more powerful and efficient refrigerating machines. The essential feature in the process of cooling by the performance of external work is the expansion of the gas by its own elastic force. If the work neces- sary for the increase of volume under the external pressure be supplied by an engine, or if all such work be prevented by making the gas expand into a vacuum, there is no external work to absorb the heat energy of the gas itself, and no cooling from this cause is produced. The gas, however, still has to supply any work needed to separate its own particles against any mutual attractive forces, and, if such forces exist, cooling can still be obtained at the expense of the heat-energy of the gas. On the other hand, if the inter-molecular forces are forces of repulsion, expansion will be aided by their action, and will, in the absence of external work, be ac- companied by an increase of temperature. Thus, by arranging for free expansion, as it is called, we can examine the nature of the inter-molecular forces by observing whether a gas is cooled or heated.

THE LIQUEFACTION OF GASES 53

In such experiments, it is necessary to prevent the performance of external work by the gas itself, and this can be done in either of the two ways in- dicated above. Gay Lussac, and afterwards Joule, filled one vessel with gas under high pressure, and then allowed the gas to expand into another vessel previously exhausted. Here, in expanding into a vacuum, no external pressure has to be over- come, and no external work is done. Any thermal change will be the equivalent of the internal work. The vessels were placed side by side in water, which was stirred after the experiment, and tested with a sensitive thermometer. At ordinary tem- peratures no heating or cooling could be observed with any of the gases examined.

The apparatus just described is clearly not adapted to detect small thermal changes, and it was not till about the year 1850, when Thomson and Joule devised a continuous method, that satisfactory results were obtained. Instead of preventing ex- ternal work by allowing the gas to expand into a vacuum, these physicists performed the external work needed to expand the gas against the pressure of the atmosphere by means of an air-pump driven by an engine. By this method a continuous current of gas was forced through a porous plug of compressed wool or silk, fixed in a wooden tube. Here the engine does the external work, and con-

54 PHYSICAL SCIENCE

sequently none of that work draws on the heat energy of the gas itself.

All the external work is done by the engine, but, as we have seen, another source of energy-change exists. When a gas expands, whether or not it performs external work, the various parts of it become separated further from each other, since, on the whole, the gas occupies after expansion a larger volume than before. If, then, there is any attraction between the parts of the gas, work must be done in separating them ; in terms of the molecular theory, work is done against the inter- molecular forces. For the performance of this internal work, energy must be drawn from the heat-supply of the gas, which will therefore cool, and the amount of cooling, if access of heat from outside be prevented, measures the intensity of the inter-molecular forces. On the other hand, if the inter-molecular forces be repulsive ones, they help on the expansion, and the energy so liberated appears as sensible heat, the resultant rise of temperature depending on the strength of the repulsion between the molecules.

The porous plug experiment, to which we have referred on the last page, was devised by Professor William Thomson, afterwards Lord Kelvin, and the late Dr. Joule, for the purpose of examining the amount and nature of these inter-molecular forces,

THE LIQUEFACTION OF GASES 55

and of determining the amount of deviation of various gases from the ideal state, in which no such forces exist. If a thermometer were filled with such a hypothetical ideal gas, its indications would coincide exactly with the absolute temperature scale, deduced by Thomson from the principles of thermodynamics. The knowledge of the devia- tion of any real gas from the ideal state thus enables us to compare the absolute scale with the scale of an actual thermometer, using the ex- pansion of the gas in question as the thermometric property. The great theoretical importance of the porous plug experiment will now be manifest.

Thomson and Joule found that air, and all other gases except hydrogen, were cooled slightly on passing the plug; with hydrogen, on the other hand, they obtained a still smaller heating effect. Thus in hydrogen the molecules must on the whole repel each other, while in air and similar gases, the intermolecular forces must be attrac- tive ones. The amount of the effect was found to increase in proportion to the difference of pressure on the opposite sides of the plug.

With air the cooling effect decreases as the temperature is raised, and increases if the air be cooled. The change of temperature pro- duced, which was only one-fifth of a degree per atmosphere difference of pressure in the

56 PHYSICAL SCIENCE

original experiments, can thus be increased to any extent by a preliminary cooling of the air.

This cooling by the performance of internal work underlies the third method adopted in the liquefaction of gases. It must be distinguished clearly from the second method, in which most of the cooling is effected by making the gas do external work.

Let us imagine that a stream of air, previously cooled by liquid carbonic acid, is forced through a spiral tube by aid of an air-pump and engine, and that finally it emerges through a fine nozzle at the end of the tube. The nozzle acts as a porous plug, and the air, cooled by free expansion, is lowered in temperature by doing internal work. Let us further suppose that the issuing air, so cooled, is made to flow back over the tube through which the stream of air passes. The advancing current of air is still further cooled, the effect of the expansion at the nozzle is increased, and a temperature yet lower than before attained. This cycle of opera- tions— the continual passage of the air just cooled by free expansion over the current of air before it issues from the nozzle — results in a con- stantly decreasing temperature, and eventually cools the air below its critical point, finally causing liquefaction. This self-intensifying action is sometimes referred to as the regenerative

THE LIQUEFACTION OF GASES 57

principle. It was first applied successfully to the liquefaction of air by Linde in Germany, and has since been used by Hampson and Dewar in Eng- land, and by Tripler in America.

Liquid air can be obtained in any quantity by the expenditure of power, and the necessary appa- ratus has become part of the usual equipment of physical and chemical laboratories. By this means regions of temperature before quite inaccessible have been opened up to investigation, and the use of liquid air promises to be of increasing ad- vantage in many departments of research. It would, of course, be possible to drive an engine by means of liquid air, but such a process would be very uneconomical. The statements, which have sometimes appeared in the daily papers, announc- ing impending revolutions in methods of obtaining cheap power by the application of liquid air, have originated from an imperfect comprehension of the problems involved.

When air had been successfully liquefied, hydro- gen was obviously the next gas to be attacked. Thomson and Joule's porous plug experiments had shown that, at ordinary temperatures, hydrogen suffers a heating effect on free expansion. It was therefore useless to attempt to liquefy it by re- generative cooling alone. But, just as the cool- ing effect in the case of air increases as the air

58 PHYSICAL SCIENCE

is subjected to a preliminary cooling, so in hydrogen, if it be first cooled, the Thomson- Joule heating effect first diminishes and then is reversed, becoming a cooling effect. This reversal was shown by Olszewski to take place about 80° below the Centigrade zero. Dewar then subjected hydrogen to a preliminary cooling in liquid air boiling in a vacuum at a temperature of — 205°, and afterwards forced the hydrogen through a regenerative coil under a pressure of 180 atmospheres.

By this means liquid hydrogen was first collected in an open vessel on May 10, 1898, though two years before it had been seen as spray in the jet of gas issuing from a simpler apparatus of the same essential form. When about 20 cubic centimetres of liquid had been collected the later experiment failed, owing to the stoppage of the exit by frozen air — a very common accident in dealing with liquid hydrogen.

By working with carefully purified gas, much larger volumes have since been obtained, and the writer has a vivid memory of an afternoon in June 1901, when Professor Dewar had trans- ported some five litres of liquid hydrogen from the Royal Institution to the rooms ofx the Royal Society, and gave his first public demonstration of its extraordinary properties. On that occasion

THE LIQUEFACTION OF GASES 59

liquid hydrogen flowed like water, and its pro- duction in any quantity must now be regarded simply as a matter of expense.

By carefully isolating a portion of liquid hydro- gen and preserving it, in a manner shortly to be described, from the access of heat from without, it was, when suddenly exhausted under an air-pump, transformed into a mass of solid frozen foam. By immersing a tube containing the liquid in this frozen foam, a small quantity of the clear trans- parent ice of solid hydrogen was obtained.

Kept in an open vessel, liquid air and liquid hydrogen are analogous to the water in a saucepan boiling over a fire. At the normal atmospheric pressure, water boils at 100° C., and the rate at which it evaporates depends simply on the rate at which heat enters it — depends, that is to say, on the fire below. In a similar way, liquid air has a definite boiling- point, which, under the normal pressure of the atmosphere, rises from —192° to —182° C. as evaporation proceeds. This rise is due to the fact that nitrogen is more volatile than oxygen ; and thus the liquid, as it boils away, gradually becomes richer in oxygen. Liquefied air cannot be kept in closed vessels. Its vapour pressure, equal to the pressure of the atmosphere at — 190°, becomes

60 PHYSICAL SCIENCE

enormously great as heat enters from surrounding objects and the temperature rises. In an open vessel, as heat enters evaporation proceeds, and the heat is used to effect the change of state. Thus, owing to this latent heat of evaporation which is absorbed, no rise of temperature (except the very small change already noted) occurs. But, in a closed vessel, as heat enters the pressure will rise, and the boiling-point will rise with it. The initial temperature being so low, a large rise of tempera- ture is possible, and a consequent very great in- crease in pressure. As ordinary temperatures were approached no vessel would withstand the internal pressure of the air.

In order to preserve liquid air for any time in an open vessel, it is clearly necessary to prevent as far as possible the access of heat. Evapora- tion must be proceeding continuously, but, by diminishing the rate at which it goes on, the rate of loss of liquid can be retarded.

Heat passes from one place to another in three ways : by conduction, when heat flows from one part of a body to another, or between two bodies in contact ; by convection, when air or water, heated by contact with a hot body, rises through the colder surrounding fluid, carrying heat with it ; by radiation, when heat passes directly from one body to another, as from the sun to the earth,

THE LIQUEFACTION OF GASES 61

without warming the intervening medium. Bearing in mind these three modes of transference, Pro- fessor Dewar has invented a vessel in which a liquid gas can be kept, and the effects of all three

FIG. i.

of these methods of heat-transfer be reduced to a minimum.

A double-walled glass bulb was taken, of one of the forms shown in Fig. i, and the space between the walls exhausted of air to the completest degree possible. This arrangement diminished the effects

62 PHYSICAL SCIENCE

of conduction and convection to such an extent that liquid air, placed within, evaporated at only one-fifth of the normal rate. An additional device enabled the effects of radiation to be diminished also. A polished metallic surface is the worst radi- ator and the worst absorber of radiation known, and, by coating the inner wall of the vacuum vessel with a film of bright silver or mercury, the rate of evaporation of liquid air was again reduced to the sixth part. By the combined results of the vacuum and the silvering, the rate of loss of liquid was thus reduced to the thirtieth part of its value in an ordinary open vessel. Without the use of these vessels, liquid air could not be kept for any length of time, and liquid hydrogen, at any rate, could never have been collected at all.

With the liquefaction of hydrogen the old class of so-called permanent gases disappeared. In place of them, however, a number of gases, previously unknown to science, have been discovered recently. Argon, shown by Lord Rayleigh and Sir William Ramsay to exist in the atmosphere, was the first of these gases to be detected. Its name attempts to describe its general chemical inertness ; and since this discovery several other new gases of somewhat similar chemical properties have been detected.

THE LIQUEFACTION OF GASES 63

The story of the discovery and isolation of argon is an excellent example of the importance in science of the infinitely little, and shows how striking discoveries may be made as a conse- quence of experiments which seem at first sight simply adapted to investigate, with the greatest attainable accuracy, phenomena already known to science. Since the days of Cavendish, the com- position of the air had been looked upon as an ascertained fact ; a certain proportion had been shown to be oxygen, varying amounts of carbonic acid and aqueous vapour were known to be present, while the remainder, as the result of careful in- vestigation, was supposed to be nitrogen. Caven- dish himself knew, so accurate was his work, that any undetected residue could not exceed the T^th part. But in the course of a long series of experiments, undertaken to determine afresh the densities of the principal gases, Lord Ray- leigh detected a slight difference in the density of nitrogen as prepared from ammonia and as extracted from the air. This difference, amount- ing at first to about o.i per cent., was increased on subsequent more careful examination to nearly a half per cent. It was clear that the gases pre- pared by these two methods were not identical, and that some hitherto unknown body was re- sponsible for the complication. The existence of

64 PHYSICAL SCIENCE

this new body, the inert gas now known as argon, was announced by Rayleigh and Ramsay in 1894, and shortly afterwards it was isolated from its companion.

