REESE LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 
 , igo . 
 
 ^Accession 
 
 2-33 Class N:,. 
 
 -s 
 
 
3 
 
 LECTURES ON PHYSICAL SCIENCE 
 
LECTURES 
 
 ON SOME 
 
 RECENT ADVANCES 
 
 IN 
 
 PHYSICAL SCIENCE 
 
 WITH A SPECIAL LECTURE ON 
 
 FORCE 
 
 BY 
 
 P. G. TAIT, M.A. 
 
 FORMERLY FELLOW OF ST. PETER'S COLLEGE, CAMBRIDGE 
 PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF EDINBURGH 
 
 TJNIVEBSITY j 
 
 
 THIRD EDITION, REVISED 
 
 MACMILLAN AND CO 
 
 1885 
 
lEainlmrgf) SRni&ersitg JGrcsc : 
 
 THOMAS AND ARCHIBALD CONSTABLE, PRINTERS TO HER MAJESTY. 
 
WITH THIS WORK 
 I DESIRE TO ASSOCIATE THE NAMES 
 
 SOF 
 GEORGE BARCLAY AND THOMAS STEVENSON, 
 
 FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH, 
 
 BY WHOSE EFFORTS THESE LECTURES WERE ORGANISED, 
 
 AND AT WHOSE WISH THEY ARE PUBLISHED AS DELIVERED. 
 
 P. G. T. 
 
PREFACE TO THIRD EDITION. 
 
 IN preparing a Third Edition for the press, I have 
 adhered to my original plan of publishing these Lectures 
 just as they were taken down by the short-hand writers. 
 I have, however, altered here and there a mere word or 
 two, and in a few places, where it appeared to be called 
 for, I have added an explanatory sentence. 
 
 Other brief additions [enclosed in square brackets] 
 deal chiefly with facts which have been discovered since 
 the Second Edition (a very large one) was published. 
 
 I have not reprinted the polemical part of the Preface 
 to that edition. Professor Zollner's charges, there alluded 
 to, were withdrawn by himself : while those of Professor 
 Clausius were so fully met by me in the Philosophical 
 Magazine for May 1879 tnat his reply has not, so far 
 as I know, even yet appeared. And the reference to 
 Mohr's work has been amplified, and embodied in 
 the text of the book. 
 
 Here my Preface might have ended, had it not been 
 that a new critic has appeared on the scene, in the form 
 of Professor du Bois-Reymond, who, in his capacity of 
 Secretary to the Royal Academy of Sciences of Berlin, 
 considered himself justified in speaking as follows at 
 
viii PREFACE TO THIRD EDITION. 
 
 a gala meeting of that Academy on March 28th, 
 
 ' Foreign investigators, in their ignorance of the German lan- 
 guage, often discovered for the second time things long known to us. 
 
 ' Not unfrequently, even when better informed, they took ad- 
 vantage of the presumed right of independent discovery to cite 
 their German predecessors only by the way or not at all. The 
 Germans, on the other hand, showed a perfect national impartiality 
 which was far more to their credit than their linguistic superiority. 
 Indeed they never even conceived the possibility of national 
 jealousy between learned men who seek nothing but the One Truth, 
 but live, ideally, with the investigators of all countries as with 
 their equals, without even imagining how little this . feeling is 
 reciprocated, chiefly because foreigners know so little of us. 
 
 * In other nations great pains were taken to find out among them- 
 selves the germs of new discoveries, and in one way or another 
 this always succeeded. The German man of science only wished 
 to find the true germ, whether it might be in a fellow-countryman 
 or in a foreigner, and he never hesitated to recognise, as probably 
 the first discoverer, a foreigner, if there was the slightest reason 
 for the supposition. He was far more pleased to do historical 
 justice than hurt to deprive Germany of a doubtful glory. 
 
 ' In the same way it was far from the thought of German men 
 of science to exaggerate the importance of a first chance observa- 
 tion, in order out of it to add to Germany's scientific credit. 
 
 'What weight would others not have given to the fact, quite 
 unnoticed by us, that the first galvanic phenomenon, which besides 
 gave Volta the key to Galvani's researches, was observed here in 
 Berlin by one of our predecessors ? 
 
 ' The national feeling does not blind German scientific men to 
 the fact that the seeking out of such Priority is a double-edged 
 weapon. For if an Irish physicist living in England and a 
 Scottish physicist (who need no such addition to their fame) had 
 Spectrum Analysis in their pocket ten years before Kirchhoff and 
 
 1 The obviously offensive intention which dictated this speech rendered 
 me anxious to avoid all suspicion of having heightened it in translation : 
 so, at my request, my colleague Dr. Crum Brown has kindly made the 
 subjoined version for me. 
 
PREFACE TO THIRD EDITION. 
 
 IX 
 
 Bunsen, why did they not make out of it what Bunsen and Kirch- 
 hoff did ? 
 
 'Why? A Scottish man. of science, whose name has been 
 recently much before us, tells us in his Lectures on some Recent 
 Advances in Physical Science. The German investigator knows all 
 that is going on in Science, or at least has some one by him who does. 
 If a German comes on a new idea, he can at once see, or be told, 
 whether another has it or not, and in the latter case he can print 
 the idea, and so secure the priority : the poor Britons, on the other 
 hand, make the most splendid discoveries in the world without 
 ever guessing that they have struck on anything new like the 
 Bourgeois Gentilhomme, they speak prose without knowing it, and_^ 
 let the priority slip them. The wily Germans ! who, instead of 
 contenting themselves like other innocent folks with their mother 
 tongue, sneak into foreign languages to spy out the discoveries ^ 
 that are being made. 
 
 'The unpleasant impression produced by these statements in 
 the key of national antipathy is increased by other passages in these 
 Lectures. The author makes it his special business to elucidate 
 the history of the law of the conservation of energy, and tracks 
 this law back to Newton's third law of motion, the equality of 
 action and reaction. Newton's second explanation of his third law 
 is, he tells us, a nearly complete expression of the conservation of 
 energy. 
 
 'As the science of Mechanics depends on Newton's laws of 
 motion, of course the conservation of energy can be somehow read 
 out of them, or rather read into them. And we need not doubt 
 that a head like Newton's had, in private, as much knowledge of 
 the conservation of energy as could be had in his time. It is 
 another question what view he took of it, and what was his position 
 towards it as manifested in his works. Whoever is acquainted with 
 the history of this doctrine knows Descartes's original but un- 
 successful notions ; their correction by Leibniz : Leibniz's conception 
 of the material world substantially agreeing with that now held. 
 He knows that Newton in his Optics also disproved Descartes's 
 opinion, although without mentioning its correction by Leibniz, 
 and without himself undertaking this correction ; that the Cos- 
 mogony-speculator called in God to put the planetary system right 
 when it had gone wrong in consequence of accumulated perturba- 
 
PREFACE TO THIRD EDITION. 
 
 tions, which scarcely accords with the conservation of energy. To 
 one who knows this epoch it will not seem impossible that the 
 dissensions between Leibniz and Newton disgusted the latter with 
 the subject, and formed the cause why the law of the conservation 
 of energy received then so little assent in England. Certain it is 
 that on the Continent, during the first half of last century, this law 
 in the form given to it by Leibniz was the common property of 
 scientifically educated persons, as it is now. This is no hidden 
 mystery : it is easy to make it out from the literature of the last 
 ten years. He who has all this before him can only shrug his 
 shoulders at the artificial attempts to put Newton at the head of 
 those to whom we owe the law of the conservation of energy. 
 Perhaps the author of the Lectures is not sufficiently acquainted 
 with the history on which he undertakes to throw light, and on the 
 later developments of which he passes such rough judgment, and 
 so only lays himself open to the suspicion, unfortunately not 
 weakened by his other writings, that the fiery Celtic blood of his 
 country sometimes runs away with him and makes him a scientific 
 Chauvin. 
 
 f ' Scientific Chauvinism, from which German men of science have 
 hitherto kept themselves free, is more hateful than political, inas- 
 much as one expects decent demeanour more from scientific men 
 than from politically excited masses. May it be far from us in 
 the future also ! Let us not be misled in our intellectual habits by 
 the present ebullition of national feeling in Europe. In spite of the 
 tone of irritation appearing, now here, now there, among other 
 nations, may we retain unlost the tradition of a scientific justice 
 exercised without respect of nation, and of the serious literary 
 work which this implies ! 
 
 ' May our Temple of the Muses remain a safe refuge for German 
 cosmopolitanism if the storms of the time tolerate it nowhere else ! ' 
 
 Is not this conceived very much in the spirit of the 
 well-known passage : Ich danke dir, Gott, dass Ich 
 nicht bin wie andere Leute, Rauber, Ungerechte, 
 Ehebrecher ; oder auch wie dieser Zollner ? 
 
 To any one who reads the above extract from 
 Professor du Bois-Reymond's speech, it is obvious that 
 
PREFACE TO THIRD EDITION. xi 
 
 the Chauvinism (surely Pharisaism would be the more 
 correct word) so freely denounced (in others) towards 
 the end, has been as freely practised (by the speaker 
 himself) from the beginning. 
 
 But this special form of accusation is most parti- 
 cularly unhappy as directed against my book. For the 
 book shows no Chauvinistic tendencies, properly so 
 called : its praise or blame may be deserved, or not, 
 but they are certainly awarded from considerations 
 altogether independent of nation or race ; they are used 
 throughout in favour of what I consider to be true 
 Science, and against quackery, knavery, bigotry, and 
 superstition, wherever found. 
 
 Fresnel and Carnot, Gauss and Riemann, Young and 
 Faraday, are names to be honoured to all time ; not 
 by any means because they belonged to Frenchmen, 
 Germans, or Britons ; but because they belonged to 
 men who have, each in his turn, led the van in the 
 intellectual struggles of his generation. 
 
 But when a false prophet arises, or is raised up by 
 others for the admiration of the unlearned multitude, it 
 is a duty (often, it may be, a pleasant duty) to expose 
 the hollowness of his pretensions ; and to do so with 
 sternly impartial relish whether he be French, German, 
 or British. Equally is it a duty to bring forward the 
 claims of a true prophet, be his nationality what it may ; 
 if these have suffered from his own modesty or care- 
 lessness, or from the neglect or disparagement of others. 
 
 My censor should have thought of the possible 
 application of some of his own phrases to himself. 
 
xii PREFACE TO THIRD EDITION. 
 
 Was it not this fervent denouncer of Chauvinism who 
 apologised to his students for the too Gallic sound 
 of his own name ? What but an absolutely overmaster- 
 ing antipathy to everything Gallic could have led a 
 Professor of Physiology to speak of 'the fiery Celtic 
 blood ' of a Norseman ? 
 
 And the most recent authoritative text-book of 
 Spectrum Analysis, published a year or two ago in 
 Berlin, supplies a singular comment on the above 
 eulogy of German scientific men in general. Though 
 historical details are freely given in that work, the name 
 of Balfour Stewart is not even once mentioned! I take 
 this work as an example, because it is a high-class one. 
 But, even from my own reading, which has been mainly 
 confined to standard works (so far as German is con- 
 cerned), I could supply numerous equally striking 
 examples of exceptions to the sweeping statement so 
 confidently made by my censor. 
 
 My acquaintance with Leibnitz's works may not be 
 so profound as is that of Professor du Bois-Reymond ; 
 but, such as it is, it has led me to accept the opinion of 
 Huygens on him as a man, and that of Gauss on him 
 as a mathematician. Surely even Professor du Bois- 
 Reymond will allow that these (especially as neither 
 was Gallic) were competent judges. 
 
 P. G. TAIT. 
 
 COLLEGE, EDINBURGH, 
 Dec. 2tyh, 1884. 
 
PREFACE TO FIRST EDITION. 
 
 THE following Lectures were given in the spring of 
 1874, at the desire of a number of my friends, mainly 
 professional men, who wished to obtain in this way a 
 notion of the chief advances made in Natural Philosophy 
 since their student days. 
 
 The only special requests made to me were, that I 
 should treat fully the modern history of Energy, and 
 that I should publish the Lectures verbatim. 
 
 The reader will judge for himself how far the first 
 request has been attended to. As to the second, it is 
 necessary to explain that, being very busy, I had not 
 time to do more than arrange a few notes for each 
 lecture ; so that the course was entirely extempore, and 
 was taken down by excellent short-hand writers. 
 
 Besides necessary corrections, only one large change 
 was made in the M.SS., viz., the excision of a great 
 many of those repetitions which are indispensable in 
 extempore lecturing, but are intolerable in a book. 
 Professors Clerk-Maxwell and Balfour Stewart have 
 been kind enough to read the proofs, and to suggest 
 several valuable improvements. 
 
 The work must, however, be regarded as in no sense 
 
xiv PREFACE TO FIRST EDITION. 
 
 whatever a finished production, though I hope it will 
 be found not only accurate but also readable. In fact, 
 I could not possibly have found time to rewrite the whole 
 in the form in which I should like to have presented it 
 for publication ; so that the reader is requested to 
 remember, if he desires to find fault, that the non- 
 removal of many defects whose correction would have 
 required large changes, was the condition under which 
 alone the book could have appeared. Still, I should 
 not have allowed it to be published had I not been 
 assured by competent judges that in spite of its neces- 
 sary imperfections it is calculated to be useful. 
 
 P. G. TAIT. 
 
 COLLEGE, EDINBURGH, 
 February 1876. 
 
CONTENTS. 
 
 LECTURE I. 
 
 INTRODUCTORY. 
 
 r 
 
 Classification of Recent Advances in Physical Science. General State- 
 ment of the Objects of Physics. Time and Space. Matter, Position, 
 Motion, and Force. Digression upon a priori reasoning. Instances 
 of modern or revived fallacies Uniformity of Earth's Rotation, Sta- 
 bility of Solar System, Heat developed the equivalent of work spent 
 in compressing a gas, Causa czqiiat effectum. Gilbert the true origi- 
 nator of Experimental Science. Test of the reality of Matter fails 
 when applied to Force not when applied to Energy. Conservation, 
 Transformation, and Dissipation of Energy. Ignorance and Inca- 
 pacity alike of Spiritualists and Materialists, .... 
 
 LECTURE II. 
 THE EARLY HISTORY OF ENERGY. 
 
 Newton's services to the subject only of late recognised. Second Law 
 There is no balancing of forces ; but only of the effects of forces 
 Geometrical composition of velocities. Third Law Its second in- 
 terpretation an all but complete statement of the Conservation of 
 Energy Arithmetical composition of the squares of velocities. 
 Experimental results of Rumford and Davy, filling up the lacuna 
 in Newton's statement. Their proofs that Heat is not matter. 
 Davy's statement of the true theory of Heat. Speculations of Sguin 
 and Mayer, . . . . 2 7 
 
CONTENTS. 
 
 LECTURE III. 
 ESTABLISHMENT OF THE CONSERVATION OF ENERGY. 
 
 PAGE 
 
 Further inquiry into the asserted claims of Mayer. Opinions of Colding 
 and Joule on Mayer's first paper. [Insertion (1884) on the prior 
 claims of Mohr.] Colding's Experiments. Joule's Experiments. 
 Numerical value of the Dynamical Equivalent of Heat. Helmholtz's 
 argument from the Perpetual Motion. Transformation and Dissi- 
 pation of Energy. Illustrative experiments, . . . . 52 
 
 LECTURE IV. 
 TRANSFORMATION OF ENERGY. 
 
 Experimental Illustrations Heating of wires, and decomposition of 
 water, by a Galvanic current Electro-magnetic Engine Rotating 
 Disc Magneto-electric Machine Induction-Coil and Geissler Tube 
 Higher and Lower Forms of Energy. Work transformed wholly 
 into Heat Only a portion of the Heat can be reconverted into 
 Work. Carnot's Cycle of Operations and his Reversible Cycle. 
 Effect of pressure upon Ice, . . . . . .81 
 
 LECTURE V. 
 
 TRANSFORMATION OF HEAT INTO WORK. 
 
 Carnot's Cycle continued. Watt's Diagram of Energy. The Impossi- 
 bility of the Perpetual Motion is an experimental truth. Conditions 
 of Reversibility. Absolute definition of Temperature. Second Law 
 of Thermodynamics. Absolute zero of temperature, or temperature 
 of a body devoid of heat. Efficiency of the best steam-engine. Effect 
 of pressure on the freezing point of water. Mechanism of Glacier 
 motion, .... ... 107 
 
 LECTURE VI. 
 TRANSFORMATION OF ENERGY. 
 
 Further consequences of Carnot's ideas. Anomalous behaviour of water 
 and of india-rubber. Application to rock masses, and the state of 
 
CONTENTS. 
 
 PAGE 
 
 the earth's interior. Availability of energy, and loss of availability. 
 To restore the availability of one portion of energy, another portion 
 must be degraded. Dissipation of energy. Sources of Terrestrial 
 and of Solar Energy. Energy of plants and animals. Measure of the 
 Sun's Radiant Energy. Energy now in the Solar System, . . 133 
 
 LECTURE VII. 
 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 Available Sources of Energy on the Earth. Whence these have been 
 derived. Uniform itarian School of Geologists. Sir W. Thomson's 
 arguments as to the length of time during which life has been possible 
 on the earth. Transference of Energy through Solids, Fluids, and 
 through the Ether. Test of the Receptivity of a body or system for 
 energy in a vibratory form. Physical ' Analogies introductory to 
 Spectrum Analysis, ....... 162 
 
 LECTURE VIII. 
 RADIATION AND ABSORPTION. 
 
 History of the discovery of the Physical Basis of Spectrum Analysis. First 
 result of Spectrum Analysis applied to non-terrestrial bodies ; There 
 is Sodium gas in the Sun's Atmosphere. Elaborate experiments of 
 Stewart and Kirchhoff. Identity of Light and Radiant Heat. Dis- 
 tinctive characters of a particular ray. Application of Carnot's 
 principle to establish the equality of radiating and absorbing powers. 
 Black, transparent, and perfectly reflecting bodies, . . . 187 
 
 LECTURE IX. 
 
 SPECTRUM ANALYSIS. 
 
 Spectrum of incandescent black body ; of incandescent gas or vapour. 
 Absorption by vapour of parts of spectrum of incandescent black 
 body. Application to sunlight, and starlight. Solar spots and pro- 
 tuberances. Period of life of various stars. Fluorescence, . .214 
 
xviii CONTENTS. 
 
 LECTURE X. 
 SPECTRUM ANALYSIS. 
 
 PAGE 
 
 Change of colour of Light by relative velocity of source and observer. 
 Analogy from sound. Causes of broadening of spectral lines. 
 Spectrum of Solar Corona ; of Double Stars ; of Comets. Probable 
 nature of Comets ; of Saturn's rings ; of the Zodiacal Light, . 237 
 
 LECTURE XL 
 CONDUCTION OF HEAT. 
 
 Fourier's Mathematical Theory. His Definition of Conducting Power. 
 Analogy between Thermal and Electric Conductivities. Forbes's 
 method and results. Angstrom's method. Penetration of Surface 
 temperature into the earth's crust. Analogy between conduction of 
 heat and conduction of electricity. Diffusion also analogous to these. 
 Diffusion of matter, of kinetic energy, and of momentum, . . 265 
 
 LECTURE XII. 
 STRUCTURE OF MATTER. 
 
 Limits of Divisibility of Matter. In physics the terms great and small 
 are merely relative. Various hypotheses as to structure of bodies 
 Hard Atom Centres of Force Continuous but Heterogeneous 
 Structure Vortex-atoms [Digression on Vortex- Motion.] Lesage's 
 Ultramundane Corpuscles. Proofs that matter has a grained struc- 
 ture. Approximation to its dimensions from the Dispersion of Light : 
 from the phenomena of Contact Electricity, . . . 287 
 
 LECTURE XIII. 
 STRUCTURE OF MATTER. 
 
 Approximation to dimensions of grained structure from capillary 
 phenomena from properties of gases. Mathematical consequences 
 
CONTENTS. xix 
 
 of the supposition that a gas consists of constantly impinging 
 particles Gaseous Diffusion. Results of Maxwell's investigations. 
 Physical reason of Dissipation Andrews' results as to the continuity 
 of the liquid and gaseous states of matter. Conclusion, . . 317 
 
 LECTURE XIV. 
 
 FORCE. 
 
 Evening Address to the British Association, Sept. 8, 1876, . . 343 
 
LECTURE I. 
 
 INTRODUCTORY. 
 
 Classification of Recent Advances in Physical Science. General Statement of 
 the Objects of Physics. Time and Space. Matter, Position, Motion, and 
 Force. Digression upon a priori reasoning. Instances of modern or 
 revived fallacies Uniformity of Earth's Rotation, Stability of Solar 
 System, Heat developed the equivalent of work spent in compressing a 
 gas, Causa <zquat effectum. Gilbert the true originator of Experimental 
 Science. Test of the reality of Matter fails when applied to Force not 
 when applied to Energy. Conservation, Transformation, and Dissipa- 
 tion of Energy. Ignorance and Incapacity alike of .Spiritualists and 
 Materialists. 
 
 IN considering what may be designated as * Recent 
 Advances in Physical Science,' it is well to remember 
 that many things which have become almost popularly 
 known within the last twenty-five years are much 
 older in the minds and writings of the foremost scien- 
 tific men. We cannot, however, treat them intelligibly 
 without reference, sometimes pretty full, to what was 
 known even earlier still : so that you must not be sur- 
 prised if I have a good deal to say of Davy and Rum- 
 ford, and even of Newton. 
 
 I shall, for the sake of clearness, attempt roughly to 
 classify these recent advances under five well-marked 
 heads ; but I shall do so very briefly, deferring expla- 
 nation even of new scientific terms till I have to treat 
 each of these heads in detail. 
 
 First and foremost, advances connected with the 
 
 A 
 
INTRODUCTORY. 
 
 modern notion of Energy. Just as Gold, Lead, Oxygen, 
 etc., are different kinds of Matter, so Sound, Light, 
 Heat, etc., are now ranked as different forms of Energy, 
 which, as we shall presently see, has been shown to 
 have as much claim to objective reality as matter has. 
 This grand idea enables us to co-ordinate all the parts, 
 however apparently diverse, of the enormous subject 
 of Natural Philosophy. It has not only thus enabled 
 us to exhibit the science in a complete and connected 
 form, but it has also, specially by the application of the 
 laws of Thermo-dynamics (to which a large part of this 
 course will be devoted), enabled us to find those points 
 where rapid advance was most easily to be secured. 
 
 Secondly. The advances which have arisen, more or 
 less directly, from the requirements felt in practical 
 applications. To take but a single instance : think of 
 the immense improvements in instruments for the 
 measurement of electric charges and electric currents, 
 such as electrometers and galvanometers, which have 
 been effected because called for by the recent exten- 
 sions of submarine telegraphy. It is not too much to 
 say that the instruments now employed, and which 
 were primarily devised for practical telegraphic pur- 
 poses, are hundreds of times more sensitive, as well as 
 more exact, and therefore more useful for purely 
 scientific purposes, than the best of those which were 
 in use thirty years ago. Thus it is that a development 
 of science, in a practical direction, leads to the construc- 
 tion of instruments which have, as it were, a reflex 
 action on the development of the pure science itself. 
 
 Thirdly. Those which arise from the assistance ren- 
 dered to one another by pure sciences, such as astro- 
 nomy, chemistry, and physiology, where, in fact, the 
 
INTRODUCTORY. 
 
 improvement of one branch has led, almost immedi- 
 ately, to important extensions of other branches. 
 Under this head we may also include those very great 
 advances which are due to improvements in our mathe- 
 matical methods. 
 
 Fourthly. What may be called casual discoveries, 
 though they are often of very great importance ; such 
 as, for instance, the discovery of fluorescence, with its 
 manifold consequences, and the invention of the pro- 
 cesses of photography. Such discoveries, instead of 
 being, as in old days, wondered at and left isolated, are 
 now at once attacked on all sides by numberless en- 
 thusiastic experimenters. 
 
 Fifthly. There is another class, very numerous but 
 more difficult to exactly describe. As a single ex- 
 ample of this class, I may mention the modern statis- 
 tical methods of treating certain problems of physical 
 science, especially those connected with the movements 
 of particles of gases and liquids, to which I shall advert 
 at considerable length in the course of these lectures. 
 
 I have now to consider how I should best commence 
 the analysis of these various heads ; and I think the 
 proper method will be first to sketch the subject as if 
 from a distance to point out a few of the principal 
 peaks which we have to ascend, and of the more formi- 
 dable abysses which we have to avoid ; striving all the 
 while to introduce as early as possible some of those 
 new technical terms which are absolutely indispensable 
 to accuracy and definiteness, and which, therefore, can 
 not be too soon mastered. 
 
 Natural Philosophy, as now regarded, treats generally 
 of the physical universe, and deals fearlessly alike with 
 quantities too great to be distinctly conceived, and with 
 
INTRODUCTORY. 
 
 quantities almost infinitely too small to be perceived 
 even with the most powerful microscopes ; such as, for 
 instance, distances through which the light of stars or 
 nebulae, though moving at the rate of about 186,000 
 miles per second, takes many years to travel ; or the 
 size of the particles of water, whose number in a single 
 drop may, as we have reason to believe, amount to 
 somewhere about 
 
 io 26 , or 100,000,000,000,000,000,000,000,000. 
 Yet we successfully inquire not only into the composi- 
 tion of the atmospheres of these distant stars, but into 
 the number and properties of these water-particles, nay, 
 even into the laws by which they act upon one another. 
 
 The fundamental notions which occur to us when we 
 commence the study of physical science are those of 
 Time and Space. A measure of time may be obtained 
 by physical methods, as in fact is done incidentally in 
 Newton's First Law of Motion, wherein he asserts that 
 a mass left to itself moves uniformly. That is, equal 
 times are the times in which such a mass describes 
 equal spaces. Of space, we can ascertain by observa- 
 tion the properties. But we cannot inquire into the 
 actual nature of either space or time, except in the way 
 of a purely metaphysical, and therefore of necessity 
 absolutely barren, speculation. We have, however, 
 mathematical methods specially adapted to the treat- 
 ment of these two abstract ideas ; Algebra, which has 
 been called (by Sir W. R. Hamilton) the science of pure 
 time ; and Geometry, which may be designated the 
 science of pure space. 
 
 The common measurement of time primarily depends 
 upon the rotation of the earth about its axis. This, 
 however, as will be seen when we advance a little 
 
INTRODUCTORY. 
 
 further, is by no means a uniform quantity, and there- 
 fore ultimately the measurement of time must be based 
 upon some motion depending on a physical property of 
 matter which we have every experimental reason for 
 believing to be unchangeable by time, and invariable 
 throughout the universe. Probably such an ultimate 
 standard for the measurement of time will be found in 
 one of the periods of vibration of the molecules of a 
 heated gas, such as hydrogen, under given conditions. 
 
 The properties of space, involving (we know not why) 
 the essential element of three dimensions, have recently 
 been subjected to a careful scrutiny by mathematicians 
 of the highest order, such as Riemann and Helmholtz j 1 
 and the result of their inquiries leaves it as yet un- 
 decided whether space may or may not have pre- 
 cisely the same properties throughout the universe. 
 To obtain an idea of what is meant by such a state- 
 ment, consider that in crumpling a leaf of paper, which 
 may be taken as representing space of two dimensions, 
 we may have some portions of it plane, and other 
 portions more or less cylindrically or conically curved. 
 But an inhabitant of such a sheet, though living in 
 space of two dimensions only, and therefore, we might 
 say beforehand, incapable of appretiating the third 
 dimension, would certainly feel some difference of 
 sensations in passing from portions of his space which 
 were less, to other portions which were more, curved. 
 So it is possible that in the rapid march of the solar 
 system through space, we may be gradually passing to 
 regions in which space has not precisely the same pro- 
 perties as we find here where it may have something 
 in three dimensions analogous to curvature in two 
 
 1 See Helmholtz' paper in Mind, No. III. 1876. 
 
INTRODUCTORY. 
 
 dimensions something, in fact, which will necessarily 
 imply a fourth-dimension change of form in portions 
 of matter in order that they may adapt themselves to 
 their new locality. But for the full discussion of a 
 question like this it would be necessary to introduce 
 mathematical reasoning of a transcendental character. 
 
 In addition to these fundamental notions of time and 
 space, the next four which force themselves upon us in 
 the physical universe are those of Matter, Position, 
 Motion, and Force. As with these ideas commences 
 the study of physics proper, I leave them for a moment 
 to consider in what way or in what spirit we ought to 
 treat problems of physical science. Remember that 
 the subject of my lectures is the Advances of Physical 
 Science. It is well then to inquire briefly to what we 
 are indebted for such advances. And every one who 
 has with any attention studied the history of scientific 
 progress sees at once that 
 
 These advances come or not according as we remember 
 or forget that our science is to be based entirely upon ex- 
 periment or mathematical deductions from experiment. 
 
 There is nothing physical to be learned a priori. We 
 have no right whatever to ascertain a single physical 
 truth without seeking for it physically, unless it be a 
 necessary consequence of other truths already acquired 
 by experiment, in which case mathematical reasoning 
 is alone requisite. 
 
 Let us consider for a moment to what fearfully absurd 
 consequences a neglect of this self-evident principle has 
 led in former times, and too often even in modern days. 
 Men were told by the antients that the planets move in 
 circles because circular motion is perfect ! They were 
 told also in the middle ages that the sun cannot pos- 
 
INTRODUCTORY. 
 
 sibly have spots ! They were told that the earth was 
 at rest ; that Nature abhors a vacuum, etc. etc. And 
 all these dogmas were enuntiated by otherwise reason- 
 able men. Within the last fifty years we have had 
 philosophers like Hegel saying that the motion of the 
 heavenly bodies is not a being pulled this way and 
 that : that they go along, as the antients said, like 
 blessed gods. Further, that pressure, gravity, etc., are 
 true only of terrestrial, not of celestial matter. Hegel 
 winds up this truly wonderful statement by saying 
 that both are matter, just as a good thought and a bad 
 one are both thoughts, but the bad is not therefore good 
 because the good one is a thought. 1 
 
 As instances of still more recent, in fact quite modern, 
 fallacies of a somewhat similar kind, I shall take but 
 four, two of which are in their very nature excusable, 
 the other two utterly unpardonable. 
 
 First, there is the assumption that the earth's rotation 
 is absolutely uniform. Now, to say nothing of the 
 effects of cooling and consequent shrinking, the effects 
 of volcanic disturbances and upheavals, the effects of 
 degradation of mountains, and various other causes 
 
 1 Naturphilosophie, 269. [The passage is so incredibly absurd that I 
 feel bound to quote it.] Die Bewegung der Himmelskorper ist nicht 
 em solches Hin- und Hergezogenseyn, sondern die freie Bewegung ; sie 
 gehen, wie die Alien sagten, als selige Cotter einher. Die himmlische 
 Korperlichkeit ist nicht eine solche, welche das Princip der Ruhe oder 
 Bewegung ausser ihr hatte. Weil der Stein trage ist, die ganze Erde 
 aber aus Steinen besteht, und die andera himmlischen Korper eben derglei- 
 chen sind ist ein Schluss, der die Eigenschaften des Ganzen denen des 
 Theils gleichsetzt. Stoss, Druck, Widerstand, Reibung, Ziehen und der- 
 gleichen gelten nur von einer andern Existenz der Materie, als die himm- 
 lische Korperlichkeit. Das Gemeinschaftliche Beider ist freilich die Ma- 
 terie, so wie ein guter Gedanke und ein schlechter beide Gedanken sind : 
 aber der sclilechte nicht darum gut, weil der gute ein Gedanke ist. 
 
INTRODUCTORY. 
 
 which must tend more or less to affect the earth's rota- 
 tion (shrinking and degradation accelerating it, while 
 upheavals retard it, according to a mechanical principle 
 which is involved in Newton's Third Law of Motion), 
 there has been recently revived the study, first pointed 
 out by Kant, of the effect of tidal retardation upon the 
 length of the day. In fact, the earth with the tide-wave 
 upon it, pointing on the average almost axially towards 
 the moon, is virtually revolving in a friction-brake or 
 collar ; and so long as it moves with reference to this 
 tidal wave, so long must it move subject to friction, and 
 therefore of course with continually decreasing velocity. 
 Then, again, we had the confident assertion of the 
 absolute stability of the solar system ; that is to say, 
 grand arguments were founded by the Teleologists on 
 the assumption that the eccentricities and inclinations, 
 and so on, of the planetary orbits, though constantly 
 varying, fluctuated between certain definite, and in 
 general very narrow limits, and that after a by no 
 means long series of ages all bodies in the solar system 
 would return to almost precisely their former configura- 
 tion as to position and velocity. Now, in arriving at 
 this result, which of course they themselves under- 
 stood in its true sense, Laplace and Lagrange confess- 
 edly employed approximate methods of solution only. 
 They left out of account what are termed technically 
 the squares of disturbing forces ; that is to say, of two 
 planets, each of which has disturbed the other's position, 
 the effects of the first upon the second were calculated 
 by leaving out of account the disturbance of the posi- 
 tion of the first, and vice versd. In order to improve 
 upon this approximation, at least without enormous 
 labour, mathematical methods of a far more powerful 
 
INTRODUCTORY. 
 
 order than have yet been invented are requisite, and 
 therefore it is not from this point of view that the solu- 
 tion can at present be improved ; nor can we well form 
 an idea of the nature of the modification which the 
 results of the approximate method would undergo. But 
 the idea which I have just mentioned with reference to 
 tidal friction, which has not yet been taken account of in 
 the solution of these planetary problems, shows at once 
 that so long as the parts of any moving integral portion 
 of the system are capable of being displaced relatively 
 to one another, and so moving relatively with friction, 
 so long must there be a cause tending constantly to the 
 degradation of the rates of motion in the system, and 
 therefore that stability of the planetary system is im- 
 possible under present conditions. Remember that it 
 was in the imagined interests of religion that the earth's 
 motion was denied. History repeats itself here. An 
 ill-informed Teleologist, however good his intentions, is 
 far more dangerous to the cause he has at heart than 
 the bitterest of its declared enemies. 
 
 Then let us take the question of the heat developed 
 by compressing a gas. You all know that a piece of 
 tinder can be set on fire when it is enclosed in a cylin- 
 der in which the air is suddenly compressed by pushing 
 in a tight-fitting piston. Great credit has recently been 
 claimed for two speculators, Seguin and Mayer, who 
 independently propounded the hypothesis that the heat 
 developed in such a case is the equivalent of the work 
 spent in compressing the air ; or its converse, that the 
 heat lost in expansion is the equivalent of the work done 
 by the expanding material. To make such hypotheses 
 without preliminary experimental measurements, is 
 simply to fall into the fatal error to which I have already 
 
io INTRODUCTORY. 
 
 adverted, the a priori assertion of physical principles. 
 To see that it is so, we have only to consider that a 
 gas might (for all we can tell without experiment) have 
 the properties of a spiral spring. Suppose, in fact, in- 
 stead of air, the cylinder above spoken of to be filled 
 with a number of spiral springs so adjusted as not to 
 interfere with each other's motions. In compressing 
 such a set of springs, exactly the same amount of work 
 may be spent as in compressing air, and yet we may 
 find no trace whatever of heat generated. It therefore 
 appears obvious that until we know for certain the ulti- 
 mate nature of a gas, the only way (independent of mere 
 guessing) to discover the relation between the heat 
 developed by compression and the work spent in pro- 
 ducing it, is to experiment ; and that without experi- 
 ment it is impossible to lay down any general relation 
 between them. The modern view of the constitution of 
 a gas, in which its particles are supposed to be flying 
 about with great velocity in all directions, and constantly 
 impinging upon one another and upon the sides of the 
 vessel, leads us almost directly to many valuable conclu- 
 sions, among which I will refer for the moment only to 
 the result known as Boyle's law, where we contemplate 
 the compression of a gas whose temperature is kept con- 
 stant. Suppose, for instance, the particles to be moving 
 with a certain velocity in every direction, we find that if 
 the piston could be moved half way down the cylinder, 
 and the velocity of the particles not thereby increased, 1 
 the number of impacts per second upon the ends of the 
 cylinder must become twice as great as it was before, 
 
 1 This would be a violation of the principle of Dissipation of Energy, as 
 will be seen by the reader of Lecture VI. But that does not invalidate its 
 usefulness as an illustration of the present argument. 
 
INTRODUCTORY. n 
 
 because the length of the cylinder is only half as great. 
 Also, the number of impacts per second per square inch 
 upon the curved sides of the cylinder must likewise 
 be doubled, simply because there is the same number 
 of particles as before, impinging with the same velo- 
 cities, but upon only one half of the surface. If we 
 could manage to advance the whole piston by infini- 
 tesimally small stages, so as at each such advance to 
 take advantage of the absence of all molecular pres- 
 sure upon the piston, or to advance at every instant 
 those parts of the piston upon which for the moment 
 no impact was impending, we should produce this dimi- 
 nution of bulk without altering in any respect the velo- 
 cities of the particles of gas ; and therefore, according 
 to Boyle's law, and according to the analysis just given, 
 we should have the case of a gas doubled in pressure, 
 and occupying exactly one half the bulk which it occu- 
 pied at first, but without increase of temperature. Here 
 then is another mode of contemplating the compression 
 of a gas without any production of heat. This question 
 is one of great importance, and I intend to treat it 
 pretty fully in the course of these lectures. 
 
 The only other fallacy which I shall mention for the 
 present, is that of basing physical results upon the old 
 dog-Latin dogma, causa <quai effectum. It is difficult to 
 decide whether the Latinity or the (semi-obscure) sense 
 is in this dogma the more incorrect. The fact is, that 
 we have not yet quite cast off that tendency to so-called 
 metaphysics which has often completely blasted the 
 already promising career of a physical inquirer. I say 
 'so-called' metaphysics, because there is a science of 
 metaphysics ; but from the very nature of the case, the 
 professed metaphysicians will never attain to it. In fact 
 
1 2 IN TROD UCTOR Y. 
 
 if we once begin to argue upon such a dogma as the 
 above, the next step may very naturally be to inquire 
 whether cause and effect are simultaneous or succes- 
 sive : and then we shall have become so mystified 
 about the meaning of the word Cause that we may well 
 be ready to inquire (as many have already done) what 
 is the necessarily ever acting cause of the uniform 
 motion of a body upon which no forces act ! 
 
 The originator of true experimental science seems 
 to have been Gilbert of Colchester, whose deservedly 
 celebrated treatise De Magnete was published 300 years 
 ago. After him came Galileo and Newton, each making 
 gigantic strides in the true direction, and by them this, 
 the ONLY way of attaining to a discovery of physical 
 laws, was permanently established. The proof of this 
 is, that the last two centuries and a half have achieved, 
 in purely physical science, million-fold what had been 
 accomplished before them. And it is not that we are 
 now more able, nor that we have more leisure cer- 
 tainly not : 
 
 ' . . . for Romans now 
 Have thewes and limbs like to their ancestors'.' 
 
 It is rather that whenever the direction given to inquiry 
 is a proper one, the men come forward. This direction 
 was good in Britain at certain memorable times, as when 
 Newton and Hooke were contemporaries ; in the days 
 of Maclaurin and Cotes, and in those of Cavendish and 
 Watt. At intervals it broke down entirely as regards 
 mathematical physics, partly as regards experimental 
 physics, and once again it has become good ; and conse- 
 quently, since the ever-memorable days of Young and 
 Davy, we have had Green and Hamilton, Faraday and 
 Graham, and we can still rejoice in the possession of 
 
INTRODUCTORY. 
 
 Stokes and Thomson, Adams and Clerk-Maxwell, Joule 
 and Andrews. This list is as good as either of the 
 others, and might be considerably increased. Other 
 countries have had their similar fluctuations, all I be- 
 lieve traceable to similar causes. Little more than 
 half a century ago, France had such mighty names as 
 Ampere, Laplace, Lagrange, Poisson, Fresnel, Fourier, 
 Carnot, Cauchy, etc. I name them just as they occur 
 to me. We cannot do much in the way of classifying 
 men like these. Germany now has Helmholtz, Weber, 
 Kirchhoff, and has but recently lost Gauss, Jacobi, Dir- 
 ichlet, Plucker, Riemann, and Magnus. 
 
 The sad fate of Newton's successors ought ever to 
 be a warning to us. Trusting to what he had done, 
 they allowed mathematical science almost to die out 
 in this country, at least as compared with its immense 
 progress in Germany and France. It required the 
 united exertions of the late Sir J. Herschel and many 
 others to render possible in these islands a Boole and 
 a Hamilton. If the successors of Davy and Faraday 
 pause to ponder even on their achievements, we shall 
 soon be again in the same state of ignominious in- 
 feriority. Who will then step in to save us ? 
 
 Even as it is, though we have among us many names 
 quite as justly great as any that our rivals can pro- 
 duce, we have also (even in our educated classes) such 
 an immense amount of ignorance and consequent cre- 
 dulity, that it seems matter for surprise that true sci- 
 ence is able to exist. Spiritualists, Circle-squarers, 
 Perpetual-motionists, Believers that the earth is flat 
 and that the moon has no rotation, swarm about us. 
 They certainly multiply much faster than do genuine 
 men of science. This is characteristic of all inferior 
 
14 INTRODUCTORY. 
 
 races, but it is consolatory to remember that in spite of 
 it these soon become extinct. Your quack has his little 
 day, and disappears except to the antiquary. But in 
 science nothing of value can ever be lost ; it is certain 
 to become a stepping-stone on the way to further truth. 
 Still, when our stepping-stones are laid, we should not 
 wait till others employ them. ' Gentlemen of the Guard, 
 be kind enough to fire first/ is a courtesy entirely out 
 of date ; with the weapons of the present day it would 
 be simply suicide. 
 
 To come back to our second set of elementary ideas, 
 Matter, Position, Motion and Force. Of these, the 
 second (Position) is a purely space relation, or geo- 
 metrical conception, and must necessarily be relative, 
 unless something like the idea of Riemann already 
 referred to have an actual existence in the universe. 
 The third (Motion) is mere change of position, but as 
 that change may take place more or less rapidly, it 
 involves the idea of time as well as of space. But both 
 of these ideas are quite independent of the remaining 
 two (Matter and Force) ; and in fact their study forms 
 the subject of a special mixed science of Time and 
 Space, called Kinematics, which takes its place beside 
 the older sciences, Geometry and Algebra, which I have 
 already adverted to as the sciences of pure Space and 
 pure Time. 
 
 The grand test of the reality of what we call Matter, 
 the proof that it has an objective existence, is its in- 
 destructibility and uncreateability if the term may be 
 used by any process at the command of man. The 
 value of this test to modern chemistry can scarcely be 
 estimated. In fact we can barely believe that there 
 could have existed an exact science of chemistry had it 
 
INTRODUCTORY. 
 
 not been for the early recognition of this property of 
 matter ; nor in fact would there be the possibility of 
 a chemical analysis, supposing that we had not the 
 assurance by enormously extended series of previous 
 experiments, that no portion of matter, however small, 
 goes out of existence or comes into existence in any 
 operation whatever. If the chemist were not certain 
 that at the end of his operations, provided he has taken 
 care to admit nothing and to let nothing escape, the 
 contents of his vessels must be precisely the same in 
 quantity as at the beginning of the experiment, there 
 could be no such thing as chemical analysis. Some 
 substance might suddenly appear, 1 or some substance 
 might suddenly vanish, and no reasoning whatever could 
 lead to a deduction from the results of experiments 
 under such conditions. This, then, is to be looked 
 upon as the great test of the objective reality of matter. 
 There remains to be treated Force, the last of the 
 fundamental four. The notion is suggested to us di- 
 rectly, by the so-called ' muscular sense,' which gives us 
 the feeling of pressure, as when we move a body with our 
 hand or foot. But we must be particularly cautious as 
 to the way in which we treat the evidence of our senses 
 in such matters. Think of Sound and Light, for in- 
 stance which, till they affect a special organ of sense, 
 are mere wave-motions. The sensation is as different 
 from the cause in such cases as are the bruise and the 
 
 1 Hegel believed in such possibilities. Witness, among others, the 
 following almost the raciest of the manifold absurdities of the Naturphilo- 
 sophu. It occurs in 332. Ebenso werden die kaustischen Kali wieder 
 milde ; man sagt dann, sie ziehen Kohlensaure aus der Luft ein. Das ist 
 aber eine Hypothese ; sie machen vielmehr aus der Luft erst Kohlensaure, 
 um sich abzustumpfen. 
 
1 6 INTROD UCTOR Y. 
 
 pain produced by a cudgel or a cricket ball from the 
 mere motion of those portions of matter before impact 
 on a part of the human body. In all likelihood a 
 similar (probably a more sweeping) statement is true 
 of force. [This subject is treated in a special Lecture, 
 appended to the present work.] 
 
 The definition of force in physical science is implicitly 
 contained in Newton's First Law of Motion, and may 
 thus be given : 
 
 Force is any cause which alters a bodys natural state 
 of rest or of uniform motion in a straight line. 
 
 The only difficulty, and it is a serious one, which we 
 feel here, is as to the word 'cause ;' for this, amongst 
 material things, usually implies objective existence. 
 Now we have absolutely no proof of the objective ex- 
 istence of force in the sense just explained. In every 
 case in which force is said to act, what is really observed, 
 independent of the muscular sense (whose indications, 
 like those of the sense of touch in matters concerning 
 the temperatures of bodies, are apt to be excessively 
 misleading), is either a transference, or a tendency to 
 transference, of what is called energy from one portion 
 of matter to another. Whenever such a transference 
 takes place, there is relative motion of the portions of 
 matter concerned, and the so-called force in any direc- 
 tion is merely the rate of transference, or of trans- 
 formation, of energy per unit of length for displacement 
 in that direction. Force then has not necessarily 
 objective reality any more than has Velocity or Posi- 
 tion. The idea, however, is still a very useful one, as 
 it introduces a term which enables us to abbreviate 
 statements which would otherwise be long and tedious ; 
 but, as Science advances, it is in all probability destined 
 
. 
 
 UK! VF.IU -:T 
 
 INTRODUCTORY. 17 
 
 to be relegated to that Limbo which has already 
 received the Crystal Spheres of the Planets, and the 
 Four Elements, along with Caloric and Phlogiston, the 
 Electric Fluid and the Odic or Psychic Force. 
 
 It is only, however, within comparatively recent years 
 that it has been generally recognised that there is some- 
 thing else in the physical universe which possesses to 
 the full as high a claim to objective reality as matter 
 possesses, though it is by no means so tangible, and 
 therefore the conception of it was much longer in forcing 
 itself upon the human mind. The so-called ' imponde- 
 rables,' things of old supposed to be matter such as 
 heat and light, et cetera^ are now known by the purely 
 experimental, and therefore the only safe, method to be 
 but varieties of what we call Energy, something which, 
 though not matter, has as much claim to recognition 
 on account of its objective existence as any portion of 
 matter. The grand principle of Conservation of Energy, 1 
 which asserts that no portion of energy can be put out 
 of existence, and no amount of energy can be brought 
 into existence by any process at our command, is sim- 
 ply a statement of the invariability of the quantity of 
 
 1 Great confusion has been introduced into many modern British works 
 by a double use of the word Force. It is employed, without qualification, 
 sometimes in the sense of force proper (as above defined), sometimes in the 
 sense of energy ! The two things (if force proper can be called a * thing, ' 
 having probably no objective existence, and certainly no conservation, 
 except possibly in a highly refined sense, which Faraday in vain attempted 
 to realise experimentally, but which, even if it were proved, would have 
 no connection with conservation of energy) are of as different orders as 
 miles and square miles, though perhaps they are not quite so incomparable 
 as minutes and yards or pence. Even a mere want of precision in the 
 use of terms of such fundamental importance is altogether incompatible 
 with the existence of true scientific method. [See Lecture xiv. (on Force) 
 at the end of this volume.] 
 
 B 
 
1 8 INTRODUCTORY, 
 
 energy in the universe, a companion statement to that 
 of the invariability of the quantity of matter. 
 
 The laws of energy differ from those of matter in one 
 most important respect, so far at least as we yet know 
 by experiment. Matter cannot, so far as we yet know, 
 be transmuted from one kind to another, though in 
 some cases it assumes what is called an allotropic form. 
 The great characteristic of energy, on the other hand, 
 is that in general we can readily transform it (in fact it 
 is of use to us solely because it can be transformed), but 
 in all its transformations the quantity present remains 
 precisely the same. 
 
 Energy may be defined as the power of doing work, 
 or, if we like to put it so, of doing mischief. I have 
 already pointed out to you that the notion of energy is 
 harder to seize than that of matter. Wherein, for in- 
 stance, consists the difference between a mass of snow 
 lying on the mountain side and the same mass when it 
 has fallen and rests in the valley below ? Obviously, 
 so far as the matter present is concerned, the two sub- 
 tances are identical, except in so far as molecular 
 changes, such as melting, may have altered the state 
 of some portions of the mass during or after its descent. 
 Yet the elevated mass possesses, in virtue of its eleva- 
 tion alone, a power of doing work or mischief, which it 
 has lost entirely when it has descended as far as it can. 
 By the mere fact, then, of its elevation, it possesses a 
 power which it does not possess when it has descended. 
 This is called energy of position, or Potential Energy. 
 Other examples of it are to be found in a wound-up 
 spring or weight, as in a clock, a bent bow ; or in gun- 
 powder ; and various others might easily be mentioned, 
 ferhaps the most striking of all instances that we can 
 
INTRODUCTORY. 19 
 
 give is that of the food of animals, including as one of 
 the principal constituents the oxygen of the atmosphere. 
 But when the snow is detached from the mountain 
 side, in descending it acquires another form of energy, 
 depending entirely on its motion ; and thus we distin- 
 guish between energy of position and energy of motion 
 or Kinetic Energy. To those who have acquired the 
 intelligent use of the terms it is matter of common 
 observation that as the one of these quantities becomes 
 less, the other becomes greater. The velocity of the 
 falling snow increases constantly as it gradually de- 
 scends ; and exact calculation, according to physical 
 experiment, shows us that the amount of potential 
 energy lost in every stage of the operation is precisely 
 equal to the amount of Kinetic energy gained. The 
 process may be inverted if we consider Kinetic energy 
 to be originally communicated to a body, suppose, for 
 simplicity, in a vertically upward direction. We know 
 that a stone thrown into the air gradually loses velocity 
 as it ascends higher and higher ; for an instant, when it 
 has lost all velocity, it pauses, and then returns, gradually 
 regaining velocity, as it in turn loses its advantage of 
 position ; and calculation, applied to this case, shows 
 that at every stage, whether of the ascent or of the 
 descent, the sum of the Potential and the Kinetic 
 energies remains precisely the same, except in so far 
 as it is modified by the resistance of the air. This, 
 however, gives us no exception to the general truth of 
 the principle of conservation of energy, because any 
 energy lost by the stone is communicated without loss 
 of quantity to the surrounding air. 
 
 We contemplate, therefore, with reference to energy, 
 its conservation, which merely asserts its objective 
 
20 IN TROD UCTOR Y. 
 
 reality ; its transformations, which render it indispens- 
 able to the existence of life and the physical changes in 
 the universe ; but it has in addition another and even 
 more curious property. We have seen that change is 
 essential to the existence of phenomena such as we 
 observe : and, that this change may take place, it is 
 necessary that there should be constant transformations 
 of energy. But some forms of energy are more capable 
 of being transformed than others ; and every time that 
 a transformation takes place, there is always a tendency 
 to pass, at least in part, from a higher or more easily trans- 
 formable to a lower or less easily transformable form. 
 
 Thus the energy of the universe is, on the whole, 
 
 constantly passing from higher to lower forms, and 
 
 therefore the possibility of transformation is becoming 
 
 smaller and smaller, so that after the lapse of sufficient 
 
 time all higher forms of energy must have passed from 
 
 the physical universe, and we can imagine nothing as 
 
 remaining, except those lower forms which are incapable, 
 
 so far as we yet know, of any further transformation. 
 
 The low form to which all transformations with which 
 
 we are at present acquainted seem inevitably to tend, 
 
 is that of uniformly diffused heat : or, more precisely, 
 
 heat so diffused as to produce uniform temperature. 
 
 We know, in fact, that in order to make any use of heat 
 
 to transform.it into mechanical power or into any 
 
 other form of energy it is absolutely necessary that we 
 
 should have bodies of different temperatures. We must, 
 
 as it were, have a source and a condenser. Now, when 
 
 all the energy of the universe has taken the final form 
 
 of heat so diffused as to produce uniform temperature, 
 
 it will obviously be impossible to make any use of this 
 
 heat for further transformation. Thus, so far as we can 
 
INTRODUCTORY. 21 
 
 as yet determine, in the far distant future of the universe 
 the quantities of matter and energy will remain ab- 
 solutely as they now are the matter unchanged alike 
 in quantity and quality, but collected together under 
 the influence of its mutual gravitation, so that there 
 remains no potential energy of detached portions of 
 matter ; the energy also unchanged in quantity, but 
 entirely transformed in quality to the low form of heat 
 so diffused as to produce uniformity of temperature. 1 
 
 This, the Dissipation of Energy, 2 is by no means well 
 understood, and many of the results of its legitimate 
 application have been received with doubt, sometimes 
 even with attempted ridicule. Yet it appears to be at the 
 present moment by far the most promising and fertile 
 portion of Natural Philosophy, having obvious applica- 
 tions of which as yet only a small percentage appear to 
 have been made. Some, indeed, were made before the 
 enuntiation of the Principle, and have since been recog- 
 nised as instances of it. Of such we have good ex- 
 amples in Fourier's great work on Heat-conduction, in 
 .the optical theorem that an image can never be brighter 
 than the object, in Gauss's mode of investigating elec- 
 trical distribution, and in some of Thomson's theorems 
 as to the energy of an electromagnetic field. But its 
 discoverer has, so far as I know, as yet confined himself 
 in its explicit application to questions of Heat-conduc- 
 tion and Restoration of Energy, Geological Time, the 
 Earth's Rotation, and such like. Unfortunately his long- 
 expected Rede Lecture* has not yet been published, and 
 
 1 Thomson On a Universal Tendency in Nature to Dissipation ofEnei-gy. 
 Proc. R.S.E. 1852. 
 
 2 What follows is extracted from my address as President of Section A 
 at the British Association Meeting of 1871. 
 
 3 Delivered in the Senate House, Cambridge, in 1866. 
 
22 INTRODUCTORY. 
 
 its contents (save to those who were fortunate enough 
 to hear it) are still almost entirely unknown. 
 
 But there can be little question that the Principle 
 contains implicitly the whole theory of Thermo-electri- 
 city, of Chemical Combination, of Allotropy, of Fluor- 
 escence, etc., and perhaps even of matters of a higher 
 order than common physics and chemistry. In Astro- 
 nomy it leads us to the grand question of the age, or 
 perhaps more correctly the phase of life, of a star or 
 nebula, shows us the material of potential suns, other 
 suns in the process of formation, in vigorous youth, and 
 in every stage of slowly protracted decay. It leads us to 
 look on each planet and satellite as having been at one 
 time a tiny sun, a member of some binary or multiple 
 group, and even now (when almost deprived, at least at 
 its surface, of its original energy) presenting an endless 
 variety of subjects for the application of its methods. 
 It leads us forward in thought to the far-distant time 
 when the materials of the present stellar systems shall 
 Jiave lost all but their mutual potential energy, but 
 shall in virtue of it form the materials of future larjger 
 suns with their attendant planets. Finally, as it alone 
 is able to lead us, by sure steps of deductive reasoning, to 
 the necessary future of the universe necessary, that is, 
 if physical laws for ever remain unchanged so it enables 
 us distinctly to say that the present order of things has 
 not been evolved through infinite past time by the 
 agency of laws now at work, but must have had a 
 distinctive beginning, a state beyond which we are 
 totally unable to penetrate ; a state, in fact, which 
 must have been produced by other than the now 
 [visibly] acting causes. 
 
 Thus also it is possible that in Physiology it may, ere 
 
INTRODUCTORY. 23 
 
 long, lead to results of a different and much higher 
 order of novelty and interest than those yet obtained, 
 immensely valuable though these certainly are. 
 
 It was a grand step in science which showed that just 
 as the consumption of fuel is necessary to the working 
 of a steam-engine, or to the steady light of a candle, 
 so the living engine requires food to supply its expen- 
 diture in the forms of muscular work and animal heat. 
 Still grander was Rumford's early anticipation that the 
 animal is a more economic engine than any lifeless one 
 we can construct. Even in the explanation of this 
 there is involved a question of very great interest, still 
 unsolved, though Joule and many other philosophers of 
 the highest order have worked at it. Joule has given a 
 suggestion of great value, viz., that the animal resembles 
 an electromagnetic- rather than a heat-engine ; but this 
 throws us back again upon our difficulties as to the 
 nature of electricity. Still, even supposing this ques- 
 tion fully answered, there remains another perhaps 
 the highest which the human intellect is capable of 
 directly attacking, for it is simply preposterous to sup- 
 pose that we shall ever be able to understand scientifi- 
 cally the source of Consciousness and Volition, not to 
 speak of loftier things there remains the question of 
 Life. Now it may be startling to some of you, especi- 
 ally if you have not particularly considered the matter, 
 to hear it surmised that possibly we may, by the help 
 of physical principles, especially that of the Dissipation 
 of Energy, some time attain to a notion of what con- 
 stitutes Life mere Vitality, I repeat, nothing higher. 
 If you think for a moment of the vitality of a plant 
 or a zoophyte, the remark perhaps will not appear so 
 strange after all. But do not fancy that the Dissipation 
 
24 INTRODUCTORY. 
 
 of Energy to which I refer is at all that of a watch or 
 suchlike piece of mere human mechanism, dissipating 
 the low and common form of energy of a single coiled 
 spring. It must be such that every little part of the 
 living organism has its own store of energy constantly 
 being dissipated, and as constantly replenished from 
 external sources drawn upon by the whole arrangement 
 in their harmonious working together. As an illustra- 
 tion of my meaning, though an extremely inadequate 
 one, suppose Vaucanson's Duck to have been made up 
 of excessively small parts, each microscopically con- 
 structed, as perfectly as was the comparatively coarse 
 whole, we should have had something barely distin- 
 guishable, save by want of instincts, from the living 
 model. But let no one imagine that, should we ever 
 penetrate this mystery, we shall thereby be enabled to 
 produce, except from life, even the lowest form of life. 
 Sir W. Thomson's splendid suggestion of Vortex-atoms, 
 if it be correct, will enable us thoroughly to understand 
 matter, and mathematically to investigate all its pro- 
 perties. Yet its very basis implies the absolute necessity 
 of an intervention of Creative Power to form or to de- 
 stroy one atom even of dead matter. The question 
 really stands thus : Is Life physical or no ? For if it 
 be in any sense, however slight or restricted, physical, it 
 is to that extent a subject for the Natural Philosopher, 
 and for him alone. 
 
 There must always be wide limits of uncertainty 
 (unless we choose to look upon Physics as a necessarily 
 finite Science) concerning the exact boundary between 
 the Attainable and the Unattainable. One herd of 
 ignorant people, with the sole prestige of rapidly in- 
 creasing numbers, and with the adhesion of a few fana- 
 
INTRODUCTORY. 25 
 
 tical deserters from the ranks of Science, refuse to admit 
 that all the phenomena even of ordinary dead matter 
 are strictly and exclusively in the domain of physical 
 science. On the other hand, there is a numerous group, 
 not in the slightest degree entitled to rank as Physicists 
 (though in general they assume the proud title of Philo- 
 sophers), who assert that not merely Life, but even 
 Volition and Consciousness are merely physical mani- 
 festations. These opposite errors, into neither of which 
 it is possible for a genuine scientific man to fall, so long 
 at least as he retains his reason, are easily seen to be 
 very closely allied. They are both to be attributed to 
 that Credulity which is characteristic alike of Ignorance 
 and of Incapacity. Unfortunately there is no cure; 
 the case is hopeless, for great ignorance almost neces- 
 sarily presumes incapacity, whether it show itself in the 
 comparatively harmless folly of the Spiritualist or in 
 the pernicious nonsense of the Materialist. 
 
 Alike condemned and contemned, we leave them to 
 their proper fate oblivion ; but still we have to face 
 the question, where to draw the line between that which 
 is physical and that which is utterly beyond physics. 
 And, again, our answer is Experience alone can tell 
 us ; for experience is our only possible guide. If we 
 attend earnestly and honestly to its teachings, we shall 
 never go far astray. Man has been left to the resources 
 of his intellect for the discovery not merely of physical 
 laws, but of how far he is capable of comprehending 
 them. And our answer to those who denounce our 
 legitimate studies as heretical is simply this, A reve- 
 lation of anything which we can discover for ourselves, 
 by studying the ordinary course of nature, would be an 
 absurdity. 
 
26 INTRODUCTORY. 
 
 A profound lesson may be learned from one of the 
 earliest little papers of Sir W. Thomson, published while 
 he was an undergraduate at Cambridge, where he shows 
 that Fourier's magnificent treatment of the Conduction 
 of Heat [in a solid body] leads to formula: for its distri- 
 bution which are intelligible (and of course capable of 
 being fully verified by experiment) for all time future, 
 but which, except in particular cases, when extended 
 to time past, remain intelligible for a finite period only, 
 and then indicate a state of things which could not 
 have resulted under known laws from any conceivable 
 previous distribution [of heat in the body]. So far as 
 heat is concerned, modern investigations have shown 
 that a previous distribution of the waiter involved may, 
 by its potential energy, be capable of producing such 
 a state of things at the moment of its aggregation ; 
 but the example is now adduced not for its bearing on 
 heat alone, but as a simple illustration of the fact that 
 all portions of our Science, and especially that beautiful 
 one, the Dissipation of Energy, point unanimously to a 
 beginning, to a state of things incapable of being 
 derived by present laws [of tangible matter and its 
 energy] from any conceivable previous arrangement. 
 
 I conclude by quoting some noble words used by 
 Stokes in his Address to the British Association at 
 Exeter: 'When from the phenomena of life we pass 
 on to those of mind, we enter a region still more pro- 
 foundly mysterious. . . . Science can be expected to 
 do but little to aid us here, since the instrument of re- 
 search is itself the object of investigation. It can but 
 enlighten us as to the depth of our ignorance, and lead 
 us to look to a higher aid for that which most nearly 
 concerns our wcllbcing.' 
 

 LECTURE II. 
 
 THE EARLY HISTORY ,OF ENERGY. 
 
 Newton's services to the subject only of late recognised. Second Law 
 There is no balancing of forces ; but only of the effects of forces Geome- 
 trical composition of velocities. Third Law Its second interpretation 
 an all but complete statement of the Conservation of Energy Arithme- 
 tical composition of the squares of velocities. Experimental results of 
 Rumford and Davy, filling up the lacuna in Newton's statement. Their 
 proofs that Heat is not matter. Davy's statement of the true theory of 
 Heat. Speculations of Se"guin and Mayer. 
 
 THOUGH the subject which has been proposed to 
 me is, ' The Advances of Physical Science within the 
 last thirty years/ we must look upon the calling atten- 
 tion to valuable though neglected or misunderstood 
 discoveries of old time, as being quite as much an 
 advance in the present age as anything that has been 
 done for the first time within the last few years. I 
 cannot commence better than with those two of the 
 great advances made by Newton, which were unfor- 
 tunately very little recognised during his life, but which 
 within the last ten or twelve years have been brought 
 prominently before the world, and have shown us how 
 enormously in advance of his time and perhaps in some 
 respects even of our time Newton was. 
 
 The first of these is contained in his simple state- 
 ment of the Second Law of Motion. I shall read it, 
 not in his own words, but in a translation. He says : 
 
28 THE EARL Y HISTOR Y OF ENERG Y. 
 
 ' CJtange of motion is proportional to force, and takes 
 place in the direction of the straight line in which the 
 force acts' Now, for the century and a half since 
 Newton's time, mathematicians and natural philo- 
 sophers have been puzzling themselves to invent 
 various proofs so-called statical proofs of the law 
 of composition of forces ; the law which informs us 
 how we are to find a single force which will produce 
 precisely the same effect upon a body as two simul- 
 taneously acting forces applied at one point. All these 
 different schemes have been, I may say, one more 
 complex than another ; and they have finally landed 
 the student in utter confusion. Out of that confusion 
 we have only recently escaped by coming back to the 
 simple, but extraordinarily complete, statement of 
 Newton's which I have just read. 
 
 Newton tells you, * Change of motion is proportional 
 to force.' He says nothing whatever as to what the 
 motion was to begin with. He says nothing whatever 
 as to the force being alone. There may be as many 
 forces acting as we please ; and of every one of them 
 he says the change of motion which it produces is pro- 
 portional to it, and takes place in its direction. 
 
 Moreover, in that statement Newton tells us that a 
 force, according to him, always produces an effect 
 There is no such thing as two or more forces balancing 
 one another preventing one another from acting, as 
 it were. Newton's notion is, if there is a force at all, it 
 is doing something ; and what it does is, it produces a 
 change of motion, or, in modern language, a change of 
 momentum, proportional to itself and in its own direc- 
 tion. So that, according to Newton, there is practi- 
 cally no such thing as Statics. There is no balancing 
 
THE EARLY HISTORY OF ENERGY. 29 
 
 of forces. There is balancing of the effects of forces, 
 which is quite another thing. A force always produces 
 its effect, and if two forces or more produce effects 
 which balance one another, then we shall have perpetual 
 balancing ; but we have no balancing forces, merely 
 a balancing of the effects they produce. We have the 
 very simplest case of this where a weight is lying on a 
 table. Gravity is constantly acting : the weight is con- 
 stantly being pulled down by the attraction of the 
 earth, but it is as constantly being pressed upwards by 
 the resistance of the table ; and each of these is pro- 
 ducing in each second a certain quantity of momentum. 
 The one is producing momentum in a vertically down- 
 ward direction ; the other is producing momentum in 
 a vertically upward direction. These correspond to 
 equal velocities in an upward and a downward direc- 
 tion ; but it is the velocities, not the forces, which 
 balance or neutralise one another. 
 
 To extend this statement to the case of the funda- 
 mental proposition in statics, which tells us how to 
 compound two forces, and to find their resultant, all we 
 have to do is to consider the two forces as acting upon 
 a single particle of matter. If one of them acted alone, 
 for a certain time, it would give it a velocity of a certain 
 amount, and in a certain direction. If the other acted 
 alone, for the same period of time, it would equally 
 give a velocity definite in amount, and definite in direc- 
 tion ; but a particle cannot be moving in more than one 
 direction at a time, so that what we have to consider is 
 this : as Newton virtually tells us that the presence of 
 a second force in no way interferes with the action of 
 the first, we have to seek first what are the effects of the 
 two separately, and then what, in consequence of these 
 
30 THE EARLY HISTORY OF ENERGY. 
 
 effects supposed simultaneous, will be the actual motion 
 of the particle. It comes then to be a question merely 
 of compounding velocities a purely geometrical (or, 
 more strictly, kinematical) question instead of a physical 
 one. The Second Law of Motion, therefore, enables us 
 to commence with the purely kinematical notion of 
 compounding two velocities, and thereafter to translate 
 that into the compounding of two forces. 
 