Argon is slightly more soluble in water than nitrogen, hence a rather larger proportion of it than might be expected is found in rain water. It is also contained to a small extent in the gases liberated from certain thermal springs. Recently traces of three other gases, neon, krypton, and xenon, which much resemble argon in chemical properties, have been detected in the atmosphere. The total amount of these three substances is almost immeasurably small, and does not altogether exceed the four-hundredth part of the argon present.

The spectrum of the sun shows lines which do not coincide with those of any chemical element in conditions usually known on the earth. Among these lines many are due to terrestrial elements in solar circumstances, but a bright line in the yellow part was detected in the spectrum of a solar prominence, and was examined carefully by Frankland and Lockyer during the eclipse of August 1868. To explain its presence they called into existence a hypothetical element, placed it in the sun, and gave to it the name helium. For many years the line in the sun's spectrum was the only evidence for the existence of helium ;

THE LIQUEFACTION OF GASES 65

but in 1895 its presence on the earth was an- nounced by Ramsay, who had detected it in the spectroscopic analysis of the gases dissolved in the mineral clevite, together with the other new gases krypton and neon. Since this discovery, helium has been isolated and collected in appreci- able quantities, and its physical and chemical properties are now well known. Of all substances investigated, helium has proved the most difficult to liquefy. But in July 1908, Professor Kamer- lingh Onnes, of Leyden, obtained about 60 cubic centimetres of liquid helium by the use of a regenerative apparatus and a plentiful supply of liquid hydrogen.

It will be seen from the foregoing account that the difficulty of obtaining these low temperatures is very great. While a temperature of many hundred degrees above the freezing-point of water is easily reached in a common fire or gas flame, to cool hydrogen to 250° below that point needs the use of powerful engines, of elaborate and costly apparatus. The difference is very marked. More- over, it becomes more and more difficult to cool a substance through one degree as we pass down the scale. This fact suggests that there is some lower limit of temperature towards which we may

strive, but with the prospect of encountering in-

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66 PHYSICAL SCIENCE

creasing difficulty as we approach ; it suggests, that is to say, the existence of an absolute zero of temperature.

Our knowledge of an absolute scale of tem- perature is due to the genius of Lord Kelvin, who, with Clausius, Rankine, and Helmholtz, may be said to have founded the modern science of thermodynamics about the year 1850. It may be shown that Lord Kelvin's absolute scale of tem- perature coincides with the scale of an ideal gas — a gas, that is, such as air would be if its molecules exerted no forces on each other, and, conse- quently, its porous - plug - effect were nil. As a matter of fact, at ordinary temperatures and pressures, such gases as air or hydrogen conform very nearly to these conditions — so nearly that, for all ordinary purposes, their deviations may be neglected. Now, if we keep a gas at constant pressure, its volume changes from i to 1.366 as it is heated from the freezing to the boiling-point of water. Similarly, if it be kept at constant volume, its pressure increases in the same ratio. If we use either of these changes as our thermo- metric property, and divide the interval between the freezing and boiling-points into 100° in the Centigrade manner, there will be a change in

pressure, for example, of 0.00366 or — of the

Photo by Window &* Grove

To face fage 66

OF THE

UNIVERSITY

OF

THE LIQUEFACTION OF GASES 67

pressure at o°, for each degree through which the gas is heated. If we call the pressure at o° unity,

then at i° the pressure will be i+—~, at 2° it will

be iH -- , and so on. Similarly, if we cool the gas below the freezing-point, at — 1° the pressure

becomes i— ~r, at ~2° tne pressure is i~r

If, while we carry on this process, the properties of the gas remain unchanged, as they would were it the ideal gas we have supposed, at a temperature

of —273° the pressure will fall to I~-> that is,

i — i, or zero. At —273° C., therefore, the pres- sure of an ideal gas would vanish absolutely, and no further cooling could make it smaller. On the temperature scale which uses the pressure of an ideal gas as the thermometric property, — 273° C. represents an absolute zero, the lowest conceivable degree of cold. But, as we said, such a scale coincides exactly with the true absolute or thermodynamic scale, which, as can be shown, unlike all other temperature scales, is independent of the properties of any particular substance, whether real or imaginary. On the thermo- dynamic scale also, then, —273° C. represents the absolute zero.

We thus see that the idea of an absolute zero,

68 PHYSICAL SCIENCE

at which all bodies would be deprived entirely of heat energy, is not a mere figment of the mathe- matical imagination, derived from the study of a hypothetical air thermometer. It has a real phy- sical meaning, and the attainment of the absolute zero is, at all events, theoretically possible.

From the practical side, however, difficulties accumulate and increase as the absolute zero is approached. As Professor Dewar has remarked, " the step between the liquefaction of air and that of hydrogen is, thermodynamically and practically, greater than that between the liquefaction of chlorine and that of air." The boiling-points of chlorine, air, and hydrogen under the atmos- pheric pressure are —33°, —193° and —253° C. re- spectively. If we express these temperatures on the absolute scale, they become 240°, 80° and 20°. The interval between the boiling-points of chlorine and air is 160°, but the ratio of the absolute tem- peratures is 240 : 80, or 3 : i. On the other hand, while the interval between air and hydrogen is only 60°, the ratio of the absolute temperatures is 80 : 20, or 4 : i. The difficulty of the transition from one to the other temperature is much more nearly proportional to the ratio than to the dif- ference between them.

The absolute boiling-point of hydrogen is, as we have said, about 20°, and at present this tern-

THE LIQUEFACTION OF GASES 69

perature is the lowest at which we can continuously keep a body long enough to examine its properties. Any further advance towards the absolute zero must be made by the help of helium. By the sudden expansion of helium at a pressure of 100 atmospheres and at the temperature of solid hy- drogen, it is estimated that a transient temperature of 9° or 10° absolute has been reached. When that gas was liquefied, Professor Onnes found that its boiling-point under the normal atmospheric pressure was about 4°-5 on the absolute scale. This temperature is about one-fourth the boiling- point of hydrogen, and it has proved at least as hard to pass the interval between hydrogen and helium as it was to pass from air to hydrogen.

But, as was foreseen, the liquefaction of helium was effected by an extension of methods previously successful with other gases. A preliminary study of its properties showed that, after cooling in liquid hydrogen, it should cool further when sub- jected to a regenerative process. After attempts by several investigators had failed, Professor Onnes succeeded, and the year 1908 saw the last known refractory gas reduced to the state of liquid.

The liquefaction of helium will give command of a steady temperature of about 4°.5 absolute, its boiling-point in open vessels. That tem- perature, within 5° of the absolute zero, is thus

;o PHYSICAL SCIENCE

almost within sight; but there, with our present methods and materials, seems to come the end of any possible advance. If, in the future, a new gas, similar to helium but of less density, should be discovered, we should find that it was still more difficult to liquefy. By using liquid helium as a means of preliminary cooling, the resistance of this hypothetical gas may possibly be overcome, and, by collecting it in open vessels under the atmospheric pressure, a steady temperature of i° or 2° absolute may some day be placed at the disposal of the physicist.

With this forecast, the present brief historical account of low temperature research will be closed that attention may be drawn to the methods of measuring the temperatures therein obtained.

Mercury freezes at a temperature of — 40° C., and, at such temperatures as those now under consideration, a mercury thermometer clearly is useless. The resistance of a metallic wire to the passage of an electric current is a quantity which can be measured easily and accurately. This re- sistance, diminishing as the wire is cooled, depends on the temperature. With some alloys the diminu- tion of resistance with temperature is very small, but with pure metals it is considerable, and roughly, at any rate, proportional to the change

THE LIQUEFACTION OF GASES 71

of temperature. The metal most usually employed is platinum, since it is not attacked by acids, and is very infusible. Platinum resistance thermo- meters are now used extensively for physical research ; they have a very large range, and are probably susceptible of greater sensitiveness than any other form of thermometer. At ordinary tem- peratures a difference of temperature of one ten- thousandth of a degree can be detected with moderate ease, while, with great precautions, the hundred-thousandth of a degree can be estimated. At high or low temperatures such accuracy is im- possible, but measurements, correct to the nearest degree, can be made up to about 1100° C. and as low as —200° C. Below the latter tem- perature the rate of change of -ie resistance alters in a manner not yet fully investigated, and the instrument ceases to be trustworthy.

The standard to which the readings of all other thermometers are referred, as we have indicated when considering the absolute scale of tempera- ture, is the gas thermometer containing nitrogen or hydrogen. Not only is the hydrogen thermo- meter thus used for purposes of reference, but it can also be employed as a practical instru- ment at temperatures too low to be measured by the platinum resistance thermometer. It might be thought that, as the point of lique-

72 PHYSICAL SCIENCE

faction was approached, a gas would cease to be trustworthy as a thermometric substance, but experiment has shown that, as long as the pressure of the gas is kept well below the saturation value at which condensation would occur, the gas still expands or contracts propor- tionally to the absolute temperature. Dewar has found that thermometers, filled with oxygen and carbonic acid at low pressures, gave correct tem- peratures as low as the boiling-points of those gases at the normal atmospheric pressure. He used therefore a constant volume hydrogen ther- mometer, working at low pressure, to determine the boiling-point of liquid hydrogen itself, and confirmed the result obtained, — 252° C., by ex- periments with a similar thermometer filled with helium.

Some very remarkable effects are obtained with liquid hydrogen. A vessel containing it is so cold that the air in contact with it immediately freezes. A snow-shower of solid air is thus pro- duced. This process may be applied to the pro- duction of very high vacua. If the vessel to be exhausted be sealed to a long tube, one end of which is plunged into liquid hydrogen, the air in the vessel is frozen out almost completely. The

THE LIQUEFACTION OF GASES 73

air in the cooled end of the tube first condenses, but, as it is removed, the residual air in the vessel expands, again fills the whole tube, and again that portion of it in contact with the cold part of the tube is frozen. This process continues till the pressure within the tube falls to the millionth of an atmosphere or less, a pressure so low that an electric discharge will only pass through the vessel with extreme difficulty. A vacuum nearly com- plete may also be obtained by using charcoal cooled by liquid air in place of the hydrogen.

The liquefaction of air and hydrogen has led to the making of many experiments on the influence of low temperature on chemical action, and it is found that the rate of change is very greatly affected at these temperatures. In many cases, where the reaction proceeds rapidly at ordinary tempera- tures, the rate is reduced to such an extent that in liquid air it becomes too small to be observed. In other cases action may cease altogether, and reagents which would otherwise undergo chemi- cal change are maintained in false equilibrium by chemical forces analogous to those of friction. Fluorine, for instance, which attacks glass violently at ordinary temperatures, has no effect on it when cooled to -i 80° C.

As yet, for the purposes of physical research,

74 PHYSICAL SCIENCE

a beginning only has been made in the use of the low temperatures now at our disposal. Neverthe- less, Dewar, as well as Dewar and Fleming working together, have already obtained some interesting results. It is found that the elasticity of materials is greatly affected by these low temperatures. On the one hand, iron, lead, and tin, as well as ivory, showed a considerable increase in this property, balls of these substances rebounding to a much greater height than usual. On the other hand, a ball of india-rubber became brittle, and was broken by the fall. Connected with the increase in the elasticity of metals is their increased strength ; wires, for example, will stand a much greater load without pulling out or breaking.

Low temperatures also affect the magnetic pro- perties of iron, cobalt, and other metals, which are usually magnetic at ordinary temperatures, gene- rally increasing the magnetic moment. Oxygen, slightly magnetic as a gas, as a liquid becomes strongly magnetic. The alteration of magnetic properties with temperature has been studied in detail for many years where high temperatures are concerned, and this extension of the research has been of great interest.

From the point of view of the popular lecture- room, some of the prettiest effects given by liquid

THE LIQUEFACTION OF GASES 75

air depend on its power of imparting phosphores- cence to many substances which do not usually possess this property. Ivory, egg-shells, paper, cotton-wool, and many other things glow brightly in liquid air after they have been exposed to light. On the other hand, certain sulphides of calcium, phosphorescent at ordinary temperatures, cease to be so when cooled. Some crystals, such as those of uranium nitrate, become self-luminous in liquid hydrogen, apparently owing to intense electric forces set up by the cooling. These forces may become so intense that discharges take place which are powerful enough to be visible in the dark.

It will be seen from this account that the changes in the properties of matter are more striking and complete in the range of temperature below the freezing-point of water than in the correspond- ing range of temperature above that point. The difference in the character and intensity of these changes emphasises the importance of the ratios of temperature as measured on the thermodynamic or absolute scale, and accounts for the greatly in- creased difficulty of manipulation created by every nearer approach to the absolute zero. On the other hand, it is very striking that in biological problems, more especially in those connected with

76 PHYSICAL SCIENCE

the lowliest forms of animal and vegetable life, a hundred degrees above the freezing-point is pro- ductive of a more complete and destructive change than a hundred degrees below. While exposure to the boiling-point of water, or to a temperature a few degrees higher, suffices to kill all known forms of living organisms, many forms of bacteria merely have their vitality temporarily suspended in liquid air. Even seeds of barley, peas, &c., were not permanently affected ; in fact, they have been placed for six hours in liquid hydrogen with no effect on their subsequent power of ger- mination.

In closing this account of low temperature research it may be of interest to tabulate some of the more important temperature-constants now known to mankind. In doing so, we cannot fail again to be struck by the high temperatures easily obtainable. On the other hand, to cool an object through 250° of the 273° which separates the freezing-point of water from the absolute zero has taxed the skill of experimenters for several genera- tions. Temperatures, as already pointed out, are more justly compared by considering their ratio on the absolute scale than by consider- ing the number of degrees Centigrade or Fahren- heit which separate them.

THE LIQUEFACTION OF GASES 77

	Temperature.
	On Absolute	On Centigrade
	Scale.	Scale.
Zero of the absolute scale .	O°	-273°
Lowest temperature yet reached	10°	-263°
Boiling-point of liquid hydrogen	20°	-253°
Critical-point of hydrogen	30°	-243°
Boiling-point of liquid air	8i°to9i°	- 192° to - 182°
Boiling-point of liquid carbonic acid	195°	-78°
Freezing-point of water	273	0°
Boiling-point of water	373°	100°
Melting-point of tin Melting-point of lead	f5 601	23i°-7 327°- 7
Boiling-point of sulphur	7i8°	444°. 5
Melting-point of silver	1234°	960°. 7
Melting-point of gold	1335°	io6i°.7
Melting-point of copper Melting-point of platinum	1354° 2073°	1080°. 5 1800°

Low red heat .... White heat .... Temperature of furnace Temperature of electric arc Estimated temperature of the sun

Approximate Temperature on Centigrade Scale. 500° to 600° 1500° to 1800 1500° to 1600° 3000° to 4000° 5700° to 7000°

CHAPTER III

FUSION AND SOLIDIFICATION

" For more is not reserved

To man, with soul just nerved To act to-morrow what he learns to-day : Here work enough to watch The Master work and catch

Hints of the proper craft, tricks of the tool's true play." — BROWNING, Rabbi Ben Ezra.

IN the previous chapter we have discussed chiefly the methods employed to bring about a change of state, especially that change of state which consists in passing from the gaseous to the liquid or solid condition in the case of those substances which at ordinary temperatures and pressures exist as gases. The methods employed and the principles under- lying them were the points of interest, and the whole subject belonged to that branch of physical science which consists in recognising and over- coming difficulties of manipulation, and, as it were, of asserting by force the superiority of mind over matter.

But, throughout the investigations to be pursued in the present chapter, our attitude is altered.

There is no need for such attempted assertion of

78

FUSION AND SOLIDIFICATION 79

supremacy. The changes of state to be examined are already under our control, and we are able to investigate further details, and probe more deeply into the intimate nature of the processes involved. We patiently seek to trace connections between, for example, the mechanical properties of metals and their microscopic structure when solidified ; and, from the complicated relations which declare themselves, we may hope to throw light on the pro- cesses of fusion and solidification, and construct a theory that will hereafter prove of some use to the engineer and the metal-worker.

In the first place it is well to remark that we are seldom dealing with pure materials. Nearly the whole of the phenomena we shall consider depend on the admixture of two or more substances, one for the most part predominating. It follows that the result of the inquiry is specially applicable in all cases where traces of some impurity are the determining factor ; that is, to the majority of cases, since the attainment of chemical purity is more often a pious hope than an accomplished fact.

Our investigations will lead us far afield, and we shall pass in review combinations of many of the principal metals. It is well, however, that the starting-point should be on familiar ground ; if, indeed, by such a term it is permissible to indicate

8o PHYSICAL SCIENCE

the ice that occasionally covers our ponds and perpetually caps our globe.

It is well known that sea-water remains liquid at temperatures low enough to freeze ponds and lakes, and, long ago, it must have been recognised that this behaviour was due to the dissolved salt, though it was not till the year 1788 that Blagden, the first worker in the field, published a systematic series of observations on the freezing-points of salt solutions.

If we cool the solution of some substance such as sodium chloride, that is, common salt, the ice which freezes out is the solid form of pure water. The process can be illustrated in a very striking manner by using the solution of a coloured salt. If, for example, a dilute solution of the purple- coloured potassium permanganate be placed in a glass bottle and be surrounded for some hours by a freezing mixture, most of the water solidifies to form a hollow cylinder of perfectly colourless ice, while the permanganate is concentrated in an intensely coloured liquid core along the axis of the cylinder.

Similar phenomena occur in other cases where the separation is not so clearly visible.

If the ice be frozen rapidly, some trace of salt may be deposited also ; but experiment has shown that

FUSION AND SOLIDIFICATION 81

it does not enter into the composition of the crystals, and is entangled merely mechanically in their interstices. Essentially, then, the salt remains in the liquid solution, and, as the solvent is gradu- ally frozen out, the concentration of that solution must increase. The stronger the solution becomes, the lower is its freezing-point ; but, if the tem- perature at our disposal be low enough, we can go on freezing out water till the residual solution is saturated with salt at the temperature of its freezing-point. Any further abstraction of heat, by removing some of the necessary solvent, must then be accompanied by the simultaneous deposi- tion of salt; ice and salt will be precipitated together, and the residual solution will retain the constant composition of saturation.

Since, as the process of freezing goes on in these conditions, there is no change in the composition of the residual liquid, there can be no change in the freezing-point. The mixture of salt and water of this particular con- centration will solidify completely at a constant temperature into a mixture of salt and ice of the same composition. But pure chemical elements like lead, or pure compounds like water, also fuse and solidify at constant temperatures without change of composition. In these respects, then, the particular mixture of salt] and water which we

F

82 PHYSICAL SCIENCE

are considering behaves like a pure element or compound. For this reason Guthrie, who first systematically examined such mixtures, classed them as compounds, and named them cryo- hydrates. It is, however, now evident that their properties are explicable in other ways.

The phenomena we have traced, and the exist- ence of a cryohydric point, must be borne in mind if we wish to understand the structure of natural ice, the properties of metallic alloys, or the pro- cesses which occur when, in the cold of an Arctic winter, sea-water becomes coated with a solid covering.

Natural waters, even when known as fresh, con- tain some amount of solids in solution. When such waters are cooled to the freezing-point, how- ever, the crystals which appear form the ice of pure water. As the crystals grow, the dissolved salts become concentrated into the liquid which remains ; and the freezing-point of this liquid falls as its concentration rises. Unless the temperature of the cryohydric point is reached, some liquid must always remain, though, with fairly pure water, it may exist only as a thin film between the solid crystals. If the temperature sink below the cryo- hydric point, these liquid films themselves solidify ; but> even then, the mass is not a homogeneous solid, for the cryohydric conglomerate forms a

FIG. 2 Magnification 45

FIG. 3 Magnification 200

FIG. 4 Magnification 50

FIG. 5 Magnification 120

To face page 83

FUSION AND SOLIDIFICATION 83

cement-like connection between the primary crys- tals of pure ice. We see now the explanation of the fact that a block of natural ice, taken from a glacier or lake, has a definite structure, and may be resolved into a heap of separate crystals by exposure to the sun. The cryohydric cement dissolves first at the lower temperature, and thus the primary crystals of pure ice fall away from each other before the temperature rises to their melting-point.

Phenomena precisely similar to those we have described appear when a fused metal is allowed to solidify. Crystalline structures of pure metal form in the liquid, and grow till the whole mass becomes solid. These primary crystals usually start as fern- like forms, of which a beautiful example is shown in Fig. 2. This represents the microscopic struc- ture of a bronze ingot, suddenly chilled from a temperature of 644° C. If the crystals be allowed to grow by very slow cooling, they may come to fill nearly the whole mass, as in the case of the section of iron shown in Fig. 3. Even in this case, with a substance nearly as pure as can be obtained, the lines of separation between the primary crystals are clearly visible ; the primary crystals are differently orientated, and their faces reflect the incident light at different angles. The

84 PHYSICAL SCIENCE

crystals of zinc are often remarkably large and well-defined, and fine specimens can be seen on surfaces of so-called galvanised iron, such as is used for water-cisterns, &c. When, instead of a single metal, traces of others are present, the lines of separation between the primary crystals are much emphasised, and, when the quantity of other substances is considerable, there arise the com- plicated structures, which we shall presently study under the head of alloys.

The process of the freezing of sea-water under the influence of the intense cold of an Arctic climate is an interesting example of the application of the same principles. The phenomena have been described by the explorer, Weyprecht, whose account is quoted by Mr. J. Y. Buchanan in his " Chemical and Physical Notes." When a new surface of sea-water is exposed to the cold air, in a short time the surface of the water begins to get thick, threads like a spider's web running out from the old ice. Brine is entangled in this struc- ture, and its concentration constantly becomes greater as the quantity of ice increases. At this stage the ice is a pasty mass, and follows every motion of the water on which it floats. With a temperature of — 40° C. the new ice, even after twelve hours, is still so soft that, in spite of its thickness, a stick can easily be thrust through it.

FUSION AND SOLIDIFICATION 85

As soon as a layer of ice is formed over the sur- face, the cooling of the underlying water proceeds much more slowly, and less salt is entangled in the crystals. The lower layers of sea-water ice give therefore, when melted, a much fresher water than can be obtained from the upper layers. Even when strong enough to walk on, the surface of new sea-ice, frozen by air at —40°, is still moist and soft, the residual liquid consisting of a concen- trated solution of various salts, chiefly calcium chloride. The cryohydric point of calcium chloride, an extremely soluble substance, is very low, and that of a mixture of salts will be lower than that of either component. This lowering of the cryo- hydric temperature, which corresponds with the lowering of the freezing-point of water by the addition of salt, was observed by Buchanan in experiments conducted in the Engadine.

So far the components of the system we have been considering are not miscible with each other in all proportions ; only a limited amount of salt can be dissolved in a given quantity of water. A system not subject to any such restriction, in which the phenomena are as simple as possible, is found in mixtures of the metals silver and copper. The equilibrium of these substances has been studied by Mr. C. T. Heycock and Mr. F. H.

86 PHYSICAL SCIENCE

Neville, who have determined the melting-points, or rather the points of solidification, of mixtures of various proportions of the two metals. At the high temperatures involved, it would, of course, be impossible to use a mercury thermometer, and the measurements were consequently made by means of a platinum resistance thermometer, with which the temperature is determined by observing the electrical resistance of a coil of platinum wire. The metals in the required proportion are fused in a crucible and allowed to cool. As soon as solidifica- tion sets in, the rate at which the temperature falls always becomes less ; and, in the case of pure metals and other systems where the solid has the same composition as the liquid, the temperature remains constant till solidification is complete, just as the temperature of a mass of ice and water remains constant till the whole is frozen. Thus, by watch- ing the thermometer, the temperature at which solid begins to form can be estimated.

The melting-point of silver is 960° C. and the addition of copper lowers it just as the addition of salt lowers the freezing-point of water. This is best shown by plotting the observations on a diagram, as in Fig. 6, in which the horizontal axis denotes the composition of the mixture expressed in percentage numbers of atomic equivalents of silver and copper, and the verti-

FUSION AND SOLIDIFICATION

87

cal axis the temperatures. On the other hand, pure copper melts at 1081°, and the admixture of silver lowers its freezing-point. The two curves in the diagram cut each other at a point which corresponds with a temperature of 777°, and a composition of 40 atomic percentages of silver and 60 of copper. At other points on the curves, the process of freezing consists in the separation of primary crystals of one or other of the pure metals

20 30 4O SO

70 80 90

800

Silver

Copper

FIG. 6.

in the manner we have traced for solutions in water.* The point of intersection of the curves corresponds with the point of saturation both of silver with copper and of copper with silver.