 But the law of composition deserves a word or two. 
 The compounding of two velocities is of course seen at 
 once to be equivalent to this : If one body, such as a 
 carriage, for instance, be moving in a certain direction 
 with a certain velocity, and if some object in the carriage 
 be simultaneously moving with reference to the carriage 
 in a certain other direction, and with a certain other 
 velocity, you can consider each of these separately 
 the motion of the carriage, or the motion of this body 
 relatively to the carriage ; but when you take the two 
 simultaneously, the result is that, with reference to the 
 ground supposed fixed, there is a perfectly definite 
 direction and velocity with which the body is moving. 
 This is an obvious truth ; and the geometrical result is 
 that, If we represent in magnitude and direction one 
 of the two velocities by a line AB, and the second 
 velocity by another line BC, drawn from the extremity 
 of the first, then the single velocity, which is equivalent 
 to the simultaneous existence of these two velocities, is 
 found by drawing the third side AC of the hitherto 
 uncompleted triangle. It follows then that (turning 
 to the forces which produce these motions) as AB 
 multiplied by the mass of the body is the change 
 of motion produced by one of the forces, and BC 
 multiplied by the same mass represents the change of 
 
THE EARLY HISTORY OF ENERGY. 31 
 
 motion produced by the second force, the change of 
 motion produced by the two forces acting simultane- 
 ously is the product of the mass moved into the third 
 side A C of the triangle. But Newton's Law tells us 
 that changes of motion are proportional to the forces 
 which produce them. Therefore if AB be now taken 
 to represent on a certain scale one of the forces, and 
 BC the other, the single force which is represented on 
 the same scale by the third side of the triangle will 
 produce precisely the same effect upon the body as 
 would be produced by the simultaneous action of the 
 two separate forces. And you will see at once how it 
 is that this law of geometrical composition of forces 
 
 (what is called the triangle of forces), is merely a slightly 
 different mode of expressing what you may be more 
 familiar with under the designation of the parallelogram 
 of forces, the so-called fundamental principle of statics. 
 There, then, is the law of the geometrical composition 
 of forces, and also of velocities. We have in this case 
 two sides of a triangle (taken consecutively and in the 
 same way round), which may be said in a sense to be 
 geometrically equivalent to the third side (taken the op- 
 posite way round), but the sum of their lengths is not 
 equal to the length of the third side. This is the law of 
 composition of what Sir W. R. Hamilton called vectors, 
 and it is obviously generalisable into a similar construe- 
 
32 THE EARL Y HIS TOR Y OF ENERG Y. 
 
 tion for the composition of any number of velocities or 
 forces in any directions in space. I leave it, without 
 further comment for the moment, until I have made 
 some remarks on Newton's Third Law, and then you 
 will see how there is a physical sense in which we must 
 take the sum, not of two sides themselves, but of the 
 squares of two sides ; how, in fact, the 47th proposition 
 of the first book of Euclid comes in as part of the inter- 
 pretation of Newton's Third Law of Motion. 
 
 Newton's Third Law of Motion, to which I have just 
 referred, is expressed in very simple words : ' To every 
 action there is always an equal and contrary reaction? 
 These terms, ' action ' and * reaction,' Newton proceeds 
 to explain. He tells us that there are two senses, quite 
 different from one another, in which you may interpret 
 each of these words ; and yet that this same simple 
 statement of the equality of action and reaction holds 
 for each of these two perfectly distinct meanings. 
 
 The first form of action is that of an ordinary force 
 or pressure ; and Newton's statement then is equivalent 
 simply to this : that if a weight presses upon a table, 
 the table must react upon the weight with an equal and 
 opposite pressure, and this whether the table is moving 
 or not. Even supposing I were to lay so large a mass 
 upon a table that the table were to give way, still while 
 it was giving way, in the act of moving, if there were 
 pressure at all between them, the load would press 
 at every instant upon the table with an exactly equal 
 and opposite force to that with which the table presses 
 upon the load, and the same will hold however you 
 may connect two bodies together. If you connect 
 them either by mere contact, or by strings, or chains, 
 or rods, or girders, anything wherever there is a con- 
 
THE EARL Y HISTOR Y OF ENERG Y. 33 
 
 nection between two bodies if there be any action 
 whatever along that connecting link, there always is an 
 equal and opposite reaction. And a visible or tangible 
 link is not necessary. The same law is true of gravita- 
 tion-attraction, and of electric and magnetic attractions. 
 So far, then, this is merely a question of forces ; but 
 it seems to have entirely escaped the notice, not only 
 of Newton's contemporaries, but of those who have 
 succeeded him during the last 150 or 200 years, until 
 quite lately, that Newton's second explanation, his second 
 mode of interpreting his Third Law, is something per- 
 fectly different from this, and leads us into a new order 
 or range of phenomena. This second interpretation is"" 1 
 so important that I must bestow considerable time upon 
 it, because in reality it shows Newton to have been in 
 possession of many of the principal facts of the conser- 
 vation and transformation of energy. One or two of 
 these facts escaped him, simply because he did not 
 know what heat is, but he was very, very near attaining 
 even that. He has given us all the mathematical mate- 
 rials that are required for the treatment of it ; but he 
 missed one great point, simply because experiment had 
 not gone far enough in his time. Of course I need 
 not say that he knew nothing (not even the name) of 
 electro-magnetism and other recently discovered phy- 
 sical agents, all of which we can now classify under 
 energy ; but for everything that was known in his time, 
 with the exception of heat, light, and electric energy, he 
 gave us a complete statement. That complete state- 
 ment, strange to say, has only been found in his great 
 work within the last few years. It is this, literally 
 translated : ' If the activity of an agent be measured [not 
 by the agent itself, as in the case of a force, but] by the 
 
 C 
 
34 THE EA RL Y HIS TOR Y OF EN ERG Y. 
 
 ^ product of its force into its velocity, and if similarly the 
 counter-activity of the resistance be measured by the veloci- 
 ties of its several parts multiplied into their several forces, 
 whether these arise from friction, cohesion, weight, or 
 acceleration ; activity and counter-activity in all combina- 
 
 ^tions of machines will be equal and opposite' Now, in 
 order to see the full force of this statement, let us con- 
 sider what is meant by the product of a force into its 
 velocity. Newton, as he has shown in a previous defini- 
 tion, understands, by the velocity of a force, not the 
 whole velocity of the point to which it is applied, but 
 the component of that velocity which is in the direction 
 of the force. If, for instance, a horse is dragging a canal 
 boat along, you are not to multiply the force of tension 
 of the rope by the velocity of the canal boat, because 
 the canal boat moves in one direction, and the tension 
 of the rope is in general in a different direction. What 
 you must do then is this : you must find out how much 
 of the velocity of the boat is in the direction of the action 
 of the force ; resolve it, as it is called, multiplying the 
 amount of the velocity of the boat by the cosine of the 
 angle between its direction and the direction of the 
 force which is applied by the rope. Then, what Newton 
 says is this : if you so treat it multiply each force by 
 the velocity (in this sense) of its point of application 
 you will find that the sum of the activities will be equal 
 to the sum of the counter-activities. 
 
 A word or two more about this before I consider the 
 very admirable statement of various cases which Newton 
 gives, Let us see what we mean now-a-days by what 
 Newton calls here ' the action of the agent' It is the 
 product of the force into the resolved part of the velo- 
 city in the direction of the force. Therefore it is the 
 
THE EARL Y HISTOR V OF EJSTERG Y. 35 
 
 product of the force into the rate at which the point of 
 application moves in the direction of the force. The 
 product of a force into the space through which it 
 moves its point of application in its own direction is 
 what we now call the amount of Work done by the 
 force. But in Newton's statement it is not the amount 
 of work done, but the rate at which work is being done, 
 so that what he contemplates is really what we now-a- 
 days measure, after Watt, by the unit called a horse- 
 power the rate at which an agent works when doing 
 33,000 foot-pounds of work per minute. 
 
 Now, you will particularly notice that he says the 
 several parts of the resistance, ' whether these arise from 
 friction, cohesion, weight, or acceleration.' 
 
 I shall take, first, cohesion and weight. You can 
 easily see how a resistance may arise from cohesion, 
 which simply means what we now call molecular forces 
 in general, as, for instance, when work is spent in 
 changing the shape of a body when it is employed 
 in producing a shear, for instance. There you have 
 the elastic forces of the body worked against ; and what 
 Newton says is, that the amount of work spent, or the 
 rate of spending work in distorting the body, is equal 
 to the amount of work done or the rate of doing work 
 against the elastic forces. It is thus stored up in the 
 distorted body as Potential Energy. 
 
 Then he says 'weight :' the rate at which an agent 
 works in lifting a mass is exactly equal to the rate 
 at which work is done against gravity : and the work 
 so done is stored up as Potential energy of the raised 
 mass. 
 
 Then he says ' acceleration ; ' and that is by far the 
 most important of those I have yet mentioned. When 
 
36 THE EARL Y HISTOR V OF ENERG Y. 
 
 work is spent on a body where there is no resistance 
 from friction or from weight, or from cohesion, Newton 
 says that work will always be spent against a resistance 
 due to acceleration ; that is, work is spent in overcoming 
 the inertia of a body and increasing its velocity. This 
 is a statement of very great importance ; and when we 
 interpret it according to Newton's previously laid down 
 definitions, we find that his Third Law here asserts that 
 the rate at which the agent works is the rate at which 
 the kinetic energy of the body increases. For it is an 
 immediate consequence of Newton's words that the rate 
 at which work is spent is measured by the product of 
 the momentum into the acceleration in the direction of 
 motion. Hence the Kinetic Energy (which is half the 
 product of the mass into the square of its velocity) is 
 increased by an amount equal to the work spent. Work 
 spent against resistance to acceleration is thus stored up 
 in the body in the form of an increase in the kinetic 
 energy. 
 
 That is very important ; but there is a still more 
 important point, which Newton takes account of, and 
 that is, work spent against friction. Whenever work is 
 spent against friction, we all know now-a-days that 
 heat is produced, and it has been proved by elaborate 
 experiments, which I shall presently discuss, that the 
 amount of heat produced is precisely proportional to 
 the amount of work spent in producing it. If Newton 
 had known that such is the case, he could have had no 
 difficulty whatever, after this extremely lucid statement 
 of his, in passing to the general modern statement of 
 the conservation of energy. So near had he arrived at 
 it, that it wanted only experiments like those I am 
 presently to describe, to have enabled him at once to 
 
THE EARL Y HIS TOR Y OF ENERG Y. 37 
 
 take a full grasp of the subject, at least so far as we 
 know it in the present day. 
 
 Before I leave this matter, however, I must say a 
 word or two as to the result of compounding two 
 amounts of Kinetic energy. Suppose we have a 
 southward velocity amounting, let us- say, to 3 feet 
 per second, and simultaneously an eastward velocity 
 amounting to 4 feet per second, then we know by 
 Kinematics, how to construct the single velocity, which 
 is the resultant of these two. All we have to do is 
 to draw a line of length 3 southwards, and from its 
 extremity a line of length 4 to the eastward, and 
 then complete the triangle. In a geometrical sense, 
 therefore, a velocity of 3 southwards and a velocity 
 of 4 eastwards will be equivalent to a velocity which, 
 if you calculate what the third side of that triangle will 
 be, is represented by 5 on the same scale. It will 
 then be a velocity of 5 in a direction which makes 
 an angle, whose sine is |, with the south line. So 
 far the geometrical conception of composition is 
 perfectly definite. But now let us see what this in- 
 volves in the case of Kinetic energy. If a mass were 
 moving with a velocity of 3 southwards, and simultane- 
 ously with a velocity of 4 eastwards : its Kinetic 
 energy, being proportional to the square of the velocity, 
 is in the southward direction proportional to 9, the 
 square of 3, while in the eastward direction it is pro- 
 portional to 1 6. But the same mass moving with the 
 resultant of these velocities has Kinetic energy pro- 
 portional (on the same scale) to 25 the arithmetical 
 sum of the other two. So that there are two ways of 
 compounding these combinations of the velocity and 
 mass of a body. When it is a question of Momenta 
 
38 THE EARL Y HISTOR Y OF ENERG Y. 
 
 that is to say, when it is a question of the application 
 of Newton's first meaning of the word actio when the 
 actio means a simple force or its time-integral, then you 
 are to compound geometrically, and two sides of a 
 triangle are in that sense equal to the third ; but when 
 it comes to compounding Kinetic energies which are 
 proportional to the square of the velocity, then you are 
 limited to right-angled triangles, and having to add the 
 squares of the two sides, you obtain the square of the 
 third side. The difference then between the geometrical 
 composition and the simple arithmetical addition is a 
 difference depending upon the use of the first or second 
 power of the velocity. When, as in momentum, the 
 first power is involved, the magnitude is essentially a 
 directed one, and two directed magnitudes must be 
 compounded geometrically. But Kinetic energy, de- 
 pending as it does upon the square of the velocity, is 
 essentially non-directional, and its various parts, when 
 independent of one another (as they are when they 
 depend upon motions in directions perpendicular to 
 one another), are to be compounded by simple addition. 
 These two things, then, Momentum and Kinetic Energy, 
 perfectly distinct from one another, having no reference 
 to one another that we can trace at present, are both 
 included in the simple form of statement of Newton's 
 Third Law, only with a corresponding difference of 
 meaning to be attached to two of the words involved. 
 
 What Newton really wanted then was to know what 
 becomes of work which is spent in friction. Now, the 
 first successful answerer of that question was un- 
 doubtedly Count Rumford, and from his paper of 1798 
 I shall read some extracts, because it is one of the 
 most valuable experimental papers that perhaps ever 
 
THE EARL Y HISTOR Y OF ENERG Y. 39 
 
 was published. It is most admirably philosophical in 
 its mode of experimenting, and it is throughout entirely 
 opposed to that d priori style of reasoning which (as I 
 showed you in my last lecture) is so fatal to progress 
 in natural philosophy. Count Rumford says : 
 
 1 It frequently happens, that in the ordinary affairs and occupa- 
 tions of life, opportunities present themselves of contemplating 
 some of the most curious operations of Nature ; and very interest- 
 ing philosophical experiments might often be made, almost with- 
 out trouble or expense, by means of machinery contrived for the 
 mere mechanical purposes of the arts and manufactures. 
 
 4 1 have frequently had occasion to make this observation ; and 
 am persuaded, that a habit of keeping the eyes open to everything 
 that is going on in the ordinary course of the business of life has 
 oftener led, as it were by accident, or in the playful excursions of 
 the imagination, put into action by contemplating the most common 
 appearances, to useful doubts, and sensible schemes for investiga- 
 tion and improvement, than all the more intense meditations of 
 philosophers, in the hours expressly set apart for study.' 
 
 Then again he says : 
 
 * Being engaged, lately, in superintending the boring of cannon, 
 in the workshops of the military arsenal at Munich, I was struck 
 with the very considerable degree of Heat which a brass gun 
 acquires, in a short time, in being bored ; and with the still more 
 intense Heat (much greater than that of boiling water, as I found 
 by experiment) of the metallic chips separated from it by the borer. 
 
 'The more I meditated on these phenomena, the more they 
 appeared to me to be curious and interesting. A thorough investi- 
 gation of them seemed even to bid fair to give a further insight 
 into the hidden nature of Heat ; and to enable us to form some 
 reasonable conjectures respecting the existence, or non-existence, 
 of an igneous fluid; a subject on which the opinions of philoso- 
 phers have, in all ages, been much divided. 
 
 * From whence comes the Heat actually produced in the mechani- 
 cal operation above mentioned ? 
 
 4 Is it furnished by the metallic chips which are separated by the 
 borer from the solid mass of metal ? 
 
40 THE EARL Y HISTOR Y OF ENERG Y. 
 
 1 If this were the case, then, according to the modern doctrines 
 of latent Heat, and of caloric, the capacity for Heat of the parts of 
 the metal, so reduced to chips, ought not only to be changed, but 
 the change undergone by them should be sufficiently great to 
 account for all the Heat produced.' 
 
 He sees the difficulty : he catches at once really what 
 is wanted the true method of upsetting the old notion 
 that heat is matter. The explanation which was 
 given of the heat produced by friction by those who 
 believed that heat is matter was simply this : The 
 body in its solid state, or rather in its massive state, 
 before you began to abrade filings from it, possessed 
 in that state a certain quantity of heat. It had a 
 certain capacity for heat at a certain temperature ; 
 in other words, it required so much heat to be mixed 
 up with its particles in order to make the tempera- 
 ture of the whole that which was observed. But if 
 you could make it more capacious if you could give it 
 greater capacity for heat then it would hold more 
 heat without becoming of a higher temperature. On 
 the other hand, if by any process whatever you could 
 diminish its capacity for heat, then, of course, it would 
 become hotter itself, and even give out heat to sur- 
 rounding bodies, so that, according to the notion of the 
 supporters of the caloric theory (as it was called), the 
 production of heat by friction or abrasion is due to the 
 fact that you make the capacity of a body for heat 
 smaller by reducing it to powder. For of course, when 
 its capacity for heat is thus made smaller, it must part 
 with some of the heat it had at first ; or if it retains it, 
 it must necessarily show the effect of the heat more than 
 it did before, and must therefore rise in temperature. 
 Now, this reasoning is, so far, perfectly philosophical. 
 
iv K 
 
 C/I.Cf 
 
 77/ ^tfZ Y HISTOR Y OF ENERG Y. 41 
 
 We can say nothing against a mode of reasoning of 
 that kind. The only fallacy in it was the assumption 
 that heat is a substance. Now, see how well Rumford 
 laid hold of that point, and how he proceeds by ex- 
 periment to try if possible to satisfy his doubts about it. 
 He says : 
 
 ' If this were the case, then, according to the modern doctrines 
 of latent Heat, and of caloric, the capacity for Heat of the parts 
 of the metal so reduced to chips, ought not only to be changed, 
 but the change undergone by them should be sufficiently great to 
 account for all the Heat produced.' 
 
 Rumford found no difference, so far as his form of 
 experiment enabled him to test it, between the capacity 
 for heat of the abraded metal and the metal before 
 the abrasion had taken place ; so that if this experiment 
 had been only a satisfactory one and Rumford did 
 not see how to make it thoroughly satisfactory the 
 fact that heat is not matter would have been con- 
 clusively established. What Rumford really did want 
 was this : he wanted a process by which to bring the 
 abraded metal and the non-abraded metal, if possible, 
 to the same final state. He tried to do this by throwing 
 them into water equal quantities of the lumps and of 
 the filings, equally hot, into equal quantities of water 
 at the same lower temperature to see whether they 
 would produce different changes of temperature, each 
 in its own vessel of water. But then they were not in 
 the same final state. The filings, remember, were in 
 a distorted state ; they might have been very con- 
 siderably compressed, or they might have been distorted 
 in shape by shearing or something of that kind, in virtue 
 of which they might have had a certain quantity of latent 
 heat which he could not discover by this process. The 
 
42 THE EARL Y HISTOR Y OF ENERG Y. 
 
 only legitimate and practicable process which we know 
 of for completely answering that question, which was 
 Rumford's sole difficulty, is a chemical process. Dissolve 
 your lumps and an equal weight of your filings in equal 
 quantities of the same acid. At the end of the operation, 
 of course, there can be no doubt that the chemical sub- 
 stances produced will be precisely the same, whether 
 you begin with lumps or with filings. You will have 
 the same chemical substance ; but if there be any 
 mysterious difference as to the capacity for heat in 
 them, that will be shown during the process of solution. 
 In general, in dissolving a metal in an acid, there is a 
 development of heat ; but if there were any difference 
 in the quantity of heat which the lumps and an equal 
 weight of filings contained that is to say, if heat could 
 by any possibility be matter then there would neces- 
 sarily have been an escape of heat more in one vessel 
 than the other. If Rumford had tried that one additional 
 experiment, he would have had the sole credit of having 
 established the non-materiality of heat. 
 
 The details of Rumford's experiments are given in 
 full, but I shall not describe them to you. I merely 
 mention that they show extraordinary skill and care in 
 experimenting, and wonderful precaution in trying to 
 avoid, as far as possible, the necessary losses in the 
 experiments. When losses were unavoidable and of a 
 large amount, the same skill is shown in making separ- 
 ate side experiments, in order to enable the operator 
 to allow for them in the main experiments. The 
 whole work itself is a model of experimental science. 
 I shall now pass on to the final reasoning, merely 
 mentioning in passing that Rumford actually managed 
 to boil a large quantity of water, though an immense 
 
THE EARL Y HISTOR Y OF ENERG Y. 43 
 
 amount of heat was lost in spite of all his precautions. 
 Still the work of a single horse for two hours and twenty 
 minutes was found sufficient to boil about 19 Ibs. of 
 water, besides heating a large casting of the cannon, 
 and all the machinery that was engaged in the process. 
 He says : 
 
 * It would be difficult to describe the surprise and astonishment 
 expressed in the countenances of the by-standers, on seeing so 
 large a quantity of cold water heated, and actually made to boil, 
 without any fire. 
 
 ' Though there was, in fact, nothing that could justly be con- 
 sidered as surprising in this event, yet I acknowledge fairly that it 
 afforded me a degree of childish pleasure which, were I ambitious 
 of the reputation of a grave philosopher, I ought most certainly 
 rather to hide than to discover. 3 
 
 Here is his final reasoning : 
 
 A 
 ' In reasoning on this subject, we must not forget to consider 
 
 that most remarkable circumstance, that the source of the Heat 
 generated by friction in these experiments, appeared evidently to 
 be inexhaustible. 
 
 ' It is hardly necessary to add, that anything which any insu- 
 /atedbody or system of bodies can continue to furnish without limi- 
 tation^ cannot possibly be a material substance. It appears to me 
 to be extremely difficult, if not quite impossible, to form any dis- 
 tinct idea of anything capable of being excited and communicated 
 in the manner in which the heat was excited and communicated in 
 these experiments, except it be motion. I am very far from pre- 
 tending to know how or by what means or mechanical contrivance 
 that particular kind of motion in bodies which has been supposed 
 to constitute Heat is excited, continued, and propagated ;' 
 
 and then he proceeds to apologise for the minutiae 
 given in his paper. 
 
 Now, when we make a calculation from the data fur- 
 nished by Rumford's paper, we find this : that, supposing 
 heat to be a form of energy, and taking 30,000 foot- 
 
44 THE EARL Y HISTOR Y OF ENERG Y. 
 
 pounds per minute as the work of a horse (that is 
 something like an ordinary estimate), the mechanical 
 equivalent of heat is 940 foot-pounds. The meaning of 
 that statement is, that if you were to expend the 
 amount of work designated as 940 foot-pounds in stirring 
 a single pound of water, then that pound of water when 
 brought to rest at the end of the operation would be one 
 degree Fahrenheit hotter than before you commenced. 
 [Rumford throughout uses Fahrenheit's degrees.] We 
 can put it in another form, which is perhaps still more 
 striking. If you had a cascade or waterfall 940 feet 
 high, then, in the fall of the water down that cascade, 
 there would be 940 foot-pounds of work done by gravity 
 upon each pound of water ; and therefore if all the 
 energy which the moving water has, as it reaches the 
 bottom of the fall, were spent simply in heating the 
 water, the result would be that the water in the pool at 
 the bottom of the fall would be I deg. Fahrenheit hotter 
 than the water at the top of the fall. 
 
 I may remind you here, that Rumford's experiments 
 were published in 1798, so that they are of considerably 
 old date ; but, like those which I am just going to 
 advert to, they were barely noticed, or noticed only to 
 be laughed at, until somewhere about the year 1840. 
 
 Now, in the very year after the experiments of Rum- 
 ford were published, we had the experiments of Davy. 
 I need not go into minute details about them, because 
 they were not by any means such models of careful 
 experimental work as Rumford's. But, for all that, 
 Davy gave conclusive proof (if he had only at the time 
 seen it himself) that heat is not matter. His proofs 
 were of this kind. He first showed that by rubbing 
 two pieces of ice together by simply expending work in 
 
THE EARL Y HISTOR Y OF ENERG Y. 45 
 
 the friction of two pieces of ice you could melt the ice. 
 Now, supposing heat had been matter, this is the sort 
 of argument that a believer in the caloric theory would 
 have used : two pieces of ice when rubbed together 
 cannot possibly melt one another, because in order to 
 melt them you will have to furnish heat to them. But 
 the heat can only come from themselves when they are 
 rubbed together ; it cannot come from surrounding 
 bodies, and therefore they cannot possibly melt to- 
 gether, because to melt one another, they would have 
 first to part with some of their heat in order to produce 
 the melting. Davy showed, however, that the mere 
 rubbing together of two pieces of ice by proper 
 mechanical processes was sufficient to melt the surface 
 layer of each. There still was this possible objection, 
 that the heat might have come from some external 
 source, so that his second experiment was of this kind. 
 He rubbed two pieces of metal together, keeping them 
 surrounded by ice, and in the exhausted receiver of an 
 air-pump, so as if possible to avoid radiant heat, heat 
 carried by convection-currents of air, and so on, and to 
 remove every possible disturbing cause, or even source 
 of suspicion, from his experiment ; and still he found 
 that these two pieces of metal, when rubbed together 
 thus, constantly produced heat and melted the ice, every 
 precaution having been taken to prevent heat from 
 getting at them from every side. It is curious that his 
 reasoning upon the subject is extremely inconclusive, 
 although his experiments themselves completely settle 
 the question. He says : 
 
 ' From this experiment it is evident that ice by friction is con- 
 verted into water, and according to the supposition its capacity is 
 diminished ; but it is a well-known fact that the capacity of water 
 
46 THE EARL Y HISTOR Y OF ENERG Y. 
 
 for heat is much greater than that of ice ; and ice must have an 
 absolute quantity of heat added to it before it can be converted 
 into water. Friction, consequently, does not diminish the capa- 
 I cities of bodies for heat ;' 
 
 and there he stops. [Sir W. Thomson remarks on 
 this passage (Encyc. Brit., last edition, art. Heat), as 
 follows : Delete from ' and according to the supposi- 
 tion,' to 'greater than that of ice,' inclusive; and 
 delete the lame and impotent conclusion stated in the 
 last eleven words. The residue constitutes an unanswer- 
 able demonstration of Davy's negative proposition that 
 heat is not matter.] But some years afterwards he came 
 to this conclusion from these experiments : 
 
 ' Heat, then, or that power which prevents the actual contact of 
 the corpuscles of bodies, and which is the cause of our own sensa- 
 tions of heat and cold, may be defined as a peculiar motion, pro- 
 bably a vibration of the corpuscles of bodies tending to separate 
 them. It may with propriety be called the repulsive motion. 
 Bodies exist in different states, and these states depend upon the 
 action of attraction and of the repulsive power on their corpuscles, 
 or, in other words, on their different quantities of repulsion and 
 attraction.' 
 
 Now, we see at a glance how he explains by these 
 experiments what is the difference between a solid and 
 a liquid, and the difference again between a liquid and 
 a gas. In general, the melting of a solid is produced 
 by communicating heat to it. In other words, accord- 
 ing to Davy's explanation, the particles of the solid 
 are set in vibration, and thus, in consequence of the 
 repeated impacts upon one another, they push one 
 another side. And, as he also says, you may consider 
 this repulsive motion to have a complete analogy to 
 the so-called centrifugal force in a planetary orbit, for 
 the faster one particle is moving about another, the 
 
THE EARL Y HISTOR Y OF ENERG Y. 47 
 
 larger necessarily is the orbit into which it will be forced. 
 The particles of a solid then are forced from one another 
 by this repulsive action of heat, and the action of the 
 heat upon it puts it into a liquid state. When you 
 increase still further the amount of heat communicated 
 to the body, you at length overcome altogether the 
 cohesive forces, and you have free particles, as in a gas, 
 flying about and impinging upon one another, but only 
 for very brief periods coming near enough in the course 
 of their gyrations to bring into play the molecular 
 forces again. Whenever, however, the molecular forces 
 do come into play for a moment, you may have two 
 particles adhering together, but they are soon knocked 
 asunder by a blow from a third particle. 
 
 There is one other sentence, however, which I must 
 quote from Davy, and then I shall have finished my 
 account of his contributions, which were later than 
 1799, when his first paper was published. In fact, in 
 1812 he enounces this proposition : 
 
 { The immediate cause of the phenomenon of heat, then, is motion, i\\ 
 and the laws of its communication are precisely the same as the 
 laws of the communication of motion.' 
 
 Now, we see at a glance to what an immense extent 
 the science had been advanced in Davy's time. When 
 Davy was in a position to make that statement, one 
 had only to take it in addition to the second interpreta- 
 tion of Newton's Third Law, and the dynamical theory 
 of heat was in his possession. Still, that publication 
 of Davy's in 1812, like the earlier ones of Rumford and 
 of Davy himself, remained almost unnoticed looked 
 upon, perhaps, as an ingenious guess, or something of 
 that sort, but as something which it was not worth the 
 trouble of philosophers to consider; and it was not 
 
48 THE EARL Y HISTOR Y OF ENERG Y. 
 
 until Joule's time, somewhere about 1840, that the 
 subject was fairly taken up, and that justice was 
 rendered to their real value. Notice how distinctly 
 these two great leaders were men who based their work 
 directly upon experiment. There is no a priori guess- 
 ing, or anything of that kind, about either Rumford's or 
 Davy's work. They simply set to work to find out what 
 heat is. They did not speculate on what it might be. 
 But both before and after their time, there have been 
 numbers of philosophers who have, without trying a 
 single experiment, or at best trying only the roughest 
 forms of experiment, endeavoured to discover by a 
 priori reasoning what heat is. The list is a very long 
 one, and includes names such as Locke and Bacon, which 
 are distinguished in very different subjects, as well as 
 to some extent in physics. These both express their 
 complete conviction that heat consists in a brisk agita- 
 tion of the particles of matter ; but then, as this was 
 based upon no experiment whatever, it can simply be 
 looked upon as a happy guess. In the present day 
 when a philosopher comes forward and makes similar 
 statements, without any experiment, we simply put 
 him in the same category as Locke and Bacon, we 
 justly refuse to give him any credit for a matter of that 
 kind. 
 
 There was one man of this class, however, M. 
 Seguin, a nephew of the celebrated Montgolfier, who 
 all but redeemed himself from being so classified. 
 Seguin himself says he got from his uncle his idea that 
 heat is certainly not matter, but corresponds to a 
 certain kind of energy ; and he says that he had made 
 various experiments with a steam-engine, in order to 
 test whether the same quantity of heat reached the 
 
THE EARL Y HIS TOR Y OF EN ERG Y. 49 
 
 condenser as had left the boiler. He was, unfortunately, 
 unsuccessful in all his experiments. He was certainly j 
 on the right track, and had he succeeded there he 
 would have been entitled to be considered as an inde- 
 pendent discoverer of the non-materiality of heat. For 
 it is obvious that if we can show by any experiment 
 whatever that heat is put out of existence, or that fresh 
 heat is brought into existence, either of these at once 
 destroys all possibility of its being material. Now, if 
 Seguin could have proved, by his actual measurements, 
 that less heat in any case reaches the condenser than 
 left the boiler, he would have completely settled the 
 question. From that point of view experiments have 
 been made, and made very carefully, in recent times, 
 by Him. Hirn has actually measured, in an ordinary") 
 working steam-engine, by most careful experimental 
 methods, the quantity of heat which leaves the boiler 
 and the quantity which reaches the condenser. He has 
 measured also the quantity which is lost by radiation, 
 conduction, and currents of air over all parts of the 
 machine, and he has found, as a final result, that when 
 the engine is at work, as, for instance, when a number 
 of spindles are being turned, there is a greater difference 
 between the quantity of heat which leaves the boiler 
 and the quantity which reaches the condenser than when 
 the steam is simply blown through the engine without,, 
 doing any work. In the latter case the greater part of 
 it reaches the condenser ; in the former case there was 
 less of it that reached the condenser more of it, in 
 fact, was put out of existence, or, to speak more cor- 
 rectly, more of it was converted into work done by the 
 engine during the operation. 
 
 But what I chiefly wish to impress upon you is that 
 
 D 
 
50 THE EA RL Y HIS TOR Y OF EN ERG Y. 
 
 Seguin, although he went to work in a correct manner, 
 reasoned from an utterly unsound basis. His reason- 
 ing was of this kind, that when a body expands and 
 thereby becomes colder, it loses heat, and that the heat 
 so lost is necessarily the equivalent of the work done 
 during the expansion. 
 
 Another of the speculators on the dynamical theory 
 of heat, but who did not publish till 1842, three years 
 after Seguin, was Mayer, who in very many quarters 
 still gets the credit of being the real author of the 
 whole science of Energy, including Thermo-dynamics. 
 Mayer's speculation was based on precisely the con- 
 Averse of that of Seguin. Seguin said the amount of 
 work done by an expanding heated body is the equi- 
 valent of the heat which it loses. Mayer said the 
 amount of heat which is produced by compressing 
 a gas or any other body is the equivalent of the work 
 u spent in compressing it. You will see at once that these 
 two statements are precisely the same, only the one is 
 the converse of the other. If the one be true, the other 
 necessarily will be true also ; but both are a priori 
 assumptions, and we now know by experiment that 
 neither of them is true under any realisable circum- 
 stances whatever ; though in certain cases they are ap- 
 proximately true. Each of the two speculators, Seguin 
 and Mayer, tried to apply his hypothesis by calculation 
 to the properties of a particular substance. Seguin tried 
 steam, because he was more familiar with steam ; Mayer 
 tried air, because he had some physical data for it. 
 Seguin's calculations were very far wrong on the one side 
 of the truth ; Mayer's were very far wrong on the other 
 side of the truth ; but Mayer's substance, namely, air, 
 has been since experimentally proved by Joule to be 
 
THE EARL Y HISTOR Y OF EN ERG Y. 5 1 
 
 capable of giving an almost exact result. Mayer by 
 chance, then, in the middle of his a priori speculations, 
 lit upon a method although he got it from a false 
 principle which Joule afterwards proved to be a good 
 one, and used as one of his modes of obtaining the 
 value of the dynamical equivalent of heat. Still, we 
 must give Mayer no credit for that, for although he laid 
 down his law quite generally, air was the only substance 
 he had data for, and he chose it on that account. But 
 even with this, his data were so bad that he got a result 
 as far from the truth as the one obtained by Seguin. 
 Only Seguin has this great credit, to which Mayer has 
 no claim, that, seeing that if heat be not matter, some 
 of it must disappear in the working of an engine, he 
 tried to measure the quantity of heat coming to the 
 condenser, in order to show that it was less than that 
 which left the boiler. 
 
 I find that I have now exhausted my time, and there- 
 fore I shall merely mention that, in my next lecture, I 
 shall take up the history of the theory of energy, as it 
 was developed by the sound methods of Colding and 
 Joule in papers published about 1843 \ an< ^ I shall then 
 endeavour, with the facilities which this room affords 
 me, to illustrate my explanation by a few experiments. 
 
 \Note to J^hird Edition. The last three or four pages have been left in 
 their original form, as expressing what was well known in 1874. But, of 
 late, attention has been called to the services of Mohr, whose date is prior 
 to that of Seguin, and still more so to that of Mayer. In the next lecture, 
 a notice of these services will be inserted. ] 
 
LECTURE III. 
 
 ESTABLISHMENT OF THE CONSERVATION OF ENERGY. 
 
 Further inquiry into the asserted claims of Mayer. Opinions of Colding and 
 Joule on Mayer's first paper. [Insertion (1884) on the prior claims 
 of Mohr.] Colding's Experiments. Joule's Experiments. Numerical 
 value of the Dynamical Equivalent of Heat. Helmholtz's argument 
 from the Perpetual Motion. Transformation and Dissipation of 
 Energy. Illustrative experiments. 
 
 IN my last lecture I showed you in what state Newton 
 left the grand question of conservation of energy, what 
 an enormous step he took, and what was the sole great 
 difficulty remaining in his way. Then I showed you 
 how, in regard to the particular branch of it which we 
 call the dynamical theory of heat, Rumford and Davy 
 had, at the very end of last century, almost completely 
 settled the question that heat is not matter. A little 
 was wanting in the work ot each. Rumford wanted 
 only one small chemical experiment in addition to his 
 grand physical experiments. Davy wanted a little more 
 conclusive reasoning than he showed at the time. Had 
 one or other of these been furnished before the end of 
 the last century, it would have been to the last century 
 that we should have been indebted entirely for the 
 dynamical theory of heat. It was not, however, until 
 1812 that Davy applied correct reasoning to his experi- 
 ments, and obtained the correct deductions from them ; 
 and then he stated in a distinct form the important 
 
THE CONSER VA T1ON OF EN ERG Y. 53 
 
 propositions that heat is motion, and that the laws of its 
 communication are precisely the same as the laws of 
 communication of motion. Then I showed you that 
 Seguin, although he was altogether wrong in his d priori 
 idea, had a true sense of what was really wanted to this 
 question, and that he made a correct, but unhappily 
 unsuccessful, experimental attempt to supply it. Then 
 we came to Mayer, a man who has, especially of late, 
 been persistently held up as the discoverer, not merely 
 of the dynamical theory of heat, but of the whole sub- 
 ject of conservation of energy. Of him, I may remark 
 because the question is one of importance though 
 at the present day we are hardly perhaps far enough 
 advanced in time calmly and dispassionately to consider 
 the relative claims of these authors ; still, I may remark 
 that a great deal of the eulogy which has been bestowed 
 upon Mayer is altogether undeserved, and that Joule 
 has even yet received far too little credit for the enor- 
 mous advances he made. In the first place, Mayer 
 was altogether wrong in his a priori idea. On that Sir 
 William Thomson and I made, in 1862, the following 
 remarks, which no one has ventured directly to challenge 
 in the slightest particular : 
 
 * Mayer's method is founded on the supposition that diminution 
 of the volume of a body implies an evolution or generation of heat ; 
 and it involves essentially a false analogy between the natural fall 
 of a body to the earth, and the condensation produced in an elastic 
 fluid by the application of external force. The hypothesis on which 
 he thus grounds a definite numerical estimate of the relation be- 
 tween the agencies here involved, is that the heat evolved when an 
 elastic fluid is compressed and kept cool, is simply the dynamical 
 equivalent of the work employed in compressing it. The experi- 
 mental investigations of subsequent naturalists have shown that 
 this hypothesis is altogether false for the generality of fluids, espe- 
 
54 THE CONSER VA TION OF EN ERG Y. 
 
 cially liquids, and is at best only approximately true for air ; 
 whereas Mayer's statements imply its indiscriminate application 
 to all bodies in nature, whether gaseous, liquid, or solid, and show 
 no reason for choosing air for the application of the supposed prin- 
 ciple to calculation ; but that at the time he wrote, air was the only 
 body for which the requisite numerical data were known with any 
 approximation to accuracy.' 
 
 Then, in addition to these two absolute errors which 
 are mentioned in this passage, I may call attention to 
 the preposterous a priori principles upon which he 
 reasons. There are two of them ; the one is causa 
 cequat effectum, to which I have never been able to attach 
 any meaning, and the other ex nihilo nihil fit. These 
 may be a basis for scholastic disquisitions, such as the 
 celebrated old question of the number of angels that 
 can simultaneously dance on the point of a needle, but 
 they are altogether unfit for introduction in any shape 
 whatever into physical reasoning. Then, again, Mayer's 
 work was altogether destitute of experiment. He sug- 
 gests, no doubt, the carrying out, on a larger scale, an 
 experiment which he says he tried, namely, shaking 
 a little phial of water for a considerable time, to find 
 it at the end of the time warmer than it was at the com- 
 mencement : merely, I may say in passing, a bad sub- 
 stitute for a hint due to Rumford, that the churning of 
 water would be a good experimental method, I daresay 
 most of you will see that such an experiment as Mayer's, 
 unless proper precautions were taken to prevent con- 
 duction of heat from the hand to the bottle of water, 
 would very probably have resulted in the heating of the 
 water considerably, even without the shaking : so that, 
 in order to prove that the heat was due to the shaking, 
 we should have required at all events a statement 
 on Mayer's part of the precautions he had taken to 
 
THE CONSER VA T1ON OF EN ERG Y. 5 5 
 
 prevent one known source of heat from affecting the 
 water. 1 
 
 But, in addition to this, Mayer did not even believe 
 that heat depends on motion ; and this is perhaps the 
 most wonderful comment that can be made upon the 
 consistency of those who, while constantly speaking of 
 heat as a ' mode of motion/ call him the discoverer of 
 the modern theory of heat. To effect this must surely 
 have involved (to use the vigorous and expressive 
 language of one of the most prominent popularisers of 
 science) the necessity of * wrangling resolutely with the 
 facts !' Mayer himself says, in his very earliest paper, and 
 he never afterwards to my knowledge modified this state- 
 ment (I translate freely), ' We might much rather assert 
 the opposite, that motion, whether it be a simple one or 
 a vibratory one like light, like radiant heat, and so 
 on must, in order to become heat, cease to be motion.' 
 He actually says it must cease to be motion in order to 
 become heat! Then he makes another and a very 
 curious statement, the absolute erroneousness of which 
 you will see in the course of another lecture. He says, 
 sneeringly : ' Let any one try to melt ice by pressure, 
 however enormous.' I shall show you that, as a con- 
 sequence of the second law of thermo-dynamics, the 
 melting of ice by pressure was predicted beforehand, 
 and was verified afterwards by actual experiment. 
 
 It is time, then, I say, that Mayer, even with our as 
 yet imperfect means of judging, should be ranged, so 
 far as we can, in his true place. He has been injudi- 
 ciously praised, and he has been an unfortunate man, 
 
 1 Even this experiment, but carried out with something like philo- 
 sophical precautions, was long before described.by Reade in Nicholson's 
 Journal, 1808, p. 113. 
 
56 THE CONSER VA TION OF EN ERG Y. 
 
 and therefore, of course, there will be an outcry against 
 any one who undertakes the necessary task of pointing 
 out his real demerits. However, there is no such thing 
 in scientific history as the argumentum ad misericor- 
 diam. The blame, if any there be in such a matter, is 
 due to those who preposterously gave him credit for 
 what he did not do. The real merits of Mayer, how- 
 ever, which are extremely great, but which are in 
 danger of being forgotten or ignored in consequence of 
 the unwarrantable claims made for him, depend upon 
 his having, after getting a true theory by false reason- 
 ing from inadequate and sometimes inadmissible pre- 
 mises, reasoned rightly upon it, and developed it widely 
 in its applications. Language has lost all meaning, 
 however, if this can be called a claim to establishment 
 of the theory itself. The fact is that in 1839 Faraday, 
 and in 1841 Liebig, and about the same time others 
 of the great philosophers who have lately died, made 
 close approaches to the true theory by methods far 
 more sound than those of either Mayer or Seguin ; and 
 yet, curiously enough, they have scarcely at any hand 
 got the slightest recognition. 1 
 
 The true modern originators and experimental demon- 
 strators of the conservation of energy in its generality 
 were undoubtedly Colding of Copenhagen and Joule of 
 Manchester. It is interesting to see in what light these 
 men regard Mayer and some others of those who pre- 
 ceded them. I shall presently give you a quotation or 
 two bearing on that point. 
 
 In the meantime I may say, with regard to Colding, 2 
 that he began by being metaphysical, but saw at once, 
 
 1 See Phil. Mag. 1864, II. p. 474; 1865, I. p. 217 ; and 1876, II. p. no. 
 a See his very interesting letter, Phil. Mag. Jan. 1864. 
 
THE CONSERVATION OF ENERGY. 57 
 
 or very soon, that metaphysics was not the proper 
 basis on which to found a search for physical facts. 
 His metaphysics led him to form certain opinions, but 
 before publishing one of them he set to work and 
 laboriously brought it to the test of fact. Joule, on the 
 other hand, seems to have begun by experimenting 
 with the view of determining certain physical constants. 
 He does not tell us whether he had any metaphysical 
 opinion about their relations or not. He set to work 
 experimenting, and it was only after a great and varied 
 series of his experiments had been fully carried out, and 
 valuable results obtained, that he began to make cer- 
 tain applications of metaphysical reasoning to the con- 
 nections which he had discovered. He did not apply 
 metaphysics to discover anything, but to try and 
 co-ordinate with other things the discoveries he had 
 already made. Colding's work is by no means so exten- 
 sive as Joule's. It is very nearly simultaneous with 
 it, but it is neither so exact nor so extensive. Still, 
 although Colding is hardly to be compared with Joule, 
 he stands enormously high in comparison with any of 
 the others who had experimented up to that time upon 
 the conservation of energy. I will read you one or two 
 extracts from Colding, and you will see from them how 
 properly he went to work. He says : 
 
 ' It was in accordance with this idea that I twenty years ago pre- 
 sented to the Royal Society of Science here in Copenhagen, a trea- 
 tise in which I explained my idea that force is imperishable and 
 immortal ; and, therefore, when and wherever force seems to vanish 
 in performing certain mechanical, chemical, or other work, the force 
 then merely undergoes a transformation and reappears in a new 
 form, but of the original amount as an active force. 
 
 * In the year 1843 tms idea, which completely constitutes the new 
 principle of the perpetuity of energy, was distinctly given by me, 
 
58 THE CONSER VA TION OF EN ERG Y. 
 
 the idea itself having been clear to my own mind nearly four years 
 before, when it arose at once in my mind by studying LfAlemberfs 
 celebrated and successful enunciation of the principle of active and 
 lost forces j but of course the new principle was not as clear to me 
 from the beginning as it was when I wrote my treatise in 
 1843-' 
 
 I may here parenthetically observe that Colding 
 speaks of D'Alembert's celebrated and successful enun- 
 tiation of a certain principle. This is nothing more or 
 less than a particular case of that principle of Newton, 
 which I gave you in a former lecture j 1 so that you see 
 Colding really got his idea suggested to him by New- 
 ton's work : 
 
 r ' According to the view which led me to this principle, its future 
 importance, in case it were really true, was perfectly clear to me 
 from the first instant. But this made me very anxious not to pub- 
 lish it as a new law of nature until I should be able to give experi- 
 mental proof of its truth ; and scientific men to whom I explained 
 my idea, and especially our celebrated professor, H. C. (Ersted, 
 agreed with me and advised me to be safe in this respect before I 
 wrote ; and it was for this reason that I departed from my original 
 intention of explaining it to a meeting of Natural Philosophers held 
 >,_in Copenhagen in 1840. 
 
 ' In my first treatise, of 1843, the title of which is " Theses con- 
 cerning Force " (Nogle S&tninger om Krcefterne\ I therefore not 
 only presented my idea to the Royal Society (of Copenhagen) as a 
 thing that most likely would hereafter be found to be a general law 
 of nature, but, after stating that the only trustworthy decision of 
 the question was to be got from the experimental investigation of 
 nature itself, I went on to call attention to several old experi- 
 ments made previously to my time, the first of which was Dulong's 
 celebrated discovery respecting the heat disengaged or absorbed 
 during the compression or expansion of a great number of different 
 airs and gases, and I then showed how perfectly these experi- 
 ments proved the truth of the said principle for bodies of that 
 
 d.' 
 
 Ante, p. 33. See Thomson and Tail's Natural Philosophy, 264. 
 
THE CONSER VA TION OF EN ERG Y. 59 
 
 Then he goes on to say that having established the 
 proposition for elastic fluids, he proceeded to try ex- 
 periments in conjunction with QErsted upon the com- 
 pression of water ; and that next he advanced, just as 
 Joule did about the same time, to experiments upon 
 the compression of solids. He also says : 
 
 ' I closed my discussion by showing that the discovery of a 
 perpetuum mobile would be possible if my principle was wrong.' 
 
 This shows that, to a certain extent at least, he had 
 anticipated Helmholtz, of whose great services to this 
 branch of science I shall presently speak. 
 
 The remarks he makes about Mayer deserve to be 
 quoted. He desires the republication, in an English 
 journal, of his first paper, in order that it might be com- 
 pared, as he says, with the paper of Mayer, which 
 was most loudly vaunted in England at the time when 
 his letter was written : 
 
 ' I need scarcely say that such a comparison would be of great 
 interest to me, as I believe it would convince your readers of the 
 fact that M. Mayer wrote his remarks in 1842, before he was able 
 to support them by a single experiment or by anything like a proof 
 of their exactness, whilst I thought it to be my duty, before I wrote, 
 to prove that my suppositions concerning the forces were confirmed 
 by nature itself, as a law of nature. 3 
 
 He also says of his own experimental approximation 
 to the dynamical equivalent of heat, that it is 
 
 'very near the proportion that M. Mayer in 1842 supposed, but 
 did not prove, to be right.' 
 
 Joule's remarks 1 upon the subject of Seguin and Mayer 
 are also deserving of quotation : 
 
 ' Seguin gives data from which the mechanical equivalent of heat 
 may be readily deduced on his hypothesis, the result being too 
 1 Phil. Mag. 1864, II. p. 151 ; see also 1862, II. p. 121. 
 
60 THE CONSER VA TION OF EN ERG Y. 
 
 great in consequence of the thermal effect of the compression of 
 vapour being understated. Neither in Se"guin's writings of 1839, 
 nor in Mayer's paper of 1842, were there such proofs of the hypo- 
 thesis advanced as were sufficient to cause it to be admitted into 
 science without further inquiry. I believe that the experiment 
 attributed to Gay-Lussac was not referred to by Mayer previously 
 
 H:o the year 1845. Mayer appears to have hastened to publish his 
 views for the express purpose of securing priority. He did not 
 wait until he had the opportunity of supporting them by facts. 
 My course, on the contrary, was to publish only such theories as 
 I had established by experiments calculated to commend them to 
 the scientific public, being well convinced of the truth of Sir 
 J. Herschel's remark, that "hasty generalisation is the bane of 
 
 i science."' 
 
 To these it would be easy to add several even more 
 telling passages to the same effect. 
 
 [In 1876 my attention was called to a paper by 
 Mohr (Journal fur Pharmacie), of which I published a 
 translation in the Phil. Mag. for August of that year. 
 The date of the paper is 1837, or ^ ve years before 
 Mayer, and it contains, in a considerably superior form, 
 almost all that is correct in Mayer's paper. Though it 
 contains many mistakes, it avoids some of the worst 
 errors of Mayer, especially his false analogy and his 
 a priori reasoning. The very process (for determining 
 the mechanical equivalent of heat from the two specific 
 heats of air) for which Mayer has been so extravagantly 
 lauded : although it is in principle, albeit not in 
 practice, utterly erroneous : is here stated much more 
 
 ! clearly than it was stated five years later by Mayer. 
 
 In December 1877, I received by post a copy of a 
 work Allgemeine Theorie der Bewegung imd Kraft, etc. 
 (Braunschweig 1869), with the inscription, in a bold hand, 
 ' dedicated by the author, Dr. Mohr.' This work is con- 
 clusive against Mayer's first paper. It leaves absolutely 
 
THE CONSER VA TION OF EN ERG Y. 6 1 
 
 nothing to him save his blunders. For it contains a 
 reprint of an article by Mohr, published in 1837 in 
 Baumgartner* s und v. Holger's Zeitschrift fiir Physik (of 
 which the paper above alluded to was, it seems, a mere 
 resume). One sentence, only, need be extracted from 
 this article (which ought certainly to be translated into 
 English verbatim) to show how definitely in 1837 Mohr 
 put into words a clear statement of the truth which 
 Mayer vainly attempted to express clearly five years 
 later. 
 
 'Ausser den bekannten 54 chemischen Elementen 
 gibt es in der Natur der Dinge nur noch ein Agens, und 
 dieses heisst Kraft: es kann unter den passenden 
 Verhaltnissen als Bewegung, chemische Affinitat, Co- 
 hasion, Electricitat, Licht, Warme und Magnetismus 
 hervortreten, und aus jeder dieser Erscheinungsarten 
 konnen alle ubrigen hervorgebracht werden. Dieselbe 
 Kraft, welche den Hammer hebt, kann, wenn sie anders 
 angewendet wird, jede der ubrigen Erscheinungen her- 
 vorbringen.' 
 
 This notable article did not obtain insertion in 
 Poggendorff's Annalen, to which it was first sent. One 
 of the earliest and most valuable of Joule's papers met 
 a similar fate at the hands of the Royal Society] 
 
 Having said this much with regard to the relative 
 merits of these men, and having shown you that Joule 
 is far the foremost, while Colding is the only one who 
 deserves mention in comparison with him, so far as the 
 present part of our subject is concerned, I proceed to give 
 a rough general statement of what Joule really did, and 
 then you will see what enormous advances he made 
 within a few years from 1840. Joule, in 1840, published" 1 
 his first paper, which was with reference to the heat 
 
62 THE CONSERVATION OF ENERGY. 
 
 produced by electric currents under various circum- 
 stances. He was led by these experiments to see that 
 there must be some relation between the heat produced 
 and the quantity of zinc consumed in the battery ; thus, 
 as it were, eliminating the mysterious agent, electricity, 
 altogether from the final result. The novelty and value 
 of this idea can hardly now be realised by us. Then, 
 again, Faraday's grand discovery of induced currents 
 suggested to Joule the measurement of the amount of 
 mechanical work we require to spend in order to pro- 
 duce a given amount of electric current, which in its 
 turn shall be frittered down into a given amount of heat. 
 We should thereby have, as it were, not an immediate 
 conversion of work into heat, as in the case of friction 
 (which appears at least at first sight to give an imme- 
 diate transformation from work into heat), but we should 
 have a mediate transformation by induction of currents 
 we should transform the work of driving the mag- 
 neto-electric machine into the energy of so much 
 electric current, and then let that again turn itself 
 into heat You have first the work, then the electric 
 currents, and finally the heat. Now, Joule seems to 
 have observed that the same amount of heat was 
 produced from this amount of work, whether the 
 work was first employed in producing electricity, and 
 then the electricity employed in producing heat, or 
 whether the work was simply spent directly in produc- 
 ing heat by friction ; and from that time he began to 
 experiment, with the view of determining exactly what 
 is the mechanical equivalent of heat, because he saw 
 that unless it were certain, experimentally, that in all 
 cases of friction, where there is nothing but heat to show 
 for the work that has been spent unless there could 
 
THE CONSERVATION OF ENERGY. 63 
 
 always be found the same amount of heat for the same 
 amount of work, whatever were the bodies which were 
 made to rub against each other unless something of 
 that kind could be established, it would be vain to seek 
 for any such thing as conservation of energy, or even for 
 the much lower and in fact mere particular case of the 
 equivalence between heat and work. If work and heat 
 be equivalent in any sense, and if you spend work 
 wholly in producing heat, you must get always the same 
 amount of heat for the same amount of work, whatever 
 be the nature of the engine which you employ. I may 
 parenthetically remark (as it gives an inkling of what is 
 to follow) that it is quite another question when you 
 come to the conversion of heat into work ; when it comes 
 to be a question of beginning with the heat, and con- 
 verting that into work, the conversion cannot be wholly 
 accomplished. Begin with work, and you can convert it 
 all into heat. Begin with heat, and you cannot convert 
 it all into work. The one case is perfectly definite, and 
 therefore Joule, reasoning upon it, virtually said : ' If 
 there be nothing but heat to show for a certain amount 
 of work spent, then unless we always get, with every 
 apparatus, the same amount of heat for the same amount 
 of work, conservation cannot possibly hold.' He proved 
 that this equivalence does subsist ; and his determination, 
 finally published with all his latest improvements in 
 1849, was 772 foot-pounds for a unit of heat ; that is to 
 say, a pound of water which has fallen 772 feet, and had 
 the whole of the energy of its fall, or the whole excess of 
 potential energy which it had before falling, converted 
 into heat, will simply be I deg. Fahr. hotter than it was 
 before it fell. As I pointed out to you in my last lec- 
 ture, Rumford's estimate was considerably above that ; 
 
64 THE CONSER VA TION OF EN ERG Y. 
 
 but it was confessedly only an estimate, while Joule's 
 was the final result of an extended and laborious series 
 of experiments. This leads us then to the statement 
 of what is called the First Law of Thermo-dynamics. 
 It may be put in very many forms, but I shall take the 
 form which seems to be the most effective. The first 
 law of thermo-dynamics, then, really established by 
 Davy and Rumford, but altogether neglected and for- 
 gotten, re-established by Joule and supplied by him 
 with a definite numerical datum, for the purpose of cal- 
 culation, may be put in this form : 
 
 When equal quantities of mechanical effect are pro- 
 duced by any means whatever, from purely thermal 
 sources, or lost in purely thermal effects, then equal quan- 
 tities of heat are put out of existence or are generated : 
 and for every unit of heat measured by the raising of a 
 pound of water I deg. Fahr. in temperature, you have to 
 expend 772 foot-pounds of work. 
 
 It is possible that that last figure of the 772, which is 
 for the latitude of Manchester, may be wrong. The 
 true number may be, for instance, 771*5 or 772^5, or 
 something of that kind, but there is little doubt that 
 Joule's determination is at all events considerably within 
 one per cent, of the truth. It is particularly noteworthy 
 that in 1843, from the heat developed by the friction of 
 water in narrow tubes, Joule had given 770 foot-pounds 
 as the mechanical equivalent. 1 
 
 In addition to all this, Joule gave an experimental 
 extension of the principle of conservation to other forms 
 of energy, that is to say, in addition to heat he enabled 
 us to take current electricity, electro-magnetism, etc., 
 into the same category. In fact, even in 1840, before 
 
 i Phil. Mag. 1843, II. 
 
THE CONSERVATION OF ENERGY. 65 
 
 he had come to definite conclusions as to the generality 
 of the principle of conservation, he had established ex- 
 perimentally a grand series of particular cases of it ; and 
 one of the most remarkable was this : 
 
 When any voltaic arrangement, whether simple or compound, 
 passes a current of electricity through any substance, whether an 
 electrolyte or not, the total voltaic heat which is generated in any 
 time, is proportional to the number of atoms which are electro- 
 lysed in each cell of the circuit, multiplied by the virtual intensity 
 of the battery. l 
 
 Therefore, even at that -early time, his experiments (and 
 his reasoning was entirely based ^jpon experiment) 
 had led him to this conclusion, that 'whenever some- 
 thing that was imponderable disappeared, and there 
 appeared some other imponderable which could have 
 no other origin, then the quantity of the one was 
 directly proportional to the quantity of the other, and 
 the ratio between these two had only to be determined 
 by accurate measurement in order that you might 
 know the mechanical equivalent of so much current 
 electricity, or of so much heat, or even of the poten- 
 tial energy of so much zinc and dihite sulphuric acid, 
 or of any other substances in a state fit for chemical 
 combination. 
 
 Another most valuable experimental research of 
 Joule's bears on the question of the mechanical value 
 of Light?' He compared the heat evolved in the wire 
 conducting a galvanic current, when the wire was ignited 
 by the passage of the current, with that evolved when 
 (with an equal current, suppose) it was kept cool by im- 
 
 1 Phil. Mag. 1841, II. p. 275. Paper read before the Royal Society, 
 December 17, 1840. 
 
 z Phil. Mag. 1843, I. p. 207. 
 
 E 
 
66 THE CONSER VA TION OF ENERG Y. 
 
 mersion in water. These experiments showed a small, 
 but unmistakeable, diminution of the heat when light 
 also was given out. However, all that was necessary 
 in order to extend the principle of conservation to light 
 was to show that light, like heat, electric currents, and 
 so on, is a form of energy and not a form of matter ; in 
 other words, to establish what is called the undulatory 
 theory instead of the corpuscular theory. 
 
 I may digress for a little to say a word or two as to 
 how that was done. It is one of the important advances 
 made within the period to which my lectures chiefly 
 refer. 1 It was established in France by Fizeau and 
 Foucault, working originally by independent processes, 
 but afterwards working together. The proposition then 
 to be decided upon is : Does light, as it comes to us from 
 the sun, for instance, consist in the transference of par- 
 ticles of something luminiferous ? Is it matter, in fact, 
 which is shot out from the sun ? or is it a propagation 
 of disturbance of some kind or other which may be 
 assimilated, for purposes of illustration, to wave-motion ? 
 Is it, in short, a propagation of energy in some form 
 or other, whether wave-motion or not, or is it a 
 propagation of matter ? Now, Newton and Huyghens 
 had, long ago, each from his own point of view, assigned 
 
 1 I am aware that many excellent authorities attribute the establishment 
 of the undulatory theory to Young and Fresnel saying that interference 
 as in the phenomena of diffraction, etc. , had, in their hands, completely 
 upset the corpuscular theory. But, as a fact, some of the more noted 
 supporters of that theory (including Biot) were not convinced by these 
 experiments, but were led to make further modifications of their favourite 
 theory, while there can be little doubt that they would have accepted 
 Fizeau and Foucault's results as decisive against them. Of course, such 
 a statement as this in no way impugns the value of the magnificent work 
 done by Young and by Fresnel. 
 
THE CONSER VA TION OF ENERG Y. 67 
 
 the means of perfectly settling this question. Newton, 
 in fact, had shown that if light be matter, then, on 
 being refracted into a dense body, it will move more 
 nearly in a direction perpendicular to the surface, 
 provided it move faster in the dense body than in the 
 rare one outside. That is to say, that, since we know 
 that an oblique ray of light falling upon the surface of 
 water, for instance, which is denser than the air, is 
 refracted more nearly to the vertical, Newton had 
 mathematically demonstrated that if light consist of 
 particles, it must move faster in water than in air. 
 Huyghens, on the other hand, showed that if light consist 
 of wave-motion, and be refracted towards the vertical, 
 at the horizontal surface of a dense body such as water, 
 then its velocity in the dense body must be less than its 
 velocity in the rare body. Thus there was a distinc- 
 tion of the most marked character between the two 
 theories. If therefore you can discover by experiment 
 whether the velocity of light is greater or less in water 
 than in air, you settle for ever the question whether 
 light consists in the propagation of matter or in the 
 propagation of motion or energy. Now the experiments 
 separately made by Fizeau and Foucault both gave the 
 result, that in water light moves slower than in air, and 
 therefore it necessarily followed that light is a form of 
 energy. 
 
 So far, then, we have come to the complete establish- 
 ment experimentally of the classification of the impon- 
 derables under the head of energy, and we have arrived 
 at a general notion of relations of equivalence between 
 them. The mere fact of conservation, of course, at once 
 establishes that there must be relations of equivalence. 
 So much of the one is equivalent to so much of the 
 
68 THE CONSERVATION OF ENERGY. 
 
 other, provided you can effect the conversion of the one 
 into the other. Of course it will always, or at least for 
 a very long time, remain an extremely difficult problem 
 to measure the equivalent of an amount of light. Still, 
 it has been approximated to, and, among other processes, 
 in this way : Light, when absorbed by an opaque body, 
 is found to make the opaque body hotter. Here is an 
 example of the principle of conservation. The energy 
 of the light is not destroyed, but its vibratory motion 
 cannot pass through this opaque body as light. It is 
 employed in agitating the particles of the opaque body, 
 and that body becomes hotter in consequence. We can 
 measure, then, the quantity of light in terms of the heat 
 which it produces, or to which it is equivalent, and then 
 we can measure that quantity of heat in terms of 
 mechanical work, so that, as Sir William Thomson did 
 many years ago, shortly after Joule's discoveries appeared 
 in print, we can calculate what he calls the mechanical 
 value of a cubic mile of sunlight ; we can calculate how 
 many foot-pounds of work are equivalent to the sunlight 
 which a cubic mile of the earth's atmosphere, filled with 
 direct sunlight, has in consequence of that luminous 
 energy which is passing through it at the instant. 
 
 Before I leave for the moment the subject of the con- 
 servation of energy, I must .speak of one additional 
 name in connection with its discovery and early develop- 
 ment, that of Helmholtz, the great physiologist of Berlin, 
 who has now, at least nominally, ceased to be a physio- 
 logist, but who remains one of the foremost of living 
 mathematicians and natural philosophers. One of his 
 early works was published in 1847, shortly after Joule 
 and Colding had published their discoveries. It seems, 
 however, that he was barely acquainted with the writings 
 
THE CONSERVATION OF ENERGY. 69 
 
 of either, but had set to work himself, from a mathe- 
 matical point of view, to settle the principle of conserva- 
 tion of energy. In fact, the German title of his book is 
 precisely an equivalent to our English phrase ' conserva- 
 tion of energy.' He based the principle upon one or 
 other of two propositions, and it is interesting in the 
 highest degree to consider what these propositions are, 
 and to see how a man who was fully acquainted with the 
 whole science of the time looked at a subject of this sort, 
 and pointed out in what direction experiment ought to 
 be turned in order to verify the conclusions of theory. 
 He says, in effect, that if you take Newton's principle 
 the principle you have already heard [p. 33]- i -and if you 
 combine it with one or other of the two following postu- 
 lates, you will establish completely the conservation of 
 energy. The first postulate is : Let us suppose matter 
 to consist of ultimate particles which exert on each other 
 forces whose directions are those of the lines joining each 
 pair of particles, and whose amounts depend simply on 
 the distances between the particles. Suppose, in fact, 
 that something akin to gravitation-force exists amongst 
 all the particles of matter in the universe, that each 
 particle attracts every other particle with a force which 
 depends only upon the distance between them, not in 
 any way upon the sides which are turned to one another, 
 so that if you know the distance between them you 
 know the amount of the attraction, and that the attrac- 
 tion shall also be (in accordance with Newton's Third 
 Law of Motion) in the direction of the line joining them. 
 If you make that assumption, then it is a mere con- 
 sequence of the ordinary laws of motion of gross matter 
 that, if all forms of energy depend upon motion or 
 position of such particles, the conservation of energy 
 
70 THE CONSER VA TION OF ENERG Y. 
 
 must hold, and also that the so-called perpetual motion 
 would be impossible under any circumstances. 
 
 As an alternative, Helmholtz shows that we may take 
 as our postulate this consequence of the first postulate. 
 Take the impossibility of the so-called perpetual motion 
 as a postulate, and take along with it Newton's grand 
 statement of his second interpretation of the Third Law 
 of Motion, these two together would, by themselves, 
 enable you to prove the principle of conservation of 
 energy. Now it had for many years back been an 
 accepted matter among men of science (as typified by 
 the long-since announced determination of the French 
 Academy to consider as not having readied it, any paper 
 whatever upon the perpetual motion), it had been 
 accepted by men of science, I say, almost universally 
 that experiment had conclusively demonstrated the 
 perpetual motion to be impossible. So Helmholtz, by 
 showing that if you simply begin with that experimental 
 fact, and take in addition to it Newton's statement, 
 you can establish the conservation of energy, had 
 made, independently of Joule and Colding, a dis- 
 covery of this great principle for himself. You will 
 notice that he did, almost as distinctly as either Joule 
 or Colding, insist upon the necessity of experiment for 
 the establishment of such a principle, but he brought in 
 his experiment in the form of an universally accepted 
 result of the experiments of others, namely, the im- 
 possibility of the perpetual motion, while they preferred 
 to make perhaps more direct experiments for themselves. 
 
 I shall have occasion to say a word or two more about 
 the so-called perpetual motion, because it has really 
 been for natural philosophy and it remains even to 
 this day as important in its influences, especially in 
 
S) 
 
 THE CONSER VA TION OF EN ERG Y. 7 1 
 
 aiding us to simple proofs of important theorems, as, for 
 instance, the notion of alchemy has been in chemistry. 
 We all know that if there had not been a pursuit after 
 the philosopher's stone, chemistry could not yet have 
 been anything like the gigantic science it now is. In 
 the same way, we can say that modern physics could 
 not yet have covered the ground it now occupies had 
 it not been for this experimental seeking for the so- 
 called perpetual motion, and the consequent establish- 
 ment of a definite and scientifically useful negative. 
 
 We notice, then, as a deduction from what I have just 
 explained about the work of these three independent dis- 
 coverers of conservation of energy, that all physical phe- 
 nomena are necessarily transformations of energy of some 
 kind or other ; and we may carry our deduction so far as 
 to say that even that mysterious thing, whatever it may 
 be, the life of plants and animals, is, so far as it is 
 physical, entirely an exhibition of transformations of 
 energy. There are things connected even with life 
 which may not be purely physical. There are other 
 things associated with living beings which, of course, no 
 one in his senses can regard as physical. Even such 
 things as Consciousness and Volition we have abso- 
 lutely no reason, however vague, for classifying, even in 
 the smallest degree, under the head of physics. But 
 everything which is really physical in life and we are 
 beginning to find many things that are so is merely 
 an example of some form of transformation of energy. 
 
 Having said so much, it will be obvious to you that 
 our proper course now will be to consider the principle 
 of transformations, and then inquire in what direction we 
 must seek for more light. We shall find that the ques- 
 tion which is suggested by all these tentative experi- 
 
72 THE CONSERVATION OF ENERGY. 
 
 ments is, What is the law of transformation of energy ? 
 From a given quantity of a given kind of energy, how 
 much of another assigned kind of energy can be pro- 
 duced by a given process ? 
 
 This question breaks up into two. The first is, 
 How much of a given kind of energy can be trans- 
 formed into some other given kind ? And then there 
 is a second question : When you have got so much of 
 it transformed, to how much of the other kind will it 
 correspond ? That is the question of equivalence again. 
 I have already discussed that, so I confine myself now 
 to the first question. The first question fully stated 
 is : Given a certain quantity of energy in one form and 
 under given conditions, how much of it can you, by 
 means of a given kind of apparatus, convert into some 
 other definitely assigned form, the rest being either 
 untransformed, or transformed in whole or in part into 
 some third form ? Now, you will see at a glance that 
 there is something very important under this. Just think 
 for a moment of the enormous amount of waste which 
 is known to take place in an, ordinary steam-engine. 
 In the very best engine, even if it were theoretically per- 
 fect, and working at ordinary ranges of temperature, it 
 has been satisfactorily demonstrated that only some- 
 where about one-fourth very rarely so much as that, 
 but at the best about one-fourth of the heat which is 
 actually employed is converted into work ; that is to say, 
 three-fourths of the coals, or three-fourths of the heat 
 employed, are absolutely wasted under the most favour- 
 able circumstances. Now, what is it that determines 
 this ? Why is it that if I have a quantity of work or 
 potential energy I can convert the whole of it, if I 
 please, into heat ; but when I have got it converted into 
 
THE CONSER VA TION OF ENERG Y. 73 
 
 heat, I cannot convert the heat back again, except in 
 part, into the higher form of work or potential energy ? 
 The answer is included entirely in that word ' higher! 
 which I have just used. When you are converting energy 
 from the high form into the low, you can carry out 
 the process in its entirety, but when it comes to be a 
 question of the reversal going up-hill as it were then 
 it is only a fraction, in general (even under the most 
 favourable circumstances) only a small fraction, of the 
 lower kind of energy which can be raised up again into 
 the higher form. All the rest sinks down still lower in 
 the process. When you have got it low already, and 
 when you are to elevate part of it and transform it into 
 a higher order, you must inevitably still further degrade 
 a large part of it ; in general the larger part of it. 
 This, as we shall find later, is one of the most impor- 
 tant scientific discoveries ever made : having most 
 stupendous bearing on the future of the whole visible 
 Universe. 
 
 I shall conclude this lecture by showing some 
 examples of conservation of energy with the apparatus 
 before me. I shall necessarily at the same time give 
 some illustrations of transformation of energy, inde- 
 pendent altogether of the particular physical experi- 
 ments which are employed for the purpose. I am 
 merely giving you these experiments as illustrating 
 conservation of energy, and incidentally, in addition, 
 transformation and dissipation 'of energy, so that we 
 are not concerning ourselves with what is the branch 
 of physical science to which any particular experiments 
 belong, but simply with how far the experimental results 
 help to illustrate the transformation. 
 
 Take, then, first of all, the simplest form the case of 
 
74 THE CONSER VA TION OF ENERG Y. 
 
 an ordinary pendulum. When the pendulum is vibrating, 
 there is constantly going on transformation of energy of 
 the very simplest kind transformation from the poten- 
 tial form which I give it by drawing it aside (and there- 
 fore lifting it), and which it gradually loses as it falls 
 back, getting more and more kinetic energy instead, until 
 at the middle of its course, when it is moving fastest, 
 it has its greatest amount of kinetic energy, having lost 
 for an instant all its potential energy. Then it gra- 
 dually loses the kinetic energy as it is climbing up 
 again, and regaining potential energy, then the energy 
 is all potential, then it becomes kinetic again, and so on. 
 Of course if there were no air-resistance, and if the stand 
 itself were absolutely rigid, and the cord supporting the 
 mass flexible and inextensible, this process would go on 
 absolutely for ever. It would be perpetual motion, but 
 it would not be the perpetual motion. Remember the 
 distinction there. Perpetual motion is simply a state- 
 ment of Newton's First Law of Motion. All motion 
 is perpetual until force interferes to alter or modify it. 
 But this is not the perpetual motion, because, although 
 under the favourable circumstances I spoke of just now, 
 the pendulum would remain for ever moving with the 
 same quantity of energy it has at present, yet it could 
 not help you to drive machinery, except at the expense 
 of that energy. It cannot drive anything else without 
 losing part of its own energy, and when that occurs, the 
 case does not come under the head of what is called the 
 perpetual motion, although, when there is no drain upon 
 it, it may be a perpetual motion. 
 
 Now, as we know by experience that this vibration 
 will not go on for ever, let us consider why it is that its 
 energy is gradually being lost. What becomes and, 
 
THE CONSERVATION OF ENERGY. 75 
 
 according to the principle of conservation of energy, we 
 ought to be able to trace it what becomes of all the 
 energy I gave it at first ? Well, we see in a short time 
 that it is communicating motion to the air around it ; 
 every time that it vibrates backwards and forwards 
 it sends alternately a wave of compression and one of 
 dilatation through the air of the room. These waves do 
 not sufficiently rapidly succeed one another to produce 
 an impression upon our sense of hearing, but they are 
 sufficient to agitate the air of the room. They are pro- 
 pagated through the air of the room with the velocity of 
 sound, and they are gradually frittered down into heat 
 because air is not a perfect fluid. Because then there 
 is something producing effects akin to those of friction 
 amongst its particles, these waves are gradually rubbed 
 down into heat, and if we had a sufficient number of 
 such pendulums set into vibration to begin with, and 
 all sufficiently resisted by the air, we should be able to 
 warm the air of the room, no doubt to an extremely 
 small extent, but still so that the quantity of heat 
 produced should be precisely equivalent to the quantity 
 of energy which you had communicated to the pen- 
 dulums at starting. But then this suggests another 
 question. At present the pendulum, hanging at rest, 
 has no potential energy, that is, if the string cannot be 
 cut. It has at present potential energy if you can cut 
 the string, because it will drop on the table, or at least 
 it will have the power of falling. But suppose the 
 string is absolutely inextensible, and cannot be cut, then 
 we must consider it in this position as having no poten- 
 tial energy at all, because it cannot get down any lower 
 than it is at present. How is it, then, that I can give it 
 energy ? because if there be conservation of energy, and 
 
76 THE CONSERVATION OF ENERGY. 
 
 if we so put it that it has none to begin with, and it gets 
 some, there must be some other energy spent in com- 
 municating it. Now, that leads us to the grand con- 
 sideration of the source of animal energy, because, by 
 pressing the pendulum with my hand, and thus elevat- 
 ing it, I must have done work, for I have exerted a 
 pressure through a certain space. Work has been done, 
 and therefore something has been expended in my body 
 for the purpose of producing it. This raises the ques- 
 tion of how the animal supplies the work ; and the 
 further one, in what form does the animal get the work 
 supplied to it, which it is constantly giving out even 
 when in repose ? Of course you can at once see that it 
 must be in some way or other connected with food. 
 That, then, will lead us, in another lecture, back to the 
 consideration of whence the food derives its energy, and 
 so on in succession. So you see that even so simple an 
 experiment as setting this pendulum in vibration leads 
 us to a train of consequences, both back and forward, 
 in reasoning, which might well occupy us for a whole 
 series of lectures. Nothing is better calculated to show 
 at once the profundity of Nature's secrets, and the firm 
 grasp we have already taken of some of them, than an 
 example like this so simple and yet so complex. 
 
 Instead of taking the case where the motion of the 
 air is not capable of being perceived by the ear, let us 
 take a case in which we use a special instrument for the 
 purpose of communicating vibrations to the air in such 
 a form that the ear can seize them. If I were to take 
 this tuning-fork and strike it against the table, or start 
 it in any of the ordinary ways, and it were not provided 
 with this sounding-board, the amount of surface which 
 it presents to the air is so slight that the amount of 
 
THE CONSER VA TION OF EN ERG Y. 77 
 
 energy which it would spend in a given time in the form 
 of sound would be exceedingly small ; and therefore 
 the sound would be hardly audible at any considerable 
 distance. But when we furnish it with a resonant 
 cavity, as it is called, such as this, every part of which 
 is set in vibration by the motion of the fork in exactly 
 the same period as the fork ; and when, moreover, the 
 dimensions of this cavity containing air are exactly 
 adjusted, so that when it is set in vibration, it tends to 
 vibrate in exactly the same time as the fork, then we 
 have got a sensitive apparatus which enables us, as it 
 were, to lay hold^of the air, and to dissipate or spend at 
 a very great rate the energy which we give to the fork. 
 The pendulum here spends it at a very slow rate, but in 
 this fork we have applied our knowledge of physics 
 so to construct an apparatus as to make it spend its 
 energy or communicate it to the air as rapidly as pos- 
 sible. We have it now in the form of sound affecting 
 our ears, but you will notice that the sound gradually 
 dies away. The vibrations of the tuning-fork die away 
 far faster than those of the pendulum, because if you 
 will give out the energy at a great rate, the original 
 stock can last only for a short time. The greater the 
 rate at which you give it out, the shorter the time for 
 which it will last. But there is another cause in this 
 case for the very speedy cessation of the sound. The 
 greater part of the energy which I gave to the tuning- 
 fork by muscular work done in forcing these prongs 
 asunder for a moment, the greater part of that energy 
 is spent in heating the body of the fork itself. Steel- 
 however startling this may appear to some of you is 
 exceedingly imperfect in its elasticity. When a steel 
 bar, such as this, is rapidly changing its form, there is 
 
78 THE CONSER VA TION OF ENERG Y. 
 
 an enormous amount of internal friction, and thus is 
 consumed a great part of the energy which is given to 
 it, so that only a part of the energy originally communi- 
 cated is given back in the form of sound, even with the 
 help of the resonant cavity. 
 
 To take another instance. I have got a galvanic 
 battery under the table, and it is connected with a 
 certain electrical apparatus. Now, whenever I allow 
 the electric current to pass through this apparatus, 
 there is for the moment a certain quantity of zinc con- 
 sumed, or, as we may put it, a certain quantity of 
 potential energy in the battery has been converted into 
 the kinetic energy of a current of electricity. That 
 current of electricity passes round some yards of copper 
 wire, coiled round a bar of iron or a number of fine 
 iron wires which are standing vertically inside this 
 apparatus. The moment the current passes, these iron 
 wires are converted into magnets, but, in consequence 
 of the conservation of energy, while this is going on 
 they weaken the current. The current of electricity 
 becomes weaker in the act of making the magnet, 
 but the moment the magnet springs into existence it 
 again is weakened, because, from the necessities of 
 its position, its mere coming into existence necessitates 
 the passage of a new current of electricity in another 
 coil of wire which surrounds this externally. So that 
 here are a number of transformations : First, we have 
 a certain amount of zinc dissolved, i.e. a certain amount 
 of potential energy lost ; then a certain current of 
 electricity produced in consequence ; then that current 
 of electricity weakened by producing magnetism in 
 certain iron wires ; then the magnetism of these iron 
 wires re-acted upon to produce a new current in 
 
THE CONSER VA TION OF EN ERG Y. 79 
 
 another set of wires ; and finally, we can use that 
 induced current, as it is called, to produce heat, or light, 
 or sound. Let us try it, for instance, in such a form as to 
 produce heat. Every time you hear that click [of the 
 contact-breaker], a fresh amount of zinc has been dis- 
 solved, and in consequence that series of transforma- 
 tions I have just described has taken place. You will 
 notice that the zinc is burning, though without almost 
 any development of heat, in the battery, but we can 
 have the fire wherever we please. We have no heat, at 
 least nothing to speak of, in the battery. The heat that 
 would be produced by the dissolving of the zinc is not 
 developed inside the battery at all ; if we had a couple 
 of Atlantic cables here, between the battery and this 
 apparatus, we should be able to produce it at a distance 
 of 3000 miles from the place where the fire burned. In 
 order to show that heat is produced largely in such a 
 case as this, my assistant will hold a piece of paper 
 between the poles. [You see it is at once ignited.] 
 You will notice that the burning of the zinc is below 
 the table, but it might have taken place 3000 miles off 
 if we had had good enough conductors. There you see 
 it has at once produced a development of heat sufficient 
 to inflame the paper. Now, I may easily alter this in 
 a striking manner. Use the same amount of zinc as 
 before, or as nearly as possible the same amount of zinc, 
 but instead of the spark being a quiet one, make it 
 noisy and luminous, as you see is easily done by attach- 
 ing the coatings of a Leyden jar to the ends of the 
 secondary coil. Then we shall find that it is not so hot 
 as before (at least so far as the paper test can inform 
 us). Of course it could not be expected to be so hot, 
 because, if conservation of energy be there, and if there 
 
8o THE CONSERVATION OF ENERGY. 
 
 is a certain quantity only of energy that the spark can 
 have, and if it be made to spend the greater part of 
 that energy as sound and light, you cannot expect it to 
 have as much heat as before. You see it now im- 
 mensely brighter than before, and accompanied by a 
 sharp crack, but we might go on with the experiment 
 indefinitely, and never set the paper on fire. 
 
 This is a very excellent instance of multifold trans- 
 formations, and furnishes also, as you have seen, a rough 
 illustration of conservation. 
 
LECTURE IV. 
 
 TRANSFORMATION OF ENERGY. 
 
 Experimental Illustrations Heating of wires, and decomposition of water, by 
 a Galvanic current Electro-magnetic Engine Rotating Disc Magneto- 
 electric Machine Induction-Coil and Geissler Tube Higher and Lower 
 Forms of Energy. Work transformed wholly into Heat Only a portion 
 of the Heat can be reconverted into Work. Carnot's Cycle of Operations 
 and his Reversible Cycle. Effect of pressure upon Ice. 
 
 IN my last lecture I showed you how, mainly by 
 Joule's grand experiments, it had been conclusively 
 demonstrated that conservation holds for every form of 
 energy, and therefore that all physical phenomena con- 
 sist in mere transformations of energy. There cannot 
 be a destruction or creation of energy. All that we 
 can have is a modification or transformation of it ; and 
 therefore we must to-day consider more fully the laws 
 of such transformation. I shall begin the consideration 
 of them by taking one or two experiments, and point- 
 ing out in each of them the various forms in which the 
 energy appears, how it was first introduced into the 
 apparatus, under what successive forms it passed through 
 the various parts of the apparatus, and in what final 
 forms it was thrown out. 
 
 Galvanic Battery with stout copper terminals. The 
 first and simplest experiment of this kind is the pro- 
 duction of heat directly by chemical combination. As 
 in all or most of the experiments I am about to show, 
 
 F 
 
82 TRA NSFORMA TION OF ENERG Y. 
 
 I intend to begin with a galvanic battery, I may say a 
 word or two as to the form in which its energy appears. 
 The energy in the battery consists mainly in the fact 
 that we have zinc which is capable of being burned, 
 as it were, by being dissolved in dilute sulphuric acid. 
 Now, if we were to burn the zinc, as can easily be done 
 by simply allowing it to dissolve (that is, by not taking 
 the precautions we have here taken against its dissolv- 
 ing without permission in the sulphuric acid), we should, 
 simply in consequence of the potential energy which is 
 lost by the zinc and the acid when they combine, have 
 a certain amount of heat generated by their combina- 
 tion, and this would be developed in the cell of the 
 battery. But instead of permitting this, we can cause 
 the combination to take place without almost any 
 development of heat. We can have practically all of 
 it in the form of some other manifestation of energy. 
 We can have it in the form, for instance, of current elec- 
 tricity ; and we can employ the kinetic energy of that 
 current for the purpose of producing various other forms 
 of energy by suitable transformations. In consequence 
 of the amalgamation of the zinc, and the other precau- 
 tions taken in the cells of the battery, very little com- 
 bination goes on in this battery until the circuit is 
 closed, as it is called ; but as soon as we close the 
 circuit, by joining together the terminal wires, a current 
 of electricity passes. A current of electricity is now 
 passing through the circuit, and chemical action (both 
 decomposition and combination) is going on to exactly 
 the same extent in every one of the cells. But the 
 chemical action now going on is attended with the 
 development of a large quantity of heat in the cells, 
 almost precisely the same amount of heat as would have 
 
TRANSFORMA TION OF ENERG Y. 83 
 
 been developed if we had dissolved the same quantity 
 of zinc in the sulphuric acid without any production of 
 electricity at all ; the reason being that the conducting 
 power of this wire which I have for the moment used to 
 close or complete the circuit is so great that the small 
 resistance it offers to the electricity scarcely fritters any of 
 the electricity down into heat. The heat which is equi- 
 valent to what would be produced by the direct burn- 
 ing of the zinc, is all or almost all produced in the cells 
 themselves, because it is in them that the current suffers 
 resistance. But if I interpose in the path of the elec- 
 tricity an imperfect conductor, which shall resist a great 
 deal more than the copper wire, or even than the cells 
 themselves (as I do by inserting in the circuit a long 
 fine iron wire), then you notice that we get the heat (which 
 is really due to the chemical action taking place in the 
 cells), we get that heat produced in another locality 
 altogether, and we could have transferred that locality 
 as far away as we pleased, if we had simply made our 
 copper wires thick enough and long enough. By simply 
 making them Jhiqk enough, so as to waste as little as 
 possible~6Tthe kinetic energy of the current electricity, 
 by friction" on" tHe way, we should have kept it all or 
 nearly all for the purpose of developing as far as we 
 please from the battery the heat really due to the com- 
 bustion there. 
 
 Voltameter introduced in circuit. Instead of using 
 the current electricity for the purpose of producing 
 heat, let us endeavour to ascend again from the kinetic 
 energy of the current to potential energy of combus- 
 tibles. Remember that it was the chemical potential 
 energy of combustibles which we had in the battery to 
 begin with. By allowing the zinc to dissolve, we got 
 
84 TRANSFORMA TION OF ENERG Y. 
 
 our current electricity, and now we shall use that cur- 
 rent for pulling asunder two substances in chemical 
 combination. We shall use it simply for the purpose 
 of decomposing water. By causing the current to pass 
 through a vessel of water, you notice that we cause 
 bubbles of gas in large quantities to ascend from the 
 ends of the conducting wires ; and we have the kinetic 
 energy of the current spent entirely, or almost entirely, 
 in pulling asunder, against their chemical attraction, the 
 particles of oxygen and hydrogen which form the water. 
 You see that a quantity of the water is being decom- 
 posed, for you see how the gas is bubbling up through 
 the water from the end of this collecting tube. Now, 
 supposing there to have been no loss during the opera- 
 tion no frittering down of the electricity into heat 
 but that the whole energy of the electric current has 
 been spent in decomposing the water, then the potential 
 energy of the separated oxygen and hydrogen which I 
 collect in this way should be precisely equivalent to the 
 amount of potential energy which was consumed in the 
 battery, or rather was there transformed into the energy 
 of the current. In order to show (with as little risk as 
 possible) that there is a large amount of potential energy 
 in these mixed gases, all we have to do is to employ 
 them to produce froth in the form of a multitude of 
 small soap-bubbles blown with the mixture. By apply- 
 ing a lighted match, we shall be able to produce from the 
 potential energy of the mixed gases a violent explosion, 
 which of course represents a certain amount of energy. 
 That explosion gives you light, heat, and a very loud 
 sound. The sum of all these energies taken together, 
 provided nothing has been lost during the process 
 that nothing has been frittered away (by breakage of 
 
TRANSFORMA TION OF ENERG Y. 85 
 
 the mortar, for instance) will represent precisely the 
 amount of energy corresponding to the amount of zinc 
 which has been dissolved during the operation. You 
 notice that here we have now in another form and a 
 form which affects the air more than any of the other 
 forms of energy we have used the energy which ought 
 to have been developed in the form of heat by the 
 combustion of the zinc, but was not, because we had 
 electricity in the place of it ; then, in place of that elec- 
 tricity, we had work done in overcoming the chemical 
 attraction of oxygen for hydrogen ; then we had the 
 mixed gases, which as soon as we pulled the trigger, as 
 it were, by applying the lighted match, gave us back 
 our energy in another kinetic form, or as a mixture of 
 several kinetic forms. 
 
 Electro-magnetic Engine. You had in the voltameter 
 current electricity produced by the battery, and em- 
 ployed for the purpose of producing potential energy, by 
 separating the particles of a chemical compound. But 
 we can produce potential energy by the help of a battery 
 by another and somewhat simpler method. Suppose 
 we employ the current of electricity produced by the 
 same battery, for the purpose of setting an electro-mag- 
 netic engine at work. (We are not at present concerned 
 with the details of construction of the engine.) For this 
 purpose we do not (at least with the engine before you) 
 require anything like so powerful a battery as we used 
 for the rapid decomposition of water. Two, or at most 
 three, cells will be sufficient for our present purpose. 
 You notice that the current is now producing motion of 
 machinery, and has actually raised a weight not by 
 any means a great one, but still the fact remains that a 
 certain mass has been raised against the earth's attrac- 
 
86 TRANSFORMA TION OF EN ERG Y. 
 
 tion to a certain height above its surface ; and you can 
 easily see that, if the experiment succeeds through a 
 space of three or four feet, as it has- now done, it would 
 equally succeed (if we kept the engine working long 
 enough) in enabling us to raise the weight, by proper 
 mechanical adjustments, to any height whatever. Now, 
 let us consider what transformation of energy took place 
 as the current of electricity passed round these electro- 
 magnets, being shunted now into one of them and then 
 off it and into the next ; into each when its becoming a 
 magnet will aid the desired effect ; off it when it would 
 tend to hinder it. This is a mere detail of mechanical 
 arrangement, and is effected by different combinations 
 of machinery in different electro-magnetic engines. But 
 we are not concerned with details of machinery ; we 
 confine ourselves to the transformations of energy which 
 are going on during the working of the engine. But 
 from this point of view what takes place here ? The 
 energy of the current is to a certain extent converted 
 into the raising of weights ; that is to say, potential 
 energy is produced in place of the kinetic energy 
 which was supplied from the battery ; but if the current 
 not only drives this machinery but keeps it doing work, 
 then there would not be conservation of energy unless 
 the current itself were kept at a reduced strength, at 
 least while it is in the act of doing work. Now, that is 
 what is found to take place. It is found that while the 
 engine is working, the current is considerably feebler 
 than it is if we were simply to stop the engine, and 
 allow the current to pass without doing any work. This 
 is quite analogous to the case I pointed out to you in 
 a former lecture. When a given quantity of steam is 
 blown through the engine from the boiler into the con- 
 
TRANSFORMA TION OF ENERG Y. 87 
 
 denser without doing any work, we find that the quan- 
 tity of heat which goes into the condenser is larger than 
 the quantity of heat which goes into it while the engine 
 is doing work. In precisely the same way, then, while 
 the current of electricity is employed in actually lifting 
 a weight, or in driving an electro-magnetic engine, the 
 current which is passing along the wire is feebler than 
 before, and corresponds, according to a great discovery 
 of Faraday's, to a less amount of chemical combination 
 (that is, a less rapid consumption of zinc) in the battery. 
 The battery has really less hard work, while driving this 
 electro-magnetic engine, than it would have if we were 
 simply to stop the engine and allow the current to pass 
 and develop heat in the conducting wires and cells. It 
 must do something. The current of electricity always 
 fritters itself down into heat in time, unless you utilise 
 it and change it into a form of energy more useful than 
 heat. But what we find is this, that, though there must 
 of course always be a current passing : or else these 
 iron horse-shoes would not successively become electro- 
 magnets the current is very much weaker when the 
 engine is doing work than when it is not. And it is also 
 found that the weaker the current becomes (the more 
 the current is checked by reflex action, as it were, by 
 the resistance it meets with in doing work), the greater 
 is the percentage of the amount of energy really spent in 
 the battery which is finally converted into useful work. 
 Thus, in order to get an electro-magnetic engine of this 
 kind to do work on a large scale and at a profitable 
 rate, it would be necessary to drive it with enormous 
 rapidity ; for the faster it is driven the greater is the 
 reaction upon the current, and therefore the more is 
 the current enfeebled, and the greater the percentage 
 
TRANSFORMATION OF ENERGY. 
 
 of the driving power which is utilised. And the laws 
 discovered by Faraday and Joule respectively viz., 
 that the strength of the current is directly as the quantity 
 of zinc dissolved per second, and that the heat developed 
 is directly as the square of the strength of the current, 
 show that the efficiency of the engine is directly pro- 
 portional to the weakening of the current. The more 
 the engine weakens the current by reaction, the greater 
 is the fraction of the whole amount of fuel spent which 
 is converted into useful work. 
 
 Many of you are doubtless practically much better 
 acquainted with the subject I am now to mention than 
 I am, and therefore I shall only briefly state that, even 
 if we could succeed in making an engine of this kind 
 work at a very great speed, and thereby obtain the 
 highest efficiency possible ; and if we could, for the 
 purpose of keeping up such a speed, almost wholly 
 get over the difficulties of ordinary friction, which of 
 course become far greater and more serious as the 
 rapidity of the working of the engine increases, even 
 if all this could be done, still, if we calculate the cost of 
 the fuel here, we shall find that such an engine could 
 never economically compete with an ordinary steam- 
 engine, because of the fact that in order to smelt a quan- 
 tity of zinc, an expenditure of about sixty times its 
 weight in coal is required ; while, weight for weight, the 
 coal is far the more powerful fuel, i.e. loses far more 
 potential energy in being burned ; and therefore of 
 course there can be no comparison between the prices 
 of the fuel in the two cases, if the same ultimate amount 
 of work is done. 
 
 Copper disc with multiplying gear. The next case I 
 take is a very curious one. I have got here an arrange- 
 
TRANSFORM A TION OF ENERG Y, 89 
 
 ment (never mind the details) consisting of a driving 
 wheel and multiplying gear, by which I can communi- 
 cate an extremely great velocity of rotation to this 
 copper disc, which is mounted as freely as possible upon 
 well-oiled and well-supported axles. It is, in fact, easily 
 driven at a rate of somewhere about a couple of hun- 
 dred turns per second, if we work the driving handle at 
 the rate of about two turns per second. The disc con- 
 sists of a highly conducting material copper, and it is 
 placed between two pieces of iron which do not touch 
 it, but come very near it. These pieces of iron form 
 part of the armature of a small electro-magnet. Now, 
 the coils of this electro-magnet have at present no 
 current passing through them, and I find that, as you 
 see, there is nothing more easy than to set the disc in 
 very rapid motion indeed. You notice that when I 
 remove my hand, the inertia of the wheel-work is such 
 that the whole goes on turning for a very considerable 
 time. Now notice what the effect will be if, while I am 
 driving it, my assistant suddenly throws the current, 
 even from three cells of a battery, round the electro- 
 magnet. Then I shall be endeavouring to drive the 
 copper disc in the immediate neighbourhood of a strong 
 north pole on the one side of it, and an equally strong 
 south pole on the other. Although there is no contact 
 nothing of what we ordinarily call friction you will 
 see that this acts exactly like a friction brake of very 
 great power. There ; you observe the instantaneous 
 stoppage, and you also see that, strive as I may, I can 
 scarcely move' the driving handle. With such battery 
 power as that, it is utterly impossible for any one man 
 to drive the disc fast ; it would require perhaps four or 
 five persons to force it to rotate at even a very moderate 
 
90 TRANSFORMA TION OF ENERG Y. 
 
 speed. If I put on a single cell instead of three, you see 
 that by great exertions I manage to keep the disc 
 rotating at a slow rate for a short time ; but it is only 
 by the expenditure of a very considerable amount of 
 labour. I could keep it going perhaps for a few minutes, 
 but there is no necessity for pushing the trial further. 
 Now comes the question, What have we to show for 
 this ? What necessitates the extraordinary amount of 
 effort that is required in order to keep the disc turning 
 in the magnetic field ? In order that you may see this 
 experiment in another and perhaps a clearer light, I 
 shall take advantage of the fact that, as you saw a little 
 ago, the machinery is capable by its inertia, if once set 
 rapidly in motion, of going on for a considerable time 
 before the motion finally dies out. I start it again, with 
 the same rapidity as before, and you see the almost in- 
 stantaneous collapse as soon as the circuit is closed. 
 We have in fact a friction brake acting without contact, 
 and to force that disc to move rapidly in the neighbour- 
 hood of the magnet requires an enormous expenditure 
 of work. Now comes the question, Where does this 
 work go to ? Suppose that in spite of this enormous 
 resistance to the motion of the disc, we were to expend 
 work in turning it. The answer must simply be this, that 
 the whole, or almost the whole of the work so spent 
 goes to heat the disc : and that, simply by persistently 
 turning it under these circumstances, you can make the 
 copper absolutely red-hot, and, in fact, melt it, if the 
 experiment is carried on far enough, without any con- 
 tact whatever with the iron of the electro-magnet. The 
 mode in which this heat is produced is also very inter- 
 esting. It depends upon induced currents, one of Fara- 
 day's great discoveries. Faraday discovered, as I daresay 
 
TRANSFORMA TION OF EN ERG Y. 9 1 
 
 you are all aware, so long ago as 1831, that when a con- 
 ducting body is made to move in the neighbourhood 
 of a magnet, the relative motion of the two produces 
 currents of electricity in the conductor. Now, when a 
 current of electricity is once produced, we have seen 
 that unless it be diverted to produce work, or potential 
 energy, or some other form of energy, it always in time 
 fritters itself down into heat. If, then, you keep this 
 copper disc moving in the neighbourhood of the magnet, 
 the faster it moves the stronger are the currents pro- 
 duced in it ; and as there is no appliance here to collect 
 these currents, so as to utilise them for any other pur- 
 pose, the currents must fritter themselves away into 
 heat in the copper disc itself. A permanent magnet 
 would have precisely the same effect as our electro- 
 magnet the only reason for using an electro-magnet 
 being that it is so easy to magnetise and demagnetise 
 the soft iron, i.e. virtually to present or withdraw the 
 magnet by the mere making or breaking of contact of 
 two wires. The currents which are generated in the 
 disc, are in such a direction as always to be attracted 
 by the magnet ; or, as it may be more scientifically 
 put, in the words of Lenz, the mutual action between 
 the magnet, and the currents generated by the relative 
 motion of the conductor, always tends to diminish that 
 relative motion. Hence the work constantly required 
 to maintain the rotation of the disc. 
 
 Magneto-electric Machine. Now, still further to illus- 
 trate this part of the subject, I may refer to this magneto- 
 electric engine, which was devised to take advantage of 
 Faraday's discovery just mentioned. Here are a couple 
 of coils of wire with iron cores, which are to be made to 
 move in presence of a bundle of steel magnets. Here 
 
92 - TRANSFORMATION OF ENERGY. 
 
 we have, in a somewhat different shape, the essential 
 features of the engine I have just been using. We apply 
 a certain amount of mechanical work, in order to move 
 these coils in the presence of the poles of the magnets ; 
 and thus have currents developed in them as we had 
 them developed a little ago in the simple copper disc. 
 I am now about to collect these currents for the pur- 
 pose of producing light, instead of allowing them to be 
 frittered down into heat, as in the former apparatus ; 
 and you see that we produce a brilliant spark by 
 simply expending mechanical power or work upon the 
 driving handle, without any battery, without any electro- 
 magnet, or anything of that kind. By simply forcing 
 the conductor to move in presence of the steel magnets, 
 we can develop currents strong enough to produce that 
 brilliant spark. Of course with this little machine the 
 light is on a very small scale, but the engine is acting 
 on precisely the same principle as the magneto-electric 
 machines, driven by steam-power, which have been 
 recently employed with great effect for the purpose of 
 lighthouse illumination. 
 
 Induction Coil with Geissler-tube containing highly 
 rarefied Carbonic Acid. There is only one other illus- 
 trative experiment connected with these to which I 
 shall now advert, and that is another mode of convert- 
 ing work or potential energy into light ; that is, by 
 means of an induction coil, as it is called. I am using 
 with it the battery I have hitherto been employing. 
 We produce a current of electricity by means of it ; we 
 magnetise a bundle of iron wires by the help of that 
 current ; then we break the circuit and stop the current, 
 and the iron wires cease to be magnets. At the instant 
 that they cease to be magnetic they are virtually, as it 
 
TRANSFORMATION OF ENERGY. 93 
 
 were, suddenly pulled away to an infinite distance. Now, 
 this coil (consisting of a very long conducting wirf^ is in 
 the immediate neighbourhood of the bundle of iron wires. 
 When they become magnetic, it is as if a powerful magnet 
 were suddenly inserted in the coil. When they cease to 
 be magnetic, it is as if the magnet were instantaneously 
 withdrawn. In either of these cases, we have the 
 development of an electric current in the conducting 
 coil. Now, instead of driving that current through a 
 very small space of common air, as I did in the case of 
 the magneto-electric machine, I will drive it through a 
 considerable length of the contents of a highly exhausted 
 receiver. I do this for a particular reason, which will 
 appear as soon as we have got the room darkened. 
 You now notice the exquisite luminous effect produced 
 by resistance : but observe especially this peculiarity 
 about it, that it remains persistent for a certain time 
 after the discharge has been interrupted. You see at 
 once that the discharge has ceased, by the disappearance 
 of the purple and the blue light near the ends of the 
 tube ; while the olive green light which is in the wider 
 parts of the apparatus remains for a time visible, and 
 gradually dies away. It has scarcely yet, as it were, 
 cooled. It presents, except as to colour, exactly the 
 appearance of a heated body cooling. This remark- 
 able effect then, though due primarily of course to the 
 current, gives us a curious instance of a body which, 
 when agitated by the passage of the current, can convert 
 its energy into light, and part with it in that form. There 
 is in fact scarcely any radiation of dark heat from that 
 glowing and cooling body. I interpolated that experi- 
 ment just now, not because it has any direct connection 
 (except as to the exciting cause, the battery) with what 
 
94 TRANSFORMA TION OF ENERG Y. 
 
 we have had before, and shall have immediately after it ; 
 but because I had the apparatus ready, and it was as 
 well to show the experiment while it was at hand. 
 
 In all these cases you will have noticed that there 
 has been a transformation sometimes many transfor- 
 mations in succession ; but there is one law of nature 
 which we notice in the case of all these transformations. 
 Some kinds of energy are of a higher order than others, 
 and if you begin with one of the higher orders, you can 
 get from it any of the others, and in general you can 
 transform almost the whole of it into any of the others 
 you please ; but when you begin with one of the lower 
 forms, the reversal of the process is attended by extra- 
 ordinary difficulties. The lines 
 
 . . . facilis descensus Averno ; 
 noctes atque dies patet atri janua Ditis : 
 sed revocare gradum, superasque evadere ad auras, 
 hoc opus, hie labor . . . 
 
 seem almost to have been written by one who antici- 
 pated our knowledge of the laws of the transformation 
 of energy. 
 
 We come then to the question of the raising of 
 energy from lower to higher forms, which is the only 
 one which presents much difficulty ; and if we thoroughly 
 understand upon what conditions the utmost transforma- 
 tion of heat into work depends, and how it is that at best 
 only a small fraction of a given quantity of heat can, 
 under the most favourable circumstances, be converted 
 into work, then we shall have no difficulty whatever in 
 seeing that laws of a similar kind, although not perhaps 
 precisely the same, must hold for every other transfor- 
 mation from one form of energy to a second, espe- 
 cially if the second be the higher form of the two. Now, 
 
TRANSFORMATION OF ENERGY. 95 
 
 the ordinary conversion of work into heat you may see 
 illustrated in the most direct form in manifold ways. 
 Savages, for instance, procure a light by rubbing two 
 pieces of dry wood together, or still better by using a 
 piece of hard wood to bore a hole in a soft piece. Any 
 of us can effect that operation, and set the pieces of 
 wood on fire, by applying long enough and with suffi- 
 cient rapidity and pressure a sort of drilling motion. It 
 is quite easy, by the expenditure of a little mechanical 
 energy, to set fire to both pieces of wood. That is 
 merely of course an improvement upon the apparatus 
 used by the savage. When we stir or churn, or any- 
 how rapidly agitate a mass of water, we find that 
 the amount of work we spend upon it is at first con- 
 verted into actual or kinetic energy of the moving water. 
 You see it rotating round as you stir the vessel ; but if 
 you leave it to itself, you see that its rotation gradually 
 slackens until it comes finally to rest. In such a case, it 
 is found that the whole of the work spent upon the 
 water has been ultimately converted into heat. When- 
 ever you apply work to the production of heat by 
 friction, you have an apparatus perfect enough to get 
 the whole of the work transformed into heat. It may be 
 that part of the energy is originally not in the form of 
 motion, as when part of the surface of. rotating water 
 is raised above its mean level, but this potential energy 
 also gets frittered down into heat by degrees. It may 
 be also that, even in ordinary friction, even in such a case 
 as the friction of sand-paper against a piece of wood, the 
 first thing produced by the friction, or rather by the work 
 spent in friction, consists of electric currents in the im- 
 mediate neighbourhood of the place where the rubbing 
 is effected. We have something very similar to that, 
 
96 TRANSFORMATION OF ENERGY. 
 
 although on a more delicate scale, in the case of an 
 ordinary friction electrical machine. There is no doubt 
 that the electricity there is produced by something very 
 closely resembling ordinary friction, although it may be 
 something intermediate between it and contact ; but this 
 leads us to the supposition that it may be possible that 
 in many cases of what appears to us to be downright 
 friction, perhaps even (as Sir W. Thomson says) when 
 actually carried to the extent of abrasion of particles of 
 the two bodies which are rubbed on one another, there 
 may be, first of all, the production of electric currents 
 to a certain extent, and that these currents may be 
 almost immediately frittered down into heat by the 
 resistance or bad conducting power of the two rubbing 
 bodies ; so that in such cases work spent in friction 
 may not immediately produce heat But there is no 
 question whatever that whether heat be immediately 
 produced or whether it is produced mediately, through 
 electric currents, we can convert the whole of the amount 
 of work spent in friction into heat. 
 
 Then in the same way we know that, by hammering 
 a horse-shoe or other small piece of iron on an anvil, a 
 skilful smith can without much trouble raise it to a dark 
 red heat. The work spent in producing these im- 
 pacts is almost entirely converted into heat, and this 
 mainly in the piece of iron to which he applies his 
 blows. And you will see something of the same kind, 
 though on a grander scale, in artillery practice. When- 
 ever the huge projectiles of the modern great guns have 
 been employed for the purpose of penetrating armour 
 plates, though a great part of their energy has no doubt 
 been spent in actually penetrating the thick iron plate, 
 yet at the same time there is an immense flash of light, 
 
TRANSFORMA TION OF ENERG Y. 97 
 
 accompanied by heat and various gases produced from 
 the two metals by actual fusion and evaporation, all 
 taking place at the instant of the impact, and corre- 
 sponding to portions of the work transformed. In these 
 cases, then, there is no difficulty whatever in getting the 
 work converted directly into heat. 
 
 But we now come to the question how to get heatj ; 
 converted into work, and here our difficulties begin. 
 Even in the best steam-engine, we cannot convert into 
 useful forms more than between one-fourth and one-third 
 of the heat which is employed. 
 
 In treating of this subject, I must introduce an ad- 
 vance in scientific method which was not known to men 
 of science till within the last thirty years, although it 
 was published in 1824; the great work of Sadi Carnot, 
 a work of which it is impossible to speak in suffi- 
 ciently high terms in such a series of lectures as I am 
 giving. I need only say that without this work of Car- 
 not's, the modern theory of energy, and especially that 
 branch of it, which is at present by far the most im- 
 portant in practice, the dynamical theory of heat, could 
 never have attained in so few years its now enormous 
 development. Carnot's claims to recognition are of an 
 exceedingly high order, because they depend not merely 
 upon his method : which is one of startling novelty and 
 originality, and is not confined to the subject of heat 
 alone : but upon the fundamental principle on which he 
 based his mode of comparing the heat employed with 
 the work procured from it. Every reasoner (who has 
 applied himself to the subject of heat since Carnot) has 
 gone right, so far as he attended to Carnot's principle, 
 but has inevitably gone wrong, when he forgot or did 
 not attend to it. The fundamental blunders of Seguin 
 
 G 
 
98 TRANSFORM A TION OF ENERG Y. 
 
 and Mayer and various others whose admitted claims 
 I have pointed out in a former lecture are almost 
 entirely due to their ignoring the great principle laid 
 down by Carnot so early as 1824. 
 
 Carnot's work is upon the Motive Power of Heat. It 
 forms no inconsiderable portion of Sir W. Thomson's 
 many scientific claims that he recognised at the right 
 moment the full merits of this all but forgotten volume, 
 and recalled the attention of scientific men to it in 1848 ; 
 pointing out, among other things, that it enabled us to 
 give, for the first time, an absolute definition of Tempera- 
 ture. Although Carnot (seemingly against his own con- 
 victions) 1 reasons on the assumption that heat is matter, 
 and therefore indestructible ; and although, in conse- 
 quence, some of his investigations are not quite exact, 
 his work is of inestimable value, because it has fur- 
 nished us, not only with a correct basis on which to 
 reason but, with a physical method of extraordinary 
 novelty and power, which enables us at once to apply 
 mathematical reasoning to all questions of this kind. 
 These then are his two great claims, first, the setting 
 thermo-dynamics upon a proper physical and experi- 
 mental basis ; and, second, in the furnishing us with a 
 means of reasoning upon it which was absolutely new in 
 mathematical physics, and which has been, not merely 
 in Carnot's hands, but in the hands of a great many of 
 his successors, as fruitful in new discoveries as the idea 
 of the conservation of energy itself. 
 
 1 [Note to Third Edition. Since the publication of the last edition of 
 this work Carnot's posthumous papers have been issued, along with a 
 reprint of his great work. They indicate an amount of insight into the 
 true theory, and the proper modes of experiment, truly marvellous even 
 in comparison with the grand advances made in that work itself.] 
 
TRANSFORMA TION OF ENERG Y. 99 
 
 Now, these two grand things which Carnot intro- 
 duced, which were entirely originated by him, and 
 which left him in an almost perfect form, were the 
 idea of a Cycle of Operations, and the further idea of a 
 Reversible Cycle. 
 
 In order to reason upon the working of a heat-engine 
 (suppose it for simplicity a steam-engine), you must 
 imagine a set of operations, such that at the end of the 
 series you bring the steam or water back to the exact 
 state in which you had it at starting. That is what 
 Carnot calls a cycle of operations, and of it Carnot says, 
 then, and only then, i.e. at the conclusion of the cycle, 
 are you entitled to reason upon the relation between 
 the work which you have acquired, and the heat which 
 you have spent in acquiring it. If you were to take, 
 as Seguin proposed, a quantity of steam, and merely 
 allow it to expand, giving out heat in the process and 
 doing work, you have no right whatever to say that 
 the quantity of heat which has disappeared is the 
 equivalent of the work which you have got, because at 
 the end of the operation the steam is in a different state 
 as to pressure and temperature from that in which it 
 was at the beginning. It was saturated steam at a 
 certain temperature, let us say, to start with, but at the 
 end of the operation it may still, if you make proper 
 adjustments, be saturated steam, but it is necessarily at 
 a different temperature, and therefore you cannot tell 
 whether or not it possesses intrinsically the same amount 
 of energy as it did in its former state. You have no 
 right whatever to reason upon the quantity of heat 
 which appears to have gone, as compared with the work 
 which has been done, when your working substance 
 begins in one state and ends in another. But if you 
 
ioo TRANSFORMA TION OF ENERG Y. 
 
 can by any process bring your working substance back 
 to its initial state, then you are entitled to assert that, as 
 it has returned to its initial state, it must contain neither 
 more nor less energy than it did at first, and therefore 
 of course you are also entitled to reason upon all the 
 external things that have taken place during the 
 operation, and to determine the condition of equivalence 
 among them. You now see how completely unscientific 
 was Seguin's reasoning, though his work was published 
 fifteen years after that of Carnot. A similar remark of 
 course applies to Mayer, who was the greater, because 
 the later, sinner in this matter. 
 
 The other grand point with reference to Carnot is 
 this, that he started the notion of a Reversible Engine, 
 reversible not in the ordinary technical sense of work- 
 ing its parts backwards, not in the mere sense of back- 
 ing, but reversible in the sense that, instead of using heat 
 and getting work from it, you can drive your engine 
 through your cycle the other way round, and by taking 
 in work, pump back heat (as it were) from the condenser 
 to the boiler again, a reversing of the whole process, 
 not a mere reversing of the direction in which the engine 
 is driving. Now, Carnot introduced that notion, and 
 he showed by perfectly conclusive reasoning that if you 
 can obtain a reversible engine, it is the perfect engine, 
 i.e. that it is impossible to get an engine more perfect 
 than a reversible one reversible being taken in the sense 
 in which I have just explained it. We see at once what 
 an enormous step is gained, supposing we can establish 
 that second principle, because, as you will presently find, 
 we can settle the conditions of reversibility altogether 
 independently of the nature of the working substance in 
 our engine. You see then that we are not now bound 
 
TRANSFORMA TION OF ENERG Y. 101 
 
 down to a steam-engine, or any one working substance. 
 We are enabled now to state our conclusions in terms, 
 not of the particular engine but, of the circumstances 
 in which the engine works. All perfect engines that 
 is, all reversible engines will do exactly the same 
 amount of work with the same amount of heat, pro- 
 vided their boilers and their condensers be at the same 
 temperatures, and therefore you can define the relation 
 between the whole amount of heat which enters the 
 engine and the utmost amount of it which can be con- 
 verted into work, and this altogether independently of 
 the particular engine, but solely and simply in terms of 
 the temperature of the boiler and the temperature of 
 the condenser. These, then, are the grand claims which 
 Carnot has in Thermodynamic Science. 
 
 Now, in order to make it intelligible how we can 
 have a reversible engine at all, in this sense, it will 
 be necessary for me to go through a series of ima- 
 ginary operations explanatory of the nature of Carnot's 
 reasoning. Besides, if you once thoroughly understand 
 this, it gives the key to an enormous number of new 
 physical facts and properties of matter which, before 
 we learned from Carnot the correct method of rea- 
 soning, we might well have despaired of ever being 
 able to understand, at least in their true physical inter- 
 dependency. 
 
 Digression. Beam of ice, supported horizontally at the 
 ends, with a fine wire, stretched by weights, hung over it. 
 Before I go into a description of it, however, I may call 
 your attention to an experiment which has been going on 
 for some time in your presence, and whose result, in one 
 of its many forms, was first predicted from those very 
 principles of Carnot's. What is its direct connection 
 
102 TRANSFORMA TION OF ENERG Y. 
 
 with them I shall explain in another lecture. In the 
 meantime, the experiment is nothing more than this : 
 Take a block or bar of ice, supported horizontally : lay 
 over it a fine wire, and append equal weights to the two 
 ends of the wire. The wire, as you notice, has gradu- 
 ally, by the action of the weights, sliced through the 
 bar of ice, and there are two such slices of which you 
 can see the planes through the slab by the distortion of 
 the air bubbles. The wire has actually passed through 
 the ice in two planes parallel to one another, and yet 
 the ice is now probably stronger at these two places 
 where it has been cut than at any other place through- 
 out the block. The statement of observed fact is, that 
 as the wire was forced by the weights into the ice, the 
 pressure melted the ice, making it colder, so that the 
 water produced, passing round the chilled wire, and 
 being thus relieved from pressure, froze again. Still the 
 ice goes on melting in front of the wire, in consequence 
 of the pressure, and the water formed continually trickles 
 round it and freezes again. In that way the ice-block 
 is reunited, and you would see no trace whatever of this 
 interruption of it were it not for the fact that this 
 particular mass of ice was originally full of air bubbles, 
 and some of these bubbles having been permitted to 
 escape during the passage of the wire, have left a trans- 
 parent stratum which shows you where each section has 
 been cut. Ice, in fact, being a substance which melts 
 under sufficient pressure, behaves absolutely like a 
 viscous or plastic substance, for it melts (and contracts) 
 wherever the pressure is sufficiently great, thereby 
 handing on the pressure to another part, and in so 
 doing becoming solid again in its new form. Thus 
 Forbes' Viscous Theory of Glacier-Motion, propounded 
 
TRANSFORMA TION OF ENERG Y. 103 
 
 in 1843 as a statement of observed facts, is seen to be 
 but the necessary consequence of a remarkable physical 
 property of ice. 
 
 Now, come to the consideration of this method of 
 Carnot's. I take an ideal engine, because that is quite 
 sufficient for the purpose of our reasoning. If our rea- 
 soning be correct, it is only a question of greater com- 
 plexity to apply it to an engine of a more elaborate 
 character. Suppose then we have the cylinder of a steam- 
 engine we shall dispense with the boiler altogether, 
 because we shall, for the sake of simplicity, always 
 make the cylinder its own boiler. Let us have in the 
 cylinder a small quantity of water, and the piston pressed 
 down so as to be nearly in contact with it. Suppose, 
 then, that our piston and the sides of our cylinder are 
 absolutely impervious to heat. That is another thing 
 we cannot realise, but it will have important bearings 
 when we come to consider what are the conditions of 
 the reversibility of an engine. We shall find in fact 
 that any loss of heat by conduction through the sides 
 of the cylinder is fatal to the reversibility of the engine ; 
 but for all that, in our theoretical reasoning we assume 
 that the sides of the cylinder and the piston itself are 
 perfect non-conductors of heat. We also assume that the 
 bottom of the cylinder is a perfect conductor of heat. 
 These of course are all suppositions which cannot be 
 realised in practice, but they serve to give us a conceiv- 
 able and extremely simple engine to theorise upon. 
 Suppose, then, we have three stands, on any one of which 
 I may place this cylinder. The first of them I call A, 
 the second B, and the middle one C. Now, suppose A 
 to be a body which has a certain defined temperature, 
 S, which is to be the temperature of the boiler. This 
 
104 . TRANSFORMA TION OF ENERG Y. 
 
 body A is supposed to be constantly supplied with heat, 
 so as always to be kept up (whatever happens) to that 
 particular temperature. Then, B, which is to be used 
 as the condenser, is to be kept constantly at a definite 
 temperature T, lower than the temperature, S, of A. 
 The third body is to be used merely for the theory of 
 the operation ; it has really no effect itself. It is simply 
 a non-conductor of heat ; it is in fact a sort of second 
 bottom to be put upon the cylinder when it is not 
 placed either upon the boiler or the condenser. Now, 
 we can commence our operations in any order with this 
 apparatus. The way in which Carnot did it is perhaps 
 not the simplest, but it is historically the more im- 
 portant. We will commence, then, by setting the whole 
 of this apparatus upon the hot body. The effect of 
 this, as the bottom of the cylinder is a perfect con- 
 ductor, is that the hot body begins at once to part with 
 heat to the water inside, under the piston. The water 
 then rises to the temperature 5, and steam begins to 
 form above it. This steam is limited in quantity by 
 the space which is afforded for it, and by the tempera- 
 ture of the body. When as much steam has been 
 formed as is consistent with these conditions, it is called 
 saturated steam corresponding to the temperature S. 
 Now suppose that, when things are in that condition, 
 we allow the steam to expand or the piston to rise 
 (the atmospheric pressure above the piston being easily 
 neutralised by a counterpoise, especially in an imaginary 
 engine), we could employ it to raise weights or do work 
 of some kind or other externally. As it rises notice 
 what takes place. The temperature remains the same 
 as before, but more space is afforded for the formation 
 of steam, and therefore more steam is formed, so that 
 
TRANSFORMA TION OF EN ERG Y. 1 05 
 
 you go on keeping up saturated steam at the pressure 
 corresponding to the temperature, S, of the boiler. As > 
 more steam is formed, more work is done, and more 
 heat is absorbed from the boiler, because latent heat 
 is required for the new steam as it is formed. Then, 
 while things are in that condition the piston having 
 risen say midway up the cylinder put the whole upon 
 the body C. No heat can get into the cylinder now, 
 nor can any escape, for the contents are now completely 
 surrounded by non-conducting bodies. Ih that state, 
 however, the contents have still the temperature of the 
 boiler. Let them still further expand, they will still do 
 work, because fresh steam is formed, but the contents 
 will become colder because of the latent heat required. 
 Let them go on expanding and doing work until they 
 cool down to the temperature, T> of the condenser, and 
 then, while they are in that state, shift the whole to the 
 condenser. There will obviously be no transference of 
 heat. While things are in that condition, suppose we 
 spend work in forcing down the piston a certain way. 
 In doing so we compress the steam, and the contents 
 tend to become hotter, but cannot^ do so, because this 
 body of temperature T is in contact with them ; so that 
 part of the steam condenses, and the latent heat which it 
 gives out is transferred to the cold body. 
 
 With regard to the amount by which you must push 
 down the piston during this part of the operation, Carnot 
 said : Push it so far that you give out to the condenser 
 exactly the same amount of heat as you had taken from 
 the boiler during the first stage of the expansion. That 
 statement, however, is incorrect, and requires modifica- 
 tion, because Carnot argued on the assumption that 
 heat is indestructible. 
 
1 06 TRA NSFORMA TION OF EN ERG V. 
 
 Bearing in mind Carnot's notion of a cycle, we 
 see that the amount by which the piston is to be 
 depressed while the whole stands on the condenser, is 
 to be determined by the condition that when the 
 whole is finally placed on the impervious stand, and 
 the piston pressed home, the temperature of the con- 
 tents shall be raised to 5, the temperature of the 
 boiler. [This complete rectification of Carnot's cycle 
 was given by James Thomson in 1849.] If this be 
 effected, we can transfer the cylinder to the body A, 
 and everything is in the condition from which we 
 started, so that the operation may be repeated as often 
 as we please. 
 
LECTURE V. 
 
 TRANSFORMATION OF HEAT INTO WORK. 
 
 Carnot's Cycle continued. Watt's Diagram of Energy. The Impossibility 
 of the Perpetual Motion is an experimental truth. Conditions of Reversi- 
 bility. Absolute definition of Temperature. Second Law of Thermo- 
 dynamics. Absolute zero of temperature, or temperature of a body 
 devoid of heat. Efficiency of the best steam-engine. Effect of pressure 
 on the freezing point of water. Mechanism of Glacier motion. 
 
 You will remember that at the close of my last 
 lecture I had just given a sketch of the first part of the 
 reasoning of Carnot the most important reasoning that 
 has ever been introduced into the treatment of any part 
 of the dynamical theory of heat. I may briefly recapi- 
 tulate (but in a somewhat improved form) what I then 
 said, in order that there may be no break of continuity. 
 
 The nature of the hypothetical operation which Car- 
 not introduced for the purpose of reasoning on this 
 subject, and only for that purpose, is of this kind. He 
 said Let us have a hot body which is constantly 
 maintained at a certain temperature. Let us have a 
 cold body which is also constantly maintained at a 
 definite temperature lower than the first. Then let us 
 suppose that in addition to these we have a body which, 
 as regards other bodies, is neither cold nor hot, for the 
 simple reason that it is incapable of absorbing heat or 
 of giving it out, a body which is a non-conductor of 
 heat. Then commence your series of operations, not 
 as I did (after Carnot) in my last lecture, but with the 
 
io8 TRANSFORMATION OF HEAT INTO WORK. 
 
 non-conductor. Suppose your cylinder and your piston 
 to be non-conductors, but the bottom of the cylinder 
 a perfect conductor. If you have a quantity of water 
 and steam in the cylinder, both at the temperature of 
 
 (u the cold body, and expend work in pressing down the 
 piston, the contents will become warmer, and some 
 steam will be liquefied. 1 Continue this process till the 
 temperature rises to that of the hot body then transfer 
 the cylinder to it!~ONow allow the piston to rise, the 
 contents remaining at the temperature of the hot body, 
 fresh steam is generated, and work is done. Arrest 
 this process at any stage and transfer the cylinder to 
 the non-conducting body. .- If we now allow the contents 
 further to expand, more work is done, but the tempera- 
 ture gradually sinks. Continue this till the temperature 
 falls to that of the cold body, to which, therefore, with- 
 out loss or gain of heat, it may now be transferred. 
 
 y Next apply work to compress it at the constant tem- 
 perature of the cold body till (by condensation) the 
 contents have become exactly as they were at starting. 
 The cylinder may now be transferred to the non-con- 
 ducting stand, and everything is as it was at first save 
 that some heat was taken from the hot body in the 
 second operation, and heat was given to the cold body 
 during the fourth. Also it is evident that more work 
 has been done during the second and third operations 
 than was spent in the first and fourth, for the tempera- 
 ture, and therefore the pressure, of the contents were 
 
 1 \Note to Third Edition. This statement requires limitation, in order 
 to avoid complications not alluded to in the text. If there be too small a 
 quantity of water, as compared with the steam, pressure will vaporise some 
 of the water, instead of, as is assumed in the text, condensing some of the' 
 steam. See Tait's HEAT, 391.] 
 
TRANSFORMA TION OF HE A T INTO WORK. 109 
 
 greater during the expansion than during the com- 
 pression. Of course you can go over this operation as 
 many times as you please. 
 
 Notice particularly what the peculiarity of the opera- 
 tion is. You must always have the steam or expanding 
 substance, whatever it is, for air or anything else would 
 do equally well, in contact with bodies at its own 
 temperature, or else with non-conducting bodies. If it 
 were in contact with a body which was not at its own 
 temperature, there would be a waste of heat. Heat 
 would pass by conduction from the cylinder to external 
 bodies, and would of course be wasted as regards work. 
 The same would happen if we were to take it from, 
 let us say, the non-conducting body and place it upon 
 the cold body, before we had let it expand far enough 
 to cool down to the temperature of the cold body : we 
 should have some heat conducted away at once without 
 having any good from it. So, throughout the whole of 
 Carnot's operation, it is essential that there should be 
 no direct transfer of heat at all except while heat is 
 being taken in from the hot body or given out to the 
 cold body : the temperature of the contents of the 
 cylinder being in each of these cases the same as that 
 of the body with which they are at the time in contact. 
 
 A remark of great importance must now be made, 
 though it involves somewhat of a digression. You must 
 have noticed how much more easily we managed in 
 to-day's than in yesterday's lecture to lay down the 
 limits for the range of volume of the working substance 
 during each of the four operations included in Carnot's 
 cycle. Yet the only difference in our proceedings con- 
 sisted in the fact that yesterday, following Carnot him- 
 self, we began with expansion at the higher temperature 
 
1 10 TRANSFORMA TION OF HE A T INTO WORK. 
 
 while to-day we have preferred to commence with 
 compression on the non-conducting stand. With the 
 help of a device due to Watt it may be possible to make 
 this point much more easily intelligible. The device I 
 allude to is called the Indicator Diagram, and is even 
 now constantly employed for the purpose of ascertaining 
 the work actually done by an engine, especially that of 
 a steam-ship. 
 
 It is not my business to enter into purely mechanical 
 details, and therefore I shall only say that this diagram 
 is traced out by a pencil attached to the piston-rod of 
 the engine, and therefore sharing its to-and-fro motion ; 
 while it has also a motion in a direction perpendicular 
 to the piston-rod, such that the displacement at any in- 
 stant is proportional to the pressure in the cylinder at 
 that instant. To fix the ideas, suppose the cylinder to 
 be horizontal, and the just-mentioned transverse motion 
 vertical. Then any re-entrant line whatever (lying wholly 
 
TRANSFORMA TION OF HE A T INTO WORK. 1 1 1 
 
 between Op and Ov) may be supposed to be traced, once 
 over in each cycle of the engine, by the pencil P. For 
 reasons to be afterwards explained, I take the curvilinear 
 quadrilateral PP'QQ. Let Ov be the axis of the 
 cylinder, Op perpendicular to it ; and let PM be perpen- 
 dicular to Ov. Then, by our conditions, OM represents 
 the distance of the piston from the bottom of the 
 cylinder ; i.e. the volume of the working substance, while 
 MP represents its pressure, each upon a definite scale. 
 It follows from this, by a mathematical investigation 
 which, though very simple, I must not give in such a 
 lecture as this, that if P be any other position of the 
 pencil, and P' M be perpendicular to Ov, the area of the 
 figure PP M' M is proportional to the amount of work 
 done by the expanding substance while the pencil passes 
 from P to P '. Hence you easily see that the area of 
 the figure PP Q'Q is the excess of the work done by, over 
 that spent on, the working substance ; i.e. the equivalent 
 of the heat which disappears during the cycle. 
 
 Now, by properly regulating the temperature during 
 the cycle, it is obvious that we may make the pressure 
 what we please at each stage of the expansion and con- 
 traction. Hence any closed curve whatever might, by 
 proper arrangement, be made the diagram of energy 
 for a heat-engine. But now note particularly that in 
 Carnot's ideal engine we are carefully restricted to two 
 kinds of operations (direct or reversed), and to two only. 
 Hence the parts of the indicator-curve for each of the 
 four operations in Carnot's cycle belong to two classes 
 of curves, each of which is known, or at least can be 
 experimentally determined, so soon as we know what 
 is the working substance. 
 
 One of these is the curve representing the relation of 
 
1 1 2 TRANSFORMA TION OF HE A T INTO WORK. 
 
 pressure to volume when the working substance ex- 
 pands or contracts without change of temperature. Call 
 this a line of constant temperature PP or Q Q in the 
 diagram. 
 
 The other, PQ or P Q , represents the corresponding 
 relation when the substance expands or contracts in a 
 vessel impervious to heat. This is called, after Ran- 
 kine, an Adiabatic Line. We might conceive Watt's 
 graphical process actually applied to trace out these 
 curves. And it is obvious that we can have one, and 
 only one, of each kind, passing through each given point 
 P in the plane of the indicator diagram. For that point 
 specifies a particular volume and pressure of the work- 
 ing substance (treated as constant in quantity), from 
 which we are to start by one or other of the two pro- 
 cesses I have just mentioned. Also it is obvious that 
 as, in general, the pressure of the working substance 
 will fall off faster as it expands when no heat is com- 
 municated to it, than when its temperature is kept con- 
 stant, of the two lines passing through the point P, 
 that corresponding to constant temperature PP tends 
 less quickly to fall to the line of no pressure Ov, than 
 does the adiabatic line PQ, for equal increments of 
 volume of the working substance. 
 
 You now see that Carnot's process essentially involves 
 a cycle whose boundary (in Watt's diagram) is formed 
 by two lines of equal temperature and two adiabatic 
 lines. But, while these lines of equal temperature were 
 at once specified by the numbers S and T, we had no 
 such definite nomenclature for the adiabatic lines. 
 Hence (so far as an elementary lecture is concerned) 
 the greater simplicity of the method I have to-day used 
 over that originally given by Carnot. To-day's method 
 
TRANSFORMA TION OF HE A T INTO WORK. 1 1 3 
 
 in fact began by taking any point Q in the line of 
 temperature T, thence P was found by an adiabatic 
 line : then P' may be any point in the other given line 
 of equal temperature, and from this the adiabatic gives 
 Q '. The difficulty in yesterday's method arose in speci- 
 fying Q in the third operation, so that we should arrive 
 at a given point P, in the fourth. 
 
 We now come to another point, also perfectly novel, 
 and of importance at least proportional to its novelty. 
 If you think again of the various steps of the opera- 
 tions in Carnot's cycle, you will easily see that it is 
 possible to consider them as performed in exactly the 
 reverse order. Begin, for instance, with the hot body, 
 but do not allow the piston to rise there. Take the 
 cylinder from the hot body when the water and the 
 little quantity of steam above it have acquired the 
 higher temperature. Lift it to the non-conducting 
 body, and then allow the piston to rise. Let it rise till 
 the temperature sinks to that of the cold body ; place 
 the whole on the cold body ; allow it to expand still 
 further, it will be in that case giving out work but 
 absorbing heat : then when it has risen to its former 
 highest point, place it back again on the non-conducting 
 body, force the piston back to the same extent as that 
 to which it rose when (in Carnot's direct set of opera- 
 tions) it was first placed on that body. Everything has 
 taken place in precisely the reverse order to that in 
 which it took place before. Finish then upon the hot 
 body, and press home. From Carnot's point of view 
 you give to the hot body in that final operation precisely 
 the quantity of heat you took from the cold body ; but 
 during the two last operations you are forcing down the 
 piston, while during the two first operations the piston 
 
 H 
 
ii4 TRANSFORMATION OF HEAT INTO WORK. 
 
 was being forced up, but it was always being forced up 
 at.a lower temperature, and therefore at a lower pressure 
 than the temperature and pressure you had to overcome 
 in forcing it home again. And, therefore, in the reverse 
 method of working this engine, you take heat from the 
 cold body and deposit it in the hot body, exactly to the 
 same amount as in the direct operation ; and, on the 
 whole, you now spend as much work as you formerly 
 gained. 
 
 These are the grand ideas which Carnot introduced. 
 Their two distinctive features are, first, the idea of a 
 complete cycle of operations, at the end of which the 
 working substance, whatever it is, is brought back to 
 precisely its primary condition ; a cycle which can be 
 repeated over and over again indefinitely. Secondly, 
 The notion of making the cycle a reversible one, so that 
 you can perform all the operations in it in the reverse 
 order, and instead of taking in heat at any place it may 
 be made to give out that amount of heat, instead of 
 the engine doing work at any place that amount of work 
 can be spent upon it. With these changes in each opera- 
 tion, the whole cycle can be gone over the reverse way. 
 