* Osmond thinks that, in this particular case, the primary crystals are not perfectly pure. He adduces evidence to show that a slight trace of copper is dissolved in the solid crystals of silver. Any such effect, however, is hardly appreciable.

88 PHYSICAL SCIENCE

When the fused alloy has this proportion, crystals of silver and copper freeze out together, just as crystals of salt and water freeze out together when the composition of the solution is that of the cryohydrate. The point we are considering, then, corresponds with the cryohydric point for salt and water. The composition of the solid is here the same as that of the liquid, and therefore, as the process of solidification goes on, the residual liquid always has a constant concentration. Thus the freezing-point remains constant throughout the operation, and is identical with the melting-point at which liquid first appears when the solid alloy is heated. Similar phenomena constantly appear in the study of other metals ; and if an alloy of this composition is polished, etched with acid, and examined under a microscope, it will be seen to consist of a uniform conglomerate of the two kinds of crystals. An alloy of any other propor- tion exhibits larger primary crystals of that metal which is present in excess, and was frozen out first, connected by regions filled with the con- glomerate referred to above. On account of its more uniform texture, this conglomerate, which, as we have seen, corresponds with a so-called cryo- hydrate, is named the eutectic alloy. Fig. 4, on the plate facing page 83, represents a micro- scopic photograph of the eutectic of gold and alu-

FUSION AND SOLIDIFICATION 89

minium ; while in Fig. 5 is shown the structure of an alloy with a composition not quite that of the eutectic. H ere large primary crystals have appeared, the intervals being filled with the same eutectic which is seen in Fig. 4. The metal of Fig. 4 has been cooled more slowly than that of Fig. 5, and therefore the eutectic in Fig. 4 has larger crystals and a coarser structure.

The eutectic alloy has a constant melting or freezing-point ; but, during the process of fusion or solidification of other alloys, the temperature will generally change. As the primary crystals of one or other pure metal form, they leave the residual liquid richer in the other constituent, and thus with a lower freezing-point. This process continues till the liquid has the composition of the eutectic alloy, when any further loss of heat will precipitate crystals of both metals side by side. A thermo- meter immersed in the mixture will show the temperature at which primary crystals begin to form, and the temperature at which the composi- tion of the residual liquid reaches that of the eutectic, for the rate at which it falls becomes suddenly much slower when solid first appears, and the fall stops altogether while the eutectic is freezing out. Thus, in such a simple case as that of silver and copper, useful information can be obtained by merely drawing the curve giving the

90 PHYSICAL SCIENCE

observed relation between the time and the tem- perature for the heated alloy. Such curves have forms more or less resembling that shown in Fig. 7.

With silver and copper no chemical compounds are formed ; with many pairs of metals combina- tion occurs, and the phenomena are more com- plicated. A definite chemical compound plays a

Timer

FIG. 7.

part similar to that of a pure element. Addition of either component lowers the freezing-point of the compound. Thus the point of solidification of the pure compound must correspond with a maximum point on the equilibrium curve. If a single compound is formed by the two components, the curve must consist of three branches; a branch due to the effect of the compound being interposed

FUSION AND SOLIDIFICATION 91

between two branches similar to those in the silver- copper curve just considered. Copper and anti- mony form a single compound SbCu2, in which two atoms of copper are united with one of anti- mony. The equilibrium of the solid and liquid phases has been studied by M. Le Chatelier, whose results are illustrated in Fig. 8. In this case two

Cu,

1000 90O° 8 O0° 700*

Sb

coo*

6OO* 400° 3OO° ,

O 10 20 30 40 60 60 7O 8O 9O WO

FIG. 8.

eutectic alloys are formed ; one being a con- glomerate of crystals of the compound with those of copper, and the other containing crystals of the compound and crystals of antimony. These eutectics are represented by the points a and c in the figure, and between them rises the curve showing the effect of the compound, which exists in the pure state at b, the maximum of the curve.

92 PHYSICAL SCIENCE

In all the cases yet considered, the crystals deposited consist either of a pure metal or else of a pure chemical compound. Whichever it be, the composition of any one crystalline species is fixed and definite ; it does not vary continuously when the composition of the mass of alloy is altered, as does, for example, the composition of the fused liquid. In Fig. 6, page 87, the left-hand branch of the curve gives the composition of the liquid alloy which, at different temperatures, is in equilibrium with crystals of pure silver, while the right-hand branch represents the liquid in equili- brium with pure copper. One phase only, the liquid, can vary continuously in composition ; the other, or solid, phase is fixed and invariable. Similarly in the case illustrated in Fig. 8, the crystals of the compound SbCu2 have a fixed and , constant composition. Cases are known, however, in which the solid phase also varies continuously. Many salts, such as the different alums, are of the same crystalline form, and can replace each other gradually in a crystal, which may have any com- position between that of the two pure salts. Such structures are called mixed crystals or solid solutions. When they can exist, the phenomena of equilibrium become much more complicated, for the composition of the solid will vary as well as that of the liquid, and will introduce

J. WILLARD GIBBS

To face page 93

FUSION AND SOLIDIFICATION 93

a second curve into the freezing-point dia- gram.

It is only of recent years that it has been possible to interpret the complicated phenomena of solid solutions. Now, however, we possess a consistent theory of the subject, founded by Professor Rooze- boom of Amsterdam, on the work of the late Pro- fessor Willard Gibbs of Yale University. Long ago, in the years 1875 to 1878, Gibbs published a series of mathematical papers in the Transactions of the Connecticut Academy. For some time they remained practically unknown to European physi- cists ; then they were discovered by Clerk Maxwell, who used a few of the results in his book on the " Theory of Heat." But even then the time was not ripe, and it is only of recent years that we have realised that the whole theory of chemical and physical equilibrium is contained in Gibbs' work. Buried for so long, the seed has germinated in the minds of many investigators. It has already borne good fruit, and is probably destined to bear still more in time to come. Happily, Willard Gibbs lived to see a general recognition of his genius, and the reputations made of younger men who knew how to extract and apply even single results taken from the rich store hidden in his somewhat abstruse pages.

By the use of Gibbs' thermodynamic principles,

94

PHYSICAL SCIENCE

Roozeboom was able to trace the various possible forms which could be assumed by the two curves, representing the compositions of the liquid and solid phases in equilibrium with each other. The simplest case indicated by the theory is shown in Fig. 9. In regions above the higher curve, acb, which is called the "liquidus," all points

represent states com- pletely liquid, while be- low the curve adb, or "solidus," the alloy is entirely solid. Between these curves exist both liquid and solid in various proportions. At a definite temperature, a liquid of one com- position, say c, is in equilibrium with a solid of another composition, such as d. As the process of solidification pro- ceeds, the composition of both liquid and solid changes continuously. In the light of these theo- retical curves, the complicated experimental curves, found by observing the freezing-points of mixtures of metals and of other substances, are now being interpreted in a manner which otherwise would have been quite impossible.

ou

Concervtra&ort/

FIG. 9.

FUSION AND SOLIDIFICATION 95

One of the most successful examples of such an interpretation is given by the very thorough study which has been made by Heycock and Neville of the bronzes, that is, of alloys consisting of copper and tin. The curves in Fig. 10 show the results of their own experiments and of previous work by Roberts- Austen. Heycock and Neville examined microscopically the structure of various alloys of the two metals in conjunction with the equilibrium curves, and have given us a knowledge of the bronzes more complete than that which we possess for any other series of alloys showing phenomena of an equal degree of complexity.

Fig. 10 (p. 96) shows the equilibrium curves, from pure copper on the left to an alloy containing 80 atomic percentages of tin on the right. Above the "liquidus" ABCDEFGH the alloys consist of a homogeneous liquid, in which solid first begins to form when the temperature .falls to points repre- sented on the curve. The " solidus " curve, below which the whole mass is solid, is the complicated curve A&kme/E2E4H"M.

It has long been known that the physical pro- perties of metals, especially of alloys, depend on the way in which they are cooled from a state of fusion. The whole process of the annealing or tempering of steel depends on a perception of this fact. Many observers had studied the changes of

PHYSICAL SCIENCE

physical properties thus produced by examining microscopically the solid alloys obtained by dif- rerent treatments, and relations between the pro- perties of the alloy and its microscopic structure had been traced. But for the first time a complete investigation has been made by Heycock and

"Percentage Vy Weight of Tin

A 1000'

BOO* 800*

fkTOO*

Liquid

oc

FIG. 10.

Neville of the changes in microscopic structure produced by different methods of cooling, and studied in conjunction with the equilibrium curves by the light of the theory of solid solutions. The work was rendered possible by the fact that, if a hot metal be cooled suddenly from any tempera-

FUSION AND SOLIDIFICATION 97

ture by chilling it in cold water, the microscopic structure it possessed at that temperature is stereo- typed almost perfectly by the process of sudden chilling, and can be examined at leisure in the cold metal by polishing and etching it with acid in the usual manner.

In this way have been detected and traced equilibrium curves lying below the solidus. Such curves represent changes of structure which occur in a mass completely solid, and quite explain the changes in physical properties caused by annealing or chilling. Take as an example the two curves /x and E'X, which cut each other in the point x, and recall in their general form and relations the simple curves of equilibrium between liquid and solid for alloys of silver and copper already de- scribed and illustrated in Fig. 6 (p. 87). The analogy is more than one of mere form. Just as crystals of silver or copper separate out of the homogeneous liquid of Fig. 6, so crystals of new substances separate out of the homogeneous solid solution which exists within the triangular space /x/7 in Fig. 10 ; and, as the crystals of silver or copper are in equilibrium with the liquid alloy in states represented by points on the freezing-point curves of Fig. 6, so the new crystalline structures are in equilibrium with the homogeneous mother sub- stance lying within our present triangle.

98 PHYSICAL SCIENCE

The positions of these curves of equilibrium between solid phases are investigated chiefly by the microscopic examination of ingots of metal, which are fused, allowed to cool very slowly to the temperature to be investigated, in order that, as far as possible, equilibrium may be reached, and then suddenly chilled by immersion in cold water. A section of the ingot is polished, and etched with acid or other suitable liquid, in order to bring out the structure-pattern. Each pure metal, com- pound, or solid solution, crystallising from the mother liquid, possesses a characteristic appearance, which can readily be recognised after some practice in interpretation of the micro-photographs. Such photographs enable us to trace the formation, de- velopment, and decay of new crystal-species in a liquid or in a solid matrix.

The effect on the microscopic structure of differences in the rate of cooling is well shown in Figs, n, 12, and 13. The same alloy is represented in all these photographs, and was, in each case, chilled from about the same temperature. The differences in structure depend solely on the differences in the rate of cooling from a liquid condition to the temperature at which the ingot was chilled in cold water.

The alloy contained 13.5 atomic percentages of tin, and is represented by the vertical dotted line

OF THE

UNIVERSITY //

FIG. ii. — Magnification 18

FIG. 12. — Magnification 45

FIG. 13.— Magnification 18 FIG. 14.— Magnification 18 FIG. 15.— Magnification 18

FIG. 16. — Magnification 18

FIG. 17. — Magnification 18

To face page 99

FUSION AND SOLIDIFICATION 99

in Fig. 10. When this alloy in cooling passes the liquidus ABC, crystal skeletons of a solid solution called a appear mixed with the mother liquid. These skeletons somewhat resemble the larger fern-like structures of Fig. 2 on page 83, which, however, chosen chiefly for its beauty, was taken from a bronze of another composition.

When the alloy we are now considering passes the line /c (Fig. 10), a new kind of crystalline solid solution, called ft, begins to form ; and, if time is given it by keeping the ingot hot, the ft substance gradually eats up the existing crystals of a. This process is illustrated in Figs, n, 12, and 13. In Fig. 1 1 the residual a is seen as white cores within the grey ft, which follows the arrangement of the original a structures, while, in the particular illumi- nation employed, the part that was liquid at the instant of chilling shows as a dark background. In Fig. 1 2, where the ingot was cooled more slowly, the change has gone farther ; the ft substance ceases to follow the original skeletons of a, a higher mag- nification brings out the characteristic striated appearance of the ft, while, owing to a different illumination, the mother liquid shows as a light background. Fig. 13 is taken from an ingot which had been cooled to the same chill point exceedingly slowly, and kept many hours just above that temperature. The whole ingot is now

ioo PHYSICAL SCIENCE

filled with uniform striated /3, a tiny speck of a, seen towards the lower side of the photograph, alone remaining. In the light of these three photographs it is not surprising that the physical and mechanical properties of metals are modified profoundly by differences in the rates at which they have been cooled from a fused condition.