 Now, Carnot proceeds to reason upon this. Consider- 
 ing heat as a material substance, he says that obvi- 
 ously it has done work in the direct series of operations 
 by being let down from the higher temperature to the 
 lower, just as water does work by being let down through 
 a turbine or other water-engine, in proportion to the 
 quantity that comes down and the height through which 
 it is allowed to descend. We now know that this 
 notion of the nature of heat is erroneous, 1 but still 
 
 1 Carnot, as is now ascertained, had long ago found this out for himself. 
 See note to p. 98. 
 
TRANSFORMATION OF HEAT INTO WORK. 115 
 
 Carnot's reasoning is of the highest value, because it 
 wants only the change of a word or two to render it per- 
 fectly applicable to our modern knowledge of the subject. 
 You see at a glance one point which appears conclu- 
 sively to show that Carnot's assumption was wrong, 
 because nothing is easier than to let the heat down at 
 once without the performance of any work. If you put 
 the hot body into direct communication with the cold 
 body, the same quantity of heat might be allowed to 
 go down from one to the other, and yet give you no 
 work at all. There must be, then, something wrong in 
 that statement of Carnot. We now know what it is ; 
 but let us follow Carnot a little further, and see how 
 much more of what is eminently useful and true he 
 attained even with his false assumption. He carried it 
 further in this way. He said If an engine be reversible 
 (as this cycle of operations has been shown to be), it does 
 as much work as can be got out of a given quantity of 
 heat under the same given circumstances. So that, no 
 matter what you make your engine of, no matter what 
 be the substance which is expanding and contracting, 
 if a certain quantity of heat be let down from a source 
 at a certain temperature through your reversible engine 
 to a sink at another temperature, then the quantity of 
 useful work which can be got from that heat will be 
 absolutely the same. Reversibility is the sole necessary 
 condition of equivalence between two such engines. You 
 will see in an instant what an enormous step this is in 
 physical science. The reasoning here is independent 
 altogether of the properties of any particular substance. 
 We are not dealing with steam, or air, or ether, or any 
 one working substance in particular ; yet we have a 
 crucial test of the perfection of an engine which is abso- 
 
ii6 TRANSFORMATION OF HEAT INTO WORK. 
 
 lutely the same when applied to any working substance 
 and any heat-engine whatever. That test is, if a heat- 
 engine is reversible it is perfect, not perfect in the popular 
 sense, but in a scientific sense ; that is to say in the sense 
 that it is as good as it is possible physically to make it. 
 
 Now the proof that it is so is very easily given, but 
 before I give it I may say a word or two upon a similar 
 but somewhat simpler sort of proof which will prepare 
 you for the reasoning employed, and which bears directly 
 upon the ordinary notion of the perpetual motion. 
 
 We know (of course only by experiment) that in all 
 cases of natural laws, such as the laws of gravitation, and 
 of magnetic attraction, whatever work is spent in moving 
 a body through a certain course in one direction, you 
 get back exactly by letting it return along the same 
 track, always on the supposition that friction is avoided. 
 The reason of this is that these forces depend upon 
 relative position only, and therefore undo, at each stage 
 of an exactly reversed path, precisely the amount of 
 work which they did at the same stage of the direct path. 
 
 A 
 
 Suppose then that there could be two courses, 
 from A to B, by the one of which more work would 
 be spent on the mass than by the other. Let these 
 amounts of work be W and w. I say that if such 
 were the case you would be able at once to pro- 
 duce the perpetual motion. All you have to do is 
 
TRANSFORMA TION OF HE A T INTO WORK. 1 1 7 
 
 to apply frictionless constraint to guide the mass, so 
 that in its ascent it shall travel along the course AwB, 
 and in its descent along BWA. From A to B you 
 have to spend the amount w of work against the 
 forces of the system from B to A these forces refund 
 the amount W. On the whole, after a complete cycle, 
 the mass is restored to A with an amount W-w of 
 energy additional to what it possessed at starting. 
 Well, we have gained something by that, and every 
 time the mass goes round the double course in the 
 direction I have indicated, it gains the difference be- 
 tween the larger quantity and the smaller one, and 
 therefore you can, at the end of each complete cycle, 
 drain that amount off to turn some machine ; to do 
 useful work. If, therefore, there were one way of doing 
 a thing at less cost than another, and if the more costly 
 operation were reversible (in the strict scientific sense 
 above explained), then it would be possible for you 
 under such circumstances to get unlimited amounts of 
 useful work from nothing. Now we know that, so far 
 as experience extends, this is impossible. The multi- 
 plied experiments of some of the most ingenious men 
 who ever lived, Vaucanson and others, were directed to 
 this question. Yet these men, who constructed automata 
 which mimicked, and often copied, the motions and 
 physical functions of living animals, these men were 
 entirely baffled in attempting to get at anything like 
 the perpetual motion. We may say distinctly that all 
 really scientific experiment has led to the conclusion 
 that the perpetual motion in the old sense is absolutely 
 unattainable. 
 
 Well, let us see how this reasoning applies to Carnot's 
 engine. He demonstrates its property by almost the 
 
1 1 8 TRANSFORMA TION OF HE A T INTO WORK. 
 
 same application of reasoning as that which I have just 
 given you for a similar but very simple case. He says 
 that a reversible heat-engine is a perfect one; for, if 
 not, let us suppose there could be one more perfect. 
 Well, you can always use these two engines in conjunc- 
 tion. Let the more perfect engine (i.e. the less costly 
 one) be employed in taking a quantity of heat, conveying 
 it down to the condenser from the boiler, and giving you 
 from it a larger quantity of work than the reversible 
 engine could do. You can now use the reversible engine 
 to pump that heat back again. Every time the heat 
 goes down, it is through the more perfect engine ; every 
 time it is coming up, it is through the worse engine, and 
 therefore it does more work going down than requires 
 to be spent on bringing it up, and thus every time the 
 compound engine makes a complete stroke, or passes 
 through the double cycle of operations, you have an 
 excess of work given by the one part over what has to 
 be spent on the other. Therefore, this is not merely an 
 engine which will go for ever, but an engine which can 
 go on for ever, and besides steadily do work on external 
 bodies. 
 
 That, however, as we have seen, is inconsistent with 
 all our experimental results, and therefore we must at 
 once pronounce the supposition which led us to this con- 
 clusion, viz., that there can be a more perfect engine 
 than a reversible one, to be false. This is Carnot's 
 final proof that (on the assumption that heat is matter) 
 a reversible heat-engine is a perfect engine. It requires 
 very little indeed, as a moment's reflection will show 
 you, to make this reasoning consistent with our modern 
 knowledge of heat. 
 
 We have now to consider the cycle in the light of 
 
TRANSFORMA TION OF HE A T INTO WORK. 1 19 
 
 the conservation of energy, so that if you get work from 
 heat at all, some of that heat must have disappeared in 
 its production, and that, therefore, under no circum- 
 stances if the engine is doing external work at all 
 can the quantity of heat which reaches the condenser 
 ever be equal to that which leaves the boiler. The 
 difference between them, if none has been wasted by 
 conduction or in other unprofitable ways, the differ- 
 ence between the quantity which leaves the source and 
 the quantity which reaches the condenser during a 
 complete cycle must be precisely the equivalent of the 
 external work which has been done. Taking that into 
 account, let us suppose we could make an engine more 
 perfect than a reversible one. Work the two together, 
 as before. Make the reversible engine continually pump 
 up just as much as the other lets down. Then, as it is 
 less perfect, it will require less work to be employed on 
 it, when reversed, to restore to the source or boiler that 
 quantity of heat than the other engine will do in letting 
 it down ; and therefore, on the whole, while you have a 
 pumping up of heat and letting it down which will 
 exactly compensate one another, or appear to do so, at 
 least so far as the source is concerned, you will have a 
 gain of work. There is the one point where the difficulty 
 is to be found, if there is any. The compound engine 
 will do work ; no question of that. The more perfect 
 engine lets down a certain quantity of heat to the con- 
 denser. The other engine pumps up heat from the con- 
 denser, and deposits in the boiler precisely the same 
 quantity as the other takes out from it. How is it then, 
 that, though we know heat is not matter, this double 
 system can do work ? It can only work in one possible 
 way, and that is by expenditure of heat it must 
 
120 TRANSFORMA TION OF HE A T INTO WORK. 
 
 ultimately work, therefore, not by letting down heat 
 from the boiler, but by cooling the condenser. That is to 
 say : If there can be a more perfect engine than a 
 reversible one, then, with our present knowledge of heat, 
 and taking Carnot's cycle, modified so as to make it com- 
 patible with our modern knowledge, these two engines, 
 working together, the one restoring to the boiler pre- 
 cisely what the other took from it, can only do work, 
 on the whole, on external bodies by cooling and further 
 cooling the condenser. Hence, our result amounts to this, 
 that by taking, as the condenser for our compound engine, 
 any limited portion of the available universe, we could go 
 on getting work from that by making it constantly colder 
 and colder, till we removed all heat from it. Now, we 
 may safely assume it to be axiomatic that we cannot do 
 this ; all experimental laws are against it ; and as we see 
 that the supposition that a more perfect engine than a 
 reversible one can exist has led us to this absurdity, 
 we have it ex absurdo that there can be no engine 
 more perfect than a reversible one. What I have just 
 given you is, in a much amplified form, the gist of some 
 of Sir W. Thomson's remarks of 1851 on this point. 
 
 Clausius, in the preceding year, had endeavoured 
 to supply this defect in Carnot's work by an appeal to 
 the general behaviour of heat, i.e. its always striving to 
 pass from a warmer body to a colder one. I have else- 
 where given reasons which seem to show this proof to 
 be inadmissible. 1 
 
 However complete and satisfactory the demonstra- 
 tion just given may appear to be, you must now be told 
 
 1 See the correspondence in full in the Phil. Mag. 1872, I. pp. 106, 338, 
 443, 516, and II. 117, 240. Also 1879, I. p. 344. The last of these 
 is referred to in the Preface. 
 
TRANSFORMATION OF HEAT INTO WORK. 121 
 
 that it is possible, but possible only in a very curious 
 way, and to an extremely limited extent, to get round 
 this apparent difficulty, to make a body colder than 
 surrounding objects, and to get work from it in con- 
 sequence. This (which, alone, is absolutely fatal to 
 Clausius' reasoning, even with his later modification of 
 it) was first pointed out by Clerk-Maxwell not long ago, 
 and he showed that the mode of escape from the 
 difficulty is, that it would require the intervention of 
 beings, still finite, but infinitely more acute and able 
 than any human beings (or even than the utmost ideal 
 a human being can well conceive), to effect the object 
 on a finite scale, and thus upset the basis on which 
 Carnot's results have been re-established by Thomson. 
 Clerk-Maxwell's reasoning depends upon the mole- 
 cular theory of gases, an essential feature of which is 
 that even in a mass of gas undisturbed by currents, and 
 of uniform temperature, the particles have not all the 
 same velocity. He points out that if such imaginary 
 beings, whom Sir W. Thomson provisionally calls 
 demons small creatures without inertia, of extremely 
 acute senses and intelligence, and marvellous agility 
 were to watch the particles of a gas contained in a 
 vessel with a partition full of trap-doors, also devoid of 
 inertia ; prepared to open and close these doors so as 
 to let the quicker particles get out of the first compart- 
 ment into the second, and to let an equal number of 
 the slower ones escape from the second compartment 
 into the first, they could, without doing any work them- 
 selves, give to the system the power of doing a certain 
 amount of work without help from external bodies. 
 You must be careful, however, not to fancy that there 
 is here any gain or creation of energy not 
 
 UNIVERj 
 
 evejjK 
 
 f U 
 
 v 
 
122 TRANSFORMATION OF HEAT INTO WORK. 
 
 demon could effect that there is a gain of transforma- 
 bility, a slight rise in the scale of availability zw7 tout. 
 As you will be told in another lecture, this restoration 
 of energy is constantly going on, but on a very limited 
 scale, in every mass of gas. If there were only a few 
 hundred particles in a small vessel of gas, the chances 
 would be that if we suddenly cut off half the vessel 
 there would be a sensible difference of temperature 
 between the two parts. But, in consequence of the 
 enormous number of particles in a cubic inch, of even 
 the most rarefied gas, the amended form of Carnot's 
 reasoning just given must be taken as holding good for 
 every heat-engine. For, alas ! we are not demons (in 
 Maxwell's sense), and therefore, so far as experiment 
 goes, and practical application goes, we may take this 
 improved form of Carnot's demonstration as being abso- 
 lutely decisive of the important result, that nojigat- 
 engine can be more perfect than a reversible one. This 
 is, virtually, the Second Law of Thermodynamics, the 
 First Law being that of the Equivalence of Heat and 
 Work. 
 
 The consideration that follows immediately upon this 
 is : If all reversible engines are perfect, they must all be of 
 equal efficiency. They must all be able to give you pre- 
 cisely the same amount of work, from the same quantity 
 of heat, under the same conditions. Therefore it follows 
 that it is these CONDITIONS alone which determine how 
 much work can be produced by a perfect engine, from 
 a given quantity of heat. Now, what are the condi- 
 tions ? I have mentioned no conditions whatever but 
 the temperatures of the boiler and condenser. The tem- 
 peratures of the boiler and condenser were the only 
 things this set of perfect engines had in common. Sup- 
 
TRANSFORMATION OF HEAT INTO WORK. 123 
 
 pose they were all worked for such a period of time 
 that they would all employ equal quantities of heat, 
 then all would do the same amount of work. Therefore, 
 having established Carnot's result, independently of 
 Carnot's erroneous assumption, we are entitled to con- 
 clude that the perfect heat-engine converts into work a 
 fraction of the heat it uses, the value of which fraction 
 depends only upon the temperatures employed. Hence 
 follows immediately one of the most important conse- 
 quences of Carnot's method. It was given, as I have 
 already said, by Sir William Thomson in 1848, when he 
 first recalled attention to Carnot's work. He pointed 
 out that here we have an absolute method of measuring 
 temperature. All previous methods had depended on 
 the properties of some particular substance. It is no 
 matter what your zero and your Newtonian fixed points 
 may be, let us suppose them defined by melting ice 
 and boiling water. Take a number of carefully made 
 and calibrated thermometers ; fill one with mercury, one 
 with sulphuric acid, and so on, and one with water. All 
 of these, if properly adjusted, will agree at the zero or 
 freezing point and at the boiling point, but no two will, 
 in general, agree at any intermediate point. In fact, the 
 water thermometer would be an extremely curious 
 thing, because for a few degrees from the freezing point 
 upwards the water contracts instead of expanding. The 
 water, heated from the freezing point, would at first go 
 downwards on the scale, and then rise with increasing 
 rapidity towards the boiling point. The mercury, on the 
 other hand, would go pretty uniformly up, and so on. 
 Thus, in employing such instruments you must, in addi- 
 tion to noting the degrees on the scale, also note the 
 particular liquid employed. The temperature, then, of a 
 
124 TRANSFORMATION OF HEAT INTO WORK. 
 
 body measured by thermometers filled with different sub- 
 stances, would give generally as many different readings 
 as there are thermometers ; and, therefore, unless you 
 state what is the particular liquid employed, and even 
 what is the particular kind of glass employed, your reader 
 cannot be sure of the particular temperature which is 
 meant. But Sir William Thomson pointed out that the 
 reversible cycle gives us the means of defining tempera- 
 ture absolutely; that is, with complete independence of 
 the properties of any particular substance, because Car- 
 not's engine, if only reversible, is perfect. We do not need 
 to inquire what is the working substance air, water, 
 chloroform, or ether, or whatever it is the engines are all 
 equivalent to one another, and the fraction of the heat 
 they take in, which is converted into useful work, depends 
 solely on the two temperatures. And we have seen that 
 for a reversible engine it is only necessary that the working 
 substance should never be in contact with a body of a 
 temperature different from its own, unless indeed it be an 
 absolute non-conductor of heat. Now, suppose we could 
 keep a body at the temperature of boiling water, under 
 certain conditions, such as that the barometer shall be at 
 a height of 760 m.m., or, roughly, 30 inches. Suppose we 
 keep another body at the temperature of melting ice, 
 with the barometer at the same height. Suppose we can 
 measurewhat amountof heat is taken in and what amount 
 given out by a perfect engine working between these two 
 temperatures, we should find that they are as nearly 
 as possible in the proportion of 374 to 274. I make 
 this statement just now simply as an assertion ; we shall 
 see afterwards by what process these numbers have been 
 approximately obtained. In the ordinary Centigrade 
 scale we call the freezing temperature zero, and we call 
 
TRANSFORMATION OF HEAT INTO WORK. 125 
 
 the temperature of boiling water, under the 30 inches of 
 pressure of the atmosphere, 100. The experimental 
 numbers have been so taken that their difference is 
 100, for a reason which will immediately appear. It is 
 obvious now that we may define the temperatures of 
 the boiler and condenser of a perfect engine by any 
 functions of the relative quantities of heat taken in 
 and given out. Sir William Thomson's first suggestion 
 was not that which he finally adopted. To give as 
 slight a dislocation as possible from the common modes 
 of measuring temperature, it was found best, as it is also 
 simplest, to define as follows : When a perfect engine 
 takes in heat at one temperature and gives it out at an- 
 other temperature, then the temperatures of the source 
 and of the refrigerator are in proportion to the quan- 
 tities of heat taken in and given out, so that, as we see 
 by experiment in the case above mentioned, that for 
 374 taken in, 274 are given out, the temperature of boil- 
 ing water will on this scale be represented by 374, and 
 of freezing water or melting ice by 274, the range be- 
 tween these being the ordinary 100 of the Centigrade 
 thermometer. Therefore we have this curious result, that 
 if you could get a body cooled down far enough under 
 the freezing point we have many artificial processes 
 for such cooling : we can go nearly 140 degrees 
 Centigrade below the freezing point, if we could go 
 twice as far, or 274 degrees below zero, we should have 
 taken all the heat out of the body, we should have re- 
 duced it to the absolute zero of temperature. It would 
 be impossible to make it any colder than the absolute 
 zero of temperature just stated as 274 C. under the freez- 
 ing point of water. Otherwise an engine could be con- 
 structed which would give more work from a quantity 
 
126 TRANSFORMATION OF HEAT INTO WORK. 
 
 of heat than its dynamical equivalent And this engine 
 would work by taking heat from a body already more 
 than totally deprived of heat ! 
 
 In passing, I may say a word or two illustrative, per- 
 haps even to be regarded as corroborative, of that con- 
 clusion. It has been long known that the pressure of a 
 gas, such as air, in a closed vessel, becomes greater as you 
 make it hotter. Take a vessel enclosing a quantity of 
 gas, and shut off the connection between the interior and 
 the exterior, and then apply heat to it. We know that 
 the gas presses more strongly on the containing vessel. 
 On the other hand, if, instead of applying heat to it, we 
 immerse the vessel in a freezing mixture, we know that 
 the pressure becomes less. Now, the amount of increase 
 of pressure per degree of increase of temperature, and 
 also the amount of diminution of pressure per degree of 
 diminution of temperature, have been carefully measured, 
 and it has been found that almost exactly not quite 
 exactly, for a reason afterwards to be assigned, but quite 
 nearly enough for our present purpose if you were to 
 suppose the gas cooled down to a temperature of 274 C. 
 under freezing point, and calculate, by assuming the ex- 
 perimental results I have mentioned to hold throughout 
 that whole range of temperature, the pressure thus de- 
 duced would be almost exactly nothing. So that on the 
 assumption that the formula for its dilatation (found 
 experimentally for small ranges of temperature) holds 
 for great ranges also, a gas would cease to exert any 
 pressure upon its containing vessel if you could cool it 
 down to 274 under ordinary freezing point, the degrees 
 between the freezing and boiling points being, as in the 
 Centigrade scale, 100. This, taken in connection with 
 Carnot's result, appears conclusively to show that the 
 
TRANSFORMATION OF HEAT INTO WORK. 127 
 
 pressure of a gas is due to motion of its particles. The 
 application of heat produces this motion of its particles, 
 in virtue of which they fly about and impinge upon 
 the walls of the vessel ; the energy of their motion is the 
 heat contained by the gas. Go on cooling, and their 
 motion becomes slower ; and finally, when you have got 
 the gas to the absolute zero of temperature, their motion 
 will have ceased, and therefore we should find no pres- 
 sure upon the retaining vessel. 
 
 I may now mention, in connection with the produc- 
 tion of work from heat, and as a practical illustration of it, 
 that suppose we could get a steam-engine made to fulfil 
 Carnot's condition of reversibility that is to say, that 
 we could prevent the steam from ever being in contact 
 with bodies at other than its own temperature for the 
 time being, prevent loss by conduction, etc., in other 
 words, suppose we had a perfect engine, the fraction of 
 the whole heat employed which would be converted 
 into work would not be a large one. Using data, which 
 I take from a statement of Joule, as fairly representing 
 a practical case ; suppose the engine to be a high-pres- 
 sure one, working at 3^ atmospheres, or something 
 about 53 Ibs. pressure on the square inch, it would 
 require in the boiler a temperature of very nearly 300 
 Fahrenheit. Joule says that while working such an 
 engine at an ordinary rate of speed it is next to impos- 
 sible to keep the condenser colder than about 1 10 Fah- 
 renheit. Now the question is, what fraction of the heat 
 spent upon that engine would be converted into useful 
 work ? The answer is remembering Carnot's cycle 
 again the quantity of heat taken in is to the quantity 
 given out in the proportion of the absolute temperature 
 of the boiler to the absolute temperature of the con- 
 
128 TRANSFORMATION OF HEAT INTO WORK, 
 
 denser ; so it comes to be a question simply of arith- 
 metic. Two hundred and seventy-four degrees under 
 zero Centigrade is the point of absolute cold ; what cor- 
 responds to that upon Fahrenheit's scale ? This is 
 easily found to be 461 '2 under the Fahrenheit zero. 
 And, therefore, 76i*2 is the absolute temperature of the 
 boiler; and S7 l ' 2 will De the absolute temperature of 
 the condenser. Therefore of 761*2 units of heat which 
 go in, only 571*2 units go out; and as the engine is 
 perfect, all the rest, that is, 190 units, amounting almost 
 exactly to one-fourth, is converted into work. So our 
 engine, under these conditions, which are about as 
 favourable as any occurring in practice, and even with 
 the additional assumption that it is a perfect engine 
 a thing quite unrealisable in practice converts only 
 one-fourth of the heat from the boiler into useful work. 
 The other three-fourths are sent to the condenser, and 
 in general wholly and absolutely wasted. 
 
 I come now to the consideration of various important 
 advances in the pure science of natural philosophy, which 
 have been made possible, or have at all events been 
 brought forward sooner than they otherwise would have 
 been, in consequence of the recognition of this great dis- 
 covery of Carnot. One of the first of these, and cer- 
 tainly one of the most important, is that made by James 
 Thomson, with regard to the effect of pressure upon the 
 freezing point of water. As you will find immediately, 
 the whole effect is, even for great pressures, an extremely 
 small one, and yet, in all probability it has fitted ice 
 to be one of the most important agents in modifying 
 physical geography. 
 
 Let us consider for a moment that when water freezes 
 there is very considerable expansion. With a very 
 
[( TJKJVJ-: s 
 
 TRANSFORMA TION OF HE A T INztimRK. 1 29 
 
 slight change of temperature of water near the freezing 
 point you have a very considerable change of bulk. 
 Taking Carnot's engine again : Suppose that instead of 
 putting into our cylinder a quantity of hot water with 
 a little steam above it, we put a quantity of cold water 
 with some ice in it, which went through the same set of 
 operations ; then and this was almost precisely the way 
 in which James Thomson regarded it it is easy to show 
 that, taking account of the expansion in the act of 
 freezing, you could get, without any expenditure of heat 
 whatever, any amount of work you pleased from such 
 an ice-water engine. The only way in which you could 
 get out of this inadmissible difficulty is by assuming 
 that the freezing point of water depends upon the pres- 
 sure. If this be allowed, everything can be explained ; 
 but if not, then unquestionably an ice-engine would 
 enable us to get work from no expenditure. Thus, , 
 by simply applying Carnot's process with the change of 
 a word or two, and availing himself of the experiment- 
 ally demonstrated impossibility of the perpetual motion, 
 James Thomson made out the result, that the freez- 
 ing point of water is necessarily lowered by pressure. 
 Well, one can calculate, suppose it were not lowered, 
 how much work could be done in one stroke of this 
 compound engine. One can compare that with the work 
 done by expansion of water when converted into ice 
 and the amount of latent heat set free, and from these 
 one can calculate conversely by how much the pressure 
 must be increased in order to lower the freezing point 
 one degree, or how much the freezing point would 
 be altered by a change of one additional atmosphere 
 of pressure. Thomson made both these calculations. 
 The result was extremely small, namely this fraction 
 
 I 
 
130 TRANSFORMATION OF HEAT INTO WORK. 
 
 O'OO75 C. The freezing point of water is lower by this 
 small fraction of a degree Centigrade for every addi- 
 tional atmosphere of pressure. You can calculate from 
 this that it would require 133 additional atmospheres 
 of pressure, that is to say, 133 times 15 Ibs., or about 
 2000 Ibs. weight on the square inch, to be applied to a 
 quantity of ice which has a temperature one degree 
 Centigrade lower than the freezing point, in order that 
 the ice should melt. So that ice can always be melted 
 by applying pressure great enough ; but if you make the 
 ice very much colder than the freezing point, the amount 
 of pressure required to melt it is so great that we can 
 hardly conceive of its ever being applied. It is only 
 when ice is moderately near its melting point that you 
 can apply sufficient pressure to get its present tempera- 
 ture to represent its melting point ; and if its present 
 temperature represents its melting point, of course it 
 melts. I showed you in my last lecture one beautiful 
 method of exhibiting the melting of ice under pressure, 
 which was described last year in Nature by Mr. Bot- 
 tomley. It consisted in cutting through a bar of ice 
 with a wire, as you would cut soap or cheese. But 
 the ice behaves in a totally different way from that 
 in which soap or cheese would have behaved under 
 the same circumstances. If the ice had been one or two 
 degrees colder than the freezing point, the wire would 
 have hung inactive. It is only when the ice is near 
 the freezing point that the wire, with moderate weights 
 at its ends, is capable of melting it. As the ice melts, 
 it passes round behind the wire, and, thus escaping 
 the pressure, sets into ice again. Thus, as fresh ice 
 has pressure applied to it by the advancing wire, there 
 is a constant melting of the ice before the wire, and a 
 
TRANSFORMA TION OF HE A T INTO WORK. 131 
 
 constant re-freezing behind it; and the block of ice 
 remains practically continuous, except just at the place 
 where the wire is cutting it. Now, this property of ice 
 was known in some of its effects at all events to every 
 one who had seen a glacier for hundreds of years ; but 
 it was only within comparatively recent times that atten- 
 tion was directly called to it. The first who seems to 
 have done so was Dollfuss-Ausset, in his experiments 
 upon the Swiss glaciers, where he showed that by com- 
 pressing a number of fragments of ice in a Bramah press, 
 it was possible to melt them ; and when pressure was 
 taken off them, to allow them to revert again into a solid 
 block. But he found that with very cold ice the experi- 
 ment did not succeed. In fact, as we now see, even with 
 his Bramah press, he could not apply pressure enough. 
 Another form in which it must have been well known 
 for hundreds of years is the form in which we try the 
 same experiment every time we make a snowball. 
 Schoolboys know well that after a very frosty night the 
 snow will not 'make:' their hands cannot apply 
 sufficient pressure. But if the snow be held long enough 
 in the hands to be warmed nearly to its melting point 
 it recovers the power of 'making,' or rather of 'being 
 made.' Every time we see a wheel-track in snow we see 
 the snow is crushed, and even after one loaded cart has 
 passed over it, certainly after two or three have passed, 
 the snow has been crushed into clear transparent ice. 
 The same thing takes place by degrees after people 
 enough have walked over a snow-covered pavement ; 
 and in all these cases this minute lowering of the freez- 
 ing point has led to the result. And now we see how 
 it is that the enormous mass of a glacier moves slowly 
 on like a viscous body, because in consequence of this 
 
132 TRANSFORMATION OF HEAT INTO WORK. 
 
 most extraordinary property it behaves under great 
 pressure precisely as if it were a viscous body. The 
 pressure down the mass of a glacier must of course be 
 very great, and as the mass is especially in summer 
 freely percolated through by water, its temperature can 
 never (except on special occasions, and then near the 
 free surface) fall notably below the freezing point. Now, 
 in the motion of the mass on its journey, there will 
 be at every instant places at which the pressure' is 
 greatest, where in fact a viscous body, if it were placed 
 in the position of the glacier ice, would give way. The 
 ice, however, has no such power of yielding ; but it has 
 what produces quite a similar result wherever there is 
 concentration of pressure at one particular place it 
 melts, and as water occupies less bulk than the ice from 
 which it is formed, there is immediate relief, and the 
 pressure is handed on to some other place or part of 
 the mass. The water is thus relieved from the pressure 
 by the yielding caused by its own diminution of bulk 
 on melting. The pressure is handed on ; but the water 
 still remains colder than the freezing point, and there- 
 fore instantly becomes ice again. The only effect is 
 that the glacier is melted for an instant at the place 
 where there is the greatest pressure, and gives way there 
 precisely as a viscous body would have done. But the 
 instant it has given way and shifted off the pressure 
 from itself it becomes ice again, and that process goes 
 on continually throughout the whole mass ; and thus 
 it behaves, though for special reasons of its own, precisely 
 as a viscous fluid would do under the same external 
 circumstances. 
 
LECTURE VI. 
 
 TRANSFORMATION OF ENERGY. 
 
 Further consequences of Carnot's ideas. Anomalous behaviour of water and 
 of india-rubber. Application to rock masses, and the state of the earth's 
 interior. Availability of energy, and loss of availability. To restore the 
 availability of one portion of energy, another portion must be degraded. 
 Dissipation of energy. Sources of Terrestrial and of Solar Energy. 
 Energy of plants and animals. Measure of the Sun's Radiant Energy. 
 Energy now in the Solar System. 
 
 I SHALL commence this afternoon by taking a few 
 further consequences of the grand ideas of Carnot, which 
 I developed at full length in my last lecture. Where- 
 ever, in fact, we meet with any one anomalous physical 
 result, we almost invariably find that it is associated 
 with other anomalous results ; and perhaps it is in this 
 respect that Carnot's ideas have been of the greatest 
 use in giving us new information. 
 
 Let us take, for instance, what I incidentally men- 
 tioned in connection with thermometers in my last 
 lecture, the fact that water would be an exceedingly 
 bad substance to employ for the purpose of filling a 
 thermometer bulb, because, even supposing that it did 
 not burst the bulb when it froze, supposing that we 
 were using it from zero of Centigrade scale up to 100, 
 it would begin to contract when first heated, and would 
 continue to do so up to the temperature of 4 C, and 
 then it would expand like most other liquids. Now, 
 here is a substance, which, when heated, becomes less 
 
134 TRANSFORMA TION OF ENERG Y. 
 
 in bulk : it contracts instead of expanding. We should 
 expect, therefore, to find that water exhibits some other 
 anomaly, really the same thing if we could understand 
 exactly all about the physical question involved, but 
 appearing very startling to us when presented as some- 
 thing apparently quite new and different. 
 
 Let us look closely into the circumstances of this 
 question. We are applying heat to water, and in con- 
 sequence the water is contracting instead of expanding. 
 Suppose, then, that we take water at a temperature 
 between zero and 4 C., and apply pressure to it, what 
 should we expect ? Pressure applied to water at any 
 temperature above 4 C., and to most other liquids at 
 any temperature whatever, develops heat. Now Car- 
 not's reasoning shows that just for the same reason that 
 pressure produces a development of heat in a liquid 
 which expands by heating, so in a liquid such as water 
 between zero and 4 C., a liquid which contracts on being 
 heated, pressure produces cooling, so that water taken 
 at any temperature between these narrow limits and 
 squeezed in a Bramah press becomes colder in conse- 
 quence of the forced contraction in bulk. 
 
 Another very startling result is derived from the 
 anomalous behaviour, which I daresay is familiar to 
 most of you, of an india-rubber band. I daresay you 
 all know that an india-rubber band suddenly stretched 
 and applied to the lip feels warmer than before. Most 
 bodies when extended become colder, as air does when 
 it expands. If you pull out a steel spring it becomes 
 colder, as Joule showed by direct experiment; but 
 india-rubber is an exception : it not only becomes 
 warmer when it is pulled out, but if, keeping it still 
 pulled out you allow it to cool to the temperature of 
 
TRANSFORMA TION OF ENERG Y. 1 35 
 
 the air, and then suddenly allow it to contract again, it 
 is very much colder than before, as you feel by apply- 
 ing it again to your lip. 
 
 Now these other bodies, such as air and the steel 
 spring, when heat is applied to them, expand. A 
 steel spring supporting a weight, and with heat applied 
 to it, will expand, and allow the weight to descend. 
 On the contrary, as I hope to be able to show you by 
 a simple arrangement, when you apply heat to stretched 
 india-rubber, instead of expanding it contracts, and 
 perfectly in accordance with the theoretical prediction 
 of Sir William Thomson from Carnot's reasoning 
 applied to this case. 
 
 I suppose the 'spot of light crossed by a sharp hori- 
 zontal dark line is visible to all of you near the top of 
 the scale. The light from an incandescent lime-ball 
 passes through a lens, and (after reflection from a plane 
 mirror) is brought to a focus on the scale. The hori- 
 zontal dark line is the image of a wire stretched in 
 front of the lime-ball. This is our index, not the 
 vaguely-defined spot of light. I have here suspended 
 a piece of vulcanised india-rubber gas-tubing, with the 
 spiral wire-core removed from it. Its lower end has a 
 scale-pan attached, and is also fastened to a lever which 
 moves the plane mirror. In order to show you what 
 the movements of the apparatus indicate, my assistant 
 will put one or two additional weights into the scale- 
 pan hanging from the tube, and you will notice that 
 the effect of the additional weights, which is of course 
 to extend the india-rubber, produces a movement of 
 the reflected light up the scale. Hence, if this india- 
 rubber were to expand further by the application of 
 heat, we should see the spot of light on the scale move 
 
TRANSFORMATION OF ENERGY. 
 
 farther up ; but, on the contrary, as soon as heat is 
 applied by a spirit-lamp to the india-rubber, the spot 
 of light you see moves downwards upon the scale, 
 showing that the india-rubber is contracting instead of 
 expanding. India-rubber is a very bad conductor of 
 
 heat, so that it will require some time to cool ; but if 
 we 'were to allow it time to do so, we should find it 
 return almost exactly to its original length ; so that 
 while being heated under tension it contracts, and while 
 cooling under tension it expands. 
 
TRANSFORMA TION OF ENERG Y. 1 37 
 
 [Clerk-Maxwell has recently improved this experi- 
 ment in a most marked manner, by heating the india- 
 rubber tube by the passage of a current of steam 
 through it. The shortening produced can now easily 
 be made visible directly to a large audience.] 
 
 There are a great many other substances which 
 present anomalous properties of the same kind ; but we 
 will now go back to cases which are not anomalous, and 
 there we shall see that the application of Carnot's prin- 
 ciples leads, in these as in other cases, to results which 
 may be of the very greatest importance. Take, for 
 instance, a piece of wax. We know that when wax 
 solidifies it contracts very considerably. Paraffin and 
 many other bodies do the same ; and, therefore, in exact 
 accordance with Carnot's reasoning, their melting points 
 are raised by pressure instead of being lowered, as the 
 melting point of ice is, so that in order to melt paraffin 
 under a very great pressure, you require to heat it very 
 much above its ordinary melting point. 
 
 This is exactly analogous to the case of the conver- 
 sion of water into steam. When water is converted 
 into steam, there is an enormous increase in the bulk, 
 and we know that the temperature of the boiling point 
 of water is greatly heightened by increased pressure. In 
 a high-pressure steam-engine, and wherever we insist 
 on having steam at a high pressure, the boiler requires 
 to be raised to a correspondingly high temperature 
 above the ordinary boiling point. We all know that 
 Papin's Digester was formed upon that principle, for the 
 purpose of heating water to a very much higher temper- 
 ature than the ordinary boiling point, and therefore to 
 confer upon it solvent powers for dissolving bones and 
 such like, which it does not possess at the ordinary boil- 
 
1 38 TRANSFORMA TION OF ENERG 1 '. 
 
 ing point. And, in the same way, Alpine travellers have 
 told us of their difficulties in cooking tea and other 
 food on the top of a high mountain, because it is im- 
 possible at such altitudes, without enclosing the water 
 in a boiler with a closed lid, to heat it up to the tem- 
 perature of 1 00 C, the ordinary boiling point Water 
 boils in an open vessel at about 85 C. on the top of 
 Mont Blanc. 
 
 Now, consider the application of this on a far more 
 gigantic scale. Think of its application to the (originally 
 fluid) substances which now form the whole mass of the 
 earth. There can be no doubt whatever, from various 
 physical and geological proofs, that the interior of the 
 earth, at all events for a very considerable depth under 
 the surface, must, at some long time ago, have been in a 
 viscous or even a perfectly liquid state. Now, when that 
 mass first cooled, which it certainly would do most rapidly 
 at the surface, then if the substance were such as to con- 
 tract on cooling, so that the solid crust became denser 
 than the liquid below it, there would be an exceedingly 
 precarious state of equilibrium, as gradually the crust 
 formed, and, shrinking in, increased the pressure on 
 the liquid below, and thus produced a powerful hori- 
 zontal tension throughout its own substance. In all 
 probability the crust must have broken up by the 
 surface-tension necessary to balance this internal pres- 
 sure (as the tension of a soap-bubble balances the extra 
 pressure due to the compressed air it contains), and 
 tumbled in (and sunk) in pieces, and then solidifica- 
 tion commenced on the fresh exposed liquid surface, 
 and so on. But through the whole globe, there 
 may be, at depths even of so little as 500 miles 
 under the earth's surface, portions still left of the 
 
TRANSFORMA TION OF ENERG Y. 1 39 
 
 originally liquid mass at temperatures equivalent to a 
 red heat ; or (it may be) even a white heat at tem- 
 peratures at all events far above their melting point 
 under ordinary pressures ; and yet, as Sir William 
 Thomson has shown by means of precession, and by 
 other astronomical determinations, still solid. The 
 whole mass of the earth is virtually solid ; more rigid 
 in fact than if it had been of glass throughout very 
 nearly as rigid as if it had been a solid mass of 
 steel ; still, I say there may be portions of the interior, 
 even not so much as 500 miles under the surface, which 
 are still at a white heat, and yet solid, because in conse- 
 quence of the immense superincumbent pressure their 
 melting points have been raised so high that even a white 
 heat is insufficient to liquefy them. 
 
 The illustrations of this lecture have been mainly 
 devoted to the law of transformation of energy from 
 one form to another, and all the examples I have given 
 have been simply applications of Carnot's great result, 
 as modified slightly so as to make it agree with modern 
 knowledge as to the nature of heat. But there are other 
 reflections which we must make on the same subject, 
 and especially with reference to the necessity in Carnot's 
 process of a large portion, by far the greater portion, of 
 the heat which even a perfect engine employs, being let 
 down, without undergoing transformation, from a high 
 temperature, where it has a great deal of available 
 energy, to a lower temperature, where it has a less 
 amount of available energy. 
 
 There is, of course, the same amount of energy in a 
 given quantity of heat in whatever body and at whatever 
 temperature you have it ; for a quantity of heat, what- 
 ever its temperature, represents its equivalent of work. 
 
140 TRANSFORM A TION OF ENERG Y. 
 
 But though there is a definite mechanical equivalent 
 for so much heat, there are vast variations in its utility 
 under different circumstances. If you have the heat in 
 a very hot body, you can get a great deal of its value 
 out of it. On the contrary, if you have it in a com- 
 paratively cold body, you can get very little out of it ; 
 and therefore we are led to speak of the availability of 
 an amount of heat-energy. Availability of energy 
 simply means its capability of being transformed into 
 something more useful, i.e. of being raised higher in 
 the scale of energy ; and depends in the case of heat 
 entirely upon the temperature at which we have it. 
 
 We have seen that even a perfect engine, when it is 
 using heat, necessarily converts only a part of the heat 
 into work. We get the full benefit of that part of the 
 heat ; but the remainder is not left in the boiler, but is 
 degraded, is let down, through the range of temperature 
 corresponding to that between the boiler and the con- 
 denser ; and there, although even yet it is equivalent 
 as much as ever to work, it cannot be converted into 
 useful work ; for, in order that such a conversion should 
 take place, we must have a new engine working down 
 to a temperature lower than that of the original con- 
 denser. Therefore this heat, although quite as high 
 as the rest in its equivalent of mechanical energy, is 
 not so useful, because we have not the means of trans- 
 forming it. It has lost its standing, as it were ; it has 
 lost its availability ; and thus there is a constant ten- 
 dency, even with a perfect engine, and we cannot get 
 a perfect engine in any of our operations, to a degrada- 
 tion of the greater part of the heat employed. 
 
 This leads us, then, to the consideration of why it is 
 that such a degradation must take place. Perhaps the 
 
TRANSFORMA TION OF ENERG Y. 141 
 
 best way of studying such a question will be to take 
 as another illustration of the perfect engine, and Car- 
 not's cycle the case of compressed air, or some other 
 such source of power which does not necessarily involve 
 the direct application of heat. 
 
 The case of compressed air is a very instructive one, 
 and at the same time a very simple one. It was first 
 thoroughly worked out by Joule, and in this way. He 
 took a strong vessel containing compressed air, and 
 connected it with another equal vessel which was ex- 
 hausted of air. These two vessels were immersed each 
 in a tank of water. After the water in the tanks had 
 been stirred carefully so as to bring everything to a 
 perfectly uniform state of temperature, a stop-cock in the 
 pipe connecting the two vessels was suddenly opened. 
 The compressed air immediately began to rush violently 
 into the empty vessel, and continued to do so till the 
 pressure became the same in both ; and the result 
 was, as every one might have expected, that the vessel 
 from which the air had been forcibly extruded fell in 
 temperature in consequence of that operation. It had 
 expended some of its energy on forcing the air into 
 the other vessel. But that air, being violently forced 
 into the other vessel, impinged against the sides of that 
 vessel, and thus the energy with which it was forced in 
 through the tap was again converted into heat. Thus 
 the air which was forced into the vacuum became hotter 
 than before, while the air which was left behind became 
 colder than before. But, on stirring the water round 
 these vessels, after the transmission of air had been 
 completed, and the stop-cock closed, Joule found that 
 the number of units of heat lost by the vessel and the 
 water on the one side, was almost precisely equal to 
 
142 TRANSFORMA TION OF ENERG Y. 
 
 the quantity of additional heat which had been gained 
 on the other side. 
 
 He then repeated the experiment, putting instead 
 of two tanks of water, each holding one of the two 
 strong vessels, one larger tank also filled with water, 
 with both vessels buried side by side in it, then, on 
 allowing part of the air to escape, as before, from the 
 one into the other, and stirring till everything had ac- 
 quired exactly the same temperature, he found that there 
 was scarcely any measurable change in temperature. 
 
 These experimental methods, then, proved indisput- 
 ably that the quantity of heat lost by the one part of 
 the air was at least as nearly as that kind of experi- 
 ment enabled him to test it equal to the quantity of 
 heat gained by the other. Now, think of this for a 
 moment, and you will see that the compressed air had 
 at first a certain capability of doing work. You might 
 have used it to drive a compressed-air engine, or you 
 might have used it for propelling air-gun bullets, or 
 anything of that sort ; but in its final state, when it had 
 expanded to double its original bulk, it had not any- 
 thing like such an amount of available working power 
 stored up in it as it had before. There was, therefore, 
 dissipation of the energy, or of part of the energy, origin- 
 ally present ; and yet, as you have seen, the apparatus 
 and its contents had not lost any heat. 
 
 There was, on the whole, no heat lost, because what 
 was lost to the one vessel was gained by the other. 
 No heat was given out to external bodies, and no avail- 
 able work was done. The air was simply allowed to 
 expand to change its bulk without driving out 
 pistons, or doing anything by which it could convey 
 work to external bodies. It had, therefore, at last 
 
TRANSFORMA TION OF ENERG Y. 143 
 
 precisely the same amount of energy as at first ; and 
 yet of that not nearly so much was available. The air 
 had seized at once the chance given it of dissipating 
 part of its energy, and did dissipate it, as far as was 
 compatible with the circumstances of the arrangement. 
 
 Now the really curious point about this is, that in 
 order to restore the lost availability to the energy of the 
 air, to get that air back into its former condition, so as 
 to be capable of doing as much work as it was capable 
 of doing at first, it would be necessary to spend work 
 upon it, pumping it back from the double vessel into 
 the single one ; but the amount of work which is so 
 spent in pumping it back goes to heat the whole mass 
 of air ; and when you have expended work enough to 
 force back the air into the first vessel from the second, 
 you find that the amount of heat which is given out 
 during that process and which can be measured with 
 great exactness is almost precisely equivalent to the 
 work which is spent in forcing the air back. 
 
 Thus to restore to the energy its former availability, 
 you do not need to spend any energy, you have only to 
 degrade some. You have spent work and got instead 
 its less useful heat-equivalent. You must waste a cer- 
 tain amount of energy, or rather get a bad form of 
 energy in place of it, in order to restore to the mass 
 of air the availability of the energy which it possessed 
 originally, and which had been allowed to be lost by 
 gradual expansion. 
 
 I can illustrate this in another and very instructive 
 way by taking an experiment belonging to the domain 
 of electricity. The experiment is, I daresay, a well- 
 enough known one, so far as the mere exhibition of an 
 experiment goes, but its really important feature, its 
 
144 TRANSFORMA TION OF ENERG Y. 
 
 explanation as bearing upon the principles of energy, 
 and especially upon Carnot's results, does not appear to 
 be, at all events, very generally known. I have got here 
 a couple of Leyden jars, and, contrary to the usual 
 practice, their exterior and interior coatings are both 
 insulated. The jars are supported upon varnished glass 
 stems. Now, I am going to charge from the electric 
 machine only one of those two jars. First of all, we 
 shall charge and discharge it ; and you will be enabled 
 
 to judge roughly the amount of work which corresponds 
 to its full charge by the sound and light of the spark. 
 After that I shall charge it again as nearly as possible 
 to the same amount, and then share the charge of 
 electricity between the two jars, by putting first their 
 outer coatings together, and then their inner coatings ; 
 so that the charge shall be divided equally (because of 
 their equality) between the two. You now obtain 
 (showing) from the sound and light of that discharge- 
 
TRANSFORMATION OF ENERGY. 145 
 
 spark an idea of the amount of work stored up in the 
 jar when charged. Now, the jar being charged again, 
 I simply place a chain over the two outer coatings, and 
 then I connect the interior coatings by means of the 
 discharging-rod. But you will notice that a spark 
 passes during that process. (Shows) Now, no elec- 
 tricity has disappeared, for the jars and discharging- 
 rod are, all of them, insulated. But by separating the 
 two jars from one another, and discharging them separ- 
 ately, you find there is a charge in each (shows), and 
 that these are as nearly as possible equal, so far as can 
 be judged by the appearance and sound of the discharges. 
 But you must have noticed, also, that of the four sparks 
 which you have just heard and seen, the first was very 
 much the stronger ; it made by far the greater noise, and 
 it was also the longer and more brilliant. The second 
 spark was the next in order of magnitude, and the two 
 final sparks, as we should have expected, were about 
 equal, but not at all comparable in intensity, even to 
 the second one, which was weaker than the first. 
 
 Now, this is a beautiful illustration of exactly, or 
 almost exactly, the same principle as that I have just 
 explained. When I had the full charge of electricity 
 in the one jar, there was a certain definite quantity of 
 what, for want of precise knowledge, we provisionally 
 call positive electricity, in the inner coating, and an 
 equal quantity of negative electricity was in the outer 
 coating. Then, when I connected the outer coatings of 
 the charged and the uncharged jar by means of this 
 chain, they formed, as it were, the outer coating of a 
 single jar ; but in order to make the two inner coatings 
 correspond in electric condition, I had to put the dis- 
 charging-rod between them, and you noticed that I 
 
 K 
 
146 TRANSFORMA TION OF ENERG Y. 
 
 could not do so without allowing a spark to pass. A 
 spark necessarily passed during that operation, at least 
 it did so when a short stout metallic discharging-rod 
 was used. 
 
 Now, that spark represented a portion of energy 
 which was wasted a certain amount of work done in 
 producing sound, light, and heat. Therefore, obviously, 
 from the mere fact that such a spark passed when I 
 completed the connection between the two jars, you 
 saw that energy must have been wasted. But how 
 could the energy be wasted when there was no free 
 electricity lost? The quantity of positive electricity 
 originally in the inside of one jar was simply divided 
 between two jars ; there was just one-half the original 
 quantity of positive and one-half the quantity of negative 
 in each. The quantity of electricity remained the same, 
 and yet there was a quantity of energy dissipated during 
 the process. Now the answer is simply this (it was 
 originally made out as a very particular case of grand 
 general theorems, given first by Green and afterwards 
 interpreted and applied by Helmholtz and Sir William 
 Thomson), that the work due to a charge of electricity, 
 or the work which must be spent upon an electric 
 machine (suppose it wholly goes to producing electrical 
 charge of a conductor), depends upon the square of the 
 quantity of electricity. No matter what the form of 
 the conductor or jar is, the energy of the charge, or the 
 amount of work which it will do, depends upon the 
 square of the quantity of electricity. Now we can 
 understand perfectly our experimental result. Sup- 
 pose we call the quantity that the first jar had when it 
 was charged, one ; then, when I discharged it by itself 
 on the first occasion, you had a spark which corresponded 
 
TRANSFORMA TION OF ENERG Y. 147 
 
 to the quantity of energy, the square of one, or one 
 itself. But when I put the two jars together, and thus 
 divided the charge, so that there was only one-half 
 the quantity of positive, and one-half the quantity of 
 negative in each jar, then the whole discharge of each 
 separate jar, or the energy of it, was proportional to 
 the square of one-half, that is, to one-fourth. Each of 
 these, when the charge had been divided between them, 
 contained a quantity of energy equal to one-fourth of 
 the original store, and therefore the two together corre- 
 sponded only to one-half of that store. Now we can see 
 what it was that produced the spark when I was dividing 
 the charge : that spark was the equivalent of the other 
 half of the energy, the half which necessarily went to 
 waste. You wasted the whole quantity by discharging 
 the charged jar itself; but in merely putting the two 
 together, so as to divide the charge, you wasted one- 
 half the energy, and then the quantities that you had 
 remaining corresponded to the two remaining quarters. 1 
 Now, in all these illustrations that I have shown you 
 whether they correspond to dissipation of ordinary 
 energy, or to dissipation by sound or friction, or even to 
 the production of heat, light, and so on, by electrical 
 discharges, in all these cases, you notice that there is a 
 tendency for the useful energy, whenever a transforma- 
 tion takes place, to run down in the scale, that, the 
 quantity being unaltered, the quality becomes deterior- 
 ated, or the availability becomes less ; and from similar 
 
 1 If instead of the stout, short, discharging-rod I had used a very long, 
 fine wire or other conductor of great resistance, such as, for instance, a 
 number of persons joining hands, the second spark might have been 
 reduced indefinitely ; but then the inevitably wasted half of the energy 
 would have appeared as heat in the wire, or in the physiological effects 
 of the shock. 
 
1 48 TRANSFORMA TION OF ENERG Y. 
 
 results in all branches of physics we are entitled to 
 enuntiate, as Sir William Thomson did very early after 
 the new ideas were brought into full development, the 
 principle of Dissipation of Energy in nature. 
 
 The principle of dissipation, or degradation, as I 
 should prefer to call it, is simply this, that as every 
 operation going on in nature involves a transformation 
 of energy, and every transformation involves a certain 
 amount of degradation (degraded energy meaning 
 energy less capable of being transformed than before), 
 energy is continually becoming less and less trans- 
 formable. 
 
 As long as there are changes going on in nature, the 
 energy of the universe is getting lower and lower in the 
 scale, and you can see at once what its ultimate form 
 must be, so far at all events as our knowledge yet 
 extends. Its ultimate form must be that of heat so 
 diffused as to give all bodies the same temperature. 
 Whether it be a high temperature or a low temperature 
 does not matter, because whenever heat is so diffused 
 as to produce uniformity of temperature, it is in a con- 
 dition from which it cannot raise itself again. In order 
 to get any work out of heat, it is absolutely necessary 
 to have a hotter body and a colder one ; but if all the 
 energy in the universe be transformed into heat, and if 
 it be all in bodies at the same temperature, then it is 
 impossible at all events by any process that we know 
 of as yet to raise the smallest part of that energy into 
 a more available form. 
 
 Having seen then that this must be the ultimate end 
 of all the energy in the universe ; that so long at all 
 events as those I have just been explaining remain 
 physical laws this is the consequence to which they 
 
TRANSFORMA TION OF ENERG Y. 149 
 
 must lead, it becomes a very necessary inquiry Whence 
 is it that the enormous quantities of energy which are 
 made use of, even on the surface of our diminutive 
 planet, are supplied to us ? What are our principal 
 sources of energy, and how do we transform the supplies 
 they afford us so as to make them useful for various 
 practical purposes, especially the most practical of all, 
 the practical one of living, which, so far as mere 
 vitality is concerned, is certainly a purely physical 
 process ? 
 
 Well, the muscular work which an animal does, and 
 the animal heat which it gives out (in much larger 
 equivalents than it does muscular work), these of course 
 we all know are due mainly to food. In such a term 
 as food, I include not merely solid and liquid food, but 
 also (and this is very important) the gaseous food which 
 we inhale. All these may be classed under the general 
 title of food. These being taken in, we have certain 
 other things which are got rid of, such as carbonic acid, 
 water, and so on. These you may call the ashes of our 
 food. These have, in their chemical relations, part of 
 the degraded energy of the food which was taken in. 
 The non-degraded part of the energy corresponds of 
 course to the muscular work done, and the store of 
 muscle, etc., laid up in the system. 
 
 Now, if this process were going on continuously 
 there would be constant using up of the oxygen of the 
 atmosphere by its combination with part of the food, 
 and production of the (to the animal) useless, or rather 
 pernicious, gas, carbonic acid. Leave this part of the 
 question as a difficulty for the moment, that we should 
 have the oxygen of the air gradually taken up, and its 
 place supplied, at all events to a great extent, with car- 
 
1 50 TRANSFORM A TION OF ENERG Y. 
 
 bonic acid gas, in which an animal could not live : 
 still we have this further difficulty : Although animals 
 may live to a great extent upon animal food, yet if you 
 go on from man, who consumes a certain kind of 
 animal, while that animal also consumes animals, and 
 so on, there must be either a cycle in which the last 
 animal consumes man, or an infinite range as it were of 
 animals, so that all could live on animal food ! 
 
 We know that it is not so, that there is a large class of 
 animals which consume only vegetable food. Now, it is 
 to the wonderful difference between the application of the 
 laws and processes of energy to the nutrition of animals, 
 and to that of vegetables, that we are indebted for the ex- 
 planation of the difficulty which I have just pointed out 
 to you what becomes of this large quantity of carbonic 
 acid gas, which in time would, if not got rid of, kill off 
 all animals, either by direct poisoning, or by depriving 
 them of their oxygen. The explanation is simply this, 
 that the animal takes in the oxygen, and with it animal 
 or vegetable food, giving out the objectionable carbonic 
 acid gas ; but, on the other hand, the plant takes the 
 carbonic acid gas, with water and other things, and 
 works it up again, gives back the oxygen to the air, 
 and stores up the carbon, etc., in the form of vegetable 
 food, upon which many animals live, and in their turn 
 become man's food. 
 
 Now, it is quite obvious that if plants were not assisted 
 by some external supply of energy, here would be some- 
 thing equivalent to the perpetual motion on the grandest 
 conceivable scale. If the plant were capable, merely by 
 its own peculiar organisation, of taking the ashes as it 
 were of the fuel burnt in the animal engine, and work- 
 ing them up again into fit and proper food, without 
 
TRANSFORMA TION OF ENERG Y. 151 
 
 external assistance, then that process might go on 
 indefinitely, the animal all the time, remember, giving 
 out animal heat and doing muscular work. 
 
 This would be the perpetual motion on a scale never 
 contemplated even by the perpetual-motionists. It is 
 obvious then that in order to escape from our difficulty 
 no less than a contradiction in terms of what we 
 know to be a physical law there must be some source 
 of energy which the plant draws upon in order to help 
 it to work up that carbonic acid, etc., and store up the 
 available part of it as food for the animal. 
 
 It was long ago recognised, but first, perhaps, in a 
 nearly definite form, by Stephenson, that it was by 
 energy supplied in a radiant form from the sun, that 
 plants were enabled to decompose carbonic acid ; and it 
 is a very wonderful thing that those so-called actinic or 
 chemical radiations from the sun, which are most effec- 
 tive in promoting the decomposition of carbonic acid by 
 the leaves of plants, are the very rays which are most 
 absorbed by the green leaves. The green leaves are 
 particularly absorbent of them, and any of you may 
 convince himself of the fact by comparing the photo- 
 graph of a tree in full leaf with that of almost anything 
 else. In fact, the photographs of foliage (at all events 
 with the chemicals usually employed) are almost in- 
 variably exceedingly dull, even black, showing that the 
 chemically active rays, except those which have been 
 reflected from the surfaces of polished leaves, have been 
 absorbed at once by the green leaves, and in this act 
 have been performing their function of decomposing 
 carbonic acid and water. 
 
 In fact, we may make a rough comparison it is hot 
 by any means an exact one, but it is close enough to be 
 
152 TRANSFORMA TION OF ENERG K 
 
 sufficient for our present purpose we may compare 
 roughly the animal to the cell of a galvanic battery, 
 where you have the virtual food supplied in the shape 
 of zinc and dilute sulphuric acid ; and the cell, by means 
 of the electric current it produces, driving an electro- 
 magnetic engine or producing heat in a wire, just as 
 the animal produces muscular work or animal heat. 
 On the other hand, you may roughly, with about the 
 same degree of approximate accuracy, compare the 
 plant to a cell in which energy, in the form of a current 
 of electricity, furnished from an external source, is 
 employed in decomposing water, let us say : separating 
 it into its oxygen and hydrogen, and producing that 
 high form of potential energy which I exhibited to you 
 experimentally in a former lecture ; so that fresh 
 materials, as it were, for the battery cell are being 
 actually separated, and getting their potential energy 
 given back to them in the decomposing cell. That 
 corresponds to the plant. You supply these materials 
 again to the cell of the battery, and it again produces 
 electric currents, and so on in succession. 
 
 But it is quite obvious that a process of that kind 
 cannot go on without a supply of energy from 
 without. The raising of energy from the lower form 
 to the higher always requires external application of 
 some fresh energy, which is itself degraded in the pro- 
 cess. This idea originated with Joule at a very early 
 period of his investigations ; and he pointed out that 
 not only does an animal much more nearly resemble 
 in its functions an electro-magnetic engine than it 
 resembles a steam-engine, but he also pointed out that 
 it is a much more efficient engine, that is to say, an 
 animal, for the same amount of potential energy of food 
 
TRANSFORMA TION OF ENERG Y. 1 53 
 
 or fuel supplied to it (call it fuel, to compare it with the 
 other engines), gives you a larger amount converted 
 into work than any engine which we can construct 
 physically. 
 
 To use the vernacular of engineers on the subject, the 
 ' duty ' of an animal engine is much larger than the 
 duty of any other engine, steam, or electro-magnetic, 
 or otherwise, which we can construct to employ fuel, 
 the duty simply meaning the percentage of the 
 energy of the fuel supplied to the engine which it can 
 convert into the useful or desired form. Carefully 
 observe here that this does not necessarily hold true 
 if we contemplate water-mills, etc., for there the energy 
 supplied is in general of a higher order than that of 
 food or fuel. 
 
 Now, from what I have said, you will see that the 
 supply which the plant requires comes from the sun. 
 That leads us then to the question what is the source 
 of the sun's energy ? Now, when, with the view of 
 answering that question, we make a few calculations, 
 we find that they at once upset the first ideas that we 
 are likely to form for ourselves on the subject. Of 
 course, the old notion that the sun is a huge fire, or 
 something of that kind, is one which will only occur to 
 those thinking of the matter for the first time ; but with 
 our modern chemical knowledge, assisting the more 
 ordinary physical reasoning which I have just given you, 
 we are enabled to say, that, massive as the sun is, if its 
 materials had consisted even of the very best materials 
 for giving out heat by what we understand on the ter- 
 restrial surface as combustion,- that enormous mass of 
 some 400,000 miles in radius could have supplied us 
 with only about 5000 years of its present radiation. A 
 
1 54 TRANSFORM A TION OF ENERG Y. 
 
 mass of coal of that size would have produced very 
 much less than that amount of heat. Take (in mass 
 equal to the sun's mass) the most energetic chemicals 
 known to us, and in the proper proportion for giving 
 the greatest amount of heat by actual chemical combi- 
 nation ; and, so far as we yet know their properties, 
 we cannot see the means of supplying the sun's present 
 waste for even 5000 years. 
 
 Therefore, as we all know that geological facts, if 
 there were no others, point to at least as high -a radiation 
 from the sun as the present, for at all events a few 
 hundreds of thousands of years back, perhaps, as we 
 shall find later, even a few millions of years back, 
 and perhaps also indicate even a higher rate of 
 radiation from the sun in old time than at present 
 it is quite obvious to you that the heat of the sun 
 cannot possibly be supplied by any chemical process 
 of which we have the slightest conception. 
 
 Now, if we can find, on the other hand, any physical 
 explanation of this, consistent with our present know- 
 ledge, we are bound to take it and use it as far as we 
 can, rather than say This question is totally unanswer- 
 able unless there be chemical agencies at work in the 
 sun of a far more powerful order than anything that 
 we meet with on the earth's surface. If we can find a 
 thoroughly intelligible source of heat, which, though 
 depending upon a different physical cause from the 
 usual one, combustion, is amply sufficient to have 
 supplied the sun with such an amount of heat as to 
 enable it to have radiated for perhaps the last hundred 
 millions of years at the same rate as it is now radiating, 
 then I say we are bound to try that hypothesis first, and 
 argue upon it until we find it inconsistent with something 
 
TRANSFORMA TION OF ENERG Y. 155 
 
 known. And if we do not find it inconsistent with 
 anything that is known, while we find it completely 
 capable of explaining our difficulty, then it is not only 
 philosophic to say that it is most probably the origin of 
 the sun's energy, but we feel ourselves constrained to 
 admit it. Newton long ago told us this obligation in 
 his Rides of Philosophising. 
 
 The shortest and easiest way in which I can illustrate 
 this simple though tremendously important step is by 
 stating that if we were to take a mass of the most per- 
 fect combustibles which we know, those combustibles 
 which give the greatest amount of energy when 
 burned together, and let it fall upon the sun merely 
 from the earth's distance, then the work done upon 
 it by the sun's attraction during its fall would give it 
 so large an amount of kinetic energy when it reached 
 the sun's surface as to produce an impact which 
 would represent 6000 times the amount of energy which 
 could be produced by its mere burning. It is, in fact, 
 capable of perfectly easy and simple demonstration, 
 that a mass which would produce the utmost known 
 energy by burning, would give 6000 times more energy 
 by a simple fall from the earth's distance upon the sur- 
 face of the sim. 
 
 It appears, then, that until it is shown that there is, 
 or has been, in the physical universe, at some time or 
 other, a greater amount of kinetic energy than can be 
 accounted for by the falling together of the masses 
 which compose the sun and stars, our natural and only 
 trustworthy mode of explaining the sun's heat at present, 
 in time past, and for time to come, must be something 
 closely analogous to, but not identical with, what was 
 called the nebular hypothesis of Laplace very eagerly 
 
156 TRANSFORMA TION OF ENERG Y. 
 
 accepted when it was first proposed the hypothesis of 
 the falling together (from widely scattered distribution 
 in space) of the matter which now forms the various 
 suns and planets. We find, by calculations in which 
 there is no possibility of large error, that this hypothesis 
 is thoroughly competent to explain 100 millions of years' 
 solar radiation at the present rate, perhaps more ; 
 and it is capable of showing us how it is that the sun, 
 for thousands of years together, can part with energy 
 at the enormous rate at which it does still part with it, 
 and yet not apparently cool by perhaps any measurable 
 quantity. 
 
 Now, in confirmation of this it is well to state here, 
 that not only is the hypothesis itself capable of ex- 
 plaining the amounts of energy which are in question, 
 but also recent investigations, aided by the spectroscope, 
 of which I shall have a good deal to say in another 
 lecture, have shown us that there are gigantic nebular 
 systems at great distances from our solar system, in 
 the process of (physical) degradation in that very way, 
 by the falling together of scattered masses, and with 
 immense consequent developments of heat by impacts. 
 What are called temporary stars form another splendid 
 and still more striking instance of it, as where a star 
 suddenly appears of the first magnitude, or even brighter 
 than the first, outshining all the planets for a month or 
 two at a time, and then, after a little time, becomes 
 invisible in the most powerful telescope. Things of that 
 kind are constantly occurring on a larger or smaller 
 scale, and they can all be easily explained on this sup- 
 position of the impact of gravitating masses. 
 
 Now, holding that such may be the cause of the 
 enormous amount of radiation from the sun, let us 
 
TRANSFORMA TION OF ENERG Y. 157 
 
 inquire what fraction of that whole radiation reaches our 
 own little globe. We know what an enormous quantity 
 of solar heat reaches the earth, reaches even our own 
 small corner of the earth. That is of course a very 
 small part of what reaches the earth's whole surface ; 
 but still, if you recollect that the earth, as seen from the 
 sun, appears very much less than the planet Jupiter, or 
 even Mars, as seen by us, that is, that it would present 
 no visible disc to the naked eye, and that to an observer 
 at such a distance as that of the sun it would require a 
 telescope of some little magnifying power to show it as 
 a disc at all, considering also that the sun is radiating 
 very nearly uniformly in all directions, how much of 
 the sun's entire radiations can reach this little speck at 
 such a distance as ninety millions of miles ? A circular 
 disc of four thousand miles radius, at a distance of 
 ninety-one million miles, appears to occupy less than 
 one two-thousand-millionth part of the celestial sphere. 
 You see, then, that the quantity of heat which the 
 whole earth gets from the sun is of the order of some- 
 thing less than the two-thousand-millionth part of that 
 which the sun gives out. Now, experiments have been 
 made, and fairly satisfactory ones, to determine what 
 amount of heat we do receive what amount of energy 
 does fall upon the earth's surface in a given time. Of 
 course, they are interfered with to a considerable extent 
 by absorption of the radiation as it passes through the 
 various and varying constituents of the earth's atmo- 
 sphere in each region of the globe ; and therefore the 
 most trustworthy experimental results have been such 
 as were obtained at considerable elevations in balloons, 
 or on the tops of very high mountains, where there is 
 comparatively little absorption. 
 
1 5 8 
 
 TRANSFORMATION OF ENERGY. 
 