Following the dotted line in Fig. 10 still further, we see that, in ingots chilled from temperatures about 750°, ft alone should exist. Fig. 14 shows a chill from 740°, which was cooled to that temperature almost slowly enough to destroy all the primary crystals of a, which now only show as scattered specks of white.

Again following the dotted line in the equilibrium curve of Fig. 10, we pass the boundary /x, and again enter a region where a and /5 exist together. The facts on which this curve is based are illus- trated in Fig. 15. Here a new or secondary crop of a crystals has begun to grow. This ingot was chilled at 558°, and there is no doubt that the new growth of a took place in a mass which had solidified completely long before.

The further growth of the new a is seen in Fig. 1 6, which represents an alloy of slightly higher content of tin (14 atomic per cents) chilled from a temperature of 530°. As the alloy in cooling passes the temperature of 500°, the whole

FUSION AND SOLIDIFICATION 101

of the /3 substance is transformed into a complex consisting of a crystals intimately mixed with a new solid solution called 3. This complex is shown in Fig. 1 7 as a light background ; while, in contrast with it, the a crystals come out dark after the treatment adopted.

These changes again occur in a mass thoroughly solid throughout, and explain in a most striking manner the effect of such processes as annealing and tempering, in which the properties of a metal are altered by heating it to a temperature well below its fusion-point and then cooling it either slowly or rapidly.

Heycock and Neville's investigation of the bronzes was a very laborious undertaking. One hundred micro-photographs were published, and these represent only a selection of those taken ; many observations of freezing-points were also made. But the labour of the work is well repaid by the magnificent results finally ob- tained.

Iron and steel, as used in the arts and indus- tries, consist of pure iron alloyed with various substances, chiefly carbon. Solid solutions, similar to those we have studied in other cases, are formed between iron and carbon, and the phenomena of equilibrium between the liquid and solid phases,

102 PHYSICAL SCIENCE

even when no other component is present, are very complicated.

Owing to their industrial importance, the alloys of iron have been investigated more extensively than those of any other metal, and the various compounds and solid solutions identified have received definite names, which, in many cases, were given long before the application by Rooze- boom of the theory of solid solutions enabled the true phenomena of equilibrium to be understood. Roozeboom's diagram for alloys of iron and carbon, containing less than 7 per cent, of carbon, is reproduced in Fig. 18. Its general meaning will be clear in the light of what has been said in the case of the bronzes. Here again changes occur at definite temperatures, even in alloys which are completely solid. The viscosity of the material makes these changes very slow, and very different proportions of the various possible constituents will be found in alloys that have been cooled quickly and slowly. The effects of tempering steel and iron thus receive a physical explana- tion.

By heating iron above one of the transformation temperatures indicated in the diagram, and main- taining it at a high temperature for some time, it will obviously be possible to produce extensive changes in the physical nature of the metal.

FUSION AND SOLIDIFICATION 103

Recent work by Mr. J. E. Stead has shown, that when steel rails have become dangerously brittle and crystalline by long use, they can be recon- verted into a tough, elastic, and therefore safe

160O

15OO°-

14OO*-

13OO°

12OO*

0100°

iooo" aoo"

800* 7OO*

600*

Mart en. site

Martenjsite and

Perlite a,nd Cementite

a.nd Graphite

Cemeotite

.01

.02

.03

.04 .05

FIG. 1 8.

.06

.07

condition by prolonged heating at temperatures from 850° to 900° C. This improvement in pro- perties has been traced to the development of a constituent of the alloy known as sorbite. It is this constituent which gives the peculiar tenacious

io4 PHYSICAL SCIENCE

properties to iron which has been specially pre- pared for drawing into wire.

Microscopic studies of the alloys composing iron and steel have been very numerous. The work of Sorby, Andrews, Osmond, Le Chatelier, and Stead should particularly be mentioned. It is by such microscopic investigations that the different con- stituents of the alloys have been for the most part distinguished, the crystals of each constituent having a characteristic appearance, which usually persists throughout a series of changes.

The investigations we have described all em- phasise one point — the fact that metals possess a structure essentially crystalline. In some cases, such as that of the surfaces of zinc deposited on so-called galvanised iron, this crystalline structure is readily visible, but most of the metallic objects in common use possess polished surfaces on which no trace of crystals can be seen. The possibility of polishing a surface to such a state of perfection that it will act as a mirror and reflect a ray of light without appreciable scattering, is a matter of con- siderable interest. Any irregularities on such a surface must be small compared with the wave- length of light, and it is difficult to see how any such surface could be obtained by the use of ordinary polishing materials, if the action of these

FlG. 19.— Magnification 775

FIG. 20. — Magnification 775

FIG. 23. — Magnification 775

FIG. 24. — Magnification 775

FUSION AND SOLIDIFICATION 105

materials be regarded as a mere mechanical grinding away, of projections after the manner of a file.

Many careful observations have been made on the process of polishing. Among them should be noted those published in August 1903 in the " Proceedings of the Royal Society." Mr. G. T. Beilby has investigated the subject microscopically, and finds reason to believe that the passage over the surface of a scratched metal of a polishing substance like wash leather covered with rouge produces a kind of surface flow, the outer layers of the metal flowing like a viscous liquid under the action of the pressure on the polishing tool, and assuming an optically perfect surface under the influence of surface tension. In this way a film is formed over the surface of a metal, which film is in a state essentially different from that of the bulk of the substance below. Inside the metal the crystalline forces have full play ; at its surface, the controlling influences consist in part of surface tension, which, under the pressure of a polishing tool, is able to overcome the tendency to assume a crystalline structure. In Figs. 19 to 24 are shown six of Mr. Beilby's photographs. Fig. 19 shows the surface of crystalline antimony after rubbing with fine emery paper. The magnification is such that the photograph is 775 times life-size. Fig. 20,

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which represents the same surface after polishing with rouged leather, shows the gradual dragging of a film of metal over the pits and furrows of the first surface. The larger pits get filled with filings of metal, and the film seems to bridge them over, forming a continuous sheet over the loosely-packed fragments below. When an acid or other liquid capable of dissolving the metal is placed on the surface, the film is dissolved, and the pits and furrows reappear. This comes out in Fig. 21, in which the antimony previously polished has been etched with a solution of potassium cyanide. Fig. 22 shows a polished surface of speculum metal, an alloy used for the reflectors of tele- scopes. Here the underlying crystalline structure is faintly visible. The surface film has, in Fig. 23, been removed with potassium cyanide, and the structure is now plain, the primary crystals, separated by channels of eutectic alloy, being clearly brought out. Finally, in Fig. 24, the same surface has been repolished, and the channels bridged over with the flowing film of viscous metal.

These experiments have an interest which ex- tends further than the immediate subject to elucidate which they were undertaken — an ex- perience not uncommon in physical research. The existence of this viscous metallic film under

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certain conditions suggests that, when minute quantities of a solid alone exist — when there is in effect inside the surface film no substance beyond the range of molecular action — all crystalline structure must disappear. The initial formation of solid in the body of a saturated solution or of a fused material will, on this view, be co-ordi- nated exactly with the deposition of drops of water from a mass of air saturated with aqueous vapour, and the possibility of super-saturation will, in each case, depend on the work required to form a new surface of separation under the influence of surface tension alone. It is only when the individual solid structures attain a considerable size that crystalline forms begin to appear.

CHAPTER IV

THE PROBLEMS OF SOLUTION

"If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also ... is divided into definite elementary portions, which behave like atoms of electricity." — H. VON HELMHOLTZ, "Faraday Lecture," 1881.

To one inexperienced in the problems which confront the workers in the world of natural science, the whole question of solution and its attendant phenomena may appear, at first sight, of small account. Yet the study of these same phenomena, and the unravelling of their intricate connections, are of fundamental importance. Fur- thermore, as the work of the last twenty years has shown, the problems involved are of in- creasing interest, not only from the point of view of physics and chemistry, but also, and perhaps especially, from the physiological stand- point. More and more the reactions of inorganic substances, whether liquid or solid, are referred to their properties in a state of solution, while every process of life to be investigated by the biologist seems capable of interpretation only

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THE PROBLEMS OF SOLUTION 109

through attention to the conditions thereby in- volved. Moreover, most chemical actions, especi- ally those examined easily in the laboratory, occur between substances one or more of which are actually in the liquid state ; while the application of physical conceptions to the problems of living matter chiefly depends on the knowledge we possess of the physics and chemistry of ordinary solutions.

The earliest investigations of the subject were of a chemical nature, and, till the passage of electric currents through liquids came to be examined at the beginning of the nineteenth century, little systematic study of the physical properties of solutions was made. But since that period there has been constant progress, and many new fields of research have been opened up.

It happens constantly that light is thrown on the dark places of one science by work undertaken to elucidate those of another; and, in this case, the starting-point for the modern theory of solution is found in some experiments made by Pfeffer in 1877 in a botanical laboratory. Ten years earlier, Traube, in studying the modes of formation of the organic cells of plants and animals, had discovered how to construct artificial membranes permeable to water but not to solu-

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tions of certain substances dissolved therein. Pfeffer made a further examination of these semi-permeable membranes, as they have been called, and by their use obtained results of great importance in the study of biology.

A porous pot of unglazed earthenware, six to eight centimetres high and two or three centi- metres in diameter, is sealed by means of sealing- wax to a glass tube, as shown in Fig. 25. Having been thoroughly washed, it is filled with the solu- tion of a salt, such as potassium ferro-cyanide, and the outside is then surrounded with the solution of another salt, such as copper sulphate or ferric chloride, which gives an insoluble precipitate when in contact with the first salt. The two solutions gradually diffuse from opposite sides into the walls of the cell, and form an insoluble mem- brane, indicated by a dotted line, where they meet inside the thickness of the walls. This process can be hastened, and the resulting membrane im- proved, by forcing the salts into the porous material by means of an electric current. The solutions are washed away, and the wide glass tube is drawn out and sealed to a smaller tube in the manner shown in the figure.

Inside a cell thus prepared let us place the solution of some substance, such as sugar in water, and surround the outside with a large volume of

THE PROBLEMS OF SOLUTION in the pure solvent, in this case, water. Water will

FIG. 25.

gradually force its way into the cell, and, by placing mercury in the glass tube to use as a pres-

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sure gauge, it will be found that this influx will continue till a definite internal pressure is reached — a pressure greater than that without. This gives a measure of what is called the osmotic pressure of the solution as it finally exists in the cell after the entrance of the additional quantity of water.

Pfeffer found that this osmotic pressure was proportional to the concentration of the solution, at all events between the concentrations of i and 6 per cent, of sugar. For a i per cent, solution, the excess of pressure at 6°. 8 C. was equal to that of a column of mercury 505 milli- metres high, the normal atmospheric pressure being equivalent to 760 millimetres.

Many membranes within animal and vegetable organisms are semi-permeable, or, at all events, are more permeable to solvent than to solution. The permanent or temporary differences of pressure, which are thus set up, are being investigated extensively by physiologists, and have already been shown to play important parts in the processes of living structures.

Attention was first called to the interest and importance of osmotic pressure from a physical standpoint by the distinguished Dutch chemist, Van't Hoff, who is now Professor at Berlin. In 1885 Van't Hoff pointed out that Pfeffer's numbers showed: (i) that the osmotic pressure

To face page 112

THE PROBLEMS OF SOLUTION 113

was inversely proportional to the volume in which a given mass of sugar was confined ; and (2) that the absolute value of the pressure in the case of the solution of sugar was the same as that which would be exerted by an equal number of mole- cules of a gas when placed in a vessel having a volume equal to that of the solution. For instance, a quantity of gas of the same molecular concentration as a i per cent, solution of sugar would, at 6°. 8 C., exert a pressure equivalent to that of 508 millimetres of mercury, a number identical within the limits of experimental error, with Pfeffer's observed value for the osmotic pressure quoted above. The first result is equi- valent to the extension to dilute solutions of Boyle's law for gases, a law which states the experimental result that the volume of a gas is inversely proportional to its pressure. The second result shows that, in a dilute solution, the pressure depends only on the number of molecules present, and not on their nature — a statement which, applied to gases, is known as Avogadro's law.

But Van't Hoff did not alone call attention to the experimental basis of the new subject. He also placed the theory of it on a sound footing. The amount of a gas which dissolves in a given quantity of water is proportional to the pressure, and from this experimental result Van't Hoff

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showed mathematically by the principles of thermo- dynamics, that, when in solution, this same gas must exert an osmotic pressure of the observed value. The proof involves no assumption as to the physical mechanism by which the osmotic pressure is produced. Whether it be due to the impacts of the dissolved molecules on the semi- permeable walls, in the same way that the mole- cules of a gas exert pressure on the walls of the containing vessel ; whether it be due to chemical affinity between the dissolved substance and the solvent, affinity which causes more solvent to enter the cell ; or whether some other hitherto untraced effects come into play, remains an open question. The thermodynamic argument simply shows that, from the experimental solubility rela- tions of gases, the observed osmotic results follow for the gases when dissolved ; but the physical modus operandi of the pressure remains un- certain.

The extension of the theoretical result to the case of non-gaseous solutes like sugar involves some amount of assumption. However, since substances of all degrees of volatility are known, the extension seems reasonable ; and it is abundantly justified by Pfeffer's experimental measurements.

Another method of applying the principles of

THE PROBLEMS OF SOLUTION 115

thermodynamics to this problem has been de- veloped by Willard Gibbs, Von Helmholtz, and Larmor. Whatever view we take of the funda- mental nature of a solution, we must imagine the dissolved substance scattered as a number of discrete particles throughout the volume of the solvent. The nature of the interaction which occurs between the solute and the solvent is unknown, possibly unknowable ; but, whatever it may be, each particle of solute will affect only a minute sphere of solvent lying round it. The solution, then, may be regarded as containing a number of little systems, each composed of a solute particle surrounded by an atmosphere of solvent in some way influenced by its nucleus.

While the solution is concentrated, the little spheres will intersect each other, and the addition of further solvent will involve some change in the interaction between solute and solvent. But, in the process of dilution, a time will come when the spheres are beyond each other's reach, and the addition of more solvent merely increases their mutual separation without affecting their internal structure.

Thus, in a dilute solution, the energy-change of further dilution is merely the energy-change involved in separating the particles of the solute ; it will not depend on the nature of any possible

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interaction between the solute and the solvent. The change of energy is thus independent of the nature of the solvent, and will be the same whether that solvent be water, alcohol'/ or any other liquid. It will even be the same when, in cases where that is possible, the solvent is removed altogether, and the solute is obtained in the gaseous state.

If we imagine that the bottom of a frictionless engine cylinder is made of a semi-permeable mem- brane, separating a solution within the cylinder from a solvent without, it is easy to see that osmotic pressure may be made to do work, which will be measured by the pressure multiplied by the change of volume. Thus the osmotic pressure is measured by the change of the available energy per unit increase of volume ; that is, by the rate of change in the available energy of dilution.

In this manner we arrive again at the con- clusion, that the osmotic pressure must be equal in amount to the gaseous pressure exerted by the same number of molecules when vaporised, and must conform to the laws which describe the temperature, pressure, and volume relations of gaseous matter. The result is seen clearly to be independent of any hypothesis concerning the mechanism of the pressure or the nature of the solution.

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In the last chapter we have traced the phenomena of fusion and solidification, and, in the course of our inquiry, studied the equilibrium of liquid solutions with the different solid phases which mavf exist in contact with the liquids. The fundamental problem of the nature of a solution was untouched ; indeed, from the point of view then adopted, such a problem did not arise.

Until the last quarter of the nineteenth century, it was generally assumed that the forces which were brought into play when a solid dissolved in water were of the same nature as those involved in chemical action ; and the resulting solution was looked on simply as a chemical compound in which there happened to be no fixed relation between the masses of the components. The study of dilute solutions, and, in particular, the examina- tion of their osmotic pressures, showed that, in many respects, a dilute solution was analogous to a gas, and conformed to the same laws of pres- sure, volume, and temperature. Such results emphasised the analogy between the dissolution of a solid and the diffusion of a gas through a space in which it was not originally present, and sometimes led to the idea that the osmotic pressure of a solution, like the pressure of a gas, was due to the impact of its molecules on the containing wall. As an extreme case of this aspect of the

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phenomena, the view has been expressed that the solvent should simply be regarded as giving room for the diffusion of the molecules of the solid ; any possible interaction/ of a chemical nature or otherwise, between the solvent and solute being disregarded.

The similarity between the laws of gases and those of dilute solutions, however, does not neces- sarily connote identity in physical nature ; the account of the subject given by thermodynamics shows clearly that the essential feature, common to both cases, on which the similarity depends, is the dilution. In a gas the molecules are, on the average, too far from each other to exert appreciable intermolecular forces, and the change in energy produced by further dilution does not involve such intermolecular forces. In the same way the dissolved molecules in a dilute solution are so far from each other that, whatever be their action on the solvent, they exert none on each other. Here again, the change of energy on further dilution does not involve the forces between those molecules which alone from this point of view are to be considered, that is, the molecules of the dissolved substance. The essential point is the distant separation of the molecules in each case from each other ; any interaction between solvent and solute would not affect the result, and the result therefore

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cannot be used as evidence for or against such interaction.

The similarity in pressure-volume laws, then, cannot be regarded as determining the question whether solution is, in its essential nature, chemical or physical. To settle such a problem other evidence must be sought. Very little such evidence is yet available ; what little there is seems rather to favour the chemical view, which regards a solution, say of salt and water, as in some way a chemical compound of these com- ponents ; a compound in which the relative proportion between the components can vary continuously between certain wide limits.

The results in this case are characteristic of the methods of thermodynamic theory as applied in physical science. Thermodynamics is not con- cerned with the physical modus operandi of the phenomena. It does not involve molecular hypo- theses ; it is free from any doubt which ac- companies such hypotheses, though it gives less insight into the intimate processes of the pheno- mena than do successful molecular conceptions.

In the development of several branches of physics and chemistry two stages can be traced. It has sometimes happened that the earliest theoretical account of a subject has been given from the mechanical or molecular standpoint. In

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this way a definite working hypothesis has arisen, on the lines of which much investigation has been undertaken. Gradually, however, this preliminary scaffolding has been found to be unnecessary, and a thermodynamic theory has been developed, which connects the phenomena directly, and brings out their relations with similar phenomena in other branches of science.

The two methods may perhaps be illustrated in some such way as the following. In looking at the face of a watch, certain relations are observed between the positions of the two hands at different times. In order to explain these phenomena we make hypotheses concerning the structure of the inside of the watch. We imagine various arrange- ments of springs, wheels, and levers till we hit on one particular system which consideration shows us will give the observed result. Here we have an intimate picture of the inside of the watch, which may or may not represent the only possible arrangement, and may or may not correspond with the reality. Such a picture is analogous to a molecular theory of a physical problem.

One day, however, we notice, in the course of our studies of the watch, that, whatever be the position of the hands, one of them always moves twelve times as fast as the other. We have discovered a necessary relation between the

THE PROBLEMS OF SOLUTION 121

phenomena, which enables us, if we will, to dispense with ail hypotheses about the wheels and springs which drive the mechanism. The observed connection between the rates of motion allows us to evade all such complications, and to calculate directly the relative positions of the two hands at any future time.

So with thermodynamics. Lord Kelvin's great principle of the dissipation of energy, especially in its modern form, which states that the available energy of an isothermal system tends constantly to decrease, enables us in many cases to evade all molecular considerations, and to trace directly the connections between various physical and chemical phenomena. By this method it is possible to develop the theoretical relations of many subjects without involving the molecular hypothesis. Such treatment, using as its sole principle of co-ordina- tion the law of available energy, ultimately rests on the experimental impossibility of perpetual motion.

This way of treating physical science has recently been adopted by a certain number of chemists, as a means of presenting their subject without applying to it the language or conceptions of the atomic theory, in terms of which even its simplest experimental facts have come to be ex- pressed. In particular Franz Wald and Ostwald have explained the phenomena of chemical com-

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bination in definite proportions from the stand- point of energetics. They have shown that the existence of the two types known to us as elements and compounds may be deduced from the thermo- dynamic theory of equilibrium without reference to atomic hypotheses. But, in the present state of knowledge, such a doctrine seems limited in its scope, and cases in which it ceases to be sufficient will constantly recur in this volume. For instance, the phenomena of highly rarified gases have only been interpreted successfully by the aid of strictly molecular conceptions. The passage of electricity through gases, which will be considered in a future chapter, again suggests molecular hypotheses, and, in conjunction with the phenomena of radio-activity, gives an extended insight into the intimate structure of atoms and molecules. In such matters we are driven back to molecular theory, which offers an alternative method of correlating other phenomena also, equally definite, if in some ways more speculative.

Thermodynamic theory, as well as practical experiment, thus indicates that the osmotic pres- sure of a solution depends only on the number of dissolved particles, and not on their nature or on the nature of the solvent. The phenomena of gases show that the number of molecules in two

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systems may be compared by a knowledge of the total masses and of the chemical molecular weights. Thus, two solutions, one of sugar, let us suppose, and one of alcohol, which are prepared so as to contain the same number of molecules in the same volume, both in theory and practice, possess equal osmotic pressures. But, if equi- molecular solutions of sugar and salt be examined, the osmotic pressure of the salt is found to be greater, and, if the solutions be dilute, nearly twice as great as that of the sugar. These abnormally great osmotic pressures were discovered at an early date in the history of the subject ; and further in- vestigation showed that, at all events when the sol- vent was water, they occurred in the cases of those solutions which were conductors of electricity.

When Van't Hoff formulated the physical theory of the osmotic pressure, he treated these abnormal values as exceptions to the usual law. It was reserved for the physicists Arrhenius of Stockholm and Planck of Berlin to point out that the exten- sion of Van't Hoff's principles to these cases required the assumption of the dissociation of the molecules of salt in order that the total number of particles in solution should still be the number indicated by the observed phenomena. According to this hypothesis, in a dilute solution of common salt, the solute does not exist as molecules of

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sodium chloride, but as the dissociated parts, sodium and chlorine, which, since the solution conducts a current of electricity, must be asso- ciated with electric charges. Each salt molecule thus gives two pressure-producing particles in solution, and the double value of the osmotic pressure is explained. In stronger solutions this dissociation is not complete, and the osmotic pressure is less than twice the normal value ; but no exact correlation of pressure and dissociation can be made, for the thermodynamic theory as formulated above is only valid for very dilute solutions.

Like the thermodynamic theory of osmotic pressure generally, this extension of it does not involve any particular view as to the cause of the pressure or the nature of solution. The dissociation hypothesis is concerned simply with the difference between solutions of electrolytes and non-electrolytes, and leaves entirely open the more fundamental question, whether solution is essentially chemical or physical in its nature.

The dissociation theory of aqueous solutions of electrolytes, originally indicated by osmotic phenomena, is supported perhaps even more clearly and strongly, by the study of the elec- trical properties. During the years 1830 to 1840,

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Faraday made a series of experiments on the passage of electricity through liquids, in this way laying the foundations of our quantitative know- ledge of that subject. He showed that the transfer of a given quantity of electricity was always accompanied by the liberation of a definite quantity of one of the constituents of the solution, a quantity proportional to the total electric trans- fer, and to the chemical equivalent weight of the substance liberated. The quantity of electricity which passed, then, depended on the number of chemical equivalents of substance liberated, and not on their nature. These results led to a definite view as to the nature of the process of electrolysis. We must regard the passage of an electric current through a solution as due to the carriage by moving parts of the salt of opposite electric charges in opposite directions through the liquid. Under the influence of applied electric forces, these carriers drift through the solu- tion, and finally give up their charges to the electrodes, as the terminals by which the current enters and leaves the solution are called. With common salt, for example, a stream of positively electrified sodium drifts with the electric cur- rent, while negatively electrified chlorine passes in the opposite direction. The moving parts of the salt, with their accompanying electric charges,

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were named ions by Faraday ; the positive ion which moves down the electric current; is termed the cation, and the negative ion which travels up the electric stream is called the anion. The electrodes to which they travel are known as the cathode and anode respectively. The electric charge on a single ion of a substance like sodium or chlorine constitutes a true natural unit of electricity. No smaller quantity seems capable of existing. As Helmholtz has insisted, electricity, like matter, is not infinitely divisible ; it possesses an atomic structure.