 This instrument, the pyrheliometer, is constructed 
 for the purpose of measuring the amount of radiation 
 from the sun. It is made of silver polished on the 
 
 cylindrical part, and on the back, because this is an 
 exceedingly bad radiator of heat, so that the instru- 
 
TRANSFORMA TION OF ENERG K 1 59 
 
 ment loses by those sides very little of the heat which 
 it collects by the blackened side, which is a good 
 absorber and is turned directly to the sun. This little 
 silver vessel is filled with water, and all the radiant 
 heat and light, everything in the form of radiation that 
 falls upon this lampblack, is absorbed by it, and is 
 degraded into the form of heat and so communicated 
 to the water. In the middle of the water is the bulb of 
 the thermometer, whose stem runs down through the 
 axis of the apparatus. We can adjust it so that the 
 blackened disc shall receive the sun's rays perpendicu- 
 larly, by a very simple contrivance : a disc of metal at 
 the other end of the thermometer tube, of exactly the 
 same size as the first disc : then the whole being so set 
 that the shadows of the two discs coincide, we know 
 that it is turned directly to the sun. Take off the cap 
 of the instrument for a measured period, put it on again, 
 and after the whole has been thoroughly shaken up, so 
 that the temperature of the water is the same through- 
 out, read off the rise of temperature as shown by the 
 thermometer. Correct that for the loss of heat by 
 radiation during the performance of the experiment. 
 That can be done at once by simply watching how it 
 gradually loses heat when it is turned to the sky, but 
 screened from the sun's radiation. With this instru- 
 ment we can make a fairly approximate estimate of the 
 amount of heat which is received from the sun by the 
 blackened surface in a given time ; and by comparing 
 the surface of this disc with the surface of the whole 
 earth which is exposed to the sun, we can estimate at 
 least approximately how much radiant energy in the 
 form of heat, light, actinism, and so on, comes to us 
 per second from the sun ; and therefore we can esti- 
 
160 TRANSFORMA TION OF ENERG Y. 
 
 mate what amount of energy leaves the sun's whole 
 surface every second, that is to say, what number of 
 foot-pounds of energy the sun is spending per unit of 
 time. 
 
 According to Thomson (calculating from the data of 
 Pouillet and Herschel), the sun's radiation is equiva- 
 lent to about 7000 horse-power per square foot of his 
 surface somewhere about thirty-fold that of the same 
 area of the furnace of a locomotive and somewhere 
 about 6x io 30 units of heat (c.) leave his whole surface 
 per annum. 
 
 In addition to the data which I have just given you, 
 I shall conclude this morning by giving one or two 
 others. Let us take the case of the earth's motion in 
 its orbit. The immense mass of the earth moving round 
 in its circle of over 90,000,000 miles radius in one year 
 is moving at what we should consider an enormous rate, 
 far greater than that of a cannon ball (being in fact 
 about 80 times as great), and yet the whole kinetic 
 energy it would supply, if it were accidentally to impinge 
 upon a huge target, as an Armstrong projectile goes 
 against an iron plate, is a mere trifle to what we have 
 been considering ; it could only supply by that fright- 
 ful crash an amount of heat equal to the sun's loss 
 in about 80 days. But if instead of taking its energy 
 of motion in its orbit, you were to take its potential 
 energy, as a heavy body which, if allowed, would 
 fall into the sun, and there produce an immense 
 development of heat by impact, the calculation leads 
 us to this result, that it would acquire, on reaching 
 the sun's surface, such a speed that the energy of the 
 impact would be equivalent to the heat at present 
 given out by the sun in about 91 years. But the 
 
TRANSFORMA TION OF ENERG Y. 161 
 
 planet Jupiter is not only enormously more massive 
 than the earth, but is also very much farther away 
 from the sun, and therefore on both accounts it would 
 produce a much greater development of heat if it were 
 to fall into the sun. The calculations made on the 
 same data for the planet Jupiter give something like 
 32,000 years, that is to say, Jupiter alone falling into 
 the sun would supply its present loss for 32,000 years 
 to come. 
 
 Then, there is one final datum with which I shall con- 
 clude to-day, and it is this : I shall give more detailed 
 explanation of it in my next lecture, but I wish to men- 
 tion it before concluding, that the lowest possible 
 estimate which we can make of the capacity of the sun 
 for heat is such that, cooling at the present rate losing 
 energy at its present rate the sun cannot possibly 
 cool more than a single degree Centigrade in seven 
 years. It may be, on the highest estimate we can take, 
 one degree in 7000 years ; the data are very uncertain ; 
 but we may say that these are the limits between which 
 it must lie. Startling as are many of the matter-of-fact 
 statements I have made to you to-day, I cannot help 
 once more repeating this, by far the strangest of them 
 all : the sun has such an enormous capacity for heat 
 that it takes at least seven years, at its present enormous 
 rate of radiation, to cool by one degree Centigrade ! 
 
LECTURE VII. 
 
 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 Available Sources of Energy on the Earth. Whence these have been derived 
 Uniformitarian School of Geologists. Sir W. Thomson's arguments as 
 to the length of time during which life has been possible on the earth. 
 Transference of Energy through Solids, Fluids, and through the Ether. 
 Test of the Receptivity of a body or system for energy in a vibratory form 
 Physical Analogies introductory to Spectrum Analysis. 
 
 IN my last lecture I considered, in as great detail as 
 our necessarily limited time permitted, the origin of the 
 energy of the solar system. I must now consider in 
 part of to-day's lecture a smaller, but much more im- 
 portant matter, much more directly personal to us, 
 namely, our available sources of terrestrial energy. In 
 my little work upon Thermo-Dynamics, I have arranged 
 these sources in order as follows : 
 
 First. Our available sources of potential energy. 
 
 1st, Fuel. Under the head of fuel I should include 
 not merely coal, wood, and so on, but also all that may 
 properly be called fuel the zinc used in a galvanic 
 battery, for instance, and various other things of that 
 kind. 
 
 2d, The food of animals. 
 
 3d, Ordinary water-power. 
 
 4th, Tidal water-power. 
 
 All these are forms of potential energy. 
 
SOURCES AND TRANSFERENCE OFENEJfGY. 163 
 
 Then, Secondly, in the Kinetic form, we have 
 
 (i.) Winds. 
 
 (2.) Currents of water, especially ocean currents ; and 
 finally we have 
 
 (3.) Hot springs and volcanoes. 
 
 There are other very small sources known to us, 
 exceedingly small ; but these I have named include 
 our principal resources. 
 
 Now comes the question, what are the sources of these 
 supplies themselves ? I find I have classified them also 
 under four heads. 
 
 The first is primitive chemical affinity, chemical 
 affinity which we may suppose to have existed between 
 particles of matter from the earliest times, and still to 
 exist between them, because these portions of matter 
 -have not combined with one another nor with other 
 matter. If, for instance, when the materials of which 
 the earth is at present composed were widely separated 
 from one another, there were particles of meteoric iron 
 and native sulphur which, when the materials did come 
 together to form the earth and heated one another by 
 mutual impact, did not combine together but have still 
 remained through long periods of time separate from 
 one another, we should consider that the mutual chemi- 
 cal potential energy of the iron and sulphur remains to 
 us as a portion of energy primordially connected with 
 the universe. But of that, so far as we know, at least 
 near the surface of the earth there is very little. There 
 may be towards the interior enormous masses of as yet 
 uncombined iron and uncombined sulphur, or various 
 other materials, but towards the surface, where they 
 could be of any direct use to us, the quantities of these 
 are excessively small. 
 
1 64 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 The second source is that which I have several times 
 alluded to, solar radiation, and that is by far the most 
 abundant source we have. 
 
 Then we have two very instructive forms, viz., the 
 energy of the earth's rotation about its axis, and the 
 internal heat of the earth. 
 
 Now, if we take in turn the enumeration which I gave 
 at first of our available stock, and compare it with the 
 sources from which we derive that stock, we shall easily 
 see how the two are connected with one another. 
 
 First, we have fuel. Now, our supplies of fuel are 
 almost entirely due to the sun. That is to say, in times 
 long gone by, the sun's rays by their energy, as absorbed 
 in the green leaves of plants, decomposed carbonic acid 
 and stored up the carbon. That carbon, and various 
 other things stored up ages ago along with it, we have 
 still as an immense reserve fund of coal. 
 
 Then for the food of animals we are mainly indebted 
 to the sun again, because the food of animals must ulti- 
 mately be vegetable food, even of the animals which 
 live upon animal food. Then for ordinary water-power 
 we are also indebted to the sun, because it is mainly 
 the energy of the radiation from the sun in its heat 
 form which evaporates water from the plains or seas, 
 and allows it to be precipitated again at such a height 
 that it has potential energy in virtue of its elevation. 
 Ordinary currents of water are a mere transformation 
 of this potential energy, because water on a height may 
 convert part of its potential energy into kinetic energy 
 of visible motion as it flows down. 
 
 But when we come to tidal water-power we must look 
 to another source. If we employ tidal power for the 
 purpose of driving an engine, we take it in the rise of 
 
SOURCES AND TRANSFERENCE OF ENERGY. 165 
 
 the water as the tide-wave passes us. We secure a por- 
 tion of water at a certain elevation, wait till the tide has 
 gone back, and then take advantage of the descent of 
 that portion of water. Now, if we were to go on doing 
 that for any considerable period of time, and doing it 
 over large tracts of sea-coast, we should find that the 
 effect of it in time would be to gradually slacken the 
 rate of rotation of the earth ; so that if all our important 
 sources of power, such as coal, and direct solar radia- 
 tion, were to fail us in great part, and if we were driven 
 finally as a last resource to use tidal water-power, it 
 might come to be a very serious international question 
 between those kingdoms which possessed sea-board and 
 those which had none. For if it were largely employed, 
 the period of the rotation of the earth might be in a 
 moderate period of years seriously affected. And there 
 seems to be no known compensating advantage for 
 those nations who are not possessed of an extensive 
 sea-board within the Temperate or Torrid Zones, where 
 alone this source of power would be of much avail. 
 
 Then we have, next to these, winds and ocean cur- 
 rents. These are almost entirely due to solar radiant 
 heat. And, finally, hot springs and volcanoes, which 
 have never been employed for any direct production of 
 work, but which might possibly be so used. Their 
 energy depends, mainly at least, upon the internal heat 
 of the earth ; partly perhaps on potential energy of 
 chemical affinity. 
 
 So you see that mainly to solar radiation, but partly 
 to the other three sources of supply, are due the various 
 stores of energy which we have at our disposal. This, 
 however, is a mere bare enumeration. I might spend 
 many lectures developing small parts of this grand 
 
1 66 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 subject ; but I have given you in these few words the 
 large heads, and it is scarcely compatible with the time 
 at our disposal to devote another couple of lectures to 
 pursuing the subject into its minute details. 
 
 The next question I take up is this, intimately con- 
 nected with what we have just considered : the question 
 of how long something like the present state of things 
 has been going on on the earth's surface. This is an 
 extremely important question, and can be approached 
 from various sides, from the geological side, for in- 
 stance, by consideration of the thickness of strata, of 
 amounts of erosion, and such like ; but it can also be 
 approached directly from the point of view of energy, 
 and from that point of view alone I shall now attempt 
 briefly to treat it. 
 
 The old notion of what was called the Uniformitarian 
 school of Geology, was simply that things had been 
 going on and were to go on, both in the past for many 
 millions of years, and in the future for many other mil- 
 lions of years, at as nearly as possible the same uniform 
 rate, that we were getting a steady supply of heat 
 from the sun, that even if energy (it was not called 
 energy in those days), even if some source of supply, call 
 it what you like, was disappearing in some portion of 
 the interior of the earth, at its disappearance it was 
 producing say electric currents, and decomposing some 
 compound substance ; so that, if ever lost by chemical 
 combination at one place, electric currents would be 
 produced, and something equivalent thereby given out 
 in some other place, so that the stock should be main- 
 tained as nearly as possible at a uniform state. 
 
 Now, this is totally inconsistent with modern physical 
 knowledge as to the dissipation of energy. Transfer- 
 
SOURCES AND TRANSFERENCE OF ENERGY. 167 
 
 mations must be going on now (at least on the average) 
 at a much slower rate than they were going ages ago. 
 Just as when you take a red-hot ball from a furnace ; 
 it cools at a certain rate, but as it becomes colder it 
 cools more and more slowly. And this is not a mere 
 analogy, but an almost absolute identity, with the case 
 of the earth and the sun. There is no doubt that at 
 some period long ago the earth was so hot as to be at 
 all events plastic, if not absolutely liquid throughout 
 its mass ; and there is no doubt that at the present 
 moment, even after ages of expenditure of energy at a 
 very great rate, the sun must be still liquid in great 
 part, and even gaseous in very large part. 
 
 Now, we can apply the theory of energy, especially 
 from Carnot's point of view, to the state of things in 
 the earth and in the sun, and can at all events roughly 
 approximate to the period during which the earth has 
 been habitable for animals and plants such as we find 
 upon it now. We do not say, of course, that it was in- 
 habited for such periods by animals and plants such as 
 we see now, or find fossil remains of ; but we can trace 
 approximately backwards for how long the earth was 
 habitable by such, and that is the problem we propose 
 to solve. 
 
 This subject was taken up very carefully within the 
 last few years by Sir William Thomson, and the brief 
 resume I shall give of his results contains nearly all that 
 is accurately and definitely acquired to science upon 
 the subject. He divides his arguments upon it into 
 three heads. The first is an argument from the internal 
 heat of the earth ; the second is from the tidal retarda- 
 tion of the earth's rotation ; and the third is from the 
 sun's temperature. 
 
1 68 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 Now, as regards the internal heat of the earth, we 
 know by actual observation that as we go down a deep 
 mine we find the temperature almost invariably increas- 
 ing. We know also that whenever a body is hotter at 
 one part than another, the tendency of heat is always 
 to flow from the hotter part of the body to the colder. 
 Therefore, as the earth's crust is warmer and warmer as 
 we go farther and farther down, there must be a steady 
 flow of heat outwards from the interior to the surface. 
 The earth is therefore even now losing heat at a certain 
 perfectly measurable and calculable rate. But if it 
 is losing heat now we can calculate by known physical 
 laws and known mathematical processes, from the pre- 
 sent state of distribution of temperature, we can cal- 
 culate backwards how its heat was arranged a hundred 
 thousand or a thousand thousand years ago, just as 
 certainly if physical laws as we know them now were 
 in existence in the past as we can predict from our 
 mathematical calculations what will be its distribution 
 at any time future, if these physical laws continue to 
 hold. In working out such a question as this, it is 
 found that the rise of temperature, taken (over the 
 whole earth's surface) at an average of about one 
 degree for 100 feet of descent, leads to this conclusion, 
 that about ten millions of years ago the surface of the 
 earth had just consolidated, or was just about to con- 
 solidate; and in the course of a comparatively few 
 thousands of years after that, the surface which had 
 been consolidated had become so moderately warm 
 as to be fitted, at all events in some parts, for the exist- 
 ence of life such as we know it. That is to say, the 
 surface temperature, in certain regions at least, was not 
 greater than that which is perfectly easily borne by 
 
SOURCES AND TRANSFERENCE OF ENERGY. 169 
 
 animals and vegetables in the tropics at the present 
 day ; and the rate of increase of temperature in going 
 down below the surface was one degree in perhaps 
 every six inches, or every ten inches, or something of 
 that sort. That would not interfere very greatly with 
 the growth of vegetables ; so from this point of view 
 we are led to a limit of something like ten million 
 years as the utmost we can give to geologists for their 
 speculations as to the history even of the lowest 
 orders of fossils. 
 
 If we were to trace the state of affairs back, instead 
 of to ten millions, to a hundred millions of years, we 
 should find that (if the earth then existed at all, if that 
 collocation of matter which we call the earth was then 
 actually formed), and if the physical laws which at 
 present hold have been in operation during that 
 hundred million years, then the surface of the earth 
 would undoubtedly have been liquid and at a high 
 white heat, so that it would have been utterly incom- 
 patible with the existence of life of any kind such as 
 we can conceive from what we are acquainted with. 
 Thus we can say at once to geologists, that granting 
 this premiss, that physical laws have remained as they 
 are now, and that we know of all the physical laws 
 which have been operating during that time, we can- 
 not give more scope for their speculations than about 
 ten or (say at most) fifteen millions of years. 
 
 But I daresay many of you are acquainted with the 
 speculations of Lyell and others, especially of Darwin, 1 
 who tell us that even for a comparatively brief portion 
 of recent geological history three hundred millions of 
 years will not suffice ! 
 
 1 Origin of Species (1859), p. 287. 
 
i;o SOURCES AND TRANSFERENCE OF ENERGY. 
 
 We say So much the worse for geology as at present 
 understood by its chief authorities, for, as you will 
 presently see, physical considerations from various inde- 
 pendent points of view render it utterly impossible that 
 more than ten or fifteen millions of years can be granted. 
 
 You see, then, that the argument from the internal 
 heat of the earth depends upon working the problem 
 backwards, and finding what is the utmost limit of time 
 back at which the surface of the earth could possibly 
 have been fitted for the life of either animals or plants. 
 
 And this leads me to say a word or two about one 
 of the most remarkable results of investigations of this 
 kind, investigations conducted as purely mathematical 
 problems, and based entirely upon physical experimental 
 data, viz., upon the observed laws of conduction of 
 heat. In the great majority of problems where the 
 data are of the nature of those we have as to the under- 
 ground temperature of the earth, the question of the 
 future is a perfectly definite one. If we knew the pre- 
 sent thermal condition of every part of the earth's mass, 
 we could calculate what would be the temperature at 
 any depth below the earth's surface at any time future, 
 provided things went on under the same conditions as 
 they are going at present, and our results would be 
 always perfectly and directly intelligible. But when 
 we try to work the problem the other way, when we 
 ask what must have been the thermal state of such a 
 body as the earth at such and such a time past, then 
 we invariably, or almost invariably, find a limit of time 
 beyond which our equations become uninterpretable. So 
 far as our equations represent what would be the course 
 of nature provided the existing physical laws remained 
 true, there must have been at this definite epoch of 
 
SOURCES AND TRANSFERENCE OF ENERGY. 171 
 
 past time the introduction of a new state of affairs, 
 something which arose from a previous state by 
 means of a process not contemplated in our investiga- 
 tion. 
 
 In the case of the earth there is no particular diffi- 
 culty in understanding what might have been that an- 
 terior state of affairs. We can trace matters back to 
 the time when the earth was molten throughout. Going 
 farther and farther back, we come to a distribution 
 (which might be pretty nearly uniform) of heat through- 
 out the whole mass. Now, a uniform distribution of 
 heat throughout the whole mass could have had no 
 existence for more than an instant, so far as we know ; 
 and we cannot conceive it to have arisen from any pre- 
 vious distribution of heat in the mass. But we can 
 understand how a high temperature throughout the 
 whole mass might have been produced by the materials 
 of which the earth is composed falling together. If 
 they fell together in such a way that the whole mass of 
 the earth was agglomerated together almost at once ; 
 and if the different parts impinged together with pro- 
 perly arranged velocities, it is possible the earth may 
 have been agglomerated together, so as to have for a 
 moment the same temperature throughout, thus giving 
 us something like what we have deduced from our for- 
 mulae. But you will notice the state of things before 
 and after that moment. Before that moment it was 
 cold masses of matter, separated perhaps by millions of 
 miles, or far more than that, but having potential energy 
 of gravitation gradually being transformed into kinetic 
 energy of approach. Then, at the instant of impact, 
 came the critical change. Instead of the cold scattered 
 masses of matter, there was suddenly an agglomerated 
 
172 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 mass of almost uniform temperature throughout, and it 
 has been cooling and shrinking ever since. 
 
 The second of these arguments of Sir William Thom- 
 son depends upon the tidal retardation. In my first 
 lecture I mentioned to you that there was such an 
 effect, and that it had been actually observed by astro- 
 nomers in a very peculiar way ; because, on calculating 
 back from the known present motion of the moon, it 
 was found that there must be some unrecognised pecu- 
 liarity in that motion, which had not been deduced by 
 calculations founded upon gravitation, either as attrac- 
 tion or as disturbance. The moon, in fact, seems to 
 have been moving quicker as time has gone on, since the 
 eclipses of the fifth and eighth centuries before our era. 
 The only way, as Laplace put it, in which it could be 
 accounted for in his time, was by what he called ' secular 
 acceleration of the moon's mean motion.' In other 
 words, the average angular velocity with. which the 
 moon moves round the earth appears to have been in- 
 creasing for the last 2000 years or more. He showed 
 that there was a mode of accounting for this by planet- 
 ary disturbance of the earth's orbit, and as calculated 
 by him, this explanation seemed to account for exactly 
 the amount of acceleration which was observed in the 
 moon's motion. Using his formulae and the numbers 
 calculated from them, and working back to those old 
 days, we find we arrive at almost the circumstances of 
 those eclipses as described by historians. 
 
 Fortunately, Adams, a few years ago, revised La- 
 place's investigation, and found that he had neglected 
 a portion of the necessary terms, and that the expla- 
 nation given by Laplace, when properly corrected, ac- 
 counted for only one-half of the phenomenon observed ; 
 
SOURCES AND TRANSFERENCE OF ENERGY. 173 
 
 so that there still remained one-half of the quantity to be 
 accounted for. This could not be accounted for by the 
 disturbance of other bodies attracting the moon. Why 
 then does the moon appear every revolution to be moving 
 faster and faster round the earth ? Well, the only way 
 in which we can explain it, after we have made every 
 possible allowance for effects of disturbance by other 
 planets, is simply to inquire, Does our measure of time 
 continue the same ? 
 
 We measure the time of the moon's revolution in 
 terms of hours, minutes, and seconds ; but these hours, 
 minutes, and seconds are measured for us not by our 
 clocks, as you may at first think. We set our clocks 
 by the earth's rotation, and therefore it is in terms 
 of the earth's rotation that we measure the time of the 
 moon's revolution round the earth. So that the moon 
 will appear to be moving quicker round the earth, 
 even supposing her orbit be altogether undisturbed, if 
 the earth itself, which is furnishing the unit of time in 
 which her revolution is to be measured, is rotating 
 slower and slower from age to age. 
 
 Then comes the question, Is there a cause which 
 tends to slacken the earth's rotation ? Newton laid it 
 down, in his First Law of Motion, that motion unresisted 
 remains uniform for ever, and referred to the earth as a 
 particular instance where there is nothing in the attrac- 
 tion of the sun or moon, or the disturbance caused by 
 any of the other planets, affecting the rate of its rota- 
 tion about its axis. But it was left to Kant, first of all, 
 to point out, and even to approximate in amount to, 
 a resistance to the earth's rotation due to the tide-wave ; 
 and to show that the earth, because the tide-wave is 
 lifted up towards the moon, and on the opposite side 
 
174 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 from the moon, has constantly to rotate inside what is 
 practically a friction-brake. The water is held back by 
 the attraction of the sun and moon, and the earth has 
 to move inside this shell of water. There is therefore 
 a source of constant friction, and friction of course 
 constantly produces development of heat. The heat 
 must be accounted for by some energy transformed, 
 and what is here transformed is part of the energy of 
 the earth's rotation about its axis. So long as tides go 
 on, there will therefore be constantly a retardation of 
 the rate of the earth's rotation. 
 
 Now let us see when this relaxation of the earth's 
 rotation would cease. Obviously this would be at the 
 instant when the earth at last ceased to rotate within 
 the tide-wave ; in other words, when the tide-wave 
 rotates along with the earth, when it is always full tide 
 at one and the same portion of the earth's surface, the 
 tide-wave being fixed (as it were) upon the earth's sur- 
 face. But the ^tide-wave is always, approximately at 
 least, directed towards the moon, so this part of the sur- 
 face where the tide-wave is fixed for ever must be con- 
 stantly turned towards the moon. In other words, if 
 there were no sun producing tides, but the moon only, 
 the final effect of the tides in stopping or quenching the 
 earth's rotation would be to bring the earth constantly 
 to turn the same portion of its surface towards the 
 moon, and therefore to rotate about its axis in the same 
 period as that in which the moon revolves about it. 
 This most remarkable ultimate effect we see already 
 produced in the moon, it is precisely the same thing, 
 we see the moon turning almost exactly the same 
 portion of its surface to the earth at all times. The 
 little deviation we see occasionally is precisely ac- 
 
SOURCES AND TRANSFERENCE OF ENERGY. 175 
 
 counted for by the fact that the moon's orbit is not 
 exactly a circle, and therefore the moon does not 
 move in it with the same rapidity when it is nearest the 
 earth as it does when it is farthest away from the earth. 
 We are thus, as it were, enabled occasionally to see a 
 little round the corner. The moon is now rotating pre- 
 cisely in the way in which the earth will in time rotate 
 when as much as possible of its energy of rotation is 
 used up in producing heat by tidal friction. And that 
 the moon should already have come into this state so 
 long before the earth has arrived at it, need not sur- 
 prise us. The moon's seas (when she had them) were of 
 molten lava, far more viscous than water ; the tide- 
 raising force on her surface depended on the mass of the 
 earth, some eighty times greater than that of the moon, 
 which is the main agent in our comparatively puny tides : 
 and, in addition, the moon's moment of inertia is very 
 small compared with that of the earth. 
 
 It being thus established that the rate of rotation of 
 the earth is constantly becoming slower, the question 
 comes : How long ago must it have solidified in order 
 that it might then have the particular amount of polar 
 flattening which it shows at present ? Suppose for 
 instance it had not consolidated less than a thousand 
 million years ago. Calculation shows us that at that 
 time, on the most moderate computation, it must have 
 been rotating at least twice as fast as it is now rotating. 
 That is to say, the day must have been 12 hours long 
 instead of 24. Now, if that had been the case, and the 
 earth still fluid throughout, or even pasty, that double 
 rate of rotation would have produced four times as great 
 centrifugal force at the equator as at present, and the 
 flattening of the earth at the poles and the bulging at 
 
i ;6 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 the equator -itfould both have been much greater than 
 we find them to be. 
 
 We say then, that because the earth is so little 
 flattened it must have been rotating at very nearly the 
 same rate as it is now rotating, when it became solid. 
 Therefore, as its rate of rotation is undoubtedly be- 
 coming slower and slower, it cannot have been many 
 millions of years back when it became solid, else it 
 would have solidified into something very much flatter 
 than we find it. That argument, taken along with the 
 first one, probably reduces the possible period which can 
 be allowed to geologists to something less than ten 
 millions of years. 
 
 Then comes the third argument, it is not quite so 
 emphatic in its demands for restricted periods as either 
 of the other two, the argument from the length of 
 time that the sun can be imagined by its radiation to 
 have kept the earth in a state fit for the habitation of 
 animals and vegetables. The argument from this point 
 of view, I say, is not so trenchant as the others, because 
 we can imagine that when the sun was immensely hot, 
 as it must have been at some previous time, enor- 
 mously hotter than at present, we can imagine that 
 one effect of its heat was to throw off from its surface 
 such enormous clouds of absorbing vapour, which cooled 
 as they left the surface, that the effective amount of 
 radiation reaching the earth might not have been greater 
 than at present. So it is possible to conceive a sort of 
 uniformitarian state of radiation from the sun: account- 
 ing for it by saying that when the sun was hottest and 
 was radiating the most, it was simultaneously raising the 
 greatest amount of obstructions to the propagation of 
 radiations from its surface. A similar argument might, 
 
SOURCES AND TRANSFERENCE OF ENERGY. 177 
 
 of course, be devised with reference to the greater 
 amount of vapour which increased solar radiation would 
 raise to be condensed in the earth's atmosphere. How- 
 ever, if we make the supposition that the sun has been 
 cooling even at a uniform rate, we find that this mode 
 of calculation leads us, in spite of the enormous amount 
 of heat which must have been produced in the sun by 
 the impact of its materials when they fell together, to 
 the conclusion that on the very highest computation 
 which can be permitted, it cannot have supplied the 
 earth, even at the present rate, for more than about 
 fifteen or twenty million years. 1 
 
 This, I again say, is not so trenchant an argument as 
 either of the other two ; but the conclusion from these 
 three arguments is not, as some of Thomson's opponents 
 seem to imagine, only as strong as the weakest of the 
 three. In order to upset the conclusions drawn from 
 them, it would be necessary to disprove two of these 
 arguments, and greatly to damage the third. But each 
 of these arguments is quite independent of the other 
 two, and is for all tend to something about the same 
 to the effect that ten millions of years is about the 
 utmost that can be allowed, from the physical point of 
 view, for all the changes that have taken place on the 
 earth's surface since vegetable life of the lowest known 
 form was capable of existing there. 
 
 I leave this part of the subject for a time. This has 
 been a developed application of the theory of energy 
 
 f 1 Note to Third Edition. Several critics, as well as some writers of a 
 higher order, think they have detected inconsistency between this passage 
 and another in p. 156. There is no such inconsistency. At p. 156 the 
 whole supply was spoken of; while here we are dealing with what has 
 been already expended.] 
 
 M 
 
178 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 to the solar system first, and then in particular to our 
 own earth. 
 
 Now, I pass to one or two other applications of the 
 second law of thermodynamics, especially in the beau- 
 tiful part of it furnished by Carnot's reasoning. We 
 have now to take up the consideration of the transfer- 
 ence of energy from one body to another, not the 
 passage of energy from one part of a body to another 
 portion of the same body. That is in the main the 
 question of the conduction of heat, to which I shall 
 devote another lecture. But now we are to speak 
 of the radiation of heat and light from one body to 
 another. 
 
 But before I take up that I shall direct your atten- 
 tion to one or two experiments, some of them long 
 known but at their epoch hardly explained, others only 
 recently made. 
 
 First of all, let us take as the medium of communica- 
 tion between two bodies : the medium through which 
 the energy is to be transferred from one body to an- 
 other: a strong wooden framework such as this. I 
 have two pendulums with very massive bobs suspended 
 from it, and have carefully made these two pendulums as 
 nearly as possible of the same length, so that their 
 times of vibration are as nearly as possible the same. 
 Both pendulums are now at rest, but suppose I set 
 one to vibrate, leaving the other at rest, you will notice, 
 if you watch the second for a short time, that it begins 
 to vibrate in its turn, and as time goes on it swings 
 through larger and larger arcs of vibration, till at last 
 the first pendulum is reduced to rest. Now, this is 
 quite obviously a case of transference of energy from 
 one pendulum to the other, effected, you will see, 
 
SOURCES AND TRANSFERENCE OF ENERGY. 179 
 
 through the wooden structure ; but it has been effected 
 thus completely on account of the simple fact that the 
 two pendulums had been (as it were) previously tuned 
 together and made to vibrate in precisely equal times. 
 We shall presently try the experiment with the two 
 pendulums not tuned together, and then you will see 
 
 that there may be transference of energy for a few 
 minutes, but it will be far less complete, and in the 
 course of a very short time the whole will be given 
 back again to the first pendulum, and so on. In the 
 case before us, a short time will suffice for the whole of 
 the energy to be transferred from the one pendulum to 
 the other, and it will then be just as if we had turned 
 
i8o SOURCES AND TRANSFERENCE OF ENERGY. 
 
 the whole apparatus round through two right angles. 
 You will have the second pendulum vibrating with the 
 whole original energy in place of the first, then the 
 transference will go on again in the opposite direction, 
 and the first will get back what it lost, except what has 
 been unavoidably dissipated in producing air vibrations, 
 and in producing heat in the materials of the frame- 
 work, which is not a perfectly elastic body, and all 
 throughout which friction and various other disturb- 
 ing causes operate. Notice particularly that the mode 
 of transference in this case is through a solid body, and 
 that it is simply by vibration of the solid body that it 
 has been effected. 
 
 I pass from the consideration of transference through 
 a solid body to transference by a gaseous body ; and 
 we shall easily realise precisely the same effect by 
 means of a couple of tuning-forks. These forks are 
 tuned precisely to the same note. They are furnished 
 with resonating cavities, to enable them to communi- 
 cate to the air as much of their energy as possible. If 
 I set one in vibration, the effect of the resonating cavity 
 is to enable it to set in lively motion, at its own period 
 
SOURCES AND TRANSFERENCE OF ENERGY. 181 
 
 of vibration, the air surrounding it. But here is another 
 cavity which is tuned to that particular time of vibra- 
 tion. The tuning-fork attached to it is also tuned to 
 precisely the same note, and now we find that when I 
 first of all start the first tuning-fork, then turn it so as 
 to place its resonating cavity with the mouth towards 
 the mouth of the resonating cavity of the other, through 
 the gas-filled space between the two, there is a trans- 
 ference of energy which is such that if, after a second 
 or two, I suddenly stop with my finger and thumb the 
 vibrations of the first fork once for all, you will hear 
 the other resounding with considerable loudness. The 
 transference of energy has here been made through the 
 air instead of through a solid body, as in the case of 
 the wooden framework connecting the pendulums. 
 
 [I now call your attention once more to the massive 
 pendulums, because the first has again handed over the 
 greater portion of the energy to the second. My 
 assistant will now put them out of tune, and we will 
 try the experiment again.] 
 
 Connected with these, and to be explained on precisely 
 the same physical principles, we have another strikingly 
 
182 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 illustrative experiment. Consider this third arrange- 
 ment, where we are to have the transference of energy 
 effected, not as in the case of the pendulums through a 
 solid bar, nor as in the case of the tuning-forks, through 
 the gaseous medium between the two, but simply by 
 magnetic action : force acting between a couple of steel 
 bars ; an action which, as you all know, is not affected 
 by the interposition of any non-magnetisable body 
 whatever, and which is as energetic through what we 
 call a vacuum as through air. These bar magnets are as 
 nearly as possible of equal mass, and are supported by 
 strings or wires of equal length. If I take one of them 
 away, the time of oscillation of the other will be the 
 same, whichever I take. In their position of equili- 
 brium they hang in the same horizontal line. Now 
 they are both at rest at this moment. Suppose I com- 
 municate vibration to one of them in the direction of 
 its length. You notice how very rapidly the energy is 
 transferred from the one to the other. The magnet 
 which was at first at rest has now gained the greater part 
 of the energy, and in the course of a very few seconds 
 more you will see the other has lost it all. There it is : 
 absolutely at rest for a moment ; and now the process 
 recommences the other way. After exactly the same 
 interval of time as that which elapsed from the com- 
 mencement of the experiment to the instant of the 
 first magnet's being brought to rest, the second will 
 be brought to rest in its turn. There it is at rest now 
 for an instant only ; and the same transference will go 
 on again indefinitely. Now, what is it that conveys the 
 energy in this case ? The transference of energy is due 
 entirely to the magnetic attraction of one of those bars 
 for the other ; because, though the apparatus is con- 
 
SOURCES AND TRANSFERENCE OF ENERGY. 183 
 
 structed suspiciously like that which I employed a few 
 minutes ago for the massive pendulums, the masses of 
 these bars are not sufficient to produce any appretiable 
 effect upon the supporting beam, so that it would be 
 impossible, if we were to demagnetise these bars, to 
 obtain any appretiable transference of energy from the 
 one to the other. This then is transference of energy 
 from one body to another, not through a solid, nor 
 through a gas, as in our recent experiments, but through 
 the magnetic medium, whatever that may be, what 
 Clerk-Maxwell has given us strong reason to believe is 
 the same medium as that which conveys light and 
 radiant heat. So we have here, as it were, a third 
 mode of transference of energy from one body to 
 another ; and this resembles much more nearly than 
 either of the other two the cases to which I am about 
 to proceed. 
 
 [But before I so proceed, you will notice that I have got 
 the original pair of massive pendulums on the wooden 
 frame put out of tune, and you can now study how the 
 oscillations are handed on from the one to the other. 
 You see that the transference, if any at all, is very much 
 more slight than before, and not only is it slight, but 
 after a short time it ceases, and then sets in the other way. 
 The energy of the second pendulum is sometimes falling 
 and sometimes increasing, but it never rises to any great 
 percentage of what remains in the first. In fact, because 
 of the dissimilarity of their periods of oscillation, the 
 one comes sometimes into a position in which it can 
 gain energy from the other, and a second or two later 
 it puts itself into such a position as to lose energy, and 
 so on backwards and forwards ; whereas, when the two 
 were tuned almost exactly to one another, if they were 
 
1 84 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 at any instant in such a position that the one was giving 
 energy to the other, they would remain for a very long 
 period in such a relative position. The one would 
 always be throughout that period in the most favour- 
 able position for communicating energy to the other, 
 and this solely because their periods of oscillation were 
 alike ; whereas when their periods of oscillation differ, 
 the one is sometimes getting away from the other, and 
 sometimes getting pulled back.] 
 
 All of you must have noticed this in the ringing of a 
 massive bell. Even a child can ring an immensely mas- 
 sive bell with very slight application of force, provided 
 he perseveres in pulling exactly at the proper moments. 
 Just as the bell is about to descend, let him pull, so as 
 to quicken the motion, but let him slacken when the 
 motion is such that a pull would tend to stop it. By 
 waiting till the exact moment, and properly timing the 
 impulse, he is capable of giving large oscillations to a 
 mass which otherwise he is almost incapable of setting 
 in motion. 
 
 In the same way it is possible to check it by apply- 
 ing retardations exactly at the proper moment. This 
 would be at exactly equal intervals of time, represent- 
 ing the vibration of the bell if it were left to itself. 
 
 Thus all these experiments depend upon the trans- 
 ference of energy in a kinetic form between two bodies, 
 and the test of the capability of the one for receiving the 
 energy which is sent out by the other is this, that the 
 natural undisturbed times of vibration of the two bodies 
 shall be as nearly as possible precisely the same. I 
 have not time to enter more deeply into the subject 
 to-day, but I shall endeavour, in the few minutes which 
 remain to me, to sketch briefly what is to be our appli- 
 
SOURCES AND TRANSFERENCE OF ENERGY. 185 
 
 cation, to modern science, of these purely mechanical 
 experiments. 
 
 Suppose we have a substance which, instead of giving 
 off sound, in consequence of its vibrations, is vibrating 
 so rapidly as to be giving off some particular colour of 
 light or of radiant heat. Then the substance which 
 will be best qualified to absorb that particular colour of 
 light or of radiant heat, will be another body of pre- 
 cisely the same kind as the first, because the two speci- 
 mens of the same matter will, under the same circum- 
 stances, vibrate according to precisely the same laws ; 
 and therefore if you define a particular beam of light 
 by having it sent out from a particular substance which 
 is rendered incandescent, another specimen of the same 
 substance will find in the beam precisely those particular 
 times of vibration which most aptly suit it, and there- 
 fore will be best fitted to absorb them. 
 
 This is, briefly, the dynamical principle at which 
 Professor Stokes arrived more than twenty years ago, 
 and which, if its applications had been properly pursued 
 at the time, would have given us ten years' start in our 
 knowledge of celestial chemistry. Stokes' illustration 
 was this : He imagined a space, such as this room for 
 instance, to be filled with tuning-forks (with resonat- 
 ing cavities let us say) or with pianoforte wires stretched 
 about in all directions so as not to interfere with one 
 another, but as nearly as possible to fill the whole space. 
 If all the tuning-forks, or all the pianoforte wires, are 
 tuned to the same note, that arrangement will form a 
 medium which is capable, when agitated in the simplest 
 manner, of giving out only that particular note. Set 
 all the tuning-forks to vibrate, they all conspire to 
 strengthen one another and give out their one particular 
 
1 86 SOURCES AND TRANSFERENCE OF ENERGY. 
 
 note, and that note only. On the other hand, when you 
 use that arrangement not as a source of sound, but as 
 a medium through which you endeavour to make sound 
 pass, then from what I have just shown you, you will 
 obviously find it to be particularly opaque to that par- 
 ticular note, and to that note only. Suppose a per- 
 former with a powerful instrument (such as a cornopean) 
 placed at one side of the room, and a listener at the other. 
 Then let the player play any note he pleases except the 
 note belonging to the forks or strings, that note will 
 be heard in full intensity, except in so far as the strings 
 (merely as obstacles) intercept the passage of the sound. 
 Such a note will be heard almost as powerfully on the 
 other side of the room as if there had been no tuning- 
 forks or wires present. But as soon as he plays the 
 particular note which belongs to all the forks or all the 
 strings, it comes to be just the question of the pendulums 
 or magnets, or the two tuning-forks which I have just 
 shown you. The contents of the room gradually absorb 
 each a portion of the sound which reaches it, and are 
 set into vibration by it. If there be enough of them 
 they take all the energy of the sound, and of course 
 completely prevent the sound from passing through 
 the medium, except in so far as they give it out them- 
 selves. 
 
 Here, then, is a medium which of itself can give out 
 one definite note, and one note alone, when it is a 
 source of sound ; but which, when it is employed as 
 a sort of sifter of sound, can sift out from a mixed or 
 confused sound only that particular note. That then 
 is mechanically or physically the analogy to which 
 we shall have to reduce the fundamental principles of 
 spectrum analysis. 
 
LECTURE VIII. 
 
 RADIATION AND ABSORPTION. 
 
 History of the discovery of the Physical Basis of Spectrum Analysis. First 
 result of Spectrum Analysis applied to* non-terrestrial bodies ; There is 
 Sodium gas in the Sun's Atmosphere. Elaborate experiments of Stewart 
 and Kirchhoff. Identity of Light and Radiant Heat. Distinctive char- 
 acters of a particular ray. Application of Carnot's principle to establish 
 the equality of radiating and absorbing powers. Black, transparent, and 
 perfectly reflecting bodies. 
 
 I ENDED my last lecture by considering various modes 
 of transference of energy of vibration from one body to 
 another. I took in particular three cases, in the first 
 of which the transference took place through a solid 
 body, in the second the vehicle was ordinary air, and 
 in the third case it was the medium which propagates 
 magnetic and electric actions. But in every one of 
 these cases we found that the condition which is abso- 
 lutely necessary for a complete handing over of the 
 energy of one vibrating body to another, whatever be 
 the intervening medium of communication, was that 
 the time of vibration of the second body should be 
 adjusted to be exactly equal to the time of vibration of 
 the body which had the energy at first. 
 
 I then went on to suppose a finite space to be filled 
 with a number of such vibrating bodies, all tuned (as 
 it were) to vibrate in precisely the same time ; and I 
 showed you that if we considered a space so filled to 
 act as a medium, it would be such as when set in 
 
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190 RADIA TION AND ABSORPTION. 
 
 continuously) along a straight line on the screen ; so 
 that there must be a constant overlapping of a great 
 many of these successive spots at any one point of the 
 spectrum, and therefore it must be practically impos- 
 sible by this method to detect the absence of any one 
 particular shade of colour. 
 
 Now, though the optical method which Newton 1 
 devised for the purpose of avoiding this difficulty is 
 a very simple one, it deserves a word or two, as it will 
 help you to understand the experimental illustrations 
 I mean to give in my next lecture. Instead of using a 
 round hole we now use a narrow slit whose sides are 
 perfectly parallel to each other, and which can be made 
 (by proper mechanical adjustment) as wide or as narrow 
 as we choose. The light from the sun or electric lamp, 
 or whatever source we employ, comes through this slit 
 as a thin sheet, and falls upon an achromatic lens ; that 
 is, a lens which behaves in almost precisely the same 
 way to all the differently coloured rays falling upon It. 
 It is usually convenient to place the lens at such a 
 distance from the slit that at exactly the same dis- 
 tance beyond the lens an image of the slit, equal to 
 it in size, will be formed on the screen. If, then, 
 sunlight pass through the slit, and fall upon the lens, 
 we shall have, on a screen placed at the proper dis- 
 tance, simply an intensely bright white line, con- 
 sisting of all the different rays belonging to sunlight. 
 But if you interpose in the course of those rays, just 
 after they come through the lens, a prism, with its edge 
 parallel to the slit, the effect will be a change of direc- 
 tion of those cones of rays which are converging to- 
 wards the image. The prism will most refract the 
 
 1 Optics, Book I. Parti. Exp. u, Illustration. 
 
RA DIA TION AND ABSORP TION. 1 9 1 
 
 violet rays, and all the others will be less and less 
 refracted as their wave-lengths grow longer and longer 
 till we reach the lowest red in the spectrum ; and there- 
 fore instead of having a set of coloured discs, as by 
 the first method, succeeding one another with their 
 centres along a line, and overlapping, you will have a set 
 of parallel coloured images, each no broader than the 
 slit itself, and you can make the slit as narrow as you 
 please. In every part the consecutive images lie side by 
 side, contiguous to one another ; but if there be light of 
 any wave-length or any particular refrangibility which 
 is wanting, then the space corresponding to that will 
 be left as a dark line (an unilluminated image of the 
 slit) across the otherwise continuous coloured band. 
 
 You see hanging on the wall a coloured plate repre- 
 senting the solar spectrum, formed in the way I have 
 just pointed out, and you can see those dark lines 
 across it. Only a few of the chief ones are figured. 
 The number of those whose position is already care- 
 fully measured, or photographically registered, amounts 
 to many thousands. [See diagram, p. 192.] They were 
 first noticed by Dr. Wollaston, about the beginning of 
 this century, but he paid very little attention to them ; 
 and they were re-discovered a considerable time after- 
 wards by the great optician Fraunhofer, whence they 
 have been called Fraunhofer's lines. 
 
 Of those lines one of the most remarkable is that to 
 which Fraunhofer gave the name of D, which you will 
 see upon the picture near the boundary between orange 
 and yellow. When, however, a very perfect prism is 
 used, and a telescope is employed instead of the screen 
 to receive the spectrum, then we are enabled to see that 
 this line is double. This gives it a very remarkable 
 
192 RADIATION AND ABSORPTION. 
 
 characteristic, two almost 
 equally strong dark lines 
 across the spectrum, so close 
 together as to be quite in- 
 capable of being separated 
 from each other without the 
 use of a telescope, or of a 
 great number of prisms in- 
 stead of one. 
 
 Now,Fraunhofer observed 
 that in the flame of an or- 
 dinary tallow candle, when 
 he tested it just as he had 
 tested sunlight, there ap- 
 peared a pair of bright lines, 
 brighter than the rest of the 
 otherwise continuous spec- 
 trum, that there were no 
 other lines in the spectrum 
 but those two bright ones, 
 and that they occupied, so 
 far as his instrumental mea- 
 surements enabled him to 
 discover, precisely the same 
 place in the spectrum as the 
 two dark lines D of the solar 
 spectrum. That is to say, 
 the candlelight possessed in 
 excess precisely one of those 
 definite components in which 
 sunlight had been found to 
 be either wholly, or at least 
 to a great extent, deficient. 
 
RADIA TION AND ABSORPTION. 193 
 
 No further actiori seems to have been taken with 
 regard to this very remarkable coincidence, until Pro- 
 fessor Miller of Cambridge, in 1849 or ^S * made a 
 more exact experiment, with the view of comparing 
 these yellow lines in the flame of a spirit-lamp with the 
 dark lines of the solar spectrum, so as to test whether 
 they are exactly coincident with one another or not. 
 The result of his measurements was that the close- 
 ness of coincidence was so great that it was impossible, 
 with his finest instruments, to find any divergence 
 between them. The two bright lines exactly corre- 
 sponded with the two dark ones as to refrangibility, and 
 therefore also wave-length. It had been conclusively 
 shown by Swan, that the two bright lines in the light 
 of a candle are due to common salt, which pervades 
 the air everywhere, and of which the very minutest 
 trace is capable of producing this yellow light. It 
 was then that Stokes at once took the additional step 
 required, and explained that the glowing vapour, which 
 is capable, when it is the source of light, of giving these 
 definite bright lines, is itself, when used as an absorbing 
 medium, capable of absorbing these and these only ; 
 and therefore that Miller's test of the exact coincidence 
 of the bright and dark lines was a complete proof that 
 there exists in the sun's atmosphere this vapour of sodium. 
 
 That occurred about 1850, and ever since that time the 
 fact that sodium exists in an incandescent state in the 
 sun's atmosphere, has been taught (as an experimentally 
 ascertained truth) by Sir William Thomson and others. 
 This was the birth of Spectrum Analysis, as applied to 
 celestial objects. 
 
 It is curious to find that the deservedly celebrated 
 Foucault had in 1849 made the same experiment in an 
 
 N 
 
194 RADIA TION AND ABSORPTION. 
 
 even more convincing form than that which Miller had 
 adopted. He found that the light, of what is called the 
 electric arc, has in its spectrum these two bright lines ; 
 but that when he looked at sunlight through the electric 
 arc and allowed the sunlight to come in so strongly as 
 to overpower the electric light, then the electric light 
 actually cut out the D lines from the solar spectrum more 
 powerfully than if it had not been present. Although 
 it was there giving out these lines strongly, it was not 
 competent to fill up the wants in the solar spectrum, but 
 actually made the deficiency more glaring than before. 
 Then, to test whether it was really the case that this 
 electric arc was absorbing these particular kinds of light, 
 Foucault very ingeniously took advantage of the fact that 
 the carbon points between which the electric arc is 
 usually formed become incandescent and, reaching a 
 higher temperature, are very much more brilliant than 
 the arc itself. By means of a small mirror he reflected 
 the white light from these carbon points through the 
 electric arc, and found that whenever it passed through 
 the arc, instead of getting brighter at those places, 
 it had those very lines cut out of it ; but whenever it 
 passed beside the electric arc it had no deficiencies. 
 Curiously enough, he seems to have derived no defini- 
 tive conclusion from this. 
 
 Then, again, exactly the same statement was made in 
 Sweden by Angstrom in 1853. He says, as the result 
 of experiment, that an incandescent gas gives out 
 luminous rays of the same refrangibility as those which 
 it absorbs. 
 
 Each one of these three thus completely made and 
 recorded the discovery of the physical basis of spectrum 
 analysis before 1854; but, of the three, Stokes alone 
 
RADIATION AND ABSORPTION. 195 
 
 made the application which really constitutes celestial 
 chemistry. Fox Talbot had, long before, distinctly 
 pointed out the use of the prismatic method for dis- 
 tinguishing terrestrial substances in a flame. 
 
 As I have already told you, Sir W. Thomson has, 
 certainly ever since 1852 (probably a year or two sooner), 
 regularly given in his public lectures in Glasgow Uni- 
 versity the statement that there is sodium vapour in the 
 sun's atmosphere ; and that, to find other constituents 
 of solar and stellar atmospheres, all that is wanted is a 
 comparison of the dark lines in their spectra with the 
 bright lines in the incandescent vapours of various 
 terrestrial substances. 1 But it was not till 1859 or 1860 
 that this was known generally, or was applied to any 
 purpose further than to the mere recording of the 
 existence of sodium in the vapours around the sun. I 
 should like to read a quotation from some remarks I 
 made a year or two ago to the Royal Society of 
 Edinburgh upon this curious subject : 2 
 
 It is difficult now-a-days, when so many philosophers are en- 
 gaged almost simultaneously at the same problem, to decide which 
 of their successive steps in advance is that to which should really 
 be attached the title of discovery (in its highest sense) as distin- 
 guished from mere improvement or generalisation. You have only 
 to look at the recent voluminous discussions as to the discoverer 
 of the Conservation of Energy, to see that critics may substantially 
 agree as to facts and dates, while differing in the most extraor- 
 
 1 President's Address, Brit. Ass. 1871. See Stokes, Nature, January 6, 
 1876. Thomson writes to me with reference to this (January 23, 1876) : 
 ' I never imagined that Stokes thought I was generalising too fast, or that 
 /was generalising at all. I felt that I had learned the whole thing from 
 him on a foundation of absolute certainty. . . . All I said in my 
 Edinburgh Address on this matter is, I believe, irrefragable.' 
 
 * Proceedings R.S.E., May 15, 1871. 
 
196 RADIA T1ON AND ABSORPTION. 
 
 dinary manner as to their deductions from them. 1 Some of these 
 writers, no doubt, put themselves out of court at once by habitually 
 attributing the gaseous laws of Boyle and Charles to Mariotte and 
 Gay-Lussac. Men who persist in error on a point so absolutely 
 clear as this, show themselves unfit to judge in any case of even a 
 little more difficulty. Others, who strongly support the so-called 
 claims of Mayer in the matter of Conservation of Energy, and who 
 should (to be consistent) therefore far more strongly advocate the 
 real claims of Talbot, Stokes, Angstrom, Stewart, etc., to the dis- 
 covery or spectrum analysis, are found to uphold Kirchhoff as 
 alone entitled to any merit in the matter. 
 
 The question of priority just alluded to illustrates in a very 
 curious way a singular and lamentable, though in one sense 
 honourable, characteristic of many of the highest class of British 
 scientific men ; i.e. their proneness to consider that what appears 
 evident to them cannot but be known to others. I do not think 
 that this can be called modesty ; it is rather a species of diffidence 
 due to their consciousness that in general their accurate knowledge 
 of the published developments of science is confined mainly to 
 those branches to which they have specially devoted themselves. 
 Their foreign competitors, on the other hand (especially the Ger- 
 mans), are often profoundly aware of all that has been done, or, at 
 least, have some one at hand who is, and can thus, when a new 
 idea occurs to them, at once recognise, or have determined for 
 them, its novelty, and so instantly put it in type and secure it. 
 Neither Stokes nor Thomson, in 1850, seems to have had the least 
 idea that he had hit on anything new . . . the matter 
 appeared so simple and obvious to them and, but for the fact 
 that Thomson has given it in his public lectures ever since (at 
 first giving it as something well known), they might have thus 
 forfeited all claim to mention in connection with the discovery. 
 
 I went on to show how this lamentable state of things 
 could easily be rendered impossible for the future, by 
 the regular publication, at very short intervals, of a 
 digest of all new advances in science. 2 
 
 1 Some frantic partisans of Papin, etc., deny almost all credit to Watt 
 in the matter of the steam-engine ! No further examples need be cited. 
 
 2 [Note to Third Edition. To a great extent this desideratum is now t 
 
RADIATION AND ABSORPTION. . 197 
 
 I come now to the question of what was done on 
 this subject in 1858 and 1859. The first of these dates 
 belongs to Balfour Stewart, and the second to Kirch- 
 hoff. Balfour Stewart treated the subject almost 
 entirely from the point of view of what is called the 
 Theory of Exchanges, and he demonstrated a very 
 remarkable generalisation or extension of the law long 
 before laid down by Prevost. Kirchhoff treated the 
 subject from an, at first sight, somewhat higher theo- 
 retical point of view, and used reasoning considerably 
 more complex and a good deal more mathematical ; 
 but in reality the fundamental point upon which the 
 reasoning is based was precisely the same in both their 
 investigations. What they established by their different 
 processes was this, the absolute equality of the radiat- 
 ing and absorbing powers of a substance for every 
 definite ray. It was not merely what had been known 
 to Leslie and others, that a body which is a good 
 absorber of heat is also a good radiator of heat, with 
 many other indefinite statements of that sort ; but it 
 was the precise limitation to each and every particular 
 wave-length, and not only that, but something higher 
 than that, not merely to rays of a particular shade of 
 colour, but also to rays polarised in particular planes. 
 Stewart and Kirchhoff thus came to the conclusion 
 that if you consider any one definite colour of light, 
 and have it polarised in one definite direction, then a 
 body which has a power of absorbing that, measured in 
 any way whatever, will have an exactly equal power of 
 radiating it, if measured according to the same units. 
 So if we adopt the same units for radiating and for 
 
 supplied by the Beibldtter zu den Annalen der Physik ; for which the whole 
 scientific world is indebted to the disinterested labour of the Wiedemanns.] 
 
198 RADIA TION AND ABSORPTION. 
 
 absorbing power, in all bodies the measure of the 
 absorbing power for any particular ray (strictly defined 
 as I have just stated) is the measure of the radiating 
 power for that same ray. 
 
 Stewart shows first, by very simple reasoning, that the 
 absorption of a body at a given temperature must be 
 equal to its radiation, for every given description of heat; 
 and then he shows experimentally that a plate of rock- 
 salt, which is an exceedingly bad absorber of heat, is 
 also an exceedingly bad radiator of heat. Then he 
 shows that a body is in general more opaque to radia- 
 tions from another portion of the same body than it is 
 to radiations from other bodies at the same tempera- 
 ture ; in other words, if you measure how much of the 
 heat radiated by a piece of hot glass is absorbed by 
 rock-salt, and if you measure also how much of the 
 radiation from an equally hot piece of rock-salt, instead 
 of the glass, is absorbed by rock-salt, you find that rock- 
 salt absorbs of the heat wh.ich is radiated by rock-salt 
 a very much larger percentage than it absorbs of the 
 heat which is radiated from glass at the same tempera- 
 ture ; and this he showed to be true, with the change of 
 a word or two, for mica, glass, and other substances. 
 Then he showed also and this is a very important 
 addition that a thick plate of rock-salt radiates more 
 than a thin plate, being at the same temperature ; and 
 therefore it follows of course that the radiation from a 
 hot body is radiation not merely from its surface, but 
 also from layers under the surface, and in some sub- 
 stances it may be radiation from layers at a very great 
 distance under the surface ; so that radiatttffi, like 
 absorption, is not a mere surface phenomenon, but 
 depends (when the substance is at all transparent) upon 
 
RADIATION AND ABSORPTION. 199 
 
 the depth or thickness of the absorbing or radiating 
 stratum. 
 
 In order experimentally to show some of these results, 
 though only in a qualitative not a quantitative manner, 
 Stewart first tried a substance such as pottery ware, 
 where you have a surface in some places white and in 
 others black. If you look at such a piece of pottery 
 ware by daylight, the reason why some markings on its 
 surface are darker than others is simply that they 
 absorb more of the incident light. These are portions 
 of the body which absorb more than other portions, and 
 therefore we should expect, if this law be true, and if it 
 be capable of extension from heat rays to luminous 
 rays, that on making the piece of pottery ware itself in 
 turn the source of light, making it hot enough to give 
 off light, then, as those portions which, when it was 
 cold, appeared darkest, did so because they absorbed 
 most, they should, when it is itself a source of light, 
 appear brightest, because they ought to radiate most. 
 That is an experiment which any of you can try very 
 easily for himself with a piece of pottery which has a 
 well-marked pattern on it. You will see, as soon as 
 you have heated it to whiteness in the fire, taken it out 
 and looked at it in the dark, a white pattern on a dark 
 ground, instead of a dark pattern on a white ground. 
 And it is very striking if, while thus looking at it, you 
 suddenly flash daylight on it, when you see at once the 
 inversion. 
 
 I can show to a few at a time, but not in a marked 
 way at a distance, the same phenomenon, by taking a 
 piece of platinum foil and writing letters on it with ink. 
 When it is once heated there is a deposit, on the surface 
 of the otherwise polished platinum foil, of oxide of iron 
 
200 RA DIA TION AND A BSORP TION. 
 
 which tarnishes the surface and makes it absorb con- 
 siderably more light than a polished reflecting surface 
 will do. We should expect, then, when this is heated 
 (as I now heat it in a powerful but very slightly luminous 
 flame), and becomes in turn the source of light, to see 
 bright letters on a dark ground. The difference of 
 brightness is not so marked in this case as in the last, 
 but still those who are nearest to me will see the pheno- 
 menon distinctly enough. 
 
 But you will see another phenomenon still more start- 
 ling on looking at the back of the heated foil instead of 
 the front of it. You saw faint traces of bright letters on 
 the dark ground when I turned the inked side to you, 
 but when I turn the other side you see dark letters on a 
 bright ground. Now, the reason why on the one side 
 we have bright letters on a dark ground, while the other 
 side of the same piece of metal shows dark letters on 
 a white ground, is still more confirmatory of the result 
 of Balfour Stewart's, which I have just stated, since 
 these letters appear dark while at present cold, because 
 they are absorbing more than the rest of the polished 
 surface. They appear brighter than the polished sur- 
 face when heated, because they radiate more ; but just 
 because they radiate more they must become colder, 
 must be kept permanently colder than the rest of the 
 foil, and therefore the parts at the back of the foil, 
 behind those which are radiating most, remain perman- 
 ently colder. This is made evident when we look at the 
 side which is without any difference of surface, as we 
 then see, by the relative amounts of brightness, a marked 
 distinction between the parts which are hotter and those 
 which are colder. This is a still more complete proof 
 of Stewart's proposition. 
 
RADIA TION AND ABSORPTION. 201 
 
 Stewart extended his reasoning still further when he 
 explained the behaviour of coloured glass when heated. 
 If you look at a bright fire through a red glass (for in- 
 stance); so long as the red glass is cold, that is to say, 
 is absorbing light but not radiating any, it absorbs the 
 green and lets the red through. That is why we call it a 
 red glass, because it absorbs green and almost every ray 
 but the red. When you put it into the fire and it has 
 acquired exactly the same temperature as the coals, it 
 shows no colour, and you cannot distinguish it from 
 the coals. In fact, it is transmitting red light but is 
 radiating green and other rays : namely, those which 
 it is capable of absorbing, and it is just making up by 
 radiation for the amount which it is absorbing ; and 
 therefore the light which is coming through it from the 
 coals behind is just as much strengthened both in 
 quantity and quality by its radiation, as it is weakened 
 by its absorption, and thus on the whole it comes to our 
 eyes uncoloured. If you put in behind it, leaving it in 
 the fire at a bright heat, a less hot coal, you will see it 
 appears green, because then the glass is hotter than the 
 background, and takes from the background less green 
 than it gives out, and therefore the light which actually 
 reaches the eye, partly through it and partly from it, 
 is more green than that from the coal behind. Thus 
 the coloured glass loses its colour when exactly at 
 the temperature of the objects behind it, and takes the 
 complementary colour when it is hotter than the ob- 
 jects behind it. 
 
 KirchhofT gave a good many experimental illustra- 
 tions of the relation between emission and absorption, 
 of which I can allude to only two or three. The 
 first was the very simple one of taking a bead of a trans- 
 
202 RADIA TION AND ABSORPTION. 
 
 parent salt and heating it in a blow-pipe when supported 
 in a loop of platinum wire. When the platinum wire 
 and the bead were at the same high temperature, the 
 platinum wire glowed bright, as we all know an incan- 
 descent wire does, but the bead of melted salt remained 
 scarcely glowing at all. That is to say, this body, which 
 is exceedingly transparent, and therefore a bad absorber, 
 is also a bad radiator. On the other hand, the platinum 
 wire is perfectly opaque ; it is a good absorber, and 
 therefore a good radiator. 
 
 But Kirchhoff carried his experiments after this at 
 once to sunlight. Knowing that there is one particular 
 definite red ray which is given out by the metal lithium 
 when in a state of incandescent vapour, he noticed that 
 there was no corresponding dark line in the solar spec- 
 trum. So he attempted with full success to make a new 
 dark line in the solar spectrum by letting sunlight pass 
 through a slit, and placing near the slit an otherwise 
 slightly luminous flame (that of a Bunsen lamp) in which 
 there was a large supply of lithium vapour, which caused 
 it to give out light of one homogeneous red. When the 
 sunlight came through it, the lithium vapour cut out that 
 very red, and a new line was formed in the solar spec- 
 trum. As the sunlight was gradually weakened, the 
 line gradually disappeared, though there was still a very 
 visible supply of sunlight ; and after a further weaken- 
 ing, the lithium line came brightly out on the darker 
 background. Thus by regulating properly the intensity 
 of the sunlight you may have at pleasure a dark line or 
 a bright line, or no line at all, at this particular place in 
 the spectrum. That was conclusive as to the possibility 
 of producing these dark lines in new positions by the 
 help of some incandescent gas. 
 
RADIA TION AND ABSORPTION. 203 
 
 But Kirchhoff also showed that if you take the direct 
 radiation from a terrestrial body instead of as in the last 
 experiment I described gradually checking or weaken- 
 ing the sunlight, if you had taken the light directly from 
 a terrestrial source, then you could get the dark line 
 only when the absorbing flame is colder than the source 
 of light. In order to produce new dark lines in the sun's 
 spectrum, we must use absorbing bodies which are colder 
 than the sun. That of course presents no difficulty, 
 because we cannot produce any terrestrial temperature 
 which at all equals that of the sun ; but it comes to be a 
 point of very great importance when we wish to produce 
 these absorption bands in an otherwise continuous 
 spectrum of artificial light, as, for instance, the light 
 from an incandescent lime-ball. The temperature of 
 the incandescent lime-ball is very low, compared with 
 even the electric arc, and extremely low compared with 
 the sun, but the light from it gives a perfectly continu- 
 ous spectrum. If we try to produce in that spectrum 
 the dark lines of lithium or sodium by the process just 
 described, we find the process fail. Bright lines appear 
 in place of dark ones. A Bunsen-lamp flame is not cold 
 enough. In other words, if sodium be in the Bunsen 
 flame, though it absorbs no doubt that particular orange 
 light which comes from the lime-ball, yet in place of it 
 it gives out a great deal more of the same kind, and 
 therefore you have bright lines instead of dark ones. But 
 if, instead of a Bunsen-lamp, you take an ordinary spirit- 
 lamp, and put sodium vapour into its flame, you find you 
 get your dark line in the spectrum of the lime-ball. 
 Kirchhoff thus experimentally showed that for the pro- 
 duction of an absorption-line (at least when the source 
 and absorber are both behind the slit) it is necessary 
 
204 RADIATION AND ABSORPTION. 
 
 that the incandescent source should be at a higher tem- 
 perature than the absorbing vapour. 
 
 We shall see that this is not only in itself a very 
 important result, but that it is of the utmost importance 
 when we come to interpret the spectrum we obtain from 
 various portions of the sun's disc, and from various stars. 
 It shows whether the radiating or absorbing matter in 
 any of these cases is the hotter or the colder. 
 
 Finally, I may mention a discovery which was made 
 almost simultaneously by Kirchhoff and by Stewart ; the 
 beautiful application, to absorbing bodies, of the polarisa- 
 tion of light. There are various transparent substances, 
 which, although colourless, or but slightly coloured, 
 nevertheless absorb all vibrations of light which take 
 place in a particular direction. The simplest is a plate 
 of tourmaline, cut parallel to the axis of the crystal. It 
 is not yet absolutely certain whether the rays which it 
 absorbs are those which vibrate parallel to the axis of 
 the crystal or those whose vibrations are perpendicular 
 to it, but that does not matter to our present purpose. 
 Light which has passed through such a slice of crystal 
 is vibrating in one definite direction only, and therefore 
 is said to be polarised. As we have experimental proof 
 that common light is subject to no such restriction, the 
 portion of the incident light which has been absorbed 
 must have been that whose vibrations were in the direc- 
 tion perpendicular to that of those which passed through, 
 and therefore what was absorbed was also polarised 
 light. Here, then, is a body which absorbs polarised 
 light : make it in its turn (by heating) a source of light, 
 and it should then, if the proposition we are dealing 
 with be universally true, radiate polarised light. Now 
 the experiment has been made, and made with complete 
 
RADIA TION AND ABSORPTION. 205 
 
 success. The light radiated by the red-hot crystal, if 
 you view it against a dark background, is polarised ; but 
 if the background be itself as hot as the crystal (and be 
 of non-polarising material), no polarisation is observed. 
 The crystal transmits one part of the light unaltered, 
 and though it stops the other half, it makes up for it by 
 the light which it radiates. 
 
 Before I go further with the reasoning on this part of 
 the subject, I must make a slight digression as to our 
 knowledge, or rather our reasons for conviction, of the 
 identity of radiant heat and light. I must, in fact, show 
 how we satisfy ourselves that there is no more difference 
 between radiant heat and light, or even the so-called 
 actinic sun rays, etc., than between waves of sound or 
 waves of water of different lengths. The precise nature 
 of the vibration which constitutes a wave of light, does 
 not matter to this question at all. 
 
 We all know that sound-waves differ practically from 
 water-waves. In the case of sound-waves the particles 
 of air are vibrating back and forward in the direction in 
 which the sound travels ; but in the case of waves on 
 water, the particles are moving partly up and down 
 and partly back and forwards, so that near the surface 
 of the water each particle is describing almost a 
 circle. 
 
 In the case of luminous waves, all we know is, that 
 whatever be the precise nature of the vibration, its direc- 
 tion is transverse to the direction in which the light is 
 moving. Now, the proof that radiant heat and light are 
 the same, or only variations of the same thing, is to be 
 arrived at by comparing their properties in a great 
 number of different ways. I cannot enter very deeply 
 into this, but I can at all events mention several of 
 
206 RADIA TION AND ABSORPTION. 
 
 these properties, and show how conclusive the evidence 
 is for the identity in question. 
 
 First of all, it is to be considered they both move 
 in straight lines. The radiant heat from the sun goes 
 along with the light from the sun, and when you shut 
 one off, put an opaque screen so as to intercept the 
 one, the other is intercepted at the same time. In the 
 case of a solar eclipse, you have part of the sun's heat as 
 long as you can see the smallest portion of the sun's 
 disc. The instant the last portion of the disc is obscured, 
 the heat disappears with the light. That shows that the 
 heat and light take not only the same course, but also 
 the same time to come to us. If the one lagged ever so 
 little behind the other, if the heat disappeared sooner 
 than the light, or the light sooner than the heat, it would 
 show that though they both moved in straight lines, the 
 one moved faster than the other ; but the result of 
 observation is that we find, so far as our most delicate 
 measurements show, that heat and light pass from the 
 moon to the earth, i.e. over a space of a quarter of a 
 million miles, in sensibly the same time. Therefore we 
 have the proposition that radiant heat moves at the rate 
 of about 1 86,000 miles per second, because that is the velo- 
 city of light. Thus, even our very first analogy between 
 them seems to be almost convincing as to their identity. 
 
 Then we have, as you all know, when you use either 
 a burning mirror or a burning lens for the purpose of 
 condensing the sun's heat into a focus, to adjust this 
 by taking advantage of the sun's light. You form an 
 image by means of the light, and then you find the 
 heat rays concentrated at the same point. That is to 
 say, the laws of reflection and refraction are precisely 
 the same for light and radiant heat. 
 
RADIATION AND ABSORPTION. 207 
 
 Then again, I dare say you all know for it was 
 shown early in this century as the true explanation of 
 phenomena known to Newton, and before him that 
 two sets of rays of light can be made so to interfere 
 with one another as to produce darkness. This ex- 
 periment is conclusive 1 as to the non-materiality of 
 light, and shows that light must be something of 
 the nature of a vibration of some kind, so that two 
 opposite motions meeting in one place, or rather simul- 
 taneously affecting one part of a medium, may produce 
 simple rest or non-existence of motion. If we test this 
 with sunlight, as was done by Fizeau and Foucault, we 
 find that precisely at the places where the sunlight has 
 disappeared, at these same places the sun's heat has 
 disappeared. Radiant heat, therefore, has, as light 
 has, the property of interference ; that is to say, two 
 portions of either are, in certain circumstances, capable 
 of mutually destroying one another. 
 
 Another very striking analogy between them is fur- 
 nished by absorption. Let us take the case of light 
 first. If I take a number of pieces of the same blue glass, 
 light which has passed through one of these is capable 
 of passing in greater part or percentage through the next, 
 and what has been sifted through two of them will in 
 still greater percentage pass through the third, and so 
 on. Precisely the same thing holds with reference to 
 radiant heat. What we call colourless glass happens to 
 be extremely opaque to radiant heat, especially to the 
 lower forms ; but if you force, by using a powerful 
 source, a considerable beam of radiant heat through a 
 single plate of window glass, you will find that though 
 
 1 Compare foot-note to p. 66. The applicability of the word ' con- 
 clusive ' is matter of opinion. 
 
208 RADIA TION AND ABSORPTION. 
 
 the window glass is exceedingly opaque to such heat in 
 general, what you can force through it will pass in very 
 much increased percentage through the second plate, 
 and in still greater percentage through the third, and 
 so on. And, just as Melloni used the word Thermo- 
 chrose, we may say that a pane of window glass, which 
 is colourless or almost so as regards light, would be 
 regarded as coloured by larger beings than ourselves : 
 beings with such very coarse-grained optical apparatus 
 as to have the sense of light produced in them by such 
 waves only as to our senses produce radiant heat. Such 
 creatures would speak of our most transparent glass as 
 being exceedingly opaque, while they would speak of 
 rock-salt as being transparent, for it is found to transmit 
 heat almost as freely as it does light. 
 
 There are various other analogies, such as, for instance, 
 that the intensity of light from any source varies in- 
 versely as the square of the distance. The same thing 
 is true of radiant heat. That, however, is necessarily 
 true of all emanations in straight lines from a centre 
 when there is no absorption, so that it does not 
 strengthen the argument. It is, in fact, merely a 
 consequence of the geometrical truth that the surface 
 of a sphere is as the square of its radius. 
 
 Then again and this is perhaps the grand proof 
 we have the discovery by Principal Forbes of the polar- 
 isation of heat. You can polarise radiant heat as you 
 can light, and this is the most conclusive argument ; one 
 which, taken with what I have just told you, leaves no 
 possibility of escape from the conclusion that the differ- 
 ence between radiant heat and light is simply the 
 difference between a low note and a high one. There- 
 fore, in reasoning upon radiation, it is quite indifferent 
 
RAD I A TION AND ABSORPTION. 209 
 
 whether we speak of radiant heat or radiant light, or 
 even higher waves which are invisible to the eye except 
 through fluorescence. So we need speak of nothing 
 but radiation, under which we suppose them all in- 
 cluded. 
 
 Now comes this question By what marks can you 
 distinguish one particular radiation from every other ? 
 Well, you can do that just as you can perfectly define 
 any particular sound. You can define a sound if you 
 are told three things about it, its intensity, its pitch, 
 and its quality. Well, the quality has of late been 
 shown by the beautiful analytic and synthetic methods 
 of Helmholtz to depend upon the admixture of other 
 sounds (harmonics) with the primitive sound ; so sup- 
 pose you take the simplest quality of all, that which 
 has no admixture, then a musical sound or note is 
 completely defined if we know its intensity, if we know 
 its pitch, and if we know its quality to be the simplest. 
 Conversely, if you have any disturbance of the air which 
 has that intensity, and that pitch, and the simplest 
 quality, it will be that same sound. That, then, is our 
 mark by which we detect a particular kind of motion of 
 the air. 
 
 Now we have precisely the same sort of marks by 
 which we can distinguish a particular kind of radiation. 
 Take the simplest form, that is, the simplest quality, 
 there are other three things to be attended to. The 
 first is the intensity ; the second is the wave-length or 
 colour, what corresponds to the pitch ; and the third, 
 how it is polarised, or whether it is polarised or not. If 
 these be attended to, and if you were to specify them 
 for any one radiation, and if any other radiation what- 
 ever satisfied the same conditions, then it must neces- 
 
 O 
 
210 RADIA TION AND ABSORPTION. 
 
 sarily be the same radiation. That is the stamp of 
 equivalence between the two. 
 
 And now we come to the question how we prove that 
 the radiation from a body must be equal to the absorp- 
 tion by the same body under similar circumstances. 
 We have seen how we can test the equality or identity 
 of two radiations, and now it remains, having that pre- 
 liminary settled, to apply reasoning to see why the 
 absorbing and radiating powers are necessarily equal. 
 
 The best way we can do it is by applying reasoning 
 very similar to Carnot's, but in this case it happens to be 
 capable of being applied even more simply. Suppose 
 we have a space, the walls of which are either perfect 
 reflectors or are always kept at a definite temperature. 
 It is an experimental fact that bodies (whatever they 
 be) which have been long enough kept in either kind 
 of enclosure will at last acquire precisely the tempera- 
 ture of the enclosure. That is a fact which has been 
 ascertained over and over again. We say, in fact, that 
 bodies are at the same temperature when neither parts 
 with heat to the other, when there is on the whole no 
 transference of heat from the one to the other when 
 they are placed in contact. Suppose one of these 
 bodies more capable of absorbing than it is capable of 
 radiating. That body would be constantly taking in 
 more heat than it was giving out, and therefore though 
 the other bodies would of course absorb the heat which 
 was given out by it, they would necessarily cool, because 
 they would get back from it less than they gave to it. 
 It would be getting hotter at the expense of all the 
 other bodies inside the enclosure. 
 
 So far then the reasoning appears, at least at first 
 sight, to be nearly complete ; but it is not, because we 
 
RADIA TION AND ABSORPTION. 211 
 
 have been taking the radiations as a whole. Suppose 
 we have then inside this enclosure, between two of the 
 bodies, some body which we may call a screen, and 
 which shall allow to pass a perfectly definite kind of 
 radiation and that alone, completely reflecting every- 
 thing else. Then whatever radiation passes from the 
 first towards the second body must pass through the 
 screen, and will be, therefore, of this definite kind only. 
 It will be partly absorbed and partly rejected by the 
 second ; but if there is to be a constant equality of 
 temperature maintained and that is our fundamental 
 proposition the fraction of the amount of this definite 
 kind of radiation given out by the first and absorbed 
 by the second must be exactly equal to the fraction of 
 that given out by the second, and absorbed by the first, 
 else one of the bodies would rise in temperature at the 
 expense of the other, and that, you know, is impossible. 
 Such a screen, in fact, while (with regard to the par- 
 ticular radiation in question) it forms one of three 
 bodies in the enclosure, virtually (for all other radia- 
 tions) makes it into two separate enclosures. 
 
 You will notice that our reasoning is in reality based 
 upon Carnot's : the same which led to the second 
 law of thermo-dynamics, because it is founded on this 
 principle, that without expenditure of work we cannot 
 cool down a body below the temperature of all the 
 surrounding bodies. If a body is at the same tempera- 
 ture as the surrounding bodies, we cannot use its heat 
 to do work. In fact, we require to spend work to 
 make this body colder. Now, if it could make itself 
 colder by radiating away more than it absorbs, then we 
 should have an enclosure containing two kinds of 
 bodies, one of which heated itself at the expense of the 
 
212 RADIA TION AND ABSORPTION. 
 
 other, so that work could be got from bodies all 
 originally at the same temperature, and kept in an 
 enclosure which is throughout constantly at that 
 temperature. [But, just as we have seen that Carnot's 
 principle is only true in the statistical sense, and 
 would not hold if we could deal with individual 
 particles of matter, so this assertion of the equality of 
 radiating and absorbing powers is true in a similar 
 statistical sense only.] 
 
 A word or two about the differences between different 
 bodies. There are some bodies which absorb every 
 radiation which falls upon them. These are such 
 bodies as lamp-black, and we may call them black 
 bodies in general. Now, as a black body is capable, 
 by definition, of absorbing every kind of radiation 
 which falls upon it, so it must, by applying to it the 
 proof we have given, be a body which when heated must 
 give off every kind of radiation. There can be nothing 
 wanting, no dark lines in its spectrum when incan- 
 descent, because as it is capable of absorbing everything, 
 it is capable of radiating and will radiate everything. 
 
 The next class of bodies we may call transparent 
 bodies. A transparent body is a body which absorbs 
 nothing at all. If we had a perfectly transparent body 
 it would absorb nothing, and therefore would radiate 
 nothing if you made it hot, so that the body could not 
 be seen either by itself stopping a certain amount of the 
 light which falls upon it, nor could it be seen by making 
 itself a source of light, because, in consequence of its 
 not being able to absorb, it would not be able to radiate. 
 It might, of course, be seen in virtue of its displacing, or 
 distorting, the images of other bodies as seen through it. 
 
 Then we have, finally, a class of bodies which may be 
 
RADIATION AND ABSORPTION. 213 
 
 distinguished from the other two as those into which heat 
 cannot be absorbed at all, because it never penetrates the 
 surface, those which are perfectly reflecting bodies. 
 
 We have, then, black bodies, transparent bodies, and 
 reflecting bodies. We have none of them in perfection, 
 but we may take lamp-black as an example of the first ; 
 rock-salt for the second ; and a polished metal, such as 
 silver, for the third. None of these is perfect ; but they 
 are all approximations, and are as good approximations 
 as we find in Nature to the mathematical ideas of rigid 
 bodies and perfect fluids, and sufficiently near approxi- 
 mations to enable us to deduce from our reasoning on 
 them valuable explanations of physical phenomena. 
 
 Let us suppose for a moment that we have two 
 of these bodies inside a perfectly reflecting enclosure. 
 Suppose one to be a black body and the other a transpa- 
 rent body, only let it be imperfectly transparent. Then 
 the black body takes up absolutely any radiation which 
 may come to it, and sends out absolutely all kinds of 
 radiation ; but the transparent body is incapable of 
 absorbing any but one kind of radiation, let us say. It 
 will go on absorbing that one kind of radiation from 
 the black body, but the black body gets back by re- 
 flection and transmission, all except that one kind of 
 radiation, and therefore that must be the one kind of 
 radiation which the transparent body can give out : and 
 it must give it out, being at the same temperature as 
 the other body in the enclosure, it must give it out pre- 
 cisely at the same rate at which it absorbs it ; and thus 
 we have from a somewhat varied point of view another 
 demonstration of the same principle. I shall endeavour 
 in my next lecture to illustrate these theoretical conclu- 
 sions by experiments. 
 
LECTURE IX, 
 
 SPECTRUM ANALYSIS. 
 
 Spectrum of incandescent black body ; of incandescent gas or vapour. Ab- 
 sorption by vapour of parts of spectrum of incandescent black body. 
 Application to sunlight, and starlight. Solar spots and protuberances. 
 Period of life of various stars. Fluorescence. 
 
 THE point at which I had arrived in my last lecture 
 was the practical results of the independent discoveries 
 because we can call them no less of Foucault, Stokes, 
 Angstrom, Balfour Stewart, KirchhofT, and others, with 
 regard to the equality of the radiating and absorbing 
 powers of any one body for any definite ray of heat or 
 light. I explained very fully in that lecture how we 
 can test, by separating them from one another, all the 
 different forms of radiation that proceed from any par- 
 ticular incandescent body, and so discover whether any 
 are wanting. It only now remains that I try these 
 experiments with the help of a galvanic battery, of 
 which I have a pretty powerful specimen down-stairs, 
 connected by wires with the electric lamp here. 
 
 In an ordinary galvanic battery, if you have only a 
 moderately great number of cells, say 100, no elec- 
 tricity will pass between the terminals until you bring 
 them into contact ; but if after bringing them into con- 
 tact you then separate them, a spark will follow, and 
 heat the air between them so much that, if the battery 
 
SPECTRUM ANAL YSr$^^ 215 
 
 be powerful enough, we may have a steady current of 
 electricity passing between the two, and keeping the 
 intervening air in a state of incandescence. 
 
 Now everything in the path of this portion of the 
 current is so intensely hot that any ordinary metals 
 such as copper, would be melted at once, or at least in 
 a very short time, if placed in it ; and therefore the sub- 
 stance we employ for the poles of the battery is gas coke, 
 the hard deposit of carbon found in gas retorts. Bars 
 of this are cut and connected with the poles of the bat- 
 tery. When the voltaic arc is passing in hot air between 
 the two poles, the ends of these bars become vividly in- 
 candescent, and you have therefore two very hot black 
 bodies, and between them a hot semi-transparent body. 
 Now, you will remember from my last lecture that a 
 black body is black because it absorbs all kinds of light 
 which fall upon it. A transparent body is transparent 
 because it absorbs little of the light which falls upon it. 
 
 Therefore, if our proposition be true, and we know 
 it must be, in the same sense at least as is the second 
 law of the dynamical theory of heat, it will follow that 
 if you make the black body incandescent it will give 
 out all kinds of radiations, just as it is capable of absorb- 
 ing all kinds ; and the gaseous or semi-transparent body, 
 which is capable of absorbing only few kinds of light 
 or radiations, will be capable, when self-luminous, of 
 giving out only the same few. The contrast between 
 the two will be well seen by adopting the optical method 
 I described in my last lecture. We separate from each 
 other the various kinds of radiation given by the two 
 bodies simultaneously. 
 
 The radiation which you see just now [throwing the 
 spectrum of light from one of the carbon points on the 
 
216 SPECTRUM ANAL YSIS. 
 
 screen] is mainly, almost wholly, from one of the hot 
 carbon points, and you see that in its spectrum there is 
 no discontinuity. You have every colour, or rather 
 wave-length, of visible light, from the lowest red which 
 the eye can see, up to the highest violet which the eye 
 can see. There are irregularities of brightness in the 
 spectrum, but these are due to the fact that we have 
 the glowing gas as well as the luminous black body. 
 But if I pass to the spectrum of the glowing gas by 
 altering (as I now do) the position of the carbon points 
 inside the electric lamp, you now see in the dark in- 
 terval between the two continuous spectra on the screen, 
 each belonging to one of the carbon points, bright lines 
 showing definite kinds of radiation and those only, 
 while the black bodies give you every possible variety of 
 tint, as it were, from the lowest up to the highest visible. 
 This glowing gas, which is the arc between the two 
 poles, gives you only certain definite kinds of light. 
 At present it is very difficult to tell, without careful 
 measurement, to what particular vapour each of these 
 rays belongs, because the composition of the glowing 
 gas between the poles depends for the moment entirely, 
 or almost entirely, upon the impurities in the carbon 
 points, which have been vaporised by the intense heat ; 
 and, therefore, though I can at once see, partly from its 
 position and colour, but much more definitely from its 
 brightness, that the orange-coloured ray belongs to the 
 metal sodium, I could not, without careful measure- 
 ment, tell what other substances are incandescent in the 
 spark there to produce the other bright lines. But if I 
 were to introduce some substance into the arc (placing 
 it upon the comparatively large upper surface of the lower 
 pole), I should be able to see what lines it produces, 
 
SPECTRUM ANALYSIS. 217 
 
 whether by new lines appearing or by the strengthening 
 of those already present. To illustrate this, I shall take 
 a small piece of metallic sodium, and render it incan- 
 descent upon one of the carbon points ; then, as it is 
 highly volatile, the space between the two carbon 
 points will immediately be filled principally with vapour 
 of sodium. You see at once that the orange line, to 
 which I have already called your attention, is very 
 greatly intensified the others being but little affected, 
 though, if anything, rather weaker than before. That 
 depends upon the fact that the sodium vapour offers 
 much less resistance to the voltaic arc than does air. 
 The arc is both longer and at a lower temperature than 
 it was before I introduced the sodium. 
 
 To show the testing nature of this mode of discrimi- 
 nating between different substances, I take a small por- 
 tion of a metal which was discovered by the help of the 
 spectroscope almost immediately after this method of 
 observation was brought into practical use. You see 
 that, in addition to the feeble bands which cross the com- 
 paratively dark space between the continuous spectra of 
 the carbon poles, we have a new one of great intensity 
 and of an exquisite green colour. This is characteristic 
 of the vapour of the metal Thallium (closely allied to 
 lead in many of its physical and chemical properties), 
 a small portion of which I had placed upon the lower 
 carbon. 
 
 The final experiment I have to show in this connec- 
 tion is the converse of this. We are now going to take 
 as the source of light one of the carbon points, an incan- 
 descent black body which gives us all kinds of radia- 
 tions, from the lowest to the highest, and we are going 
 to make the sodium vapour, whose particular kind of 
 
2 1 8 SPECTR UM ANAL YSIS. 
 
 radiation we have already studied, the absorbing body, 
 and see what part of the continuous spectrum of the 
 incandescent black body it cuts out or refuses to allow 
 to pass. And in this experiment of course rests the 
 definite proof, so far as one single case of experiment 
 can give a definite proof, that the absorption and radia- 
 tion are exactly equivalent to one another in every 
 particular glowing gas. 
 
 I place near the slit of the electric lamp a powerful 
 Bunsen burner, into which my assistant will introduce 
 a pellet of metallic sodium in a little iron spoon. You 
 see first the combustion of the naphtha in which the 
 sodium was kept (to prevent its oxidation), then in a 
 few moments you have an excessively bright mono- 
 chromatic flame, whose light is due almost entirely to 
 the incandescent sodium vapour. You see the weird 
 expression of one another's countenances as this 
 snap-dragon flame becomes more and more intense. 
 I interpose a sheet of pasteboard to prevent its direct 
 light from falling on the screen where the spectrum of 
 the carbon point is for the moment seen continuous. 
 I now, move the Bunsen lamp slightly, so that the 
 carbon point must shine through the sodium flame, and 
 you see at once a dark, almost perfectly black, band 
 cut out of the otherwise continuous spectrum, just as if 
 a pencil or other opaque body had been interposed. 
 You see it is exactly a prolongation of the orange band 
 of sodium still furnished by the voltaic arc, and you 
 see that it appears and disappears exactly as I put the 
 lamp in front of the slit or withdraw it. 
 
 It would be easy to extend a series of experiments 
 of this kind, but there would be a very great deal of 
 sameness about them, because all we could do would 
 
SPECTRUM ANAL YSIS. 219 
 
 be to show over and over again that certain bodies 
 when incandescent give perfectly definite kinds of light ; 
 and that the same bodies when incandescent, but suffi- 
 ciently colder than the carbon pole of the electric lamp, 
 cut out from the otherwise continuous spectrum of the 
 carbon pole precisely the kind of light they give out 
 when they are themselves made the source of light. 
 But in order to convert this rude experiment into a 
 perfectly definite physical method of measurement and 
 proof, it is necessary to take more refined means of com- 
 parison than the methods I have just used. First of all, 
 it is important to make the slit an extremely narrow one. 
 I was obliged to make the slit moderately wide that you 
 might see the various coloured images of it ; but in 
 order that we may have a thoroughly trustworthy mea- 
 surement, I must make the slit extremely narrow, and 
 then we shall have perfectly sharp definite lines, only of 
 the breadth of the slit itself, showing these colours. You 
 see them now perhaps half-an-inch or one-third of an 
 inch broad ; but it is perfectly possible and necessary 
 for exact physical measurement, to make them exces- 
 sively narrow, and to measure with the most extreme 
 care their relative positions with regard to one another. 
 Another necessary detail is to place the prism, or prisms, 
 exactly in the position of minimum deviation as it is 
 called in which case the rays make equal angles with 
 the surfaces of the prism at which they enter and escape. 
 Then and only then are we entitled to conclude that 
 there is absolute coincidence between the dark absorp- 
 tion lines and the bright lines due to the same incan- 
 descent vapour, according as it is employed to absorb 
 or to radiate. When this is to be carried out with the 
 utmost perfection attainable in modern optics, we employ, 
 
220 SPECTRUM ANAL YSIS. 
 
 not the method of projection upon a screen, which 
 I have used just now, but a far more delicate method, 
 invented by Fraunhofer, in which the rays are received 
 by the object-glass of a telescope, so that in the air, 
 at its focus, an image of the spectrum may be formed. 
 This may be examined by means of an eye-piece, as 
 powerful as we choose, so that we may separate the 
 different kinds of light radiated by a glowing gas, by 
 telescopic power as well as by increasing the number 
 of prisms. By using telescopes more and more powerful, 
 and greater numbers of prisms, as you can easily con- 
 ceive, this method will enable us to measure with the 
 utmost nicety, to any degree of approximation that may 
 be desired, the relative distances between the various lines 
 of the spectrum. So we have the means, if we apply 
 these refined methods to light from celestial sources, and 
 also to that from known terrestrial sources, of determining 
 whether the different radiations and absorptions observed 
 belong to precisely the same wave-lengths, that is, have 
 precisely the same positions in the spectrum ; and there- 
 fore we have as complete physical proof as it is possible 
 to desire of the presence (somewhere or other in the 
 path of the light which comes to us from a celestial 
 body) of the incandescent vapour of a particular known 
 terrestrial substance. 
 
 This, then, is the basis of spectrum analysis as applied 
 to problems connected with the physical universe. I 
 shall now say a few words about the results of the 
 application of this method of investigation to the sun, 
 stars, nebulae, and comets. The literature of this sub- 
 ject has become very extensive considering how new it 
 is. Seeing that the subject is barely fourteen years 
 old in its definite applications, it is astonishing to find 
 
SPECTR UM ANAL YSIS. 22 1 
 
 that it already fills many volumes of special treatises 
 and a host of scattered papers, and still more to find 
 that a great deal of what is there contained is thoroughly 
 popular and yet thoroughly trustworthy. 
 
 On a point of this kind, therefore, most of you by a 
 little reading can acquire at least as much information 
 as I have to give you. Therefore, while I must take 
 some notice of it, I need not at all dilate upon it, 
 though it is a very important and interesting part of 
 our subject. 
 
 First of all, let us consider what we do see when we 
 treat sunlight as it comes to us from the sun, as a whole, 
 that is without specifying any particular portion of the 
 surface. Take a beam of sunlight and subject it to the 
 same scrutiny which we have employed to-day upon the 
 light of the electric arc and the carbon points. It is 
 impossible in any coloured diagram to represent accu- 
 rately the solar spectrum, and therefore no graphical 
 delineation will at all supply the place of an actual 
 examination of the phenomena. Nor will a verbal 
 description ; so I shall be very brief. We find at once 
 that the solar spectrum is crossed over by an enormous 
 number of black lines, perpendicular to its length ; 
 precisely as the black line lay which you saw a little 
 ago across the otherwise complete spectrum from which 
 it had cut out a portion. We arrive therefore at the 
 conclusion that the sunlight must have come originally 
 from some black body, or opaque body, which is in- 
 tensely self-luminous, and which may be either in a 
 solid or in a liquid state, possibly even in the state of 
 extremely compressed gas. However this may be, the 
 source of light in the sun, whatever it is, must, in so 
 far as we can see, give off all kinds of radiations, so it 
 
SPECTRUM ANALYSIS. 
 
 is practically a black body. These black lines, or gaps, 
 in what would otherwise be a continuous spectrum, must 
 therefore be due to absorption by vapours (self-luminous 
 or not) which are somewhere in the path by which 
 these sun rays arrive at our earth. 
 
 Now, the source of a part of these lines has been 
 known for a very long time, since Sir David Brew- 
 ster's early days, in fact, for he discovered that they 
 were due to absorption by the earth's atmosphere. We 
 know the earth's atmosphere does absorb a great deal 
 of sunlight. The rising sun, when we see it obscured 
 by vapours, is by no means comparable with the sun 
 in the zenith ; but that is mainly a kind of absorption 
 which would be given by neutral tinted coloured glass, 
 which would tone down the various rays in only slightly 
 different proportions, very much, in fact, as they are 
 toned down by reflection, as when you see an image 
 of the sun in a pool. The reflected sun is very much 
 less bright than the direct, and after two or three reflec- 
 tions from a glass surface may be looked at without 
 injury to the eye. But here the effect is a mere general 
 weakening of the light, there is no special or selective 
 absorption. The atmosphere might merely have 
 weakened the various kinds of sunlight in some such 
 nearly constant proportion, but Sir David Brewster 
 found it did more than that. He found that when you 
 compare the solar spectrum when the sun is high with 
 that of the same sun when it is rising or setting, there 
 are a great many more lines crossing it in the latter 
 than in the former case ; and he concluded that, as the 
 only difference of circumstances between the two cases 
 is that the same rays had to pass through a much 
 longer extent of the earth's atmosphere (and especially 
 
SPECTRUM ANAL YSIS. 223 
 
 through the dense part of it), at sunrise or sunset, than 
 when the sun is high, therefore these new lines at least 
 are due to absorption by the air, or by aqueous or 
 other vapour in the air. 
 
 It is possible, by that very simple comparison of the 
 spectrum of the sun at rising with the spectrum of the 
 sun at mid-day, to classify the missing rays, and say 
 there are some whose absence is obviously due to the 
 earth's atmosphere ; the remaining ones we cannot 
 account for by anything terrestrial, we must go either 
 to the space between us and the sun, or to the sun's 
 atmosphere for the explanation of their cause. 
 
 Now, it is obvious that if the absorption were due 
 not to the sun's atmosphere or to the earth's atmosphere, 
 but to some other medium between us and the sun, that 
 medium would treat the light of all the other stars just 
 as it treats the light of the sun ; and therefore if these 
 lines in the solar spectrum which are not accounted for 
 by the earth's atmosphere can be accounted for by 
 anything in space, all stars should have spectra con- 
 taining the same dark lines as are found in that of 
 the sun. 
 
 Now that has been found to be by no means the case. 
 Many stars have spectra totally different from that of 
 the sun, as well as from one another. Therefore the 
 spectrum given by any particular sun or star is due 
 mainly to its own atmosphere of incandescent vapour, 
 and we can thus study the chemical composition of the 
 atmosphere of that sun by simply finding what terres- 
 trial substances, put into a Bunsen flame, or rendered 
 incandescent by electricity, will produce bright lines in 
 its spectrum corresponding to the dark lines we find 
 in the spectrum of the star. Here is a small portion 
 
224 
 
 SPECTRUM ANALYSIS. 
 
 of the grand drawing made by Angstrom, a mere frag- 
 ment of his map of the solar spectrum, not above one- 
 thirtieth of the whole he has depicted. The numbers 
 above indicate the wave-length, in fractions of a milli- 
 metre. Thus the three conspicuous green lines of mag- 
 nesium, forming the group called b by Fraunhofer (see 
 diagram, p. 192), are seen here to have wave-lengths 
 of o mm 'O005i67, o mm '0005i72, and O mm> ooo5i83 respec- 
 tively. This portion, as you see, contains a number 
 
 52 
 
 t&KC&KJfa Cr Ti Cu/ n Cojfob 
 
 of dark lines. Well, when you pass sunlight through 
 one-half of the slit of the spectroscope, and light from 
 incandescent materials (in the electric arc or in an 
 induction spark, or even a Bunsen lamp) through the 
 remaining half, and examine them through the same 
 train of prisms, you get two spectra as here represented, 
 the one of sunlight and the other of the terrestrial sub- 
 stance, spread out side by side. Any two rays which, 
 
SPECTRUM ANAL YSIS. 225 
 
 in passing through a very long series of prisms, undergo 
 exactly the same treatment, must be of the same refran- 
 gibility ; and therefore, by what I have just explained 
 to you, due to the same definite substance. 
 
 In the band just below the portion denoting the solar 
 spectrum, all the full lines represent lines which are 
 actually observed in the spectrum of metallic iron. 
 Looking up, you see the exact coincidence of each 
 with a corresponding line in the solar spectrum. You 
 see there are about thirty coincidences even in this 
 small part of the solar spectrum ; and so throughout 
 the spectrum the number of coincidences between 
 actual bright lines given by incandescent iron, and 
 absorption lines in the solar spectrum, may amount 
 to several hundreds. By recording both spectra pho- 
 tographically, it appears probable, from some recent 
 experiments, that these hundreds of observed coinci- 
 dences may in a short time become thousands. Now, 
 as Kirchhoff has shown, even if there were not an 
 absolutely ascertained coincidence in any one of these 
 cases, if it were only so near a coincidence that we could 
 not be perfectly certain, by means of our instruments, 
 that it was an exact coincidence, still, looking at the 
 question from the point of view of the theory of pro- 
 babilities, the chances of iron's not existing as an 
 absorbing medium in the sun's atmosphere, as estimated 
 by a person who has seen even a moderate series of at 
 least approximate coincidences, would be represented 
 by one against a number which I cannot pretend to 
 understand, but which contains some thirty-five places 
 of figures. You can see then what extraordinary sort 
 of probability there is that iron is there ; and when I 
 say that that probability was derived from only a com- 
 
 p 
 
226 SPECTRUM ANAL YSIS. 
 
 paratively few coincidences in the solar spectrum, how 
 enormously greater would it not be were we to take 
 account of all now known. And not only this. Lines 
 which, in the iron spectrum, are strong, are correspond- 
 ingly strong in the solar spectrum to every grade of 
 nicety. So far, then, iron must be in large quantities in 
 the sun's atmosphere. We find also that nickel must 
 exist there. Every bright line shown by incandescent 
 vapour of specimens of nickel in our laboratories (whether 
 these specimens be terrestrial or cosmical, i.e. meteoric) 
 corresponds to a dark line in the solar spectrum. Not 
 only so, but the character of each bright line and the 
 corresponding absorption line is the same. Very bright 
 lines correspond with very dark ones, broad lines with 
 broad, narrow with narrow, double with double. Some 
 lines appear to be given by two different substances, 
 as iron and nickel, for instance. This is probably, in 
 the great majority of cases, due to slight impurities 
 of the specimens tried. Various other substances 
 are shown in this small portion of the spectrum, 
 magnesium, manganese, cobalt, chromium, sodium, 
 titanium, and calcium. The number of titanium lines 
 has been shown by Thalen to be very much in excess 
 of even the enormous number of iron lines I have 
 mentioned. 
 
 So far then this has been a question of the spectrum 
 of light taken from the whole surface of the sun ; but 
 it becomes an exceedingly curious question, Are there 
 local differences in the light from that surface, and if 
 so, what are they ? when we reflect that there are such 
 things as sun-spots, and also when we think of those 
 peculiar red flames, as they used to be called, which 
 are seen round the dark body of the moon during a 
 
SPECTRUM ANALYSIS. 
 
 227 
 
 total eclipse. It becomes an exceedingly curious 
 question what we shall get if we take sunlight from a 
 limited portion of the sun's surface, as we can do by 
 using a telescope lens of long focus. We form by means 
 of it an image of the sun of an inch or so in diameter, 
 and place the slit of our spectroscope successively on 
 various parts of that image. 
 
 It was to be expected that some very important addi- 
 tional information would thus be obtained. Now, such 
 information you can quite easily procure for yourselves 
 by reading works like that of Lockyer, but I may just 
 very briefly indicate its nature. In the first place, we 
 
 _ Di Da T)3 
 
 find that from sun-spots in general we have those 
 absorption lines a little thicker and darker than from 
 sunlight as a whole, so that it appears that there is 
 associated with the sun-spot something which produces 
 an excess of absorption. There is a more powerfully 
 absorbing medium at the place where the sun-spot 
 appears than at the places where faculae or bright spots 
 appear. In the particular spot, a portion of whose 
 spectrum is here figured, the lines (D l and Z> 3 ) of sodium 
 appear not only broadened over the spot, but reversed : 
 i.e. bright instead of dark : just over the middle of 
 the spot. 
 
 Then, when we come to examine the red flames or 
 
228 SPECTRUM ANAL YSIS. 
 
 prominences, we find that in general their spectra con- 
 sist simply of bright lines. Such then is the spectrum 
 of part at least of the gaseous matter which surrounds 
 the sun, and it is the upper portion of the absorbing 
 medium which cuts out these black lines from what 
 would otherwise be a continuous spectrum, and you 
 easily trace what lines it does cut out. For instance, 
 here is a dark line (C) in the red [see diagram, p. 192, 
 which shows, as through the same slit, the spectra of 
 
 the sun and of a prominence], which is due to hydrogen 
 gas. Well, we find these red flames owe their redness 
 to the particular colour of this line of hydrogen. So 
 this bright red line is one of the main features of the 
 prominences. Then we find a yellow line very nearly 
 coincident, as you see, with the lines of sodium. No- 
 body as yet knows what is the chemical substance 
 which produces this particular line. It corresponds to 
 no absorption line usually found in the sun's spectrum 
 
SPECTR UM ANAL YSIS. 229 
 
 (though you observe a trace of it in the spot spectrum 
 which I last showed you), and therefore it must be due 
 to a substance in a peculiar condition capable of radiat- 
 ing, but of having its absorption made up for, some 
 substance which possibly we may not yet know. Pos- 
 sibly it may not be a terrestrial substance at all. But 
 it occurs here, very nearly giving a coincidence with 
 sodium ; but its light is not only more refrangible, but 
 it wants the distinctive property which sodium has of 
 giving a double line. Then we find several other lines, 
 including two or I may say three more, due to hydro- 
 gen ; so that the spectrum of these flames consists 
 mainly of the spectrum of incandescent hydrogen gas. 
 Here is another drawing of a small portion of the 
 spectra of the sun and a prominence, which shows the 
 exact coincidence of the bright and dark lines. 
 
 Suppose now we had a telescope to which the spec- 
 troscope could be adjusted : on looking at a red promi- 
 nence without the spectroscope we should see one 
 image, but it would be an image which consisted partly 
 of the red, partly of the green, partly of the blue, partly 
 of the violet rays of hydrogen ; but if we combine tele- 
 scope and spectroscope, the combination would enable 
 us to separate from each other, along the line of disper- 
 sion, the various colours ; and the edge of the sun 
 would be treated in the same way. All its colours 
 would be spread out from one another, but they would 
 be spread out at a disadvantage compared with the 
 colour of a monochromatic line. Because however far 
 you separate one such line from another, you do not 
 weaken either. They remain, except in so far as re- 
 flection from the surfaces of the prisms, and ab- 
 sorption within the prisms, weaken them, as strong 
 
230 SPECTR UM ANAL YSIS. 
 
 as ever. But if you take a corresponding portion of 
 sunlight, then, since it gives practically a continuous 
 spectrum, you spread it uniformly over as long a space 
 as you choose. So by the aid of this property, as the 
 solar spectrum is practically continuous, except where 
 there are interceptions of light, you can spread it out, 
 and thus weaken it throughout as much as you please ; 
 whereas the other spectrum consists of perfectly definite 
 bright lines, which you may spread as far apart from 
 one another as you please, but which you cannot 
 individually weaken. Hence, however strong be the 
 glare of sunlight, sufficient dispersive power will enable 
 us in fine weather to examine the spectrum of the red 
 flames. 
 
 This is perfectly analogous to the observing stars by 
 daylight, which, you are aware, is done in every fixed 
 observatory by means of a good telescope. It is simply 
 because the diffused light of the sky allows itself to be 
 weakened farther and farther as we spread it over a 
 larger and larger image, while the light of the star 
 always comes from the same definite point ; because 
 no one has yet made a telescope showing a star's disc 
 (except as a delusive appearance due to diffraction), so 
 that, magnify it as you please, its light comes from the 
 same definite point. So it remains of the same bright- 
 ness, while the background may be made as dark as 
 you please by spreading it out. In that way, by com- 
 bining the spectroscope with the telescope, and widen- 
 ing, or altogether dispensing with the slit, it is possible 
 to study the phenomena of these red flames, and, in 
 fact, the whole behaviour of gaseous matters round the 
 edge of the sun's disc, without waiting for a total 
 eclipse. This is an extremely beautiful adaptation of 
 
SPECTR UM ANAL YSIS. 23 1 
 
 means first made theoretically by Lockyer, and after- 
 wards by Janssen, but brought into practice nearly 
 simultaneously by the two astronomers. 
 
 Here is the result as applied to a particular portion 
 of the sun's circumference. The body of the sun we 
 
 will suppose to be under that picture. These are simply 
 eruptions of glowing gas from the sun's apparent sur- 
 face. On the same scale there would be another image, 
 a green image, situated almost at the end of the room ; 
 then a long way beyond, an indigo, and finally a violet 
 
 one. But we have by means of the prisms separated 
 that particular image from the others, and thus we 
 have here a monochromatic representation of what is 
 above the surface of the sun, in so far at least as incan- 
 descent hydrogen gas is involved. When I point out 
 
232 SPECTR UM ANAL YSIS. 
 
 that the change from the first figure to the second took 
 place in the course of a few minutes, you will see what 
 exceedingly rapid changes are going on in these self- 
 luminous clouds ; and when I further tell you that the 
 height of this prominence, which is a stream of hydro- 
 gen rushing violently up from a rent in the surface of 
 the sun, is something like 70,000 miles, you will see on 
 what a stupendous scale, and with what tremendous 
 velocities, these phenomena are constantly taking place. 
 So far then for the sun. When we compare the 
 spectra of different stars with that of the sun, we come 
 to some very curious conclusions. We find four classes 
 of spectra, as a rule, among the different fixed stars 
 which have seemed of importance enough to be separ- 
 ately examined. The first class of spectra are those of 
 ivhite or blue stars. You see an admirable example in 
 Vega, and another in Sirius, or the dog-star. All these 
 white stars have this characteristic, that they have an 
 almost continuous spectrum with few and broad dark 
 lines crossing it, and these few for the most part lines 
 of hydrogen. These stars are in all probability at a 
 considerably higher temperature than the sun ; and 
 their atmospheres are in even more violent agitation 
 than is that of the sun. Then you come to the class 
 of yellow stars, of which our sun is an example. In 
 their spectra you have many more dark lines than in 
 those of the white stars, but you have nothing of the 
 nature of nebulous bands crossing the spectrum, such 
 as you find in the third class ; still less have you certain 
 curious zones of shaded lines which you have in the 
 fourth class of stars. This classification seems to point 
 out the period of life, or phase of life, of each particular 
 star or sun. When it is first formed, by the impact of 
 
SPECTRUM ANAL YSIS. 233 
 
 enormous quantities of matter coming together by gravi- 
 tation, you have the very nearly continuous spectrum 
 of a glowing white hot liquid or solid body (or, it may 
 be, dense gas), the sole, or nearly sole, absorbent being 
 gaseous hydrogen in comparatively small quantity, and 
 the spectrum having therefore few absorption lines. 
 As it gradually cools, more and more of those gases 
 surrounding its glowing surface become absorbent, 
 and so you have a greater number and variety of lines. 
 Then, as it still further cools, you have those nebulous 
 bands which seem to indicate the presence of com- 
 pound substances ; which could not exist in the first 
 two classes, because there the temperature is so high 
 as to produce dissociation. Still further complexity 
 of compounds will be found in the atmospheres of the 
 fourth class. But sometimes, as in the case of tem- 
 porary stars, a spectrum of the fourth class is suddenly 
 crossed by the bright lines of hydrogen showing either 
 a last effort at the discharging of red flames, or a flicker 
 due to some last chance impact of meteoric matter. 
 So that we can study, as it were, not the succession of 
 phases of life in any one particular star, but different 
 simultaneous phases in many : we can study some stars, 
 as it were starting into life, others getting older, others 
 older and older ; and we occasionally find a most re- 
 markable circumstance happening with a star that has 
 practically died out, a star which is scarcely notice- 
 able by the astronomer. Such a star occasionally has 
 an outburst, rendering it for a little time sometimes 
 for several years as bright as Jupiter itself. One 
 such case very luckily occurred within the spectro- 
 scope period. It was carefully examined by Huggins, 
 and the result of the examination was to show that it was 
 
234 SPECTRUM ANAL YSIS. 
 
 a star which had gone on cooling, or at all events had 
 reached the lowest of its cooling stages, but suddenly 
 became bright, because of an outburst of hydrogen. 
 Bright lines broke out across its spectrum, showing 
 that the incandescent gas which was in its atmosphere 
 was at a higher temperature than at least the surface of 
 the star itself. Now, this leads me to another and a 
 curious remark about the lines of hydrogen which we 
 see in the sun. Here is a portion of the solar spectrum 
 as seen under particular conditions. It belongs to a 
 solar spot, where of course the whole amount of radiation 
 is less than that from the general body of the sun 
 
 around it. Over that spot there must have floated an 
 incandescent hydrogen cloud at a much higher tempera- 
 ture than the radiating portion of the sun at the spot, 
 and therefore it was capable of radiating more of the 
 hydrogen light than there was to absorb, so it behaved 
 as a radiating medium instead of an absorbing one ; and 
 therefore the green line in the solar spectrum which is 
 due to hydrogen came out as a bright line. After 
 watching this phenomenon for a short time in this par- 
 ticular form, the observer saw it change into a line with 
 a bright portion at one side and a relatively black portion 
 
SPECTRUM ANAL YS1S. 235 
 
 at the other, one part evidently due to radiation, the 
 other to absorption, but both closely connected. Why 
 did one half become bright and the other half black ? 
 The answer to that leads us to a study of a very curious 
 kind, but I must defer this to another lecture. Mean- 
 while, as I have the electric apparatus at hand, there is 
 another experiment I wish to show, though it is not 
 directly connected with the subject I have been discuss- 
 ing. 
 
 I have here a cube of the well-known Canary glass, 
 whose colour is due to oxide of Uranium. When I place 
 it in the path of the rays from the electric arc it shows 
 brilliantly its characteristic yellowish green light. But 
 observe that this dark violet glass, when interposed 
 between you and the cube, renders it practically in- 
 visible in spite of its brilliant illumination. The violet 
 glass is practically opaque to this yellowish green light. 
 So far the experiment presents nothing very remark- 
 able. But I now close the aperture of the electric lamp 
 with the violet glass; and there, in the middle of the 
 almost invisible beam which it allows to pass, is the 
 cube of canary glass showing its characteristic colour 
 almost as brightly as before. 
 
 Obviously the canary glass has changed the light 
 which falls upon it : for light can pass through the 
 violet glass and afterwards develop the greenish colour 
 to which the violet glass is almost opaque. This is one 
 of the very beautiful experiments by which Stokes 
 physically explained Fluorescence as a change produced 
 by certain bodies on the refrangibility or, more directly, 
 on the period of vibration of light. 
 
 Here is another exquisite experiment of the same 
 kind. I illuminate (very feebly) a sheet of white paper 
 
236 SPECTR UM ANAL YSIS. 
 
 by the radiation through the violet glass. With a brush 
 dipped in a solution of sulphate of quinine, slightly 
 acidulated by sulphuric acid, I write letters on the 
 paper, and these at once shine out brilliantly with a 
 light blue colour. This also is nearly invisible through 
 the violet glass. 
 
 In both experiments the altered light is of lower 
 refrangibility, i.e. of longer vibration-period, than the 
 incident light another instance of degradation of 
 energy. 
 
 The point I shall first take up in next lecture is the 
 point left unexplained to-day, how it is possible for a 
 line which was originally dark in the solar spectrum to 
 broaden out and become bright, and then for one por- 
 tion to become dark while the other portions remain 
 bright. 
 
LECTURE X. 
 
 SPECTRUM ANALYSIS. 
 
 Change of colour of Light by relative velocity of source and observer. Analogy 
 from Sound. Causes of broadening of spectral lines. Spectrum of Solar 
 Corona ; of Double Stars ; of Comets. Probable nature of Comets ; of 
 Saturn's rings ; of the Zodiacal Light. 
 
 YOU remember I closed my last lecture by pointing 
 out to you, for the second time, a diagram of a portion 
 of the solar spectrum, in which we had side by side a 
 bright line and a dark one, due to the same substance, 
 namely, hydrogen. I told you that there is a very 
 beautiful point of theory involved in the explanation of 
 this phenomenon, and I proceed to give it. It generally 
 goes by the name of Doppler's principle, but it depends 
 upon precisely the same idea as that which led Romer 
 to the discovery of the finite speed of light. 
 
 Let us take the simplest possible analogy. Suppose, 
 for instance, that we had Mr. Perkins' steam-gun, and 
 caused it to project bullets in the same direction, suc- 
 ceeding one another once every half-second. Then, if 
 a target were held in the path of these bullets, it would 
 of course be struck 120 times per minute. But suppose 
 that the target were to move up towards the gun, while 
 the gun still kept on discharging the bullets at the 
 same rate, it is obvious that it would meet more bullets 
 in the course of a minute than it would meet if it were 
 
238 SPECTR UM ANAL YSIS. 
 
 standing still. If you were to withdraw the target 
 gradually, keeping it always however in the line of fire, 
 you would get fewer bullets per minute ; and if you 
 were to make it move away from the gun at exactly 
 the rate at which the bullets are coming, then no bullets 
 would reach it at all. One bullet would be in its neigh- 
 bourhood, and would remain constantly at the same 
 distance from it ; for, in fact, the target and the bullet 
 would be moving with the same rapidity. 
 
 Precisely the same thing may be observed in passing 
 over a set of waves. If you were steaming through a 
 set of waves in the direction in which the waves are 
 going, it is quite conceivable that you may be steaming 
 so fast as to be riding on the crest of a definite wave 
 all the way ; but steam a little more slowly, and you 
 will see waves gradually passing you ; steam still more 
 slowly, and a greater number of them will pass you per 
 minute. If, on the other hand, you are steaming so as 
 to meet the waves, then you meet more than if you 
 were not moving. The faster you go you meet the 
 more waves per minute ; and there is absolutely no 
 limit to the number you may meet per minute, if you 
 could only move fast enough to meet them. Now the 
 impression, be it of pitch or of colour, that is produced 
 upon the ear by sound, or upon the eye by a luminous 
 radiation, depends entirely, so far as our present pur- 
 pose is concerned, upon the number of these waves 
 which meet them per second. Therefore, if we are 
 moving towards a sounding body which is giving out 
 a particular note, the number of waves which reach our 
 ear per second will be greater than it would be if we 
 were standing still, or (generally) if we were at rest rela- 
 tively to the body. And as a higher note corresponds 
 
SPECTR UM ANAL YSIS. 239 
 
 to a greater number of waves reaching our ear per 
 second, it is obvious that in the former case, whether 
 we are moving to the sounding body or the sounding 
 body is moving to us, there will be a greater number of 
 waves reaching our ears than if we were at relative 
 rest ; so that we should perceive a higher pitched 
 sound than what is actually given off by the sounding 
 body. The experiment has been made by the help of 
 a railway engine first in Holland, and since in other 
 countries by stationing upon the engine a trumpeter, 
 who had beside him a musician to control exactly the 
 note that he should play. The musician, of course, 
 was moving along with the trumpeter, and therefore 
 heard precisely the note that the trumpet was sound- 
 ing. The sound, however, was also heard by other 
 musicians who were placed at the side of the line, and 
 they noted that the faster the engine came up to them, 
 the higher did they hear the note which was played by 
 the trumpet ; and the faster the engine went away after 
 passing them, the faster it retreated from them, the 
 lower did this note appear to be. I have no doubt 
 that you at all events those of you who have paid any 
 special attention to musical sounds will be able at once 
 to perceive this effect by means of such a simple instru- 
 ment as this tuning-fork, even with such comparatively 
 slight velocity as I can give it by swinging it in my 
 hand. For the success of an experiment of this kind, 
 it is better that you should close your eyes, in order 
 that you may not associate the result with any move- 
 ment which you may observe on my part ; and I shall 
 endeavour to perform the experiment without making 
 any noise which might indicate to you how I am 
 moving, or whether I am moving, the apparatus at the 
 
240 SPECTR UM ANAL YSfS. 
 
 instant. [Experiment shown.] You notice, then, that 
 during the interval that I allowed the fork to sound, 
 there was a period at which its pitch appeared to you 
 to rise ; then immediately afterwards it appeared to fall ; 
 then it rose again, and so on. We had a musical sound 
 which was alternately higher and lower in pitch as I 
 sharply moved the vibrating fork to or from you, and 
 then, when the fork was held steady, we had the original 
 sound. Now, precisely the same thing happens with 
 regard to waves of light. If you move so as to meet more 
 waves of light in a second, that will correspond to an im- 
 pression upon your retina of a higher order of colour than 
 if you were not moving to meet those waves, or if the body 
 which was sending those waves to you were not moving 
 towards you. Thus you see that the light which comes 
 to us from a star is capable, not only, as I pointed out 
 in my last lecture, of showing what chemical substances 
 are incandescent in the atmosphere of the star, whether 
 as giving out light on their own account or as absorb- 
 ing portions from an otherwise continuous spectrum, 
 but is also capable of pointing out to us whether the 
 star is moving to us or from us ; or still more minutely, 
 whether a portion of its atmosphere is moving on the 
 whole from us, and another portion on the whole to us. 
 The first application of this by the spectroscope to the 
 study of the relative motion of a star with reference to 
 the solar system, was made by Mr. Huggins with refer- 
 ence to the dog-star. Of course, in order to find out 
 from such experiments (which tell us only the relative 
 velocity of the earth and the star in the direction of 
 the line of sight) what the corresponding velocity 
 of Sirius is with regard to the sun, it is necessary to 
 consider in what part of its orbit the earth is during the 
 
SPECTRUM ANAL YS1S. 241 
 
 observation, because when the earth lies in a line from 
 the sun, making a right angle with the line drawn to 
 Sirius, the earth is moving much faster or much slower 
 towards Sirius than the sun is moving. On the other 
 hand, when the earth is 180 from that position, it is 
 moving slower or faster towards Sirius than the sun is 
 moving. When the earth is so placed that Sirius and 
 the sun are nearly on the same or on opposite sides of 
 it, it is moving transversely to the line joining the sun 
 and Sirius, and its motion relatively to the sun pro- 
 duces no modification of the observed phenomenon. 
 We should have in such a case the full effect due to the 
 relative motion of Sirius and the sun. Correcting, then, 
 for the velocity of the earth relatively to the sun, Mr. 
 Huggins found that the velocity of Sirius relatively to 
 the sun is about twenty miles per second in a direction 
 tending to increase their distance ; so that ever since 
 the time when Sirius was first observed, it has been 
 steadily moving away from the solar system at the rate 
 of something like twenty miles per second, and yet we 
 have not the least documentary or other proof that 
 the brightness or apparent magnitude of Sirius has 
 become at all diminished in consequence. It has been 
 leaving us at that tremendous rate, and yet so far is it, 
 or has it been, from us all this time, that even this in- 
 crement of distance, growing at such a tremendous 
 rate, has made during historical periods no perceptible 
 change in the amount of light that we receive from it. 
 
 The next application that was made of this principle 
 was to verify the fact of the sun's rotation about its 
 axis. It is obvious that, as the sun rotates about its 
 axis in the same direction as the earth rotates, one por- 
 tion of the solar equator, the portion to the left as we 
 
 Q 
 
242 SPEC TR UM ANAL YSIS. 
 
 look at the sun in our northern hemisphere the left- 
 hand side of the sun is coming towards us, and the 
 right-hand side of the sun is going away from us. The 
 sun's rotation about its axis takes place in what is called 
 the positive direction ; that is, the opposite direction to 
 that of the hands of a watch, as looked at from the north 
 pole side of the plane of the ecliptic. Now, although 
 the sun's rotation is very slow, that is to say, though 
 the sun takes about twenty-six days to execute a whole 
 revolution, still, because of its enormous diameter, the 
 linear velocity of all parts of its equator is very consid- 
 erable : more than a mile per second. Therefore if we 
 examine, by means of a spectroscope, the light which 
 comes from, let us say, incandescent hydrogen at different 
 parts of the solar equator, it should correspond to rather 
 higher light (more refrangible rays more waves per 
 second) from the left-hand side of the sun's equator 
 which is approaching us, than from the right-hand side, 
 which is retiring from us ; and, therefore, if we could by 
 a proper optical combination place side by side, as com- 
 ing through the same spectroscope slit, the light given 
 out by incandescent hydrogen at these two extreme ends 
 of the sun's equator as seen by us, then we should find 
 of the two hydrogen lines, the one from the left-hand 
 side shifted a little up in the scale, and the one from the 
 right-hand shifted a little downwards. Therefore we 
 should find, of course, the hydrogen line in different 
 places of the two spectra ; and by measuring the 
 amount of displacement between the two, we could 
 calculate what is the rate of the motion of these points 
 in the sun's equator to us or from us, compared with 
 the whole velocity of light in space. 
 
 Now, carry this just a step further, especially thinking 
 
SPECTRUM ANALYSIS. 
 
 243 
 
 of the enormous velocities (which I discoursed upon in 
 last lecture) with which these masses of flaming hydro- 
 gen are thrown out in explosions or eruptions from 
 below the visible surface of the sun. Think of a rate of 
 several hundred miles per second, or something like it, 
 with which these masses of glowing gas are thrown out, 
 and you can easily see that if something of the nature 
 of, but incomparably superior in dimensions to, a cyclone, 
 such as we have in our tropical regions, were taking 
 place, accompanied by down-rushes of colder gas, and 
 up-rushes of warmer gas, both of these being incandes- 
 cent hydrogen, the general down-rush of the cold will 
 correspond to absorption, and the up-rush of the hot to 
 radiation. There will be cold gas absorbing, but going 
 
 from us, and an up-rush of (on the whole) radiating gas 
 which is coming towards us ; and therefore we should 
 find the absorption correspond to a lower position in 
 the spectrum than the natural hydrogen line, while the 
 bright line corresponding to the gas coming towards us 
 will belong to a higher position in the spectrum ; and 
 so we account for the double line referred to in my last 
 lecture, the lower half of it nearest the red being dark 
 or due to absorption, and the other side being bright or 
 due to radiation. Thus, even with a slit, the motion of 
 these hydrogen clouds is easily seen by the blurred and 
 broken form presented, whether by their absorption 
 
244 
 
 SPECTRUM ANALYSIS. 
 
 lines as seen on the spectrum of the solar surface ; or 
 their radiation lines as seen in the spectrum of the 
 regions round the edge of the disc. Curious examples 
 of these two phenomena are shown in the diagrams 
 before you. Both represent appearances presented by 
 the green line of hydrogen in the first partly absorbent, 
 partly radiating, the line is on the disc in the second 
 it is seen in a prominence, parts of which are moving 
 with very great velocity. [Hence these pictures arc not 
 pictures of the prominence, as it would be seen by a 
 telescope during a total eclipse, but pictures distorted by 
 the Doppler principle.] 
 
 If we think for a moment of the whole light sent us by 
 the sun, in which absorption by hydrogen far exceeds 
 radiation by hydrogen, and think of the different rela- 
 tive rates of motion of different parts of the surface, 
 we see a physical reason for broadening of the hydrogen 
 lines altogether independent of pressure and cyclone 
 currents. Hence a star in which the absorption bands 
 are very broad may not necessarily have a dense 
 atmosphere, but may be merely rotating rapidly about 
 its axis. Thus caution is requisite in interpreting such 
 appearances. And all the more so because Lord Rayleigh 
 
SPECTRUM ANAL YSIS. 245 
 
 has called attention to the fact that even when a mass 
 of incandescent gas is at rest as regards the spectator, 
 its individual particles are in motion with sufficient 
 relative rapidity to render a very narrow bright or 
 dark line an impossibility. Even very rare hydrogen, 
 if very hot, will therefore give broad absorption bands 
 or bright lines. Other two causes, which may in 
 certain cases lead to similar results, I must presently 
 point out to you. 
 
 I may mention, before leaving this part of the sub- 
 ject, that Fox Talbot has proposed to apply the same 
 principle to double stars, in order to find what is the 
 distance of a physical system of two stars from us ; at 
 least when they have one common absorbing con- 
 stituent in their atmospheres. If we can observe a 
 double star, the plane of whose relative orbit passes 
 (let us say, for example) nearly through the earth, 
 then we may perform upon these two stars precisely 
 the same operation as I have described with reference 
 to the light coming from the two ends of the solar 
 equator ; and therefore of course we shall be able to 
 tell what is the actual velocity of the one star in its 
 orbit relatively to the other. We shall be able to cal- 
 culate the relative velocity of the two, which is in fact 
 the actual velocity of the one star in its orbit round the 
 other ; and knowing that actual velocity, we shall be able 
 to calculate, from the observed periodic time, from the 
 actual velocity thus determined, and from the apparent 
 size of the orbit, not only what the actual size of the orbit 
 is, but also how far that orbit is removed from us in 
 order to appear so small as it does. So that by the help 
 of this method, when properly applied, we shall be able 
 to get perhaps a much closer approximation to the dis- 
 
246 SPECTR UM ANAL YSIS. 
 
 tance of various fixed stars from us than we can get by 
 the only method hitherto employed, namely, by the 
 determination of what is called their annual parallax. 
 In fact, we may conceivably thus obtain a measure of 
 the distance of stars so far off as to show no measur- 
 able, or even observable, annual parallax at all. 
 
 You see, then, that the light from a heavenly body 
 can give us new information of very varied kinds, infor- 
 mation which was not sought nor even thought of as 
 attainable until the introduction of spectrum analysis. 
 We can find out, first of all, whether the light which 
 it sends to us is light from a body of the nature of a 
 solid or liquid, or at all events, a body of high general 
 absorbing power, or whether it is light from a body of 
 comparatively small and specific absorbing power, such 
 as a glowing gas. Then, we can also tell and this is 
 perhaps one of the most curious of all the applications 
 if it be a glowing gas, at what pressure and at what 
 temperature it exists in order to give off the spectrum 
 that we find, because we can operate upon terrestrial 
 hydrogen, etc., at various temperatures, and combine 
 these with various pressures, and examine the spectrum 
 under all such possible combinations, and then compare 
 these variations in the spectrum with the varieties of 
 hydrogen spectrum, which we get from the sun as a 
 whole, from different parts of .the sun^s surface, and 
 from various fixed stars. Therefore we are able to 
 assign, not merely that it is this particular chemical 
 substance, but also in what particular physical condi- 
 tions it is found in order that it may give that parti- 
 cular kind of spectrum. Then we can tell, as we have 
 just seen, the rate at which that particular radiating 
 body is coming to us or going from us. The rate at 
 
SPECTR UM ANAL YSIS. 247 
 
 which it is moving in a direction transverse to the line 
 of sight is of course to be measured by ordinary astro- 
 nomical processes, and therefore this fills up a lacuna 
 something that was wanting to ordinary astronomical 
 processes, because we could tell perfectly well how a 
 body moves transversely to the line of sight, but it 
 is quite a novelty, at all events when the body 
 is one whose dimensions are invisible in the tele- 
 scope, to find the rate at which it is moving to or 
 from us. 
 
 With reference to other possible causes (which are 
 often at work at least we may reasonably suppose so), 
 besides variations of temperature and pressure, for the 
 broadening of lines in the solar spectrum, let us think 
 first of a particular effect that may take place in conse- 
 quence of the currents of hydrogen gas in the sun's 
 atmosphere. If part of the gas were going down slowly, 
 part of it in a locality immediately contiguous going 
 down faster, and then another stream going down still 
 faster, then that part which was going down slowest 
 would give the higher absorption line, and the part 
 which is going down fastest from us will give the lowest 
 absorption line ; and you would have, therefore, instead 
 of the single definite narrow line which would be given 
 by hydrogen remaining at rest, a broad band of absorp- 
 tion, parts of it corresponding to the different velocities 
 of portions of the gas. All these absorption bands 
 may fine off, as it were, continuously into one another ; 
 so that although it is the same definite substance which 
 is producing them all, it is producing them in different 
 places in the spectrum, and filling with comparative 
 darkness a definite breadth of the spectrum, because 
 its different parts are moving from us with different 
 
248 SPECTR UM ANAL YSIS. 
 
 velocities. That is another way in which the broadening 
 of a band may occur in the solar spectrum. 
 
 But, as I said before, it may depend upon the 
 fact that differences of temperature and pressure in 
 general produce changes in the spectrum which a body 
 gives. I shall come in another lecture to the considera- 
 tion of the molecular theory of gases, when I shall speak 
 of the particles flying about with very great velocity and 
 impinging upon one another, and upon the sides of the 
 containing vessel, and so producing what we call the 
 pressure of the gas. Meanwhile, I shall anticipate so 
 far as to say that when a gas is at the ordinary pres- 
 sure of the atmosphere, each particle has to move a 
 distance, let us say, of something like a(7oVoTr tn or 
 sWowth of an i ncn n the average before it comes 
 into collision with another particle, and is sent into a 
 new path ; but if you were partially to exhaust the 
 gas in the receiver of an air-pump, there would be so 
 much fewer particles in a given space that the length 
 of the average path of any one particle, between one 
 collision and the next, would be notably increased. On 
 the other hand, if you were to compress the gas, then 
 you might bring the particles so much closer together 
 that no one would, on the average, be able to move 
 more than, let us say, ToWoTTou-th part of an inch, even 
 at its very greatest excursion, before it would come 
 into collision with another, and be sent into a new path 
 altogether. And the more you compress the gas, the 
 greater will of course be the number of such impacts for 
 every particle in a given time, and therefore the shorter 
 will be its average path between one collision and 
 the next. Now the effect of heat also is to increase this 
 number of impacts, because it makes the average velo- 
 

 SPECTR UM ANAL YSIS. 24C 
 
 49 
 
 city of the particles greater than before. The average 
 square of the velocity of the particles corresponds in fact 
 with what we call the energy of heat in the gas ; and there- 
 fore corresponds nearly to what we call the temperature ; 
 so that as you compress the gas, you give its particles 
 less way to go before they impinge upon one another, 
 and as you still heat it under compression, you make 
 them go faster and faster through the little range which 
 they can compass before collision. Therefore, by these 
 processes you make the collisions more numerous and 
 more violent, and you also make the length of time dur- 
 ing which a particle is in collision a larger percentage of 
 the whole time of its motion. If it has only a collision 
 now and then, it has a very small percentage of its 
 time occupied by the collision, because the actual time 
 of a collision is exceedingly short, and during the rest 
 of the time it is moving free ; but if collisions occur 
 with very great frequency, then the time occupied in 
 collisions becomes a serious fraction of the whole ; and 
 when a gas can be so far condensed as to approach 
 the liquid state, its particles are scarcely ever free 
 from collisions. Finally, when you get a body in the 
 solid state, its particles are practically in a permanent 
 state of collision with one another, or, at all events, 
 the time occupied in collisions is by far the greater 
 part of the whole time. Now, during a collision, a 
 particle of gas is not free ; it is jammed against an- 
 other or others ; and therefore we may expect some 
 modification to take place in the periods in which 
 it is capable of vibrating. It is vibrating not by 
 itself, but, as it were, only so far as the other or 
 others will permit it, and thus the particles inter- 
 fere with and modify one another's vibrations. Thus 
 
250 SPECTRUM ANAL YSIS. 
 
 we see that if we have a very rare gas, we may ex- 
 pect that the spectrum which it gives off when heated 
 will be in the main the spectrum due to the vibrations 
 of the individual particles of the gas as they are flying 
 about free from the others ; but as we gradually com- 
 press it, the part of the whole time which is occupied 
 in collisions increases, and then you do not get the pure 
 spectrum of the gas, what each particle would give 
 on its own account, but in addition to that, you get the 
 modification which is introduced by the action of one 
 particle upon the next ; and as you more and more 
 compress it, and also as it is more and more heated, 
 you get more and more of this interference of particles 
 with one another. From free particles we get in general 
 a few definite forms of vibration, corresponding each to 
 a fine line in the spectrum, except in so far as this is 
 modified by the relative velocities of the particles with 
 regard to one another. When there are collisions, but 
 not very numerous, we get slight modifications, gener- 
 ally as much in the way of increase of refrangibility as 
 the opposite, so these lines broaden out on both' sides. 
 But as the amount of collision becomes more and more 
 serious, and occupies more and more of the whole time, 
 these effects spread themselves over larger and larger 
 spaces in the spectrum ; and so the effect of increased 
 pressure and temperature is to make all the bands 
 broader and broader, and finally, when we compress 
 sufficiently, to reduce the gas to what is practically a 
 solid, or at all events an incandescent liquid, the bands 
 have so spread out that they have met one another, and 
 you have in fact got a practically continuous spectrum. 
 Thus the source of sunlight may not be a solid or even 
 liquid globe it may be merely a great thickness of 
 
SPECTRUM ANAL YSIS. 25 1 
 
 very hot and highly compressed gas ; in fact it seems 
 quite possible that no portion of the body of the sun 
 may be as yet even liquid. 
 