In the year 1855 Hittorf examined the changes in the concentration of a solution which occur on the passage of an electric current, and explained them by supposing that the two ions moved at unequal rates. It is evident that more salt will be taken from that end of the solution from which comes the more mobile ion, and, on the assump- tion that this is the only cause at work, Hittorf calculated the ratio between the velocities of the two ions in many cases.

The next great step was made by Kohlrausch, in 1873. The conductivity of a solution is measured by the total quantity of electricity which passes through the solution per second under the action of a given electric force ; and, since the current is carried by the motion of

THE PROBLEMS OF SOLUTION 127

charged ions, the conductivity must depend on the number of the ions, that is, on the concentration of the solution, and on the velocity with which the opposite ions move through the liquid. Thus, by measuring the conductivity, the velocities of the ions under a given electric force can be calculated.

So far the movement of the ions was visible to the mind's eye only. Their passage through a solution seemed necessary to explain the facts, and, in an indirect way, their velocities could be calculated, but no direct evidence of the reality of these hypothetical phenomena was forthcoming. However, in the year 1886 Sir Oliver Lodge, and shortly afterwards by a somewhat different method the present writer, showed how to render these molecular processes visible, and how to watch the motion of the ions as they drift through the solution under the action of the electric forces.

One apparatus which may be used for this purpose is represented in Fig. 26. Let us suppose that a solution of some coloured salt is placed in contact with the solution of some colourless one, so that a fairly sharp line of demarca- tion is produced between them. The solutions should be of the same molecular concentration, the same conductivity, and the denser solution

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must, of course, be placed below the lighter. Let us take, as an example, the case of solutions of potassium bichromate and potassium carbonate, which fulfil the necessary conditions. The colour of the former salt is due to the acid part, the bichromate ion, which has the chemical composition represented by Cr2O7; the potassium ion is colourless. When a current of electricity is passed across the junction between the liquids, the colour boundary is seen to move, and, from the rate at which it creeps along the tube, the velocity of the bichromate ion under a given electric force can be determined.

The conductivity of a salt solution, made solid by the addition of gelatine or some similar substance, is nearly the same as that of the liquid

solution without the jelly, and this fact justifies the use of such solid solutions in experiments on the migration of ions. Lodge determined the

FIG. 26.

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velocity of the hydrogen ion by watching the rate at which, passing along a glass tube, it changed the colour of an indicator, while the present writer has measured the velocity of many other ions by tracing the formation of opaque precipitates, formed in minute quantity by the ions in their path.

Of late years these methods have been im- proved and extended by Orme-Masson and B. D. Steele. The general result of the experiments is to confirm the values for the ionic velocities calcu- lated from the theories of Kohlrausch and Hittorf.

The velocities with which the ions travel, even when driven forward by intense electric forces, are very small. Hydrogen, the most mobile ion known, moves over a distance of ten centimetres, or four inches, in one hour, when the applied electromotive force is one volt per centimetre. Most other ions travel at about one-tenth this rate.

These comparatively small velocities must not be confounded with an entirely different thing : the velocity with which an electric impulse, started at one end of a tube filled with an electrolyte, reaches the other end. This velocity is very great, closely approaching the rate at which an electro-magnetic wave travels through free space, that is, the velo- city of light, about one hundred and eighty thousand miles a second.

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If we accept for the moment the common con- ception of an electric current as analogous to the flow of a liquid through a conducting pipe, the connection between the two modes of motion may be illustrated by a familiar example. Suppose that a long wooden rod is lying on the surface of the ground, and that a push is given to one end of it. The motion of the rod may be quite slow, an inch an hour if we like. But, after moving one end, the other end begins to move an extremely minute fraction of a second after the starting of the impulse. Perhaps it never has occurred to us that any appreciable time elapses between the starting of the two ends. Yet, if we think for a moment, it is clear that the initial push must travel as a wave of compression along the rod, and that the far end can only begin to move when the wave front reaches it. The bearing of the analogy is now obvious. The slow movement of the rod as a whole when once started corresponds with the slow drift of the ions ; the almost instantaneous passage of the wave of compression along the rod corresponds with the velocity of electricity in the electrolytic solution.

A picture of the phenomena, more nearly cor- responding with the facts, is obtained by considering that the rapid electric impulse travels as an electric wave through the surrounding luminiferous aether.

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On this view, due to Faraday and Maxwell, and now universally accepted, the electric forces always travel through the aether. When they act on charged matter free to move, as in metallic conductors or electrolytic solutions, they produce a drift of that matter — a drift which constitutes a current. Along the line of the drift, that is, along a conductor, energy is lost, and thus along that line, and there alone, energy is constantly flowing, being carried forward by the aether to supply the place of the energy dissipated by the current.

The mobility of any one ion is, in dilute solu- tions, independent of the nature of the other ion present, at all events in simple salts, such as the chlorides of sodium, potassium, and lithium. This independence itself indicates that the ions are free from each other, and again suggests some form of dissociation.

The phenomena of conductivity also point to the same idea. To set free an ion or its products at the electrodes requires the expenditure of a certain amount of electric work, and at the elec- trodes an equivalent reverse electro-motive force exists. When, however, this reverse force is over- come, the passage of the current through the solution is opposed by no other reversible forces, and it is found that the work expended is that

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required to force the current against the frictional resistance of the electrolyte alone. The current is proportional to the excess of the electric force applied beyond what is needed to overcome the effect at the electrodes ; this part of the conduction conforms to Ohm's law, which describes the pro- cess in metallic conductors. In the body of the solution, then, as distinct from the transition layer in contact with the electrodes, the electric forces do no reversible work, such as would be needed to separate the ions from each other. Whatever freedom is requisite between the ions for the purpose of conduction, must necessarily exist whether the electric forces act or not ; the function of the electric forces when applied is simply to force the ions, already separated from each other, against the frictional resistance of the liquid medium. A certain free- dom of interchange, at all events, is thus indicated between the ions, and the freedom of interchange exists whether the current passes or not. Such freedom, indeed, had been inferred long ago from the phenomena of double decomposition observed in the chemical reactions between solutions of different salts.

So far the conductivity relations indicate the possibility of ionic interchange between the parts of the dissolved molecules, though the conformity of

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solutions with Ohm's law does not, of itself, neces- sitate the idea of permanent ionic freedom. But on any other view the possibility of interchange must be secured by collisions between the dis- solved molecules, and consequent interchanges between their ions, which would thus work their way through the solution by a series of such col- lisions. The velocity with which this process is effected must depend on the frequency of collision, which would be proportional to the square of the concentration. The ionic velocities, then, on this supposition, would increase in pro- portion to the square of the concentration of the solution, and the conductivity, which depends on the product of the ionic velocities and the concen- tration, would vary as the cube or third power of the concentration.

But the facts are quite inconsistent with this hypothesis. The conductivity is proportional at the most to the first power of the concentration ; and the ionic velocities, instead of increasing as the square, are, in dilute solution, independent of the concentration, and in more concentrated solu- tions decrease with increasing concentration. Thus again we are driven to the belief that the ions are free from each other, and move independently of each other through the liquid under an electric force : free from union with each other, let us

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observe, not necessarily free from combination, chemical or other, with the solvent. As already indicated, the dissociation theory does not depend on any particular view as to the nature of solution in general.

For aqueous solutions, then, the evidence in favour of the dissociation hypothesis is very strong, and it can safely be used as a working hypothesis to co-ordinate the known phenomena, and to guide future research. For solutions in other solvents, less evidence is yet available; though for solutions of certain salts in alcohol, the laws of the elec- trolysis seem to be similar to those of aqueous solutions and to indicate a similar theory. In fused salts, and solid electrolytes like the filaments of Nernst lamps, which also conduct currents of electricity, the conditions are different, and we must wait for further light before we can profitably theorize about the nature of the conduction process.

Besides explaining the electrical and osmotic properties of solutions, the dissociation theory, in the domain of chemistry, has proved one of the most fruitful generalisations that has ever been formulated. Solutions of salts and acids, electro- lytes in fact, are the solutions which exhibit chemical activity in the highest degree. In them, the ions alone are concerned in chemical

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action, and so clearly is this the case, that, as soon as the subject is examined, the ordi- nary chemical tests for the presence of salts are seen at once to be, in reality, tests for the individual ions of those salts. At one time it seemed likely that all cases of rapid chemical action might be reduced to reactions between electrolytic ions, but recent work by Kahlenberg and others seems to show that in non- aqueous solvents rapid reactions may occur not in any way correlated with electrolytic conduc- tivity. However this may be, in water many chemical actions are certainly connected in a very intimate way with the electrical properties, and the dissociation theory gives a satisfactory method of co-ordinating the two sets of properties. In some reactions the actual electric charges on the ions seem to be the determining factors of the whole process.

There is a marked difference in chemical and physical properties between bodies of definite crystalline form, such as most inorganic salts, and soft or amorphous substances, such as albumen and the various kinds of jelly. Long ago Graham distinguished the two groups as crystalloids and colloids respectively, and par- ticularly examined them with regard to their

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relative powers of diffusion through water. He found that, while crystalloids diffuse comparatively rapidly, the motion of colloids is so slow that it is often almost inappreciable.

Many different kinds of chemical compounds show colloidal properties. Besides a vast number of animal and vegetable substances, some of which seem to play a great part in the pheno- mena distinctive of living matter, many of the precipitates which are formed in the course of inorganic chemical reactions appear in an amor- phous or colloidal state. The sulphides of such metals as antimony and arsenic are good ex- amples. If a solution of arsenious acid be allowed to flow into water kept saturated with sulphuretted hydrogen by means of a current of that gas, a colloidal hydrosulphide is formed. Many hydrates, too, are colloids, ferric hydrate, for instance, which can readily be prepared from the corresponding salts of iron. By treating dilute solutions of gold chloride with reducing agents, such as a few drops of a solution of phosphorus in ether, the gold is set free in the colloidal con- dition, forming a ruby-coloured solution. Silver, bismuth, and mercury can also be obtained in colloidal solution.

Crystalloids diffuse much more rapidly through water and other solvents than do colloids. If

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a mixture of crystalloids and colloids be placed in a drum covered with a colloidal membrane, such as bladder or parchment, complete separa- tion can be effected, for the dissolved colloids seem quite incapable of passing through such membranes. This process probably plays a great part in animal and vegetable physiology.

Solutions of colloids in crystalloid solvents, such as water or alcohol, seem to be divisible into two classes. Both classes appear to mix with warm water in all proportions, and the mass will solidify under certain conditions to form a solid which may be called a gel. One class, represented by gelatine and agar jelly, will, when solidified, re- dissolve on warming or dilution, while the other class, containing such substances as hydrated silica, albumen, aud metallic hydro-sulphides, will, under the influence of heat or on the addition of electrolytes, form gels which cannot be re- dissolved. The solidification of members of the first class into redissolvable substances is termed setting, that of substances in the second class, which form insoluble precipitates, is termed coagulation.

The mechanism of gelation in the first, or reversible class of colloidal systems, has been studied experimentally by Van Bemmelen and by W. B. Hardy. The process of solidification

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seems to consist in the growth of a solid frame- work containing more liquid portions. The tem- perature at which this separation into two phases occurs depends on the amount of water present.

The coagulation of irreversible colloidal solu- tions, as already stated, can be effected by the addition of small quantities of the solution of an electrolyte, such as an ordinary salt or acid. Graham, who originally investigated the subject, found that a minute trace of salt was often sufficient. Thus, hydrated alumina, prepared from a solution of the chloride, was so unstable that a few drops of well-water produced coagula- tion at once, and the same change was brought about by pouring the colloidal solution into a new glass vessel, unless the vessel had previously been washed repeatedly with distilled water.

Several experimenters, including Schulze, Lin- der and Picton, and Hardy, have recently in- vestigated this coagulative power of electrolytes, with very curious and interesting results. The coagulative power of a salt is found to vary in a remarkable manner with the chemical valency of one of its ions.1 The average of the coagu-

1 The valency of a chemical atom may be defined as the number of hydrogen atoms it will combine with or replace. Thus the normal valency of oxygen is two, since two hydrogen atoms unite with one oxygen atom to form water. Faraday's work showed that the electric charge carried by an ion is proportional to its valency.