 Attending then to this, in addition to the other pos- 
 sible causes of modification which I have just men- 
 tioned, let us consider some of the data which are 
 obtained by actual observation. I spoke to you in my 
 last lecture about the spectrum of the incandescent 
 part of the sun itself, and also of the protuberances 
 which are seen during a total eclipse. But now let us 
 consider the spectrum of what is called the corona, 
 the pearly white light which is seen round the body of 
 the moon during a solar eclipse. There are parts of it, 
 according to many drawings by accurate observers, 
 which are obviously due to motes and ice crystals and 
 various other things floating in the earth's atmosphere, 
 because, of course, when you consider the enormous 
 dimensions of the sun itself, it is quite certain that there 
 can be no solar atmosphere (in the ordinary accepta- 
 tion of the word), extending to a height of something 
 like two or three diameters above his surface. Con- 
 sider the enormous mass of the sun and its consequent 
 attraction, and you will see at once that the idea of a 
 solar atmosphere extending to anything like that dis- 
 tance is altogether preposterous. For in spite of the 
 very high temperature at the sun's apparent surface, the 
 density of the atmosphere there, due to the immense 
 pressure, would in such a case be so great that a layer 
 of moderate thickness from its lower part might easily 
 have a density exceeding that of the sun as a whole ; so 
 that the sun would thus be in unstable equilibrium in a 
 fluid denser than itself. Besides, there is a well-ascer- 
 tained fact of quite a different character which goes 
 
252 SPECTRUM ANAL YSIS. 
 
 against the notion altogether ; that is, that no two ob- 
 servers drawing such a corona, even at very short inter- 
 vals of time from one another, or at very short intervals 
 of distance from one another at the same time, ever 
 draw at all nearly the same thing. That is a complete 
 proof that at least the outer part of what has often been 
 called the corona is a phenomenon due to the state of 
 the terrestrial atmosphere in the observer's line of sight. 
 But, even when the atmosphere is in its very clearest 
 state, as it happily was in the south of India during the 
 great eclipse of 1871, when most perfect observations 
 were made, it is still found that there is a silvery 
 light surrounding the sun, but extending to a height 
 of, at the utmost, only fifteen or twenty minutes of arc 
 above the dark circumference of the moon. That light 
 has been analysed by the spectroscope, and its spectrum 
 has been found to consist of two things, one of them 
 light from a glowing gas, the other reflected sunlight, 
 so that the true corona owes its light to two sources. 
 One is self-luminous gas, of whose composition I shall 
 speak immediately ; the other, scattered particles which 
 are capable of sending back sunlight. In fact, the 
 spectrum of the corona as observed by Janssen, with an 
 instrument specially contrived for the purpose, a tele- 
 scope with very large aperture as compared with its 
 length, constructed for the special purpose of enormously 
 increasingthe brightness of the image of the phenomenon, 
 was simply a weak solar spectrum, not continuous, but 
 having the dark lines, just like the spectrum of moon- 
 light (which is merely reflected sunlight). But crossing 
 it there were bright lines of hydrogen, the C line, the 
 Ftine, and the G line, which I described to you formerly 
 [diagram, p. 192] : and, in addition to these, there was 
 
SPECTRUM ANAL YSIS. 253 
 
 a green line, which cannot as yet be assigned to any 
 known substance. That line appeared, in a detailed ex- 
 amination, to be given out even in the uppermost regions 
 of the corona, regions farther from the sun than the 
 highest in which hydrogen lines were seen. This would 
 appear to indicate a gaseous element, one not only giving 
 a simpler spectrum than hydrogen, but also a lighter 
 element, capable of rising to higher elevations against 
 the action of the sun's attraction. There must, then, be 
 in the corona a solar atmosphere extending to a height 
 of rather more than one-half the radius of the sun from 
 his surface. It is possible it may extend still farther ; 
 but in addition to that, there must be matter which is 
 capable of reflecting sunlight, and giving the continuous 
 spectrum which Janssen observed. 
 
 Some very curious observations made in America 
 upon the corona led to the detection of three bright 
 lines which were found to coincide with lines which 
 occur in the spectrum of the aurora. Now, it is a 
 very singular fact that the terrestrial substance which 
 gives these lines has not yet been discovered ; and 
 it is a problem of the most curious, interest to us at 
 present what substance it can be which, incandescent 
 by electricity no doubt, during a terrestrial aurora, 
 gives us the peculiar homogeneous green light which 
 every aurora shows, and which is almost the only light 
 given by the great majority of auroras. But the pre- 
 cise similarity and coincidence between the three auro- 
 ral lines observed by one American observer, and the 
 three lines observed by another American in the corona 
 of the sun, seem to promise us wonderful information 
 as to the similarity of the upper regions of the earth's 
 atmosphere to those of the sun's atmosphere. 
 
254 SPECTRUM ANALYSIS. 
 
 I shall now add a word or two to what I said in my 
 last lecture with reference to double stars. I spoke 
 to you about the spectra of fixed stars as indicating 
 what may be called periods of life ; but there are, be- 
 sides, some very curious observations made specially 
 upon double stars. All of you who have looked through 
 even a moderately good telescope at double stars, must 
 have noticed that many of such stars have extremely 
 fine colours, very often directly complementary colours. 
 Now, it was of course an interesting application of the 
 spectroscope to find out to what these complementary 
 colours are due. You can see at a glance when the 
 spectra of the components of a double star are placed 
 side by side, in what they differ. Now one of the first 
 pairs examined showed for the first component the 
 spectrum of a white star nearly ; but the other com- 
 ponent showed in its spectrum an enormous group of 
 bands, cutting out almost the whole of the blue and 
 green regions. Hence the group consists of a white 
 star, with a practically red star revolving round it. But 
 for an optical, or rather a physiological reason, of which 
 it is not my business now to inquire the nature, a white 
 body in the neighbourhood of a red body has a tendency 
 to appear green. It is, then, merely an effect of contrast, 
 as it were, that this double star appears in the telescope 
 as an extremely fine green star, associated with an ex- 
 tremely fine red one. For when the spectroscope is 
 appealed to, it tells us that there is a direct reason 
 obviously due to absorption in its atmosphere for the 
 one star's appearing red ; but that there is absolutely 
 no reason, except the physiological reason just alluded 
 to, for the principal star's appearing green, for we see the 
 spectrum it gives is almost devoid of absorption bands. 
 
SPECTRUM ANALYSIS. 
 
 255 
 
 A few additional remarks remain to be made, chiefly 
 with reference to comets. Unfortunately, the last very 
 fine comet that was observed came before any one was 
 prepared to apply the spectroscope to it ; and, since 
 spectroscopes have been in every observatory, no comets 
 have appeared, except small and usually mere tele- 
 scopic ones. There is no doubt, however, that the next 
 fine comet 1 that appears will, especially by the help of 
 spectroscopes, give us an amount of information as to 
 the nature of comets immensely exceeding all that we 
 have already gathered during thousands of years. 
 
 But such small comets as have been observed have 
 given spectra which are extremely well worth noticing. 
 Observations of these seem to show, first of all, that the 
 tail of a comet gives a spectrum like that of the moon 
 or other body illuminated by sunlight ; in other words, 
 that the tail of the comet is not self-luminous, that it 
 shines by scattered sunlight. But the head of the comet 
 shows in general a spectrum which indicates the presence 
 of glowing gas ; that is to say, its spectrum is not con- 
 tinuous, nor is it visibly intersected by dark lines : it 
 consists in general of a small number of bright lines 
 
 1 These lectures were given in the spring of 1874, before the appearance 
 of Coggia's comet. This was a magnificent object, but unfortunately ill 
 situated for spectroscopic observation, having to be examined either very 
 low in the horizon or in very strong twilight. 
 
SPECTRUM ANALYSIS. 
 
 standing markedly out in relief from a feeble continuous 
 spectrum. There (in the lower figure) is one of these 
 the spectrum of what is called Winnecke's comet, from 
 the discoverer. It consists of three bright bands of 
 light, each sharply terminated towards the red end of 
 the spectrum, and shading away upwards to the violet 
 end. Now Mr. Huggins, who first observed this, was 
 struck by the resemblance of this spectrum (as he saw 
 it in the telescope) to a terrestrial spectrum which he 
 had noted before ; and going over his note-book, he 
 found it closely resembled the delineation of the spec- 
 trum of a hydro-carbon such as olefiant gas, rendered 
 incandescent by passing an electric discharge through it. 
 He then adopted the method to which I have already 
 several times referred, of sending light from the two 
 sources simultaneously through the upper and lower 
 parts of the same slit, so that the spectra of light from 
 the two sources should be placed side by side, and sub- 
 jected to precisely the same series of refractions. When 
 that was done the result was as shown in the diagram. 
 The upper figure is the spectrum of some hydro-carbon, 
 as given by an electric spark through the olefiant gas ; 
 the lower is the spectrum of the comet. Now, just as 
 we had concluded that there is hydrogen in the sun's 
 spectrum from the coincidence of the bright lines of 
 terrestrial hydrogen with dark lines in the solar spec- 
 trum, here is a similar telling coincidence. Here is the 
 coincidence of the three bands : a coincidence perfectly 
 exact so far as the enlargement by the spectroscope 
 enabled Huggins to measure it, not only of the bright 
 terminations of these bands, but also in the gradual 
 shading-ofif of each of them. 
 
 Now, this is a most remarkable phenomenon. It at 
 
SPECTRUM ANAL YSIS. 257 
 
 once suggests the question How does the hydro-carbon 
 get into this incandescent state in the head of a comet ? 
 A word or two on that subject may be of considerable 
 interest, but we must lead up to it gradually. A great 
 astronomical discovery of modern times is, that meteor- 
 ites, the so-called falling stars, especially those of 
 August and November, as they are called, follow a 
 perfectly definite track in space, and that this track is 
 in each case the path of a known comet ; so that : 
 whether, as Schiaparelli and others imagine, the meteor- 
 ites are only a sort of attendants on the comet ; or 
 whether, as there is, I think, more reason to believe, the 
 mass of meteorites forms the comet itself : there is no 
 doubt whatever that there is at least an intimate con- 
 nection between the two. The path of the meteorites is 
 the path of the comet. Well, let us consider a swarm of 
 such meteorites (regarded each as a fragment of stone), 
 like a shower, in fact, of Macadamised stones, or 
 bricks, or even boulders : what would be the appear- 
 ances presented by such a cloud ? It must in all cases 
 be of enormous dimensions, because the earth takes 
 two or three days and nights to pass through even the 
 breadth of the stratum of the November meteors. 
 Consider the rate at which the earth moves in its orbit, 
 and you can see through what an enormous extent of 
 space these masses are scattered. Now, if you think 
 for a moment what would be the aspect of such a 
 shower of stones when illuminated by sunlight, you 
 will see at once that, seen from a distance, it would be 
 like a cloud of ordinary dust : and an easy mathematical 
 investigation shows that it should give when sufficiently 
 thick, except in extreme cases, a brightness equal to 
 about half that of a solid slab of the same material 
 
 R 
 
258 SPECTRUM ANAL YSIS. 
 
 similarly illuminated. The spectrum of its reflected or 
 scattered light should be the spectrum of sunlight, only 
 a great deal weaker. It is easy without calculation, but 
 by simply looking at a cloud of dust on a chalky road 
 in sunshine, to assure one's-self of the property just 
 mentioned of such a cloud of dust or small particles. 
 Remember that in cosmical questions we can speak 
 of masses like bricks, or even paving-stones, as being 
 mere dust of the solar system, and we may suppose 
 them as far separated from one another, in propor- 
 tion to their size, as the particles of ordinary dust are. 
 Whether, then, it be common terrestrial dust, or 
 cosmical dust, with particles of the size of brickbats 
 or boulders, does not matter to the result of this 
 calculation. Spread them about in a swarm or cloud, 
 as sparsely as you please : only make that cloud deep 
 enough, and illuminate it by the sun, then it can send 
 back one-half as much light as if it had been one con- 
 tinuous slab of the material. Now, look at the moon. 
 You see there a continuous slab of material, and you 
 know what a great amount of brightness that gives. And 
 a shower of stones in space at the same distance from the 
 sun as the moon, and of the same material as the moon, 
 could, if it were only deep enough, however scattered 
 its materials, shine with half the moon's brightness. 
 Now, no comet's tail has ever been seen with brightness 
 at all comparable to that of the moon ; and therefore it 
 is perfectly possible, and, so far as our present means 
 enable us to judge, it is extremely probable, that the 
 tail of the comet is merely a shower of such stones, large 
 or small. 
 
 But now we come to the question How does the light 
 from the head of the comet happen to contain portions 
 
SPECTR UM ANAL YSIS. 259 
 
 obviously due to glowing gas, in addition to other por- 
 tions giving apparently a faint continuous spectrum of 
 sunlight, and perhaps also light from an incandescent 
 solid ? The answer is to be found at least so it 
 appears to me in the impacts of those various masses 
 upon one another. Consider what would be the effect 
 if a couple of masses of stone, or of lumps of native 
 iron such as occasionally fall on the earth's surface 
 from cosmical space, impinged upon each other even 
 with ordinary terrestrial, not with planetary, velocities. 
 In comparison with these latter, of course, the velocity 
 of the shot of any of the big guns at Shoeburyness 
 would be a mere trifle ; yet we know that when a 
 shot from one of them impinges upon an iron plate 
 there is an enormous flash of light and heat, and 
 splinters fly off in all directions. Now, mere dif- 
 ferences among the cosmical velocities of the particles 
 of a comet, due to different paths round the sun, or to 
 mutual gravitation among the constituents of a cloud, 
 may easily amount to 1400 feet per second, which is 
 about the rate of a cannon-ball. Masses so impinging 
 upon one another will produce several effects, incan- 
 descence, melting, the development of glowing gas, 
 the crushing of both bodies, and smashing them up into 
 fragments or dust with a great variety of velocities of the 
 several parts. Some parts of them may be set on mov- 
 ing very much faster than before ; others may be thrown 
 Out of the race altogether by having their motions sud- 
 denly checked, or may even be driven backwards ; so 
 that this mode of looking at the subject will enable us 
 to account for the jets of light which suddenly rush out 
 from the head of a comet (on the whole, forwards), and 
 appear gradually to be blown backwards, whereas in 
 
2<5o SPECTRUM ANAL YSIS. 
 
 fact they are checked partly by impacts upon other 
 particles, partly by the comet's attraction. Other very 
 singular phenomena often presented by comets have 
 recently been explained by a general rotation of the 
 whole. And it is, of course, excessively improbable 
 that a cosmical cluster of stones should not, whatever its 
 origin, have a certain amount of moment of momentum 
 in itself. Therefore, so far as can be said until we get 
 a good comet to which to apply the spectroscope, this 
 excessively simple hypothesis appears easily able to 
 account for many even of the most perplexing of the ob- 
 served phenomena. I must warn you, however, that this 
 is not the hypothesis generally received by astronomers. 1 
 There are various other phenomena in the solar 
 system to which I might call your attention as capable of 
 similar simple explanation, but I shall mention only two 
 of them. The first is the wonderful appendage of Saturn, 
 what is known as Saturn's rings. There can be no 
 doubt now that these rings are clouds of separate 
 masses. This follows first from telescopic observation, 
 which has shown us stars through one of the rings of 
 Saturn, proving that there are numberless gaps in it, just 
 as there are such gaps not only in the tail but in the head 
 of a comet, through which we can see a star, even a small 
 star, with almost absolutely undiminished brightness, and 
 without refraction-change of apparent position. Again, 
 
 1 [See Proc. R.S.E. 1868-9, and Cosmical Astronomy, V., Good Words, 
 1875. Recent researches, mainly due to Bredichin, have thrown very 
 great additional light on this subject : but have not added any new argu- 
 ments in favour of the intrinsically improbable electrical hypothesis alluded 
 to in the text. They have, however, made it possible that an action, some- 
 what akin to that which is shown by the Radiometer, may play a consider- 
 able part in causing the outrushes of tail-dust from the comet. Added to 
 Third Edition^ 
 
SPECTRUM ANAL YSIS. 261 
 
 mathematical calculation, founded on the laws of mo- 
 tion, has proved that rings like those of Saturn, if solid 
 or liquid, would be broken up in a very short time by the 
 enormous forces which are exerted upon them. The 
 solid would either be broken up into pieces, or else it 
 would as a whole go against Saturn on one side or 
 another. The liquid would be broken up by enormous 
 forced waves travelling round it, like the waves pro- 
 duced by a canal boat, which would go on increasing 
 and increasing until they ruptured it. Clerk-Maxwell 
 has shown, in his Adams' Prize Essay, that no hypo- 
 thesis whatever will account for the form and perma- 
 nence of these rings, except the supposition that they 
 consist of clouds of stones, or fragments of matter 
 of some kind or another, flying round, each almost 
 like an independent member of a family of satel- 
 lites, but still, of course, acting upon one another by 
 their mutual gravitation. That mutual gravitation is, 
 no doubt, sufficient to produce among them impacts 
 with considerable relative velocity ; so that it is possible 
 that we may some day find bright lines in the spec- 
 trum of the light from the rings. Thus these rings of 
 Saturn, like everything cosmical, must be gradually 
 decaying, because in the course of their motion round 
 the planet there must be continual impacts amongst 
 the separate portions of the mass ; and of two which 
 impinge, one may be accelerated, butjit will be acceler- 
 ated at the expense of the other. The other falls 
 out of the race, as it were, and is gradually drawn in 
 towards the planet. The consequence is that, possibly 
 not so much on account of the improvement of tele- 
 scopes of late years, but perhaps simply in consequence 
 of this gradual closing in of the whole system, a new 
 
262 SPECTRUM ANAL YSIS. 
 
 ring of Saturn has been observed inside the two old 
 ones, what is called from its appearance the crape 
 ring, which was narrow when first observed, but is 
 gradually becoming broader. That is formed of the 
 laggards, as it were, which have been thrown out of the 
 race, and which are gradually falling in towards the 
 planet's surface. 
 
 The second instance I refer to is the zodiacal light, 
 which obviously cannot possibly be part of the gaseous 
 atmosphere of the sun, nor can it be any solid or liquid 
 body. It must be of the nature of detached portions of 
 solid or liquid, floating as separate satellites, revolving 
 about the sun, though by no means necessarily in orbits 
 nearly circular. The spectrum of the zodiacal light has 
 been examined. It is an extremely difficult thing to 
 examine it ; however, the task has been at least partially 
 accomplished. The light is far too faint to enable even 
 the most skilled observer, with the most perfect of our 
 present instruments, to say whether there are dark lines 
 across its spectrum or not The spectrum has been 
 found to be at least practically continuous ; that is to 
 say, it has been found to be probably that of reflected 
 sunlight simply. Thus the zodiacal light reveals to us 
 the existence of enormous amounts of small cosmical 
 masses which have been somehow or other detached 
 from comets or swarms of meteorites, and forced, 
 whether by planetary attraction or by resistance, to 
 revolve in orbits of moderate size about the sun. As 
 they have been seized at different times and from 
 different sources of supply, they probably move in all 
 sorts of orbits with all sorts of eccentricities and in- 
 clinations somewhere about half of them probably 
 going round in the opposite direction to that in which 
 
SPECTRUM ANALYSIS. 263 
 
 the planets move. Meteorites or aerolites, which every 
 now and then reach the earth, may often be portions 
 of this source of the zodiacal light. These scattered 
 fragments, gradually resisted, or impinging upon one 
 another, fall in age after age towards the sun's surface. 
 They must thus form a supply, although an extremely 
 small and inadequate supply, of potential energy, which 
 has the effect of, to a certain extent, maintaining the 
 sun's heat 
 
 I must now take leave of this part of the subject, and 
 I do so by recurring to what I said at the commence- 
 ment of it. I began by saying that, after studying the 
 laws of heat and thermo-dynamics, we should consider 
 some very important cases of the transference of heat 
 or energy from one body to another. We have already 
 treated of the radiation of heat and the absorption of 
 heat. Now we come to another case of the transference 
 of energy: the case in which energy is transferred 
 continuously from one part of a body to another part of 
 the same body ; and here we must deal, first of all, with 
 what is called conduction of heat. This subject was 
 very fully worked out as a mathematical problem long 
 before the period to which these lectures are professedly 
 confined, but great additional information has been 
 obtained about it within that period, and therefore I 
 propose in my next lecture to give a brief sketch of 
 the early development of it ; and then to go more fully 
 into the recent extensions and additions which it has 
 obtained. Along with the conduction of heat I shall, 
 virtually at least, treat of other things which, although 
 having apparently no connection whatever with conduc- 
 tion of heat, really have precisely the same laws. These 
 are the conduction of electricity, as, for instance, in a 
 
264 SPECTR UM ANAL YSIS. 
 
 submarine cable, and the diffusion of a salt or an acid 
 in a solution in water. Perfectly different as these 
 phenomena appear to be, they are all, when treated 
 mathematically, dependent upon the same differential 
 equation (merely, of course, because their elementary 
 laws, which are summed up with all their possible con- 
 sequences in that equation, are of precisely similar 
 form) ; and therefore by the change of a word or two, 
 any statement made with regard to the one can be 
 transformed into an equally true statement with regard 
 to either of the others. 
 
LECTURE XL 
 
 CONDUCTION OF HEAT. 
 
 Fourier's Mathematical Theory. His Definition of Conducting Power. Ana- 
 logy between Thermal and Electric Conductivities. Forbes's method and 
 results. Angstrom's method. Penetration of Surface temperature into 
 the earth's crust. Analogy between conduction of heat and conduction 
 of electricity. Diffusion also analogous to these. Diffusion of matter, of 
 kinetic energy, and of momentum. 
 
 As I promised in my last lecture, I now proceed to a 
 consideration of the subject of the conduction of heat. 
 
 A great deal was known about the conduction of heat 
 before the period to which my lectures specially refer, 
 but during that period a very great deal of quite un- 
 expected information has been obtained on the subject. 
 Perhaps it will conduce to the intelligibility of what I 
 have to say about the new matter, if I briefly run over 
 what was known about the time when Principal Forbes 
 commenced his experimental inquiries into the question 
 before us. 
 
 It was Fourier who first put the laws of conduction of 
 heat into a perfectly definite mathematical form, and 
 who invented, for the purpose of investigating detailed 
 problems on the subject, a mathematical method of ex- 
 quisite power. Fourier defined conductivity the con- 
 ducting power of a substance in a manner which has 
 not been improved since. He defines it, in fact, in this 
 
266 CONDUCTION OF HE A T. 
 
 -way. Suppose that you have a slab of unit thickness, 
 but in surface practically infinite, composed of some 
 material whose conductivity you wish to measure. Sup- 
 pose one of its sides to be kept permanently at a tem- 
 perature one degree hotter than the other side. Then, 
 as we know that there is a constant flow of heat from a 
 hot body to a colder one, there will be in this case (after 
 things have settled down to a permanent condition) a 
 definite rate of flow of heat through every unit of sur- 
 face of the slab in a direction perpendicular to the slab. 
 In fact, because we have supposed that the slab is of 
 practically infinite extent, and that its surfaces are kept 
 each throughout at a perfectly definite temperature, 
 the flow of heat will necessarily be in the common perpen- 
 dicular to the surfaces of the slab ; and the measure of 
 conductivity then, according to Fourier, is the number of 
 units of heat which pass per square unit of surface of the 
 slab from one side to the other in unit of time. You see, 
 then, how all the different units come in. You have 
 unit of length for the thickness of the slab: you consider 
 the square of this unit that is, unit of surface as the 
 portion of the slab through which the heat is passing. 
 You have the unit of heat defined as the quantity of heat 
 which can raise the temperature of a pound of water one 
 degree. You have unit, that is one degree, difference of 
 temperatures on the two sides of the slab, and you have 
 unit of time during which the process of conduction is 
 supposed to go on. Now, in an arrangement of the kind 
 described, after a time, practically very short though 
 theoretically infinite, the temperature will distribute itself 
 permanently in this way : The temperature will fall off 
 steadily by a uniform gradient from the value on the one 
 side to that on the other of the slab. It follows from this 
 
COND UCTION OF HE A T. 267 
 
 that the rate at which heat passes through the slab 
 depends only upon two things, the gradient or rate at 
 which the temperature falls off per unit of length in the 
 direction of its thickness, and the specific conductivity 
 or conducting power of the material. Now, taking this 
 datum, Fourier gave completely the mathematical 
 formulae which are necessary for applying it to any 
 case however complex of the conduction of heat, in 
 a solid of which the conductivity is not altered by 
 temperature. 
 
 But this question very naturally arose Is the con- 
 ducting power of a substance the same at all tempera- 
 tures ? It had been assumed in Fourier's calculations 
 that it was so ; but Forbes seriously shook this assump- 
 tion by pointing out a curiously complete analogy 
 between the conducting powers of metals for electricity 
 and their conducting powers for heat. It was found by 
 experiment that those metals which conduct electricity 
 well, also conduct heat well, and not only so : Forbes 
 pointed out that the order of conducting power for elec- 
 tricity is also, in the main, the order of conducting power 
 for heat. [This observation of Forbes, which had been 
 founded on the published experiments of other physi- 
 cists, was confirmed by the experiments of Wiedemann 
 and Franz, which were specially devised for the purpose 
 of testing it] Now, a point which has become of very 
 serious importance of late years, especially in conse- 
 quence of the development of submarine cables, is the 
 very great change of electric conducting power of sub- 
 stances by change of temperature. Metals, in general, 
 conduct electricity very much worse when hot than 
 when cold ; so that it occurred to Forbes that as there 
 was an analogy a prima facie analogy, at all events 
 
268 COND UCTION OF HE A T. 
 
 between the conducting powers of different metals 
 for heat and electricity, and as the conducting power 
 for electricity is rendered very much worse by increase 
 of temperature, so there might be an effect of this kind 
 upon the conducting power of metals for heat. He 
 therefore established a series of experiments, which, 
 unfortunately, he lived to develop only as regarded the 
 one metal, iron ; but the results of these experiments 
 were perfectly decisive in proving that the conducting 
 power of iron for heat becomes worse and worse as it 
 is hotter, and almost in the same proportion as it 
 becomes by heat a worse conductor of electricity. 1 
 
 I may say a word or two as to the process by which 
 we investigate the conducting power, before I describe 
 Forbes's experimental apparatus. Take an analogy 
 first : suppose we consider the stock-in-trade of a cer- 
 tain business. There are two ways of investigating 
 how that stock-in-trade may alter. One way consists 
 simply in periodically taking stock, or going through 
 the whole collection and seeing what it consists of. 
 But there is another and equally good way, provided 
 it could be carried out as well, and that is to keep 
 an account of purchases and sales ; so much has come 
 in on the whole during the period ; so much has gone 
 out during the period ; and the difference between the 
 quantity which has come in and the quantity which 
 
 1 [This, however, is true only of what is called the Thermometric Con- 
 ductivity ; in which the amount of heat conducted is measured in terms of 
 the rise of temperature which it would produce in unit volume of the 
 conducting substance at the temperature of conduction. But the specific 
 heat in all substances alters with temperature. Thus Forbes's results are 
 subject to serious modification when they are reduced to the usual thermal 
 unit implied in Fourier's definition of conductivity. Note to Third 
 Edition.'] 
 
COND UCTION OF HEA T. 269 
 
 has gone out is the quantity by which the whole stock 
 has changed during the period ; so that there are these 
 two ways of getting at it. Now, precisely the same 
 idea is applied in ascertaining the conditions of the 
 conduction of heat in a solid. We picture to our- 
 selves a small portion in the interior of the solid, 
 and for reasons of simplicity in calculation, we con- 
 sider that small portion brick-shaped. We consider 
 how much heat comes in through any one side, 
 then how much during the same period of time goes 
 out by the opposite side; and extend the process to 
 the other two pairs of parallel sides. A mathemati- 
 cal expression can easily be formed for these various 
 quantities, as I have already explained. They will be 
 expressed in terms of the gradients of temperature, 
 and the conducting powers (which may not be the 
 same in all directions), parallel to the three sets of 
 edges of the brick. But then there is the other way 
 of looking at it. Instead of thinking what comes in 
 and what goes out, think of how the temperature of 
 the whole is altered during the period. You will see 
 that in terms of the rise of temperature, the specific 
 heat of the body, and the mass of the brick-shaped 
 portion, we can make an independent calculation of 
 how much heat has come in (of course on the assump- 
 tion that no heat has been generated or destroyed 
 within the brick). The latter of these expressions de- 
 pends upon the rate of rise of temperature with time 
 at any one point ; the former depends upon the rates 
 of increase of temperature per unit of length (or what 
 may be called thermometric gradients) in three selected 
 directions at right angles to one another. The gradients 
 and the conductivity tell us how much comes in : the 
 
270 
 
 CONDUCTION OF HE A T. 
 
 rate of change of gradient, per unit of length, and the 
 conductivity, therefore, tell us how much more comes 
 in than goes out ; while the rate of rise of temperature, 
 per unit of time, gives us another expression for the same 
 quantity. It is the determination of relations between 
 these two which is the object of every experimental 
 inquiry on the subject. 
 
 Forbes's apparatus may be briefly described as 
 follows : These bars (showing), which were made for 
 my own experiments, are made exactly of the dimen- 
 
 sions of Forbes's original bar. You will notice they 
 are bars of ij inch square section, and somewhere 
 about 8 feet long, but that is not usually a matter of 
 any great consequence. Along the length of each bar 
 there are at intervals, first of three inches, and then of 
 six inches, and finally of a foot, little holes cut verti- 
 cally into the bar. In Forbes's iron bar these holes 
 were simply filled with mercury, and the bulbs of 
 thermometers were placed in them. In copper bars, 
 and in German silver bars, si^ch as those before you, it 
 
 >i^n 
 
COND UCTION OF HE A T. 27 1 
 
 was necessary that these little holes should be lined 
 with iron cups like arrow-heads, in order to prevent the 
 mercury from attacking the substance of the bar. Now, 
 matters being arranged in this way, a crucible was slid 
 on, as you see, upon one end of the bar, and filled with 
 melted metal, and a powerful lamp being applied to it, 
 the temperature of the molten metal was kept as nearly 
 as possible uniform for eight, or nine, or sometimes even 
 ten hours. There was, therefore, a constant source of 
 heat applied at one end of the bar, and all the rest of 
 the bar was exposed simply to the air of the room. In 
 the case of iron bars, Forbes found that even with the 
 highest temperature to which he raised the crucible of 
 molten metal, there was scarcely any perceptible rise 
 of temperature in eight hours at the far end of the 
 bar ; but in my own experiments, I have found that 
 because copper is so very .much better a conductor 
 than iron, it is absolutely necessary, if we keep the 
 pot of metal at any moderately high temperature, to 
 have a constant stream of cold water flowing over 
 the farther end of the bar, in order to keep it from 
 gradually increasing in temperature, even after eight 
 hours' experimenting. However, the action of the 
 cold water at the farther end introduces only a slight 
 and simple modification of the formula, and in the mode 
 of deducing the final results from it, but does not inter- 
 fere with the mode of reasoning from the experiment. 
 
 The first effect of applying heat is to produce a 
 gradual rise of temperature, which is of course observed 
 first in the holes nearest the crucible. The thermo- 
 meters farthest off are the last to give any indication 
 of increase of temperature, and (after a steady state 
 
 has been arrived at) are found to have risen the least, 
 it 
 
272 CONDUCTION OF HE A T. 
 
 What we wish to study now is the rate at which 
 heat is being conveyed along ; what our thermometers 
 tell us is the temperature at different points of the 
 bar. We must take care in making the deductions to 
 remember that while our information is about tempera- 
 tures, our conclusions require to be about heat. 
 
 Heat, then, gradually flows from the hot end of the 
 bar to the cold one ; and as the bar rises in tempera- 
 ture above the surrounding air, there is a loss of heat 
 by radiation from its surface, and also by convection, 
 by currents of heated air rising from the bar. This 
 state of matters, strictly speaking, would go on inde- 
 finitely, approximating to a steady state. The steady 
 state of temperature should (theoretically) never be 
 actually arrived at ; but practically in all our experi- 
 mental work, a sufficient approximation to the steady 
 state is arrived at in bars like these in at most eight 
 or nine hours. After that time, provided we keep 
 the temperature of the molten metal as nearly as 
 possible steady, and provided the temperature of the 
 air in the room remain unchanged, it is found that 
 the thermometers have assumed definite readings 
 from which they do not practically alter more than 
 by very small fractions of a degree. There is then 
 a steady state of temperature at every point of the 
 bar, and that is the essence of the method. In such a 
 steady state of temperature, of course, there is a steady 
 thermometric gradient maintained at each point along 
 the length of the bar ; and it is found that practically we 
 may assume, without risk of sensible error, the tempera- 
 ture to have the same value at all points of the same 
 transverse section. The process I have just described 
 to you may be applied to any thin transverse slice of the 
 
COND UCT1ON OF HEA T. 273 
 
 bar, so far as its supply, etc., of heat is concerned. First, 
 in consequence of the greater steepness of the gradient 
 of temperature at the warmer side of it, there is a greater 
 quantity of heat passing into the slice by conduction 
 than passes out of it by the same process. But be- 
 cause the temperature remains unchanged, that excess 
 of heat must be lost by radiation and convection into 
 the air. If, then, we could only measure how much 
 heat is given off by radiation and convection from any 
 given part of the bar, we should be able to measure 
 how much more heat comes in than goes out in conse- 
 quence of the difference of gradient at its ends. The 
 temperatures are observed ; from these the gradients and 
 the difference of gradients can be calculated; multiply 
 the difference of gradients by the conducting power, and 
 by the area of the cross section, and you get the excess 
 of the quantity of heat which goes in over the quantity 
 which goes out per unit of time. Now that excess is pre- 
 cisely the loss from the external surface, also during unit 
 of time. Forbes therefore made an addition to the usual 
 experiment. He took a separate bar of the same 
 material, of the same section, and in every respect similar 
 to the first, only much shorter : and having heated this 
 up, to a high uniform temperature, he allowed it to cool, 
 simply noting its temperature after the lapse of successive 
 equal intervals of time. Thence he calculated the rate 
 at which it lost heat per unit of surface by radiation 
 and convection together at each temperature. We have 
 now by these two experiments an equation between two 
 expressions, one involving, besides known quantities, 
 the conductivity which is unknown, the other consisting 
 entirely of known quantities and from this equation 
 the conductivity is found. By that very ingenious 
 
 S 
 
274 COND UCTION OF HE A T. 
 
 method, then, carried out by extremely careful experi- 
 ments, the difficulty of which you may very well judge 
 when I tell you that this pot of metal was usually 
 heated to a temperature of somewhere about 300 or 
 350 C, and had to be kept sometimes for more than 
 eight hours together without varying more than a single 
 degree from that temperature, Forbes arrived at the 
 conclusion which I have already stated, that the [ther- 
 mometric] conducting power of iron falls off very 
 rapidly with increase of temperature. He found that 
 the conducting power at various temperatures is ex- 
 pressed by the following numbers, the units being the 
 foot, minute, and degree Centigrade : 
 
 o C, 0-0133 
 
 100 C M . ... 0-0107 
 
 200 C, . . . . . 0-0082 
 showing a remarkably steady diminution with increase 
 of temperature. On looking at these numbers, we find 
 that they almost exactly agree with the empirical law 
 that the conducting power of iron for heat is inversely 
 as the absolute temperature ; that is to say, if you add 
 274 to each of these temperatures, you will find that the 
 product of temperature so altered into the correspond- 
 ing conductivity of iron is very nearly the same for each. 
 Thus the conducting power is, as far as this determina- 
 tion allows us to judge, nearly inversely as the absolute 
 temperature. This, if a general law, would appear to 
 show that could we get an iron bar cooled down to a 
 temperature of 274 under zero, its conducting power 
 would become practically infinite ; at least that, when 
 the bar is almost deprived of heat, it has the power of 
 conducting heat at an enormously great rate. That, of 
 course, is arguing from results at a certain limited range 
 
CONDUCTION OF HEA T. 275 
 
 of easily obtained temperatures to a range of tempera- 
 tures on which we have not the least prospect of ever 
 being able to make experiments at all. 
 
 I may mention, in passing, a curious form in which 
 this semi-empirical statement as to thermal conductivity 
 may be put. If we assume the principle of dissipation 
 of energy to hold not merely for cases in which heat is 
 altogether left to itself in a conducting body, but also 
 in cases of artificially-sustained distribution of tempera- 
 ture, such as in this long bar of Forbes's, we have no 
 difficulty in accounting for the fact that the conductivity 
 may be inversely as the absolute temperature. 
 
 For (to take our earliest illustration of conduction) we 
 conclude that any three consecutive slices of the infinite 
 slab, of equal thickness, will have the least available 
 energy when the absolute temperature of the middle 
 one is the geometric mean of the temperatures of the 
 others. Then the gradient will be as the absolute 
 temperature, and (to make the flow of heat uniform) 
 the conductivity must be inversely as the absolute tem- 
 perature. This is on the assumption that the specific 
 heat is unaltered by change of temperature, and must 
 be modified accordingly. 
 
 I shall now say a word or two about a repetition of 
 Forbes's experiments, and an extension of them to other 
 bodies than iron, which has been carried on for some 
 time in my own laboratory. You see there two copper 
 bars, between which it would be exceedingly difficult for 
 any of you, even with the aid of careful chemical ana- 
 lysis, to find much difference. The two bars are as alike 
 as possible in their ordinary properties in colour, 
 specific gravity, elasticity, hardness, etc., and yet this 
 mysterious energy, which we call heat, has far greater 
 
276 COND UCTION OF HE A T. 
 
 facility in passing along one of these bars than the 
 other. , One of them has somewhere about 40 per cent, 
 greater conductivity than the other. Now, the only 
 difference which we can detect between them is this, 
 that in the manufacture of one there seems to have 
 been a, very small quantity of oxide of copper mixed 
 up with the molten mass, and this small trace (which it 
 is difficult to measure by chemical processes) makes 
 the metal a very much worse conductor of heat. These 
 bars were obtained for the purpose of trying whether 
 Forbes's analogy between different metals in their con- 
 ducting powers for heat and electricity would extend 
 to different specimens of the same metal. The bars 
 were procured for me by Mr. Willoughby Smith, one 
 being made of copper of very high, the other of copper 
 of very low, electric conductivity. In fact that which 
 conducts heat 40 per cent, better than the other con- 
 ducts electricity about 73 per cent better. 1 
 
 But then there comes in another and a very curious 
 thing. You have seen that in all pure metals, as iron, 
 copper, and so on, the electric conductivity falls off as 
 the temperature rises. This is not the case with such 
 an alloy as German silver. It is, in fact, used for electric 
 resistance-coils because of the slight change produced 
 in its electric conductivity even by serious changes of 
 temperature. Here is a German silver bar of the same 
 dimensions as the iron and copper bars. We find, on 
 making the same experiments with it, that its conduc- 
 
 1 [The experiments on the bars of copper and German silver, here de- 
 scribed, had been made before these Lectures were delivered, but the 
 extremely laborious process of deducing the conductivity from them had 
 not been fully carried out. A full account of the results was given in 
 Trans. R.S.E., ifyZ.Note to Third Edition.'} 
 
COND UCTION OF HE A T. 277 
 
 tivity for heat is much less affected by temperature 
 than that of iron. 
 
 I have described one modern method by which con- 
 ducting powers have been found. I have discoursed 
 upon it so long that I must dismiss more briefly the 
 other also modern method which has been applied to 
 the purpose of experiment by Angstrom, but which had 
 been virtually employed in observations on a gigantic 
 scale long previously to his time. 
 
 He, like Forbes, employs a bar, only instead of heating 
 it steadily at one end, and waiting till a steady state of 
 temperature has been set up in it, he produces a peri- 
 odical change of temperature at one end. He heats it 
 for a certain time, then cools it for an equal period, and 
 repeats this operation until a steady state of oscillation of 
 temperature has been practically attained at all points 
 of the bar where observations are to be made. He 
 observes at selected stations the range and the epoch 
 of each wave of heat which thus travels along the bar, 
 becoming less and less marked as it proceeds. This is 
 in fact quite analogous to the process of telegraphing 
 through a submarine cable. You apply one pole of a 
 battery to the end of the submarine cable for a certain 
 time : then remove it and so on : and certain waves 
 of electric potential run along the wire, by which intelli- 
 gible signals are transmitted to the other end. Pre- 
 cisely the same thing, then, has Angstrom done with 
 reference to the conduction of heat by bars ; and his 
 method has given nearly the same conductivity as 
 Forbes's for iron, which was the only metal experi- 
 mented on by both. You will get some idea of Ang- 
 strom's method and of the results deduced from it, if, 
 instead of speaking of the more complex circumstances 
 
278 COND UCTION OF HE A T. 
 
 of the wave running along a bar, I speak of the simpler 
 case in which we have a large slab of metal, heated 
 periodically at one side, and kept cold at the other. 
 Further, instead of metal, let us take the crust of the 
 earth. Here is a diagram 1 prepared by Principal Forbes 
 from continued observations of thermometers, whose 
 bulbs were sunk, some in the porphyritic rock of the 
 Calton Hill, within the Observatory grounds, some in 
 the sandstone of Craigleith quarry, and some in the 
 sandy soil of the Experimental Gardens. The curves 
 on the diagram show the temperatures as indicated by 
 these thermometers throughout the course of a whole 
 year. The first thermometer at each locality has its 
 bulb three feet below the surface of the ground ; the 
 second six feet below, the third twelve, and the fourth 
 twenty-four feet under the surface. The observations 
 are here figured in four groups, each containing three 
 curves corresponding to the simultaneous indications at 
 the different localities given by thermometers buried 
 to equal depths under the surface. These thermometers 
 (with the exception of one which was broken by the 
 intense cold of the winter 1860-1) have been regularly 
 read since they were buried. [This very valuable series 
 of observations was interrupted by the wilful destruction 
 of the instruments (September, 1876); but new ones 
 have since been sunk, and the observations resumed.] 
 
 You will notice here that for the upper thermometer 
 in the trap rock of the Calton Hill, you have the periodic 
 wave of temperature lowest, not about the middle of 
 winter, but about the middle of February. That is at 
 
 1 It has not been judged necessary to reproduce this very elaborate 
 diagram from Trans. R.S.E. t 1846, to which the reader is referred for 
 fuller information on the question of terrestrial surface-temperature. 
 
COND UCTION OF HE A T. 279 
 
 a depth of about three feet below the surface. We 
 get the highest temperature at that depth about the 
 middle of August ; and so on down again to the lowest 
 temperature in the middle of February next year. 
 Now, another great point to be observed is that there 
 is a considerable range of temperature at this depth ; 
 for the lowest is somewhere about 39 R, and the 
 highest somewhere about 54 F. ; so that there you 
 have a range of somewhere about 15 F. And remem- 
 bering that the three lines which you see running along- 
 side one another are for three such excessively different 
 materials as porphyry, sandstone, and common light 
 sandy soil, you see their general coincidence is very 
 marked. They of course agree with one another in 
 showing slight irregularities of temperature, due to 
 periods of what we call ' change of weather ' at the sur- 
 face ; but the ranges and epochs are not very widely 
 different in spite of the variety of materials. 
 
 But see what a different state of things has been arrived 
 at when you go only three feet farther down under the 
 surface. There you find a far less range of temperature, 
 though the mean temperature is nearly the same ; the 
 lowest temperature is now somewhere about 41, and 
 the highest somewhere about 51, so that you have a 
 range of only 10 altogether. When you go still farther 
 down, to a depth of twelve feet, you will find a similar 
 modification. [The,irregularities here and there in some 
 one of the three curves of each group, but not in the 
 others, are evidently due to the percolation of water 
 from the upper surface, or to some other purely local 
 disturbance.] On the average, the twelve-foot observa- 
 tions show a range of from 44 to 49, being a range of 
 only 5. And when you come down to the 24 feet 
 
280 CONDUCTION OF HE A T. 
 
 thermometers you find barely a range of i'5 through- 
 out the whole year. 
 
 Then remark, besides, that the minimum temperature 
 arrives at the 6 feet thermometer somewhere about 
 the beginning of March instead of the middle of Feb- 
 ruary ; it arrives at the 12 feet about the 2Oth of April ; 
 and at the lowest or 24 feet thermometer just about 
 the middle of July, that is to say, the winter's cold 
 takes somewhere about half a year to penetrate twenty- 
 four feet downwards into this kind of surface material. 
 
 Now this is almost precisely the same thing as only 
 on a much larger scale than Angstrom's experiment. 
 The only difference is that Angstrom had to allow 
 for the loss of heat by radiation from the surface of his 
 bar, while in the case I have been speaking of, there 
 is no conduction except in a vertically downward or 
 upward direction. Still you notice that the character- 
 istics of the results are, on the whole, the same as 
 those for the earth temperatures, that the ranges of 
 the various thermometers diminish with great rapidity 
 as you go farther and farther from the source of heat, 
 and the periods at which the maximum and minimum 
 arrive at any point are later and later as it is farther 
 from the source. 
 
 Supposing the earth's crust to be of uniform material, 
 and to have conducting power the same at all tempera- 
 tures, the law made out by Fourier long ago was that 
 as you go down successive depths in arithmetical pro- 
 gression, the range of the thermometers for a simple 
 harmonic wave of any period, such as for instance the 
 annual one should fall off in geometrical progression. 
 If, for instance, at three feet down you had a range of 
 20, and if at six feet down you had a range of only 10, 
 
COND UCTION OF HE A T. 28 1 
 
 then on going down three feet farther, you should have 
 a range of only 5, and so on. Also the time at which 
 you have what is called a particular phase of the wave 
 of temperature (say its maximum or its minimum) should 
 be later and later in proportion simply as you go farther 
 down, so that if it be a month later at three feet, it 
 should be two months later at six feet, four months 
 later at twelve feet, and so on, a month later for every 
 three feet you go down. But notice that it would be 
 so only on the supposition that the conducting power 
 is the same at all temperatures. 
 
 In performing the bar experiment according to 
 Angstrom's method, the wave of temperature which 
 passes the thermometers does not in general give, for its 
 simple harmonic components, ranges diminishing in 
 geometrical progression as we advance along the bar in 
 arithmetical progression, nor are the periods of maximum 
 constantly later and later by equal amounts for equal 
 successive intervals along the bar ; but it would be so if 
 the surface-loss were very small, and the conductivity 
 the same at all temperatures. Any such deviations 
 then are due to these causes, and by them the amounts 
 of the causes can be separately calculated. 
 
 Precisely the same statements that I made with re- 
 ference to the distribution of temperature and the con- 
 sequent flux of heat will apply, if instead of the word 
 *heat,' we use the word 'electricity,' and if instead of 
 the word ' temperature,' we use the word ' potential,' 
 which corresponds, in the theory of electricity, precisely 
 to temperature in the theory of heat ; so that when we 
 write a mathematical formula to express the conduction 
 of electricity in any body whatever, that formula will 
 apply equally well to a corresponding case of the con- 
 
282 CONDUCTION OF HE A T. 
 
 duction of heat. There is no difference whatever be- 
 tween them till we come to the interpretations. We 
 interpret a certain symbol in them to mean in the one 
 case potential, in the other case temperature. 
 
 One of the most curious instances of imitation, on an 
 exceedingly small scale, of what takes place on a very- 
 large scale, is suggested by this analogy. If I take a 
 small piece of copper, an inch or so long, and, keeping 
 one end of it in connection with a thermo-electric junction 
 and a galvanometer, so as to measure very accurately any 
 little changes of temperature that may arrive at that end, 
 apply a lamp to the other end, just as you would apply 
 to the near end of the Atlantic cable the pole of a gal- 
 vanic battery ; if I signal with this lamp just as the 
 telegraph operator does with the galvanic battery 
 through the Atlantic cable, exactly the same results 
 may be produced on the galvanometers in the two 
 cases, the tiny dimensions of the heat-conductor being 
 necessitated by the time required to sensibly alter the 
 temperature at the far end of the bar. You require to 
 take a very short bar, indeed, in order to represent the 
 phenomena on the same time scale, but you can have 
 precisely the same effects in the two cases. And it is 
 not at the ends merely, but at all similarly situated 
 points in the two conductors, that the temperature and 
 potential are proportional to one another at each instant 
 of time. 
 
 Another illustration of the same thing is furnished 
 by what you see here the diffusion of a salt in 
 solution through clear water. Take a tall cylindrical 
 vessel, such as this, and having rilled it with clean 
 water, carefully boiled beforehand to exclude air from 
 it, then, when the water is perfectly at rest, by means of 
 
COND UCTION OF HE A T. 283 
 
 a very long-necked funnel carefully pour in a solution 
 of some deep-coloured salt, such as bichromate of potash, 
 freely soluble in water, so that it lies as a horizontal 
 stratum at the bottom, without disturbing more than 
 slightly the water above it. We find that, in spite of 
 gravity, some of the salt from the denser solution makes 
 its way gradually up through the superincumbent 
 column of water. But just as the rate at which heat 
 passes from one part of a body to another depends upon 
 the gradient of temperature, and just as the motion of 
 electricity depends upon the gradient of the potential, 
 so the rate at which this salt diffuses from one layer to 
 another depends upon the gradient of strength of the 
 solution. If there be any two places contiguous to one 
 another where the strength is the same, then there would 
 be just as much given out from the one side to the other 
 as there is from the second side to the first, and there- 
 fore, on the whole, there would be no transfer ; but 
 where there is a denser solution placed immediately 
 contiguous 'to a less dense one, then you have more 
 given out per second from the dense solution to the rare 
 one than you have from the rare one to the dense. And 
 because this takes place according to precisely the same 
 law as in the case of heat and electricity, any investiga- 
 tion whatever as to conduction of heat or electricity has 
 a possible, or at least conceivable, application to some 
 case of diffusion of a solid .in a liquid which dissolves it. 
 Now, in all these cases we have really been dealing 
 with diffusion, whether of the particular kind of energy 
 which we call heat, or of what we call electricity, or 
 of matter itself, the law of the diffusion being precisely 
 the same in the three cases. We call by the name 
 conductivity, or conducting power, the numerical quan- 
 
284 COND UCTION OF HE A T. 
 
 tity which tells us how much heat or electricity passes 
 in a given time across unit of area under a given gradient 
 of temperature or potential ; so that, in the same way, 
 we may speak of the diffusivity (if the word be per- 
 mitted) of one substance in solution in another. This, 
 again, is a definite numerical quantity, whose value is 
 in every case to be determined by experiment It 
 depends not only upon the nature of the soluble salt, 
 but also on the nature of the substance in which it is 
 dissolved. The product of this diffusivity by the gra- 
 dient of strength of the solution, gives you the quantity 
 of salt which passes in unit of time from one side to 
 another of a square unit in the liquid. 
 
 But it is not only matter and energy which can be so 
 diffused ; we can also have diffusion of momentum. I 
 conclude to-day with a brief discussion of that subject, 
 because it will form an excellent introduction to the 
 subject which I must take up in my next lecture. We 
 will take an analogy, first published I believe by Pro- 
 fessor Balfour Stewart, though it had occurred inde- 
 pendently to others. Suppose there were a railway 
 train passing through a station, and that a number of 
 individuals who were waiting on the platform should 
 jump into the train as it passed, and other passengers 
 were to jump out of the train, what would be the effect 
 on the train's motion ? Simply this some parts of the 
 train (because the passengers were at first virtually 
 parts of the train) which had a certain amount of for- 
 .ward momentum, jumped out or left the train, taking 
 their momentum with them. The train, therefore, as a 
 whole, had less momentum, but also less mass, after 
 these passengers left it than it had before. On the 
 other hand, other passengers who had no momentum 
 
CONDUCTION OF HEAT. 285 
 
 at all, simply stepped into the train as it passed them, 
 so that the train gained no momentum by them, but 
 gained mass. If a body gains mass, but does not gain 
 momentum, it must be losing velocity. Thus the effect 
 of those who jumped out is not either to increase or 
 diminish the velocity of the train, unless they gave it a 
 jerk on starting from it. If they jumped forward so as 
 to give themselves more velocity than the train, they 
 would retard the train to a certain extent, gaining in fact 
 additional momentum, which is simply taken from that 
 of the train. If they were to jump backwards, so as, if 
 possible, to deprive themselves of any forward motion 
 when they left the train, then they would quicken the 
 train. But if we suppose them simply to step out 
 transversely to the train, and take the consequences, 
 they will leave the train with precisely the same velo- 
 city it had before, but it will have less momentum 
 than before, because, although having the same velo- 
 city, it has less mass by the masses of the passengers 
 who have gone out. But those who jumped in, if they 
 jumped in in a direction transverse to the train, so 
 as to have no momentum in the direction of the rails, 
 must necessarily diminish the velocity of the train, be- 
 cause they cannot change its momentum, but they do 
 change its mass, and if enough of passengers could 
 jump into the train at once to enormously increase its 
 mass, then they would be capable of reducing its velo- 
 city to any small amount you choose. 
 
 Carry the illustration a little further by supposing 
 two long trains passing one another, and passengers 
 stepping both ways between the two, it will be obvious 
 to you that if this process could be continued long 
 enough, it would end in destroying all difference of 
 
286 COND UCTION OF HE A T. 
 
 velocity between the two trains : since only when their 
 velocities are equal can there be no alteration of velo- 
 city by shifting a part transversely from one train to 
 the other. 
 
 This illustration, of course, is a perfectly easily con- 
 ceived one ; but it will help us to understand what has 
 until very lately been an extremely obscure subject, 
 viz., how it is that there can be such a thing as friction 
 between portions of air ; how it is that streams con- 
 sisting each of detached particles flying about among 
 themselves, can act as if they were solid bodies rubbing 
 against one another. It enables us, I say, to explain 
 upon what depends friction in fluids ; in gaseous fluids 
 at all events, if it does not quite enable us to explain 
 friction in liquids. Of course the explanation of friction 
 in solids must depend on totally different principles. I 
 shall, in my remaining lectures, explain the molecular 
 motions due to heat in gases, and must therefore recur 
 in part to our present inquiry. 
 
LECTURE XII. 
 
 STRUCTURE OF MATTER. 
 
 Limits of Divisibility of Matter. In physics the terms great and small are 
 merely relative. Various hypotheses as to structure of bodies Hard 
 Atom Centres of Force Continuous but Heterogeneous Structure 
 Vortex-atoms [Digression on Vortex-Motion.] Lesage's Ultramundane 
 Corpuscles. Proofs that matter has a grained structure. Approximation 
 to its dimensions from the Dispersion of Light : from the phenomena 
 of Contact Electricity. 
 
 As I promised in my last lecture, I intend to take 
 up to-day the consideration of recent results as to the 
 ultimate nature and constitution of matter. This is a 
 problem which has exercised the intellects of philoso- 
 phers from the very oldest times. I have no doubt 
 you are all acquainted with some of the speculations 
 which, whether their own or not, Lucretius and others 
 have given forth upon the subject. These, in many 
 cases, possess even now some interest ; but in compara- 
 tively modern times such inquiries have usually led to 
 what may rather be called metaphysical than physical 
 disquisitions. It became, in fact, the question of ' Yes ' 
 or 'No' for infinite ultimate divisibility of matter. 
 Now that is a problem which, however simple it may 
 appear to the metaphysicians, is at present quite as far 
 from us physicists as it was in the time of Lucretius. 
 We have made certain steps towards the knowledge of 
 
288 STRUCTURE OF MATTER. 
 
 the nature of particles or molecules of matter ; but as 
 to the question of atoms, that is to say, whether in 
 going on dividing and dividing, if we could carry the 
 process far enough, we should finally arrive at por- 
 tions of matter which are incapable of further division, 
 that is a question, I say, whose solution seems to 
 recede from our grasp as fast, at least, as' we attempt 
 to approach it. 
 
 There is a preliminary to all inquiries of this kind 
 which, though obvious to every one worthy of the 
 name of mathematician, is by no means obvious to an 
 intellect (however naturally acute) which has no mathe- 
 matical training. It is this : that there is no such thing 
 as absolute size, there is relative greatness and smallness 
 nothing more. To human beings things appear small 
 which are just visible to the naked eye very small 
 when they require a powerful microscope to render 
 them visible. The distance of a fixed star from us is 
 enormous compared with that of the sun : but there is 
 absolutely nothing \.Q show that even a portion of matter 
 which in our most powerful microscopes appears as 
 hopelessly minute as the most distant star appears in 
 our telescopes, may not be as astoundingly complex 
 in its structure as is that star itself, even if it far exceed 
 our own sun in magnitude. 
 
 Nothing is more preposterously unscientific than to 
 assert (as is constantly done by the quasi-scientific 
 writers of the present day) that with the utmost strides 
 attempted by science we should necessarily be sensibly 
 nearer to a conception of the ultimate nature of matter. 
 Only sheer ignorance could assert that there is any 
 limit to the amount of information which human beings 
 may in time acquire of the constitution of matter. 
 
STRUCTURE OF MATTER. 289 
 
 However far we may manage to go, there will still 
 appear before us something further to be assailed. 
 The small separate particles of a gas are each, no 
 doubt, less complex in structure than the whole visible 
 universe ; but the comparison is a comparison of two 
 infinites. Think of this and eschew popular science, 
 whose dicta are pernicious just in proportion as they 
 are the outcome of presumptuous ignorance. 
 
 I shall commence by briefly sketching one or two of 
 the more plausible or justifiable opinions which have 
 been enuntiated by various philosophers as to the so- 
 called ultimate constitution of matter. The first 
 that which I have just referred to is the notion of 
 the perfectly hard atom. You meet with it, not only 
 long before the time of Lucretius, but also in all sub- 
 sequent time, even in the works of Newton himself. 
 We find Newton speculating on this subject in his 
 unsuccessful attempt to account for the extraordinary 
 fact that the velocity of sound, as calculated by him by 
 strictly accurate mathematical processes, was found to 
 be something like one-ninth too little. We find Newton 
 suggesting that possibly the particles of air may be 
 little, hard, spherical bodies, which, at the ordinary 
 pressure of the atmosphere, are at a distance from one 
 another of somewhere about nine times the diameter of 
 each ; and, he says, sound then may be propagated 
 instantaneously through these hard atoms, or particles 
 of air, while it is propagated with the mathematically 
 calculated velocity through the space between each 
 pair. This is no doubt a very ingenious suggestion, 
 and it enables him to get rid of the outstanding diffi- 
 culty, because it virtually reduces the space through 
 which the sound has to travel to -^ths of what it other- 
 
 T 
 
290 STRUCTURE OF MATTER. 
 
 wise would have been ; and therefore it enables him to 
 add ^th to the calculated velocity of sound. In fact, it 
 virtually makes sound pass over Jth more space in a 
 given time than the mathematical investigation showed 
 it should do. But, unfortunately for this explanation, 
 it implies that sound should move faster in dense than 
 in rare air at the same temperature. This is incon- 
 sistent with the results of direct measurement. 
 
 The true explanation, however, why the velocity of 
 sound is different from that given by Newton's mathe- 
 matical calculation, was furnished by Laplace, who 
 showed that during the passage of a sound-wave 
 through the air, the alternate compressions and dilata- 
 tions take place so suddenly that the air has not time 
 to part with the heat generated by the compression, or 
 to supply the loss of temperature produced by the ex- 
 pansion, and therefore its pressure increases more when 
 it is compressed, and diminishes more when it is dilated, 
 than it would do if it were kept constantly at the same 
 temperature. [In the language of Lecture V., above, 
 the compressions and dilatations by which sound is 
 propagated take place adiabatically.] And it is found 
 by experiment that the amount of heat developed by 
 compression of air, or the amount of heat absorbed in 
 its expansion, is completely and exactly sufficient to 
 account for the ninth which Newton found wanting ; so 
 that, although we have in this way Newton's authority 
 for the supposition that there may exist ultimate hard 
 particles through which sound or any motion may be 
 transmitted instantaneously, the ground upon which he 
 introduced them has now been found not to warrant 
 that introduction, and therefore we are left as much in 
 difficulty as before. 
 
STRUCTURE OF MATTER. 291 
 
 There is one point, however, which should be noticed 
 before leaving this speculation of Newton's : that if 
 the particles of matter be small hard atoms, whose size 
 bears any finite ratio to the distances between contigu- 
 ous ones, there must be a limit to the compressibility of 
 any and every body. For instance, if Newton's sug- 
 gestion had been correct ; if the particles of air at the 
 ordinary pressure of the atmosphere had a diameter 
 equal to about |th of their mutual distance from one 
 another (i.e. -^th of the distance from centre to centre), 
 then it is obvious that if you were to compress a mass 
 of air into Yo^- n P ar t each way in each of three dimensions, 
 you would bring the particles in the various layers into 
 contact with one another. That is to say, when a mass 
 of air, taken at the ordinary pressure of the atmosphere, 
 is compressed to T Vth of ^th of T Vth, or T ^oo tn of its 
 original bulk, then the particles are in contact with one 
 another, like cannon-balls in a pile ; and as they are, 
 according to Newton's supposition, infinitely hard and 
 incompressible, it would be impossible to compress the 
 group further. Hence air could not be compressed to a 
 smaller bulk than TTJ Vo tn f tne bulk ^ nas at ordinary 
 pressures and temperatures. 1 Now, we know that air 
 has been compressed by Natterer and others far beyond 
 that, and therefore, tested from this point of view also, 
 Newton's explanation or suggestion is seen to be quite 
 
 1 This supposes the particles to be arranged in cubical order, so that 
 ach is in contact with only six others. But they can be packed closer, 
 by arranging every three contiguous spheres in triangular order, so that 
 
 each is in contact with twelve others. The density in this case is greater 
 
 than in the former in the ratio of ^/2 to I ; so that Newton's group of 
 spherical particles could be compressed to T ii?th part of the space they 
 originally occupied. (Proc. JR. S. ., Feb. 1862.) This, however, does 
 not invalidate the remarks above. 
 
292 STRUCTURE OF MATTER. 
 
 indefensible. It is obvious, however, that if there are 
 such small infinitely hard particles as atoms, they must 
 be in all bodies at a distance from one another, because, 
 so far as experiment has guided us, there is no portion 
 of matter whatever that is not capable of further com- 
 pression by the application of sufficient pressure ; and 
 of course, compression of a group of infinitely hard 
 particles must presuppose that they have certain in- 
 terstices between them, so that they are capable of 
 being brought still nearer. 
 
 Another school of philosophers and experimenters, 
 recoiling from the notion of the hard atom, took up the 
 following idea. All that we know of atoms will be 
 perfectly well accounted for if we dispense altogether 
 /with the notion of an atom dispense with anything 
 y material in the ordinary sense of the word matter : but 
 suppose merely a centre of force, such as we are accus- 
 tomed to in those mathematical fictions which we meet 
 with in our text-books. Suppose, in place of an atom, 
 a mere geometrical point, which can exert repulsive or 
 attractive forces ; or rather suppose such forces tending 
 towards or from a certain point, but nothing at the 
 point ; except, in some unexplained way, mass. So far 
 as external bodies are concerned, this point will behave 
 just as an atom would do. But here we are met by the 
 gigantic difficulty of accounting for Inertia. This 
 hypothesis was taken up and developed to a great 
 extent by Boscovich, and was to a certain extent 
 adopted in later times even by Faraday. It is, as 
 I have stated at the outset, a mathematical fiction, 
 but it is often an extremely convenient one for the 
 purpose of enabling us to make certain mathematico- 
 physical investigations of what takes place in the 
 

 STRUCTURE OF MATTER. 293 
 
 interior of bodies in their various states of solids, 
 liquids, and gases. 
 
 Then there is a third notion that the matter of any 
 body, where it does not possess pores, like those, for 
 instance, of a sponge (which obviously does not occupy 
 the whole of the space which its outline fills), fills space, 
 continuously, but with extraordinary heterogeneous- 
 ness. But if, even in such a body as a sponge, we were 
 to take a part so small as to be without pores, according 
 to this notion, such a part is continuous but intensely 
 heterogeneous. 
 
 In order to make this more plain, let us think of it 
 on a greatly magnified scale ; let us think of an enor- 
 mous mass like a pyramid, for instance, or like the 
 whole earth, built up of bricks and mortar ; or, rather, 
 like a huge mass of rubble, built of irregular stones, 
 with mortar filling the interstices. Or, to take a body 
 of intermediate size, suppose the moon were built up of 
 materials of that kind. Looked at with our most power- 
 ful telescopes, it would appear to be perfectly homo- 
 geneous in texture. We could not possibly see the 
 heterogeneity, the passing from the bricks to the mortar, 
 or from the stones to the mortar, unless we could im- 
 prove our telescopes so as to magnify enormously more 
 than we can at present have any hope of. And unless 
 we could obtain almost infinitely more perfect tran- 
 quillity of the air than has ever been noticed by observ- 
 ing astronomers (even when, as suggested by Newton, 
 they have observed from the tops of high mountains), 
 the possession of the requisite enormously high optical 
 power would be impotent to reveal to us that the moon 
 was not homogeneous throughout, but that it was really 
 intensely heterogeneous when closely enough examined. 
 
294 STRUCTURE OF MATTER. 
 
 Now, what the moon presents to us at its distance of 
 240,000 miles enormous from one point of view, but 
 very small in comparison with other distances even in 
 the solar system very much the same thing is pre- 
 sented to us by a single drop of water. Our difficulty 
 there is not on account of its distance, but on account 
 of the extreme minuteness of the heterogeneity which 
 we desire to measure. No microscope has yet enabled 
 us to see anything of the nature of heterogeneity in a 
 quantity of water, magnify it as we please, but yet there 
 must be heterogeneity, and that of by no means incon- 
 ceivably small dimensions, as you will see by many 
 proofs which I shall soon proceed to give. 
 
 As, however, I am at present merely classifying the 
 various more plausible suppositions as to the ultimate 
 structure of matter, I do not now give that illustration, 
 but leave it for a few minutes. 
 
 Finally, as the only other of these hypotheses which 
 it is necessary to bring forward, I mention that quite 
 recently suggested by Sir William Thomson the notion 
 tjzat what we call matter may really be only the rotating 
 ^portions of something which fills the whole of space ; that 
 is to say, vortex-motion of an everywhere present fluid. 
 
 The peculiar properties of vortex-motion were mathe- 
 matically deduced, for the first time, by Helmholtz, 1 
 some fifteen years ago only, in a most beautiful investi- 
 gation, in which he broke ground in a department of 
 hydro-kinetics, the difficulties of which had, up to his 
 time, kept mathematicians almost completely aloof. 
 
 So far, at all events, as concerns the motion of a per- 
 fect incompressible liquid, Helmholtz made out a great 
 many thoroughly novel and excessively interesting pro- 
 
 1 Crelle, 1857. Translated in Phil. Mag., 1867. 
 
STRUCTURE OF MATTER. 295 
 
 positions, and upon these Sir William Thomson based 
 ,his notion of possible vortex-atoms. 
 
 It will be necessary that I should give a brief sketch 
 of the nature of these results of Helmholtz, in order 
 that you may easily follow my explanation of Sir Wil- 
 liam Thomson's suggestion, and I do so the more 
 readily because it is, or, at all events, it appears to my- 
 self to be, by far the most fruitful in consequences of all 
 the suggestions that have hitherto been made as to the 
 ultimate nature of matter. Especially does it give us 
 a glimpse, at least, of an explanation of the extraordi- 
 nary fact, that every atom of any one substance, where- 
 soever we find it, whether on the earth or in the sun, or 
 in meteorites coming to us from cosmical spaces, or in 
 the farthest distant stars or nebulae, possesses precisely 
 the same physical properties. So convinced are we, by 
 experiment and observation, that a particle of hydrogen, 
 in the farthest nebulae, in the farthest stellar system, 
 vibrates (when heated) in precisely the same fundamental 
 modes, and in precisely the same periods, as it does in a 
 Geissler's vacuum-tube in our laboratories ; that, as we 
 have already seen, any apparent exception to this is 
 hailed as a certain source of information about the 
 relative motion of such bodies with regard to the earth, 
 and in some cases may give an invaluable method of 
 obtaining their actual distances from us. 
 
 As a preliminary illustration, I shall show the forma- 
 tion of a simple circular vortex-ring : exhibiting one or 
 two of its more important properties ; and then we shall 
 get rid of the apparatus for producing it as fast as we can. 
 