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lative powers of salts of univalent, divalent, and trivalent metals are found to be proportional to the numbers i : 35 : 1023 respectively. Most properties which depend on the valency vary in the ratios 1:2:3, an<^ the great differ- ence in the numbers now under consideration is very striking. An explanation of these unusual relations has been given by the present writer.

Let us frame a mental picture of a solution as it is represented by the dissociation theory, A certain number of the dissolved molecules are regarded as dissociated into charged ions, which wander, free from each other, through the liquid, perhaps by successive combinations with solvent molecules in their path. When an electric force is applied, though still moving sometimes in one direction and sometimes in another, the ions, on the whole, drift in the direction indicated by the force, and we may imagine, therefore, that two processions of oppo- sitely charged ions pass each other, drifting in opposite directions through the solution.

When there is no electric force, the ions are sub- ject to no steady drift, and must move sometimes in one direction, sometimes in another, as the chances of their life direct. Any one ion will be passing sometimes from one solvent molecule to another, carrying its electric charge with it ;

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sometimes it will come across an ion of the opposite kind in such a way that combination occurs, and, for a time, an electrically neutral molecule is formed. By collisions of unusual violence, or by other means, soon this molecule will be dissociated, and its ions again set free from each other, to be handed backwards and forwards by the solvent molecules as already described.

Let us suppose that, in order to produce the aggregation of colloidal particles which constitute coagulation, a certain minimum electric charge has to be brought within reach of a colloidal group, and that such conjunctions must occur with a certain minimum frequency throughout the solution. Since the electric charge on an ion is proportional to its valency, we shall get equal charges by the conjunction of 2n triads, 3;* diads, or 6n monads, where n is any whole number.

The chance conjunctions of a large number of particles moving like the ions of an electrolytic solution can be investigated by the principles of the kinetic theory of gases. If i/x denote the chance of one ion colliding with a colloidal particle, the chance that two ions should collide with it is the product of their separate chances, or i/#2, and so on. When applied to the case in hand, these principles lead to the

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conclusion that the relative coagulative powers of univalent, divalent, and trivalent ions will be proportional to the ratios i : n : n2. The value of «, which depends on a number of unknown factors, remains arbitrary. If we assume that n is 32, n2 is 1024, and we get the numbers i : 32 : 1024 to compare with the experi- mental values of the relative coagulative powers i : 35 : 1023.

When we consider the difficulty of the experi- ments, and remember that the coagulative powers of different solutions containing ions of equal valency are not exactly equal, but vary as the equivalent conductivities of the solutions, we see that these results show a remarkable agreement with the calculated numbers, and give strong evidence in favour of the hypothesis that coagu- lation depends on the presence of a minimum electric charge, which is brought into action by the chance conjunction of the ions of an electrolyte.

The particles in solutions of colloids in water generally move slowly when acted on by electric forces, the direction of motion depending on the nature of the colloid and on that of the solvent. Hardy found that the direction of movement of certain proteids could be changed by changing the solvent from a very dilute acid to a very dilute alkali. This reversal implied a change in the sign of

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the charges on the colloid particles ; and, if the sol- vent was very carefully neutralised, an iso-electric point was reached at which the solution became very unstable, and coagulation seemed to occur spontaneously. The same observer also found that, in the case of colloids travelling with the current, it is the acid ion which is active in causing coagulation, and not the metallic ion as in the experiments of the older experimenters, who all used colloids which travel against the electric current. Thus it is always the ion possessing a charge of opposite kind to that on the colloid particle which is effective in producing coagulation.

These results are of great importance, not only from the point of view of physiology, from which they were undertaken, but also as throwing light on the nature of colloid solution — perhaps, indeed, of solution in general. It looks as though colloid particles, at any rate, could exist in solution only when charged electrically. If, by the conjunction of more mobile ions, their charge is neutralised and the iso-electric point reached, coagulation must im- mediately follow.

It is probable that these effects depend on changes in the surface of separation between the colloidal particles and the more liquid phase which surrounds them. Such a surface of separation must exhibit the well-known

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phenomena of surface-tension, and will possess an amount of available energy proportional to its area, which therefore tends to become as small as possible. A number of separate par- ticles would, in these conditions, tend to coagulate into larger ones, just as small rain- drops tend to coalesce into larger ones. If the colloidal particles are electrified, the electric energy is greater when the charge is concen- trated on a small area, and, on this account, the area will tend to increase. The effect of the electric charge is thus opposite to that of the natural surface-tension, and diminishes the tendency to coagulate. Thus an electric charge may enable the colloid to dissolve, while neutrali- sation of the charge may result in coagulation.

Modern physiology finds some reason for believing that a wave of this electrolytic coagu- lation is the physical accompaniment of a nerve impulse, while permanent and irreversible coagulation results from the action of certain poisons. This, however, is not the place to follow in detail such an interesting inquiry, which deals with matters outside the present scope of physical science.

Much discussion has taken place about the nature of liquid colloidal solutions, and their relations with ordinary solutions of mineral salts

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and other crystalloids. They may either be regarded as ordinary solutions, in which the dissolved particles are similar in kind to those of crystalloid solutions, though of much higher mole- cular weight, or they may be considered to be systems of two phases, composed of suspensions of particles in the liquid, the particles being different in kind from the liquid, and of much greater than molecular dimensions.

In some colloid solutions the presence of suspended particles can be detected readily by ordinary means. Sometimes they are visible under a good microscope ; in other cases, while too small to be directly visible, they are large enough to scatter and polarise a beam of light. This means that their size must be comparable with the wave-length of light, about 5 x io~5 cm. Such particles would be too few in number to exert a measurable osmotic pressure, and the absence of such pressure does not necessarily mean that solutions of colloids are different in kind from solutions of crystalloids.

It is worthy of note that turbid suspensions of clay, kaoline, &c., in water are rapidly cleared by the addition of small quantities of metallic salts. This action, which is almost certainly of the same nature as the coagulation described above, pro- bably helps in the formation of sand-banks at the

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mouths of rivers ; the salts of the sea-water clear the suspensions of clay brought down with the fresh water, and precipitation is then aided by the diminished velocity.

The conditions which determine the colloid or crystalloid nature of a substance are still not fully understood. The persistence of colloid properties, when a substance passes from the dissolved to the non-dissolved state, shows that the determining conditions must be of fundamental importance. The molecular forces seem to be much less active in colloids, but the freedom with which some of them disintegrate and dissolve in presence of water and other liquids indicates that some interaction between them and their solvent must occur. It seems likely that the forces which are involved in crystalloid solution are of the nature of those classed as chemical or molecular, while, when colloids dissolve, the actions between solvent and solute are conditioned also by the phenomena studied under the names of capillarity and surface tension. It is not likely that any sharp line of demarcation can be drawn ; though, as the size of the dissolved particles increases, the importance of the chemical forces probably diminishes, and that of the capillary forces grows.

If colloid and crystalloid solution are but the

extreme limits of a continuous series of phenomena,

K

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the study of dissolved colloids of varying degrees of aggregation should throw much light on the general problem of the fundamental nature of solution.

The explanation of the coagulation of colloidal solutions as an effect on the surface conditions at the junction between colloid and solvent, brought about by the chance conjunctions of dissociated electric ions, is an illustration of a course of history which indeed constantly repeats itself in scientific inquiry. An observation is made, per- haps long series of experiments are carried out, before the general state of knowledge enables a satisfactory explanation of the phenomena to be formed, or a theoretical co-ordination of them with other phenomena to be traced. Even Graham's acute and powerful mind, in the absence of the dissociation theory of electrolytes, and of the knowledge of the surface relations of two phases which we now possess, could frame no complete theory of the coagulation effects which he examined with such skill. By experiments on coagulation alone it is probable than an explana- tion could never have been reached. But by the advance of other observers, led by Gibbs on one far-off flank, and by Van't Hoff and Arrhenius on the other, almost out of touch with

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the original attack, the position of the adversary — ignorance — was turned ; and when, at a later time, a new frontal assault was made, the way proved easy and obvious.

" For, while the tired waves, vainly breaking,

Seem here no painful inch to gain, Far back, through creeks and inlets making, Comes, silent, flooding in, the main.

And not by eastern windows only,

When daylight comes, comes in the light ;

In front the Sun climbs slow, how slowly ! But westward, look ! the land is bright."

CHAPTER V

THE CONDUCTION OF ELECTRICITY THROUGH GASES

"It is difficult to think of a single branch of the physical sciences in which these advances are not of fundamental importance. . . . The physicist sees the relations between electricity and matter laid bare in a manner hardly hoped for hitherto. . . . But it is the philosopher that these researches will affect most profoundly. As much by the aid of a perfect mastery over the properties of materials as by the sheer intellectual power of abstract reasoning, some of the fundamental problems of the constitution of matter are here presented as on the verge of solution." — Times. January 22, 1904.

UNLIKE the liquid solutions and other electrolytes studied in the last chapter, gases, in normal conditions, are almost perfect insulators of elec- tricity. Telegraph wires are insulated by the air which surrounds them, and, if leakage occurs to any measurable extent, it can always be traced to the solid supports to which the wires are attached. Nevertheless, by delicate instruments, a slight leakage of electricity through air can be detected. This air leakage is usually extremely small, but it can be increased greatly in many ways. The passage of Rontgen rays, the incidence of ultra- violet light on a metal plate, the neighbourhood

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of flames, incandescent metals, or of radio-active bodies such as radium, are among the agencies whereby the condition of the surrounding air is modified so that it can rapidly conduct away the electric charge.

In general, the currents through gases are too small to be investigated by means of a galvano- meter. By the aid of an electrometer, however, or by the use of some form of gold leaf electro- scope, the passage of electricity may be detected, and the amount of the current determined.

The quadrant electrometer consists of a light but rigid strip of aluminium or silvered paper, suspended horizontally by a fine quartz fibre. This strip is kept permanently charged with elec- tricity, and is therefore deflected when other charges are given to brass quadrants which sur- round it. By the rate at which the deflection diminishes, it is possible to estimate the rate at which the charge on the quadrants, and on any conductor connected with them, disappears or increases.

Still simpler and yet more sensitive is the gold leaf electroscope, in which a thin strip of gold leaf is attached to a brass plate, and charged with electricity. Owing to the repulsive forces between portions of the same charge, the gold leaf is repelled from the plate and stands out at an

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angle. By observing through a microscope the rate at which the leaf falls, we can determine the rate at which its charge leaks away.

Whichever apparatus be adopted, the natural leak, due to the apparatus itself and the air sur- rounding it; must first be determined, and sub- tracted from the leakage afterwards found under the influence of an ionizing agency.

In the last chapter we have seen that the properties of conducting solutions have been successfully co-ordinated and explained on the hypothesis that the passage of a current is effected by the motion of charged particles called ions. A similar supposition has been adopted to explain the conductivity of gases, although it will be clear that, in many respects, the ions in the case of electric discharge through gases must be endowed with properties different from those which pertain to the ions of liquid solutions.

After a period of activity on the part of some ionizing agency, such as Rontgen rays, the resultant conductivity does not cease simultaneously with the action of the rays. It persists for some little time ; it can be blown about with currents of air ; and in all respects acts as though it were due to the presence of material particles, formed somehow in the gas through which the rays had passed. The conductivity is destroyed if the gas be passed

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through a plug of glass wool or bubbled through water ; it is also removed if the gas be subjected to the action of an electric field. Such experi- ments, and many others of somewhat similar nature, are readily explained by the conception of charged particles, which, produced in some way by the action of the ionizing agency on the molecules of the gas, are afterwards driven through the gas by an electric force, just as the ions of a salt solution are driven through the liquid. Unlike the ions of liquids, however, those of gases do not long persist after the cessation of the outside ionizing agency. Left to themselves, the ions gradually disappear. Such a disappearance might be anticipated on the view that the opposite ions re-combine and neutralize each other, and also on the assumption that they give up their charges to the solid objects with which they come in con- tact as they move about under their own motions of diffusion, and that they are driven towards an electrode by the action of an electric force.

The non - persistence of gaseous ions and the consequent need of their perpetual renewal ex- plains the relation between current and electro- motive force — a relation different from that observed in liquid solutions. In solutions, as we saw, the conduction conforms to Ohm's law — the current is proportional to the electro-motive force.

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In gases this is not the case. For an ionizing agency of constant intensity, such as a layer of<