 The apparatus consists, as you see, of a very homely 
 arrangement, merely a wooden box with a large round 
 hole made in one end of it, while the opposite end has 
 
296 STR UC TURE OF MA TTER. 
 
 been removed, and its place supplied by a towel 
 tightly stretched. In order to make the air which is 
 to be expelled from this box visible, we charge it first 
 with ammoniacal gas, by sprinkling the bottom of the 
 box with strong solution of ammonia. A certain 
 quantity of ammoniacal gas has now been introduced 
 into it, and we shall develop in addition a quantity of 
 muriatic acid gas. This is done by putting into the 
 box a dish containing common salt, over which I pour 
 sulphuric acid of commerce. These two gases combine, 
 and form solid sal-ammoniac, so that anything visible 
 which escapes from the box is simply particles of sal- 
 
 
 ammoniac, which are so very small that they remain 
 suspended by fluid-friction, like smoke in the air. Now 
 notice the effect of a sudden blow applied to the end of 
 the box opposite the hole. There you see a circular 
 vortex-ring, moving on its own account through the 
 room as if it were an independent solid. 
 
 I shall now try to show you the effect of one vortex-ring 
 upon another, just as I showed it here to Thomson, when 
 he at once formed his theory. You notice that when 
 two vortex-rings impinge upon one another, they be- 
 have like solid elastic rings. They vibrate vehemently 
 
STRUCTURE OF MATTER. 297 
 
 after the shock, just as if they were solid rings of india- 
 rubber. It is easy, as you now see (shows), to produce 
 such vibration of a vortex-ring without any impact from 
 another. All we have to do is to substitute an elliptical, 
 or even a square, hole for the circular one we have hither- 
 to employed. The circle is the equilibrium form of the 
 simple vortex, and thus, if a simple vortex be produced 
 of other than a circular form, it vibrates about that 
 circular form as about a position of stable equilibrium. 
 Another curious result which, as you see, is easily pro- 
 duced (skozvs), is to make one vortex-ring pass through 
 another. Helmholtz showed theoretically that if two 
 vortex-rings be moving with their centres in the same 
 line, and their planes perpendicular to that line, then : 
 first if they are moving in the same direction, the 
 pursuer contracts and moves faster, while the pursued 
 expands and moves slower, so that they alternately 
 penetrate one another : second if they are equal and 
 moving in opposite directions, both expand indefinitely 
 and move slower and slower, never reaching one an- 
 other. In fact, the one behaves to the other like its 
 image in a plane mirror. And this, as you now see, is 
 the fate of a vortex-ring which impinges directly on a 
 plane solid surface. 
 
 Now, the first vortex-ring which you saw sailing 
 up through the class-room, contained precisely that 
 particular portion of air, mixed with sal-ammoniac 
 powder, which had been sent out of the box by the blow. 
 It was not merely sal-ammoniac powder which was 
 going through the air, but a certain definite portion of 
 the smoky air, if we so may call it, from the inside of 
 that box, which, in virtue of the vortex-motion which it 
 had, became, as it were, a different substance from the 
 
298 STRUCTURE OF MATTER. 
 
 surrounding air, and moved through it very much likeVa 
 solid body. 
 
 In fact, according to the result of Helmholtz's re- 
 searches, if the air were a perfect fluid, if there were 
 no such thing as fluid-friction in air, that vortex-ring 
 would have gone on moving for ever. 1 Not only so, 
 but the portion of the fluid which contained the smoke, 
 which was, as it were, marked by the smoke, would 
 remain precisely the same set of particles of the fluid as 
 it moved through the rest ; so that those which were 
 thus marked by the smoke were, by the fact of their 
 rotation, distinguished or differentiated from all the 
 rest of the particles of air in the room, and could 
 not by any process, except an act of creative power, be 
 made to unite with the fluid in the room. 
 
 That is a point which appears to me to be one of the 
 most striking characteristics in the foundation of this 
 suggestion of vortex-atoms. Granted that you have a 
 perfect fluid, you could not produce a vortex-ring in it ; 
 nor, if a vortex-ring were there, could you destroy it. No 
 process at our command could enable us to do either, 
 because in order to do it, fluid-friction is essentially 
 requisite. Now, by the very definition of a perfect fluid, 
 friction does not exist in it. 
 
 Thus, if we adopt Sir William Thomson's supposition 
 that the universe is filled with something which we have 
 no right to call ordinary matter (though it must possess 
 inertia), but which we may call a perfect fluid ; then, if 
 any portions of it have vortex-motion communicated 
 
 1 Of course, in air, fluid-friction, which depends upon diffusion, soon 
 interferes with this state of things. But, in the experiment as shown, 
 the ring (of some six or eight inches in diameter) was not sensibly altered 
 by such causes in the first twenty feet of its path. 
 
STRUCTURE OF MATTER. 299 
 
 to them, they will remain for ever stamped with that 
 vortex-motion ; they cannot part with it ; it will remain 
 with them/ as a characteristic for ever, or at least until 
 the creative act which produced it shall take it away 
 again, i 1 ' Thus this property of rotation may be the basis 
 of all that to our senses appeals as matter. 
 
 The properties which Helmholtz showed that such 
 a vortex-filament must possess are these first, that 
 every part of the core of the filament is essentially 
 rotating. A vortex-filament may have infinitely many 
 shapes besides the simple one which I showed you just 
 now. Unfortunately it appears impossible for us to 
 form, even with an imperfect fluid like air or water, a 
 vortex-filament of any more complex character than 
 that simple circle. Theoretically, a vortex-filament can 
 exist with any amount of knots and windings upon it, 
 but then unfortunately we cannot devise an aperture by 
 which to allow the smoky air to escape so as to give us 
 such a knotted vortex. If we could devise the requisite 
 form of aperture, and produce the vortex, then so long 
 as the friction of the air did not seriously come into 
 play, that vortex would retain its characteristics as com- 
 pletely as did the circular one which I sent out, and 
 not only that, but it would possess that same elasticity 
 about a definite form of equilibrium which you noticed 
 the circular vortices possessed. They not merely keep 
 their portion of air always in the vortex state, but they 
 also have a definite form, in virtue of which they possess 
 elasticity, so that when the form was altered for a mo- 
 ment by a sudden shock between two of them, each 
 oscillated about its definite form, to which it finally 
 settled down again. 
 
 In such a vortex-ring (as you will easily understand 
 
300 STRUCTURE OF MATTER. 
 
 by thinking how it came out of the round hole in the 
 box), the motion of the particles of air is of this kind. 
 Suppose it to be coming forward towards you, then 
 every portion of the air on the inner side of the ring is 
 moving forward, and every portion on the outer side is 
 going backward, so that the whole is turning round 
 and round its linear circular core. The air all about it 
 is in motion according to a simple law which, how- 
 ever, I could not explain without mathematics ex- 
 cept in the particular case of that within the annulus, 
 which is moving forward faster than the ring itself. I 
 shall afford any of you who desire it (after the lecture) 
 
 an opportunity of convincing yourselves of the fact. 
 Each of you will find that, if he places his face in the 
 path of one of these large air vortex-rings, there is no 
 sensation whatever until the vortex-ring is almost close 
 to him, and when it reaches him he feels a sudden blast 
 of wind flowing through the centre of it. Thus, this 
 vortex-ring not only involves in itself rotating elements 
 which are thereby distinguished altogether from the 
 other elements of the fluid, but it also is associated 
 necessarily with other movements through the non- 
 differentiated air, and especially a forward rapid current 
 of air passing through its centre in the direction in 
 which it is going. 
 
STRUCTURE OF MATTER. 301 
 
 Helmholtz showed that if vortex-filaments exist in a 
 continuous medium, one of two things must follow : 
 either they must be ring-shaped that is to say, endless 
 after any number whatever of knottings or twistings, 
 the ends must come together ; or else the ends must be 
 in the free surface of the medium. Now, you can easily 
 form half a vortex-ring. I dare say many of you have 
 seen such a thing over and over again without thinking 
 what it was. You must all have seen that when you draw 
 a teaspoon along the surface of a cup of tea, and lift it 
 up from the surface, there are a couple of little eddies 
 or whirlpools going round in the tea rotating in opposite 
 directions, the two moving forward (as do their sides 
 which are nearest one another) in the direction in which 
 the teaspoon was drawn. These two little eddies are 
 simply the ends of a half vortex-ring. There can be ends 
 in such a case as that, because these two ends are in 
 the free surface of the liquid. A vortex-ring, then, can- 
 not have ends, it must be a ring or a knot in fact, 
 except these ends be in the free surface of the liquid ; 
 and if we adopt Thomson's notion of a perfect fluid 
 filling infinite space, of course there can then be no 
 ends. All vortex-rings and therefore, according to 
 Sir William Thomson, all atoms of matter -must 
 necessarily be endless, that is to say, must have their 
 ends finally united together after any number of convo- 
 lutions or knottings. 
 
 Secondly, though this is really involved in what we 
 have just seen, Helmholtz shows that such a ring is 
 indivisible : you cannot cut it. Do what you like : bring 
 the edge of the keenest knife up to it as rapidly as you 
 please, it cannot be cut ; it simply moves away from or 
 wriggles round the knife ; and, in this sense, it is literally 
 
302 STR UC TURE OF MA TTER. 
 
 an atom. It is a thing which cannot be cut : not that 
 you cannot cut it ; but that you cannot so much as get 
 at it so as to try to cut it. 
 
 This idea of vortex-atoms enables us to explain a 
 great many properties of matter ; but it has introduced 
 us unfortunately (perhaps I ought rather to say fortun- 
 ately) to a series of mathematical difficulties of incom- 
 parably superior order to those suggested to us (at least 
 at so early a stage) by any of the other ideas as to the 
 nature of matter. 
 
 The fact is that Helmholtz's investigation, made 
 fifteen years ago, was the very first attempt to take 
 more than a single step into the wide and very diffi- 
 cult subject of hydro-kinetics, without the preliminary 
 assumption that the motion should be differentially 
 irrotational. 
 
 The subject of rotatory fluid motion is such a for- 
 bidding one, from a purely mathematical point of view, 
 that no one had done more than take a look at it, as it 
 were, until Helmholtz gave us these fundamental pro- 
 positions ; splendid as they are, they are only a first 
 step. Indeed, to investigate what takes place when 
 one circular vortex-atom impinges upon another, and 
 the whole motion is not symmetrical about an axis, is 
 a task which may employ perhaps the lifetimes, for the 
 next two or three generations, of the best mathe- 
 maticians in Europe ; unless, in the meantime, some 
 mathematical method, enormously more powerful than 
 anything we at present have, be devised for the purpose 
 of solving this special problem. This is no doubt a 
 very formidable difficulty, but it is the only one which 
 seems for the moment to attach to the development 
 of this extremely beautiful speculation ; and it is the 
 
STRUCTURE OF MATTER. 303 
 
 business of mathematicians to get over difficulties of 
 that kind. 
 
 But there is more than this. In general, vortex- 
 atoms, if they be at a moderate distance from one 
 another, will not exhibit, in their behaviour to one 
 another, anything of the nature of gravitation. That 
 result at all events we can derive by our modern im- 
 provements of mathematics. How, then, is gravitation 
 to be accounted for on this theory ? The theory of 
 vortex-atoms, being as it were complete in itself, must 
 be rejected at once if it can be shown to be in- 
 capable of explaining this grand law of nature, which 
 tells us that every particle or atom in the universe 
 attracts every other with a force proportional to their 
 masses conjointly, and to the square of their distance, 
 inversely. Now the only even plausible explanation 
 of gravity which has yet been propounded, was given 
 long ago (at the beginning of the century) by Lesage 
 of Geneva. He showed that gravitation can in all 
 cases be accounted for by the not improbable supposi- 
 tion that, in addition to the gross particles of matter 
 I should, perhaps, rather say the particles of gross 
 matter ; but, as you will see, the term gross particles 
 of matter also comes in as specially applicable to the 
 hypothesis we are dealing with : in addition to these 
 grosser particles which are the atoms of tangible or 
 sensible matter, infinite as these are in number, there 
 is an infinitely greater number of much smaller ones 
 darting about in all directions with enormously great 
 velocities. Lesage showed that, if this were the case, 
 the effects of their impacts upon the grosser particles 
 or atoms of matter would be to make each two of 
 these behave as if they attracted one another with a 
 
304 STRUCTURE OF MATTER. 
 
 force following exactly the law of gravity. In fact, 
 when two such particles are placed at a distance from 
 one another, each, as it were, screens the other from a 
 part of the shower which would otherwise batter upon 
 it. If you had a single lone particle, it would be equally 
 battered on all sides, but when you bring in a second 
 particle, it, as it were, screens the first to a certain 
 extent, in the line joining the two ; and the first in 
 turn screens the second, so that, on the whole, each of 
 these two is battered more on the side opposite to the 
 other one than it is on the side next the other one ; 
 and, therefore, on the whole, there is a tendency to 
 bring the two together by the excess of battering 
 outside over that inside. Now, it is a very easy mathe- 
 matical deduction to show that the result of this is 
 equivalent to an attraction, inversely as the square of 
 the distance ; and, therefore, that it exactly agrees with 
 the law of gravity. But it is necessary also to suppose 
 that masses of matter have a cage-like form, so that 
 enormously more corpuscles pass through them than 
 impinge upon them ; else the gravitation action be- 
 tween two bodies would not be as the product of their 
 masses. 
 
 This supplementary hypothesis requires, from Thom- 
 son's theory, an explanation of the supply of energy 
 to these smaller particles ; which must, of course, be 
 smaller vortices. This has, as yet, not been fully given, 
 though certain advances have been made. With a 
 little further development the theory may perhaps be 
 said to have passed its first trials at all events, and, 
 being admitted as a possibility, left to time and the 
 mathematicians to settle whether, really, it will account 
 for everything already experimentally found. If it 
 
STRUCTURE OF MATTER. 305 
 
 does so, and if it, in addition, enables us to predict 
 other phenomena, which, in their turn, shall be found 
 to be experimentally verified, it will have secured all 
 the possible claim on our belief that any physical theory 
 can ever have. 
 
 Although we cannot as yet attempt to settle the 
 question whether there are atoms or not, we can, at 
 all events, by the help of chemistry, take one step 
 of immense consequence as regards the much simpler 
 question of heterogeneity, to which I alluded a little 
 ago. 
 
 We know that, taking water as the most familiar 
 of all substances to talk about, we know that a drop 
 of water can be divided and divided to an enormous 
 extent, whether to an infinite extent or not we don't 
 know, but there is still a finite amount of division to 
 which a drop of water can be subjected, in which the 
 parts, which are finally separated from one another, 
 are no longer the same as portions of the whole. By 
 means of a galvanic battery, we can decompose water 
 into its constituent gases. Now, this shows at once 
 that there must be some limit to the division of a drop 
 of water ; a point which we cannot pass without pro- 
 ducing something different from water. The drop must 
 be capable of finite, though excessively minute, division 
 into parts quite alike, similar and equal to one another, 
 but so small that if any one of these parts is again 
 divided, the halves or parts of it could no longer be 
 similar to one another. This similarity must necessarily 
 go on to a certain extent, and to an extent far beyond 
 what the microscope can show us ; but there must at 
 last come a state of division when any further inter- 
 ference with one of the particles will make each frag- 
 
 U 
 
3 o6 STRUCTURE OF MATTER. 
 
 ment something other than water, will take away a 
 part of its oxygen or a part of its hydrogen, leaving too 
 much of the one and too little of the other. 
 
 Whenever we come to that point, we have got down 
 to what we may call the grained structure of the whole. 
 Without any assumption at all about atoms, this is 
 obviously something which exists, and which we reach 
 in thought far sooner than we reach the atom. We 
 know as yet nothing whatever as to whether oxygen 
 and hydrogen consist of ultimate atoms or not ; but we 
 do know that water and all other compound substances 
 certainly do consist of ultimate parts, ultimate in this 
 sense, that if you go any further with the division of 
 them they cease to be parts of the substance. 
 
 Take a number of such similar parts of the substance 
 as are capable, when mixed together in any numbers, 
 of forming a mass of the substance. Perform the same 
 sort of operation upon each of them, an operation which 
 shall make it different from what it was before, by 
 taking off a part of one of its constituents only ; then 
 if you mix all these similar parts together, you do not 
 get the original substance. You get something else, if 
 indeed you get a chemically stable compound at all, 
 rather than a mere mixture of several different things. 
 That shows, then, that without going infinitely far, you 
 have arrived at a place at which heterogeneity begins 
 to come in. 
 
 Now, it is a very great step indeed in science to 
 determine at about what distance heterogeneity sets 
 in. To take the former illustration which I gave, if the 
 moon were built up, like a wall, of stones and mortar, 
 into how many pieces must it be broken, so that these 
 pieces shall not be, on the whole, quite similar in aver- 
 
STRUCTURE OF MATTER. 
 
 age materials to one another ? A piece of massive 
 brickwork of the size of this room could scarcely be 
 distinguished from another piece of massive brickwork 
 of the same size, if the bricks were laid in each in the 
 same tactical order, and with the same thickness of in- 
 tervening mortar. There might be a projecting fraction 
 of a brick at one side more than at the other, and so 
 on ; but on the whole, a mass of brickwork of such a 
 size that is to say, a mass so large in its dimensions 
 compared with an individual brick might be talked of 
 as homogeneous practically, or at all events as being 
 simply and directly comparable with another piece of 
 the same materials and size. But could we break down 
 the mass into fragments : after the mortar has become 
 as strong, let us say, as the bricks : fragments about the 
 tenth part of the dimensions of the original bricks, then 
 we should have pieces quite distinguishable ; one, per- 
 haps, wholly mortar, another wholly brick, and a third 
 partly mortar and partly brick. There at last you 
 have got heterogeneity, and marked heterogeneity, 
 because two of the parts may have absolutely nothing 
 in common, the one being entirely mortar, and the 
 other entirely brick, although taken from the same solid 
 mass, as nearly as possible from the same part of it, 
 and of the same size. 
 
 It is quite obvious, then, that there is a most impor- 
 tant investigation to be made here, at what limit does 
 this heterogeneity begin ? and also that it is already, 
 to some extent at least, within our reach. The answer 
 to that question has not yet of course been definitely 
 given, but it has been approximately given by various 
 authors, and on various grounds. Loschmidt was, I 
 believe, the first who gave an estimate. Others have 
 
308 STRUCTURE OF MATTER. 
 
 since given other estimates (very nearly agreeing with 
 his) from the same point of view ; and lately Sir William 
 Thomson has not only given us an estimate from that 
 point of view, but he has given us, besides, other three 
 estimates from perfectly different grounds of reasoning, 
 yet agreeing with one another, and with the slightly 
 older results, as well at least as can be expected at the 
 outset of so novel an inquiry. 
 
 As this is one of the most important of modern dis- 
 coveries, I make no apology for dilating considerably 
 upon these various arguments, the experiments upon 
 which they are founded, and the results to which they 
 lead us. 
 
 I may take first, then, a mode of proof depending on 
 an investigation which, at the time when it was given, 
 was hardly perhaps understood in its full weight. It 
 was given considerably before the period to which my 
 present expositions mainly refer. It was an investiga- 
 tion by the great French mathematician, Cauchy, of the 
 motion of light in solid bodies and liquids ; wherein he 
 showed that, in order to account for what is called dis- 
 persion, that is to say, the fundamental phenomenon 
 discovered by Newton the separation of the various 
 colours of white light by refraction, it was absolutely 
 necessary, at least on his hypothesis, to take into account 
 the effect of the distance between particles of matter 
 (assuming that there are particles) upon the motion of 
 the luminiferous medium. He showed that there could 
 be no such separation of the various colours of light from 
 one another, unless the distance from particle to particle 
 of the substance through which the light was passing 
 were comparable with the length of the wave of light, 
 or at least were not infinitely small compared with it. 
 
STRUCTURE OF MATTER. 309 
 
 Thus, looked at from our modern point of view, 
 Cauchy's result (valeat quantum) simply shows us that 
 matter cannot be homogeneous. If matter were abso- 
 lutely homogeneous, there might be refraction, but there 
 would be no dispersion. All kinds of light would travel 
 with the same velocity in glass, just as they did in the 
 air outside ; and, therefore, the mere fact that the differ- 
 ent kinds of light can be separated from one another in 
 passing through a prism, gives, at least, a hint that the 
 matter of the prism is heterogeneous, and that its 
 heterogeneousness is not infinitely more fine grained 
 than the length of a wave of any of the kinds of light 
 which it enables us to separate in their courses. 
 
 Take this argument for what it is worth (especially 
 if we connect with it the irrationality of dispersion), it 
 gives us, at least, an approximation to the dimensions 
 of the grained structure. For the average length of a 
 wave of visible light is somewhere about, let us say, the 
 4O,oooth or 5o,oooth part of an inch. But the grained 
 structure is probably very much more minute than the 
 wave length. If it were not so, dispersion would, on 
 Cauchy's hypothesis, be enormously greater than we 
 find it. Again, we cannot suppose that it is much less 
 than somewhere about the io,oooth part of the length 
 of a wave of light ; that is, in the course of one of these 
 waves of light, which is only about the 4O,oooth part 
 of an inch in length, there cannot be much more than 
 10,000 alternations fronr brick to mortar, as it were, 
 and mortar to brick again : and, therefore, by using 
 the 10,000 and the 40,000 as factors, you may say 
 that, in an inch, this heterogeneity, or the change, if 
 you like to call it so, from a molecule to nothing, cannot 
 occur much more frequently than somewhere about 
 
3 io STRUCTURE OF MATTER. 
 
 400,000,000 times. 400,000,000 in the inch, then, will 
 be a first very rough approximation to this heterogeneity 
 or grained structure of matter. 
 
 The next which I take up, although not the next 
 in order of time, is perhaps the next in simplicity of 
 explanation to that of Cauchy. It is founded upon 
 what is called the electricity of contact of different 
 metals. 
 
 I shall first, by means of one of Thomson's electro- 
 meters, show you the fundamental experiment of this 
 subject. I do so, because the experiment is one which, 
 although perfectly well known in the time of Volta, 
 has been steadily disbelieved since Volta's time, and is 
 now received as true by a comparatively small num- 
 ber only even among physical philosophers. This is 
 the electrometer, one of those instruments to which I 
 alluded in my opening lecture as having been supplied 
 in consequence of the practical demands of the time, and 
 as having reacted in the way of enormously improving 
 our means of making physical investigations. In order, 
 first of all, to show that it is really acted upon by elec- 
 tricity, suppose I take this zinc plate, which is sup- 
 ported upon a glass stem, surrounded below by pieces 
 of pumice moistened with strong sulphuric acid, and 
 connected at present with the interior of the apparatus, 
 and touch it with my handkerchief, you notice that the 
 effect is to produce a deflection of the index-spot of 
 light, which is sufficient to throw it off the scale. We 
 know, however, that an electrified body put in contact 
 with the ground loses all its free electricity. And you 
 see now, that a touch of my finger on the zinc plate dis- 
 charges its electricity, and the spot of light comes back 
 to its original zero position. We shall study afterwards 
 
STR UCTURE OF MA TTER. 3 1 1 
 
 what kind of electricity was there developed. Mean- 
 while, I take a copper plate, which I hold by means of 
 a glass handle, touch it first to remove any free electri- 
 city it may have, touch this zinc again to remove any 
 trace of electricity, and then bring the two into contact. 
 I take the copper plate from the zinc, and you notice 
 the deflection of the spot of light to the left-hand side 
 of the zero. I touch the copper, and apply it again. 
 Taking it off, I have a still greater deflection ; and I 
 could go on doing this over and over again, and giving 
 larger and larger quantities of electricity to the zinc 
 plate. This is obviously the opposite kind of electricity 
 to that which I produced in the zinc by touching it with 
 my handkerchief. However, we shall presently test 
 what kind of electricity it is. To show that this is a 
 genuine charge of electricity, I touch the zinc, and you 
 see the charge vanishes, and the electrometer reading 
 is zero again. Let us vary the experiment, by putting 
 the zinc plate where the copper was, and the copper 
 where the zinc was. This time we are to observe the 
 electrification of the copper plate when it has come in 
 contact with the zinc. I make the contact, and with- 
 draw it, and you notice now a deflection to the right- 
 hand side instead of to the left. I perform it again, 
 touching the zinc plate every time I have withdrawn it 
 from the copper, and you notice the steadily-increasing 
 deflection. We have thus established, as far as physical 
 experiment can establish anything, that when a zinc 
 and copper plate are brought into contact with one 
 another, and then separated, the one is, in the usual 
 language of the subject, charged with positive electricity, 
 and the other with negative. To find out which is 
 which, all that is necessary is to take a stick of sealing- 
 
312 STRUCTURE OF MATTER. 
 
 wax, which produces what is called resinous or negative 
 electricity when rubbed with a piece of flannel. If this 
 be the same kind of electricity as that with which the 
 copper plate remains charged, the effect of bringing the 
 
 rubbed sealing-wax near the copper plate will be to 
 repel that electricity into the electrometer, and therefore, 
 of course, to increase the present deflection. On the 
 other hand, if it should be the opposite kind of elec- 
 
STRUCTURE OF MATTER. 313 
 
 tricity, the wax will attract some of it out of the electro- 
 meter, and so the deviation of the spot of light will 
 become less. I rub the wax and present it, and you 
 notice we have a greater deflection ; therefore, copper 
 is resinously or negatively electrified when it comes in 
 contact with zinc, and zinc is, of course, positively or 
 vitreously charged by the same operation. The large 
 amount of the charge, in this experiment, depended 
 upon the fact that the zinc and copper were put into 
 metallic contact with one another over a large surface ; 
 but I could have produced the same result in another 
 way, more pertinent to my present inquiry. It would 
 take up your time too much to exhibit the experiment, 
 but if, in place of putting the plates in direct surface 
 contact, I had supported one a small distance above the 
 other, and brought a metallic wire from the one to the 
 other, precisely the same effect would have been pro- 
 duced. 
 
 Now, to our application. When two bodies are elec- 
 trified, one with positive and the other with negative elec- 
 tricity, they attract one another. Therefore, the mere 
 fact of putting these metal plates in presence of one 
 another, with a metallic wire, however thin, connecting 
 them, introduces this force of attraction between the two, 
 altogether independent of the force of gravity a force 
 of attraction due to the dissimilarity of the two metals. 
 If they had been two plates of the same kind of metal, 
 there would have been no such effect. 
 
 It was upon this experiment of Volta, which Sir 
 William Thomson, by the help of his electrometer, was 
 enabled to put beyond all cavil, that he founded another 
 of those estimates of the dimensions of the hetero- 
 geneity of matter. The reasoning was of this kind. 
 
3 i4 STRUCTURE OF MATTER. 
 
 There is a certain amount of attraction between the 
 zinc and the copper plates when they have been put 
 into metallic contact, however thin be the plates and 
 the wire which is connecting the two. If we can 
 measure the amount of electric attraction between the 
 zinc and the copper plates, we shall be able to tell how 
 much work would be done by this electric attraction if 
 the zinc plate were allowed to come up to the copper 
 plate. There is a certain force acting through a certain 
 distance, and we can calculate how much work it would 
 do. Suppose, then, that we take an enormous number 
 of exceedingly thin plates of zinc and exceedingly thin 
 plates of copper, and that we lay down first one plate 
 of zinc, and then bring a plate of copper near it, 
 but not touching it except by one corner, then there 
 would be this electric attraction between the two. Allow 
 the copper plate to fall down upon the zinc, and there 
 would be a certain amount of work done. Then the 
 upper surface would be copper. Bring a new zinc plate 
 and repeat the experiment, and so on, you would get a 
 pile of zinc and copper plates over one another. You 
 can calculate how much work would be done in such a 
 case, but it is easy to see that the quantity of work does 
 not depend upon the thickness of the zinc or copper 
 plates ; so that, make the plates as thin as you please, 
 the quantity of work done by the pile of zinc and copper 
 plates, which together would rise to the thickness of an 
 inch, will be greater and greater as there are more plates 
 in it ; therefore, make them thinner and thinner, and 
 more numerous in the same proportion. You will get 
 more and more work done by electrical forces on the 
 same amount of mass, and, by carrying the process far 
 enough, you would reach an amount of work sufficient, 
 
STRUCTURE OF MATTER. 315 
 
 if in the form of heat, to melt the whole of the zinc and 
 the copper. Now comes the application. It is obvious 
 from the reasoning I have just given that when zinc and 
 copper are put together in fine powder, it would be pos- 
 sible, provided there were no limit to their division, to 
 make the powders so fine that they would take fire, or 
 at least melt, on being mixed. Now we know by ex- 
 periment the amount of heat which is generated when 
 copper and zinc are mixed intimately in the formation 
 of their alloy brass so that we can calculate how fine 
 must be their physical particles to account for their giv- 
 ing no more than the heat which is actually observed on 
 their thus coming together. That calculation depends on 
 a great many things, of which we have as yet no precise 
 measurement, so that such numbers as we can give must 
 be only approximate, but still we do not expect that they 
 are wrong by anything like 30 or 40 per cent, and that 
 is quite near enough for a first approximation in a ques- 
 tion of such difficulty. It appears that if the thick- 
 ness of the zinc and copper plates could be reduced to 
 about the 7OO,ooo,oooth of an inch only, there would 
 be an amount of heat produced, by piling them together 
 alternately, which would more than correspond to the 
 quantity of heat which is produced by their chemical 
 action when they are melted together. Therefore we 
 see, from this way of treating the subject, that the 
 7OO,ooo,oooth part of an inch is considerably under the 
 thickness to which you can reduce if you could do it 
 a plate of zinc or a plate of copper, without making 
 it cease to be zinc or copper as we know and handle 
 them. That is, in these metals the grained structure is 
 of dimensions considerably exceeding a 7OO,ooo,oooth 
 part of an inch. That, you see, agrees perfectly well 
 
316 STRUCTURE OF MATTER. 
 
 with the 4OO,ooo,oooth which we got from the other 
 method, depending on Cauchy's work. But there are 
 two other methods of making the approximation, which 
 I shall contrast and compare with this one in my next 
 lecture. 
 
LECTURE XIII. 
 
 STRUCTURE OF MATTER. 
 
 Approximation to dimensions of grained structure from capillary phenomena 
 from properties of gases. Mathematical consequences of the supposi- 
 tion that a gas consists of constantly impinging particles Gaseous Diffu- 
 sion. Results of Maxwell's investigations. Physical reason of Dissipation 
 Andrews' results as to the continuity of the liquid and gaseous states of 
 matter. Conclusion. 
 
 You will remember that in my last lecture I gave 
 you in detail two of the methods by which Sir William 
 Thomson approximated to the dimensions of the grained 
 structure of matter. It remains, then, in commencing 
 my present lecture, that I should briefly explain the 
 other two methods. 
 
 You will remember that the first method was founded 
 upon the dispersion of white light, or the separation of 
 its various component colours by means of a prism. 
 The second method was founded upon considerations 
 of the amount of heat which would be generated by 
 electrical action between particles of different materials 
 when they were intimately combined together. 
 
 The third method is founded upon the forces em- 
 ployed in drawing out a film of liquid, in fact (to take 
 the simplest case), in blowing a soap-bubble. When 
 we consider that the soap-film requires work to be done 
 upon it in order to enlarge it that is, to enlarge its 
 
3i8 STRUCTURE OF MATTER. 
 
 surface, and when also we consider that if we leave a 
 portion of it open to the air, the contractile force of 
 the film itself tends to make it shrink to smaller and 
 smaller dimensions, and thus gradually to expel the 
 contained air, we see that the film itself behaves to a 
 certain extent like an elastic membrane, which requires 
 work to be spent upon it in order to stretch it. But, 
 just as a gas has no superior limit to its expansion, a 
 soap-film has no inferior limit to its contraction. 
 
 Now it is a perfectly easy matter, if we know the 
 tension of the film, to calculate what amount of work 
 must be done in order to expand it from any given 
 superficial area to any other given area ; and by mea- 
 suring the height to which the soapy water rises in a 
 capillary tube of given bore, we can calculate what is 
 the amount of surface-tension of the liquid. This is 
 only one half of the amount of tension of a soap-film ; 
 for you must recollect that, thin as it is, it has two tensile 
 surfaces with a layer of water between them. Hence, 
 by experiments upon a capillary tube, we can tell what 
 is this amount of surface-tension per linear inch. Then 
 we can calculate from that what amount of work would 
 be required to pull out a single drop of water until it 
 was made into a film of any given thickness. The 
 amount of work is, in fact, numerically the product of 
 the tension per linear inch into the area of the surface. 
 
 Now it is found (in accordance with the fact that the 
 surface-tension of water diminishes as the temperature 
 rises) that in pulling out such a film, making it thinner 
 and thinner, or spending work upon it against its mole- 
 cular forces, it must become colder and colder, and that 
 it would require a constant supply of heat in order to 
 keep it at the temperature of the air. You will see then 
 
STRUCTURE OF MATTER. 319 
 
 that there we have data from which it would be possible 
 to calculate how much work would be required to pull 
 out a drop of water into a film of a given thickness, 
 keeping it always at a constant temperature. 
 
 This calculation has been made in terms of the thick- 
 ness of the film, and it appears that if you pull it out 
 to a thickness of the 5OO,ooo,oooth part of an inch 
 (supposing that could be done), you would require to 
 spend upon it, besides the amount of work requisite to 
 overcome the molecular forces, about one half as much 
 energy in addition, in the form of heat, in order to keep 
 its temperature from sinking ; so that on the whole, in- 
 cluding the heat which had to be communicated to it, 
 the quantity of work spent upon it in the operation 
 would be such that if it had all been applied to the drop 
 of water in the form of heat, it would have been capable 
 of raising it to a temperature of somewhere over 1 100 C. 
 Now, this amount of heat would of course wholly vola- 
 tilise the water in an instant. It is therefore perfectly 
 inconceivable that a film of water can be drawn out to 
 such an excessive thinness without very great reduction 
 of the molecular tension. But if the molecular tension 
 is reduced, obviously we are coming to a state in which 
 there are but a few molecules or particles in the thick- 
 ness of the film, because as long as the film contains a 
 great number of particles in its thickness, the whole 
 tension of the film will remain sensibly unaltered. 
 
 Thus the only way of reconciling these two incon- 
 sistent things is by supposing that we have erred in 
 assuming that, when we have made the film very thin, 
 there still remains the original amount of molecular 
 tension in it. Hence a film drawn out, if it were possible 
 to draw it, to anything like the ioo,OOO,oooth part of 
 
320 STRUCTURE OF MATTER. 
 
 an inch in thickness, cannot contain more than a very 
 few particles of water in its thickness. 
 
 Then finally there comes the fourth argument, which 
 is founded upon the behaviour of gases. I shall state 
 merely the result just now, because I intend to devote the 
 rest of my lecture this morning, or at least a great part 
 of it, to the consideration of the motion of the molecules 
 of gases. The result then that has been arrived at by 
 several inquirers who have considered this molecular 
 motion of gases is, that the average distance between 
 the several particles of a gas at the ordinary temperature 
 and pressure of the air must be something between the 
 6,ooo,oooth part of an inch and the io,ooo,oooth part 
 of an inch. This points (by a method which I shall 
 presently indicate) to something rather greater than the 
 5OO,ooo,oooth of an inch as the effective size of the 
 particles. 
 
 Thus you see that all these various approximate 
 estimates, differing no doubt considerably in the num- 
 bers which we obtain from them, still consistently point 
 to something, not very largely differing from the 
 5OO,ooo,oooth part of an inch, as being the distance 
 between the centres of contiguous particles of matter in 
 a liquid, or as being the measure of what I called in a 
 former lecture the coarse-grainedness of what appears to 
 our eyes, and even to our most powerful microscopes, to 
 be absolutely uniform matter. 
 
 We have now got a notion of the dimensions of this 
 coarse-grainedness, and it is possible also, by the pro- 
 perties of moving molecules constituting a gas, to find 
 approximately the sizes of the individual molecules not 
 merely how far they are from one another, but how 
 large is each particular molecule in comparison with 
 
STRUCTURE OF MATTER. 321 
 
 the average distance between any two of them. This, 
 as I shall presently explain, may 'be calculated from 
 the theory of impact of elastic particles, or of particles 
 repelling one another according to a high inverse power 
 of their mutual distance. 
 
 I shall put the result, perhaps, in the most simple 
 form by describing briefly the nature of the motion. 
 Each particle describes a straight path with uniform 
 velocity, but after going a certain distance it strikes 
 another ; then it goes off in a new direction, and after 
 some time it strikes a third, and so on. But there is an 
 average distance which it will pass through between 
 every two successive collisions. Now, if we call that 
 the mean free path, then the length of this mean free 
 path, divided by the diameter of any one particle, has 
 been shown by theory to be equal to the ratio of the 
 whole space occupied by the gas to about eight and a 
 half times the bulk of the whole particles. 1 
 
 Now, looking at this, which is a mathematical result 
 founded upon the supposition that the particles of a gas 
 are little hard bodies constantly impinging upon one 
 another, you will see that if we can get any mode of esti- 
 mating what is the average distance which one of them 
 must travel before it comes in contact with another, we 
 shall know one of the quantities in the above proportion. 
 
 We also know another, the whole space occupied by 
 the gas ; and the whole bulk of the particles will depend 
 upon their number and their diameters. These may be 
 approximated to by supposing that in the liquid state 
 the particles are nearly in contact. Thus an equation 
 
 1 Clausius says 8, assuming that all the particles have the same velo- 
 city ; but Maxwell, taking account of the law of distribution of velocities 
 among the particles, gives /</7 2 > which is nearly 8-5. 
 
 X 
 
322 STRUCTURE OF MATTER. 
 
 can be formed, by which the diameter of a particle is 
 given in terms of quantities which are all, at least 
 approximately, known. 
 
 This calculation has actually been made, and the result 
 is that the effective diameter of a particle must be some- 
 thing certainly not very different from one-25o,ooo,oooth 
 part of an inch. 
 
 Then, of course, knowing the diameter of a particle, 
 and the average distance between two contiguous par- 
 ticles, we can calculate how many particles there are in 
 a cubic inch of any gas at the ordinary temperature 
 and pressure. 
 
 Thus we can assert from measurement and calcula- 
 tion that the number of particles in a cubic inch of air 
 in the ordinary state of the atmosphere is represented 
 by a number which is approximately about 3 X io 20 . 
 This number might have been written as 3 with 20 
 cyphers after it. 
 
 [It is a very much improved method of writing large 
 numbers (when we cannot tell, or do not care, what are 
 the figures in all the various places) simply to indicate 
 the two or three most important figures of the number, 
 and then to fill up with powers of io. There is no use 
 doing it in millions, billions, or anything of that sort : 
 in fact, billions, etc., have at least two quite distinct 
 meanings with various sects of arithmeticians ; so we 
 simply take the first two or three places of figures of a 
 number, and indicate how many places there are : afar 
 more excellent way.] 
 
 Be this as it may, 3 multiplied 20 times over by ten 
 expresses a number not greatly falling short of the 
 number of particles in a cubic inch of a gas at the 
 ordinary temperature and pressure. 
 
STRUCTURE OF MATTER. 323 
 
 Now, you can see how it was that various scientific 
 men were led to the conclusion which I mentioned in 
 my first lecture as to the comparison between the actual 
 size of the coarse-grainedness in a drop of water and the 
 size of the drop itself. 
 
 If a drop of water is Jth of an inch in diameter, and 
 if those numbers I have just given represent the dia- 
 meters of its individual particles, or its grained structure, 
 what is the size of a body which bears to the whole 
 earth the same ratio as one of those particles to this 
 drop of water ? The answer is that it must be something 
 between about the size of a cherry or small plum and 
 the size of a cricket-ball. Take on the average a good- 
 sized plum or a small orange, then you get from that 
 the approximation that as the large plum is to the 
 whole earth, so- is this coarse-grained particle to the 
 drop of water ; so that if we could magnify a drop of 
 water to the apparent size of the whole earth as seen 
 from the distance at which a single plum is just visible, 
 we could just see its grained structure. 
 
 Now, what I have just said has led me to anticipate 
 a little as to the molecular structure of gases. We have 
 absolute proof that gases consist of particles of matter 
 which are perfectly free and detached from one another, 
 and which are constantly flying about in all directions. 
 The best and simplest proof that we have of this is 
 obtained by considering the process of mixture of one 
 gas with another, the way in which one gas diffuses 
 through another ; as, for instance, when any volatile 
 substance in the form of vapour or gas is allowed to 
 escape into a room, we find that it gradually mixes 
 itself thoroughly with the air of the room. This diffu- 
 sion takes place even if currents of air are prevented, 
 
324 STRUCTURE OF MATTER. 
 
 so that at last there is almost uniform distribution of 
 such a gas or vapour throughout the whole of any mass 
 of air however great. 
 
 But, by means of a simple but extremely beautiful 
 experiment, due to Dr. Graham, the late Master of the 
 Mint, I can show in a most striking way the mobility 
 and perfect independence (as it were) of the various par- 
 ticles of the same and of different gases. The appa- 
 ratus consists of a glass tube, with a hollow ball of porous 
 earthenware at its upper end, an arrangement very like 
 an ordinary air thermometer, only that the bulb is not 
 of glass but of porous clay. At present (showing} the 
 whole apparatus is full of air, and there is air outside. 
 You will notice that the open lower end being dipped 
 under the surface of water, coloured for greater dis- 
 tinctness, the water stands as nearly as may be at the 
 same level inside and outside, the reason of this of 
 course being that there is precisely the same pressure 
 in the gas inside as there is in the atmosphere outside. 
 Now what is really going on here what is keeping up 
 this constant equality of pressure inside and outside ? It 
 is this : there is a constant stream of particles of air 
 entering by all the pores of this porous clay, and a 
 corresponding stream of particles of air coming out 
 through them. We cannot, of course, mark individual 
 particles of air, even could we see them, nor have we 
 any test by which we could recognise a group of them. 
 But to test the process which must be going on here, 
 let us make a material difference between what is out- 
 side and what is inside the porous ball. Let us place 
 this bulb with its air inside in an atmosphere of ordi- 
 nary coal gas. 
 
 I shall easily obtain a quantity of coal gas by dis- 
 
STRUCTURE OF MATTER. 325 
 
 placement in this beaker. (Shows.) I find that the gas is 
 now escaping from beneath it, so that I know the beaker 
 is full. Now watch the effect the moment that I surround 
 this porous vessel containing air with the atmosphere 
 of coal gas : you see the bubbling which commences 
 
 through the liquid almost instantaneously. Great 
 quantities of gas are escaping from the liquid and from 
 the open-mouthed bell. Next, if I remove the atmo- 
 sphere of coal gas, you see almost instantly a rise of 
 
326 STRUCTURE OF MATTER. 
 
 the liquid in the tube, so that the pressure in the inside 
 has become at once notably less than the pressure out- 
 side. This process will go on for a considerable time, 
 until we get as nearly as may be the restoration of 
 equilibrium between the outside and inside pressures ; 
 but not to waste time over the experiment, although 
 it is an extremely striking one, I shall simply, having a 
 quantity of the coal gas still left in the beaker, put this 
 atmosphere of coal gas once more outside the bulb. 
 There ! notice the instant increase of pressure in- 
 side ; the coloured liquid falls at once in the stem. 
 The moment I remove the beaker, there is an instan- 
 taneous diminution of pressure, and the coloured liquid 
 rises. 
 
 This effect can be repeated as often as we choose, 
 by simply putting on and withdrawing the vessel with 
 the coal gas. Now it is perfectly obvious that the 
 explanation of this experiment must depend on the fact 
 that something gets in, in excess of what goes out, when 
 I place the vessel full of coal gas outside the ball. There 
 is then at once a great escape a great out-rush of 
 gas from the lower end of the tube, and that could only 
 take place because of an increase of pressure ; that is, 
 an increase in the quantity of gas inside this vessel. In 
 other words, the coal gas must be diffusing in through 
 the porous clay at a greater rate than the air is diffus- 
 ing out through it ; and at how great a rate you can 
 easily see, since the quantity which comes in through 
 that comparatively small surface is sufficient to give us 
 a rapid succession of large bubbles of gas passing out 
 below. And you will remember here that it is only a 
 differential effect that we are observing, because coal 
 gas is constantly going in, but air is as constantly going 
 
STRUCTURE OF MATTER. 327 
 
 out ; so that what we observe is merely the excess of 
 the amount of coal gas going in over that of the air 
 going out. 
 
 You can easily understand that methods can be de- 
 vised for the purpose of measuring precisely the relative 
 rates at which gases go in and come out through such 
 a porous substance. 
 
 This is perhaps one of the most striking illustrations 
 we can give of the great rate at which the particles of a 
 gas must constantly be moving. It is also a complete 
 demonstration of their comparative freedom from one 
 another, except at instants when they come against 
 each other in their motions. 
 
 Now, the notion that the particles of a gas are in 
 rapid motion, and that it is by their impacts that gases 
 press on other bodies, is a very old one. It was pointed 
 out not long after Newton's time by D. Bernoulli ; it 
 was afterwards revived in this country by Herapath ; 
 but it is to Joule that we owe the first precise findings 
 on the subject. Joule made a calculation as to what 
 must be the velocity with which the particles of certain 
 particular gases must move in order that, with the 
 known mass of the gaseous contents of a vessel, the 
 observed interior pressure on the vessel may be ac- 
 counted for. 
 
 If we take a vessel containing a cubic foot and fill it 
 with hydrogen gas at the ordinary pressure and tempera- 
 ture, the gas produces, by the constantly repeated impacts 
 of its particles upon the walls of the vessel, a certain 
 definite pressure which amounts to the ordinary baro- 
 metrical pressure of 1 5 Ibs. weight on the square inch. 
 Now, we know what mass of hydrogen there is in the 
 vessel. At what rate then must this rain, or rather hail- 
 
328 STRUCTURE OF MATTER. 
 
 storm of particles be going on inside the vessel in order 
 that these almost innumerable impacts may, when 
 totted up for a definite time, amount to this definite 
 observed pressure? That is a question, of course, of 
 purely dynamical reasoning, and the result, as deduced 
 by Joule, is certainly a very striking one. He arrived 
 at this result, an absolutely certain result from his data, 
 that the velocity of the particles of hydrogen must be 
 about 6055 feet per second at o C. Of course you can 
 see at once that this is a velocity far higher than that 
 of a cannon-ball, or than that of any projectile which 
 we can conveniently discharge ; but in spite of the enor- 
 mous velocity with which each individual particle of 
 hydrogen is moving, there is such an enormous number 
 of particles of hydrogen in a single cubic inch of space 
 that no one particle can ever find anything like a free 
 path from one side of a cubic inch of space to the other. 
 It is certain to be met over and over again in its course 
 by others. 
 
 Now, the number of such collisions which take place 
 during a single second can be calculated from the rate 
 at which one gas diffuses into another. If we take a 
 vessel consisting of two large receivers full of gas, with 
 a tube of known length and known diameter connecting 
 them, and [opening a stop-cock in that tube] allow the 
 two gases gradually to interpenetrate one another, we 
 can, at the end of a measured time, close the stop-cock, 
 and by a chemical process analyse the contents of each 
 of the two vessels. Thus we determine how much of the 
 one gas has passed into the other in a given time. We 
 can repeat the experiment and allow it to go on for a 
 different time, and so form a table of experimental 
 results as to the rate of diffusion of one gas into another 
 
STRUCTURE OF MATTER. 329 
 
 .' 
 
 according to the time which has elapsed since the two 
 were put into contact with one another. From such a 
 table we can, by mathematical calculation, determine 
 how far on an average any one particle of the one gas 
 penetrates in amongst the particles of the other gas 
 before suffering a collision. 
 
 Each particle advances a little way and then is driven 
 aside or back, another gets possibly a little farther, and 
 so on ; but the average penetration can be calculated 
 from the rate at which the gases are found to mix with 
 one another, and therefore we can tell what is the 
 average distance which a particle moves through between 
 two successive collisions. 
 
 By applying calculations similar to those of Joule, 
 but considerably extended by the use of more powerful 
 mathematical methods, such as the methods of the 
 theory of probabilities, Clausius first, and, a little later, 
 but far more profoundly, Clerk-Maxwell, and still more 
 recently Boltzmann, have arrived at very valuable re- 
 sults as to the motion of swarms of impinging particles. 
 One of the results arrived at is that in a mass of hydro- 
 gen at ordinary temperature and pressure, every particle 
 has on an average 17,700,000,000 collisions per second 
 with other particles, that is to say 17,700,000,000 times 
 in every second it has its course wholly changed. And 
 yet the particles are moving at a rate of something like 
 70 miles per minute. So comes this curious problem 
 given that the direction of motion of a particle is arbi- 
 trarily changed 17,700,000,000 times in every second, 
 and that the particle itself is moving 70 miles in a 
 minute, where would it be at the end of a single minute, 
 having started from any given place ? In air the number 
 of collisions for each particle is only about half as great 
 
330 STRUCTURE OF MATTER. 
 
 as, and the average velocity only about one-fourth of, 
 that in hydrogen. 
 
 You can see then to what exceedingly small quan- 
 tities, or rather to what enormous numbers, because 
 it is large numbers and not small quantities that we 
 are really dealing with, such a question as this leads. 
 I have already told you that in true physical science 
 #reat and small are mere relative terms, so far as size 
 /or duration is concerned ; but averages, such as we 
 ' are now dealing with, are of no value except when the 
 number of individual cases is very large. 
 
 The solution obtained is capable, as has been recently 
 shown, of explaining almost everything that we know 
 with reference to the behaviour of gases, and perhaps 
 even of vapours. [The chief exception is in connection 
 with the specific heats of gases. But the difficulty 
 seems to have arisen from too hasty generalisations of 
 the theory.] 
 
 As the direct results of Maxwell's investigation are 
 very important, I may just point out the three which 
 are of most importance. The first is this, that if you 
 have a mixture of particles of different kinds, as you 
 h^rve for instance in air, particles of oxygen and nitrogen 
 /mixed with one another, then after they have gone on 
 V impinging on one another for a sufficient time to have 
 attained the average state from which they will never 
 afterwards much diverge, this will be the result the 
 average energy of motion of each particle is the same 
 for each kind of gas ; so that if one of these particles 
 belongs to a light gas, that is to say, a gas whose par- 
 ticles are lighter or less massive than those of the other, 
 it will, on the average, be moving with greater velocity ; 
 so that the energy of the motion of one particle of either 
 
STRUCTURE OF MATTER. 331 
 
 gas is the same on the average as the energy of motion 
 of one particle of the other gas. That is a result which 
 can be obtained purely by ordinary mathematics of im- 
 pact of elastic spheres, generalised so as to apply it in a 
 statistical way to a great swarm of such spheres instead 
 of a finite number. For the purpose of applying it by a 
 statistical process to groups, it is necessary, in addition 
 to the ordinary methods of such kinetic problems, to 
 take into consideration the theory of probabilities. 
 Thus we are led to classify the particles into groups, 
 each group consisting of the particles whose velocity 
 lies between given limits. The velocities proper to these 
 groups range from zero to infinity, but the number 
 belonging to such extreme groups is small compared 
 with the number in the groups whose velocity is nearer 
 to that which corresponds with the average energy. 
 This average energy is the same in each of the two gases 
 which are mixed. 
 
 Then, the second result which also follows from the 
 theory of elastic particles impinging on one another is , 
 this, that if you have, as in the case of the air, oxygen '7]\ 
 and nitrogen mixed in any proportion whatever, the 
 ultimate state of distribution which they will assume, 
 after being mixed and having been left long enough to 
 get to a nearly permanent state, is the same as if each 
 gas, independently of the other, had distributed itself 
 according to its own law of pressure and density in a 
 vertical column. The oxygen and nitrogen of the air 
 so far, at all events, as gravity is concerned are free to 
 distribute themselves according to this law of mixture 
 from the surface of the earth upwards ; and, therefore, 
 in whatever proportion you find them in a cubic inch 
 near the surface of the earth, you would find (were it 
 
332 STRUCTURE OF MATTER. 
 
 not for winds, etc., which tend to mix them) rather 
 more Nitrogen and less Oxygen the higher you ascend. 
 Then another result bears upon the temperature of a 
 vertical column of gas. Of course any particles which 
 may be warmer than others, must be moving faster, 
 because the temperature of a gas depends upon the rate 
 at which its particles are moving. Now, Maxwell has 
 n that gravity has no tendency to make the quicker- 
 r moving particles go into any particular position, and the 
 slower-moving ones into any particular position. In 
 other words, an external force, such as gravity, does 
 not tend to make the lower part of a column of gas any 
 hotter than the upper part, or the upper part any hotter 
 than the lower part. If you, for a moment, interfere 
 with a state of things which has become nearly steady, 
 or has arrived nearly at the average, as, for instance, by 
 applying heat, then for a moment you make a portion 
 of the gas physically lighter than another portion, and 
 there, of course, gravity comes in, and the physically 
 lighter part bulk for bulk ascends to the top of the 
 column ; but, if you leave the thing to itself, gravity 
 has no tendency whatever to bring either the quicker- 
 moving particles that is, the warmer ones, or the 
 slower-moving particles that is, the colder ones lower 
 down or higher up ; but, whether gravity acted or not, 
 there will be the same average ratio of quick-moving 
 particles to slow-moving particles in every cubic inch 
 throughout the space. [And Carnot's reasoning, applied 
 to this result, shows that as it is true for gases it must 
 also be true for liquids and for solids : so that gravity 
 in no way directly interferes with distribution of tempera- 
 ture. Indirectly it does interfere, often in a marked 
 manner, as in processes of convection.] 
 
STRUCTURE ORJfy.TTER. 333 
 
 There is another extremely important point of this 
 statistical question as to the particles of gases which 
 I must carefully explain ; and it is this, how it happens 
 that in the enormous bulk of the whole atmosphere of 
 the earth these particles of oxygen and nitrogen, mov- 
 ing about amongst one another, should not by chance, at 
 some place or other, operate on one another in such a way 
 that in some particular cubic inch the particles of nitro- 
 gen might for a moment expel from it all the particles 
 of oxygen, so that in virtue of the great extent of the 
 earth's atmosphere, compared with the size of a particle 
 of gas, there might be, at some definite instant, a region 
 filled mainly with nitrogen, and other regions filled 
 mainly with oxygen. Now the beauty of this statistical 
 method is that it explains to us how such an event, 
 though possible, never occurs. It is a thing which is 
 in itself absolutely possible, but it never can occur in 
 practice, because the probability of its occurrence is so 
 exceedingly small. There is a probability (numerically 
 measurable) for everything which is possible, but if that 
 probability (reckoned in numbers) is as small as is the 
 probability of the accident we are considering, we never 
 expect to find it occur. And not only do we never 
 expect to find it at any time, but we can say boldly 
 from experience that it is never met with at all, how- 
 ever long our observations are conducted, or through 
 however great an extent of space we conduct them. If 
 you had originally in a box divided into two equal 
 parts, nitrogen in the one part and oxygen in the other, 
 and then allowed them to mix with one another, the 
 probability that in any assigned time you would find 
 all the nitrogen back again, even for a moment, in 
 the space where it was originally, and all the oxygen 
 
334 STRUCfggE OF MATTEK. 
 
 back again in the space where it was originally, is 
 certainly one which can be measured, but it is one 
 which is so infinitesimally small that we know perfectly 
 by experience that it never can be realised. The reason 
 lies simply in the fact that there is such an enormous 
 number of particles in every cubic inch. If there were 
 only one or two particles of nitrogen and oxygen in 
 each cubic inch of the atmosphere of this room, then it 
 would be a thing not only realisable, but actually 
 realised over and over again in the course of a single 
 afternoon, that (suppose we could see these particles) 
 we should every now and then see a space of a cubic 
 inch, or it might be even of a cubic foot, occupied (for a 
 single moment) wholly by particles of oxygen or by 
 particles of nitrogen. It would be a different cubic foot 
 or a different cubic inch the next instant, but still such 
 spaces free from oxygen or free from nitrogen would be 
 constantly occurring simply because there is a small 
 number of particles in comparison with the whole space 
 in which you are experimenting. But when you come 
 to consider this number 3 X IO 20 in every cubic inch, 
 then you begin to see how it is that the number of par- 
 ticles is so enormously great, that if there were at any 
 time the possibility of a small portion of space contain- 
 ing particles of oxygen only, or particles of nitrogen 
 only, it could have a realisable probability in the case 
 of so exceedingly small a fraction of a cubic inch 
 only, that it would not be worth speaking of. You 
 could not observe it. No doubt it does occur, but in 
 an exceedingly small fraction, less than the millionth of 
 the millionth of the millionth of a cubic inch. There 
 may occur even in this room such portions wholly 
 occupied by particles of nitrogen or by particles of 
 
STRUCTURE Ol^ MATTER. 335 
 
 oxygen for a moment, but only for a moment, in the sense 
 of some millionth of a millionth of a second, but any- 
 thing more than that could never present a reasonable 
 probability ; and the reason of this depends simply upon 
 the enormous number of particles which you have to 
 deal with : for, the greater the number of independent 
 movements the greater is the probability of their con- 
 forming nearer and nearer to the average distribution of 
 amounts of velocity as well as to the average distribution 
 of kinds of particles. 
 
 The only other point that I have time to take up is 
 the consideration of certain most remarkable experi- 
 ments which have been made recently by Dr. Andrews 
 in extension of others made long ago by Faraday, and 
 by Cagniard de la Tour, with reference to the connec- 
 tion between the gaseous and liquid states of matter. 
 We have just seen how the gaseous state is completely, 
 or almost completely, accounted for by the supposition 
 of independent particles which are absolutely free from 
 one another except at the instants when they impinge 
 upon one another. Liquids possess the property of 
 diffusing among one another just as gases do, only the 
 rate of diffusion of liquids is exceedingly small com- 
 pared with the rate of diffusion of gases, and therefore 
 we conceive that the liquid state may be represented by 
 a set of particles which are free from one another to a 
 certain extent, but not nearly so much free from one 
 another as they are in the gaseous state ; so that the 
 particles of a liquid are so much nearer together in 
 comparison with their diameters, that the average dis- 
 tance through which a particle of liquid can travel before 
 it comes into collision with another is exceedingly small, 
 even compared with the same path in the case of a gas 
 
336 STRUCT&tE OF MATTER. 
 
 Therefore in a liquid we see why the diffusion is slower, 
 because a particle can only go a much shorter way be- 
 fore it has its direction of motion completely changed 
 by impact upon another. Now, Andrews has shown 
 by experiment that it is possible to pass continuously 
 that is to say, without any apparent optical change 
 from a body which is obviously in a gaseous state to the 
 same body obviously in a liquid state, and that is certainly 
 one of the most remarkable experimental discoveries 
 of modern times. Part of the phenomena had been 
 obtained, but no complete experimental examination of 
 them, by Cagniard de la Tour, many years ago. He had 
 shown that if you take a quantity of ordinary ether in a 
 strong glass tube, so as to fill about one-half the tube, 
 leaving nothing but vapour of ether above it, and, seal- 
 ing it up, apply heat to it, you may convert the whole 
 liquid into vapour, so that the liquid contents wholly 
 disappear ; and this at a very moderate elevation of 
 temperature. Cagniard de la Tour inferred from these 
 experiments that sulphuric ether may be reduced com- 
 pletely to vapour by the combined action of heat and 
 pressure in a volume a little more than double that of 
 the liquid. The true explanation was first given by 
 Andrews, who showed from his experiments on carbonic 
 acid that when the liquid disappears as the tube is heated, 
 some state of matter is produced which is certainly not 
 liquid and certainly not ordinary vapour. Cagniard de 
 la Tour performed the same experiment with water, but 
 he found that for water it required so much stronger 
 tubes and so much higher a temperature that, partly from 
 the danger of explosions, and partly from the fact that 
 water so heated attacked the glass chemically, it was next 
 to impossible to make the experiment with precision. 
 
STIt UCTURE OF MA TTER. 337 
 
 Andrews examined the subject in another way by 
 actually compressing different gases, keeping them all 
 the time at a definite temperature, and noting the 
 relation between volume and pressure : then raising 
 them to a little higher temperature, keeping them 
 steadily at that temperature, and going through the 
 same operation, and so on. In that way he was en- 
 abled, by direct experiments of the most beautiful kind, 
 to lay down tables or charts which represented the 
 relation between pressure and volume of these gases for 
 any sets of temperatures between the limits through 
 which he could experiment. The result of his inquiries 
 may be easily seen if I roughly trace an approximation 
 to some of his diagrams. 
 
 From what I told you of Watt's Diagram of Energy 
 in a former lecture [ante, p. no], and from what I have 
 just said, you will see that Andrews made a detailed 
 study of the lines of equal temperature for all the sub- 
 stances he experimented on. His first results were 
 obtained from carbonic acid gas, and to them I shall 
 recur : but for ease of explanation, suppose we com- 
 mence with vapour of water. 
 
 Take a cylinder containing a small quantity of super- 
 heated vapour of water at any temperature, and gradu- 
 ally compress it, keeping it at the same temperature, 
 let us say, for instance, the temperature of boiling 
 water. As we gradually compress, the volume dimin- 
 ishes and the pressure rises, the steam or vapour of 
 water becomes more and more nearly saturated steam, 
 until we come to a certain bulk which corresponds with 
 its being all in the form of saturated steam. Then if 
 we compress ever so little more, taking care to keep the 
 temperature the same as before, we know what takes 
 
 Y 
 
338 
 
 STRUCTURE OF MATTER. 
 
 place : the pressure does not alter, but some of the 
 vapour is deposited in the form of water, and so we go 
 on compressing without altering the pressure, but lique- 
 fying more and more of the contents, until we find the 
 whole of the contents liquid. Then, still keeping the 
 same temperature by proper appliances, we go on com- 
 pressing ; but we now find a very great difficulty in 
 compressing any further, because we have liquid water 
 to deal with, which now fills the whole of the part 
 
 of our cylinder under the piston. The curve will now 
 show very large increments of pressure for very small 
 decrements of volume. Its course is PQRS in the 
 diagram. 
 
 In the steam the pressure is small, while the bulk is 
 large. It increases as we gradually compress, until we 
 come to the perfectly definite pressure at which, at the 
 given temperature, water begins to form. Then, how- 
 
STRUCTURE OF MATTER. 339 
 
 ever much more we may compress up to a certain limit, 
 the pressure does not alter, so that our curve then 
 runs along parallel to the horizontal line, and it does 
 so until all the steam is converted into water ; and 
 then by further application of pressure we compress the 
 water ; but exceedingly little so that in reality our 
 curve is now almost a straight line running vertically 
 upwards. 
 
 That is the case for a temperature corresponding to 
 the ordinary boiling point of water ; but suppose we 
 were to perform the same experiment on the same 
 amount of steam at a higher temperature, we should 
 find that we must now compress a good deal further 
 before there is any deposition of vapour in the form 
 of water, and that the water when formed occupies 
 a somewhat larger volume, so that, on both accounts, 
 the range through which we have part of our cylinder 
 full of steam and part full of water, extends through 
 a smaller horizontal space than before. Repeating the 
 experiment at higher and higher temperatures, we 
 come to smaller and smaller ranges of that kind, until 
 finally we reach a temperature for water at which we 
 cannot have part of the cylinder full of steam and part 
 full of water. 
 
 Now you can see that if a curve, the dotted one in 
 the figure, be drawn through all the points which ter- 
 minate the horizontal straight parts of the various lines 
 of equal temperature, we indicate on the diagram the 
 region within which our given quantity of water can 
 exist partly as vapour and partly as liquid. 
 
 Now we may, by proper application of heat and pres- 
 sure, make the steam pass from one volume to another 
 through any possible series of intermediate states. This 
 
340 STRUCTURE OF MATTER. 
 
 series can, of course, be represented by a line on Watt's 
 diagram. Take two points, A and B, both external to 
 the dotted curve, but on opposite sides of it, so that 
 in the condition denoted by A the water is obviously 
 wholly in the form of vapour, at B wholly liquid. We 
 may pass from one of these states to the other by any 
 possible path, but for our present purpose only two need 
 be considered, the first (AaB in the diagram) cutting the 
 dotted line in two points, the second (/4&#)passing wholly 
 outside it. By the first course we have vapour alone 
 till we enter the dotted curve liquid alone after we 
 pass out of it liquid in presence of vapour while we 
 are within it. On this no comment need be made the 
 passage from vapour to liquid is visible to the eye. But 
 in the second course we pass from obvious vapour at 
 A to obvious liquid at B, without its being possible at 
 any point of the journey to say the change is taking 
 place. 
 
 You can begin it absolutely as gas, and bring it abso- 
 lutely to the liquid state, but during the whole of the 
 operation it is impossible to point out the instant at 
 which it changes its character. And you can see per- 
 fectly well that the change can only be effected sud- 
 denly or in a manner marked to the eye, when you are 
 performing the operations at such a temperature that 
 the corresponding line in the diagram passes through 
 the region in which the substance can exist in the liquid 
 state in presence of its vapour. If you go beyond the 
 limits at which this is possible, then you can cause the 
 fluid to pass from the gaseous to the liquid, or from the 
 liquid back to the gaseous state, with absolute optical 
 continuity. 
 
 Or, to make it still more curious, suppose we go 
 
STRUCTURE OF MATTER. 341 
 
 through a complete cycle of operations from the state 
 B to the state A, and back again to B. Begin, for ex- 
 ample, with the lower of the two paths, BaA, and come 
 back by the higher, A bB. We begin with water ; then 
 we have water and saturated steam about a, then super- 
 heated steam, till we reach A. On our way back we 
 have no such stages though when we have again 
 reached B the contents are obviously water as at first. 
 
 Now the explanation of that phenomenon has not 
 been fully given by the help of the dynamical theory of 
 gases, but the mode of applying the dynamical theory 
 to it has been, I think, successfully pointed out. One 
 pregnant hint is given by the fact, noticed by Andrews, 
 that the capillary surface of the liquid in contact with 
 the vapour becomes less and less curved as the tem- 
 perature rises to the critical point (i.e. the temperature 
 at and above which the presence of liquid and vapour 
 together becomes impossible), the curvature becoming 
 nil when that point is reached. In all probability we 
 want only a little further application of our statistical 
 process to explain even this, which is perhaps the most 
 curious fact that any investigation has ever told us as 
 to the connection between liquids and gases. 
 
 Before concluding, I would just mention that there 
 are a great many subjects to which I should have liked 
 to direct your attention had time permitted. My 
 apology for not having introduced them is partly want 
 of time, partly the wish expressed to me that certain 
 questions of history and priority should be fully treated. 
 I have not been able to overtake during the time that 
 I could devote to it nearly the whole of the programme 
 that I at first put before me. 
 
342 STRUCTURE OF MATTER. 
 
 I shall just mention what some of these things were, 
 and you will see that although I have taken up a great 
 many interesting points, I have left still a great many 
 others equally interesting. There is, for instance, the 
 very interesting question of the explanation of vowel 
 sounds and the qualities of musical notes ; the whole in 
 fact of Helmholtz's splendid investigations in Acoustics. 
 
 There is the whole subject of contact electricity, 
 which I could only illustrate by a single experiment in 
 my last lecture. There is the important subject, grow- 
 ing in importance every day, of Atmospheric electricity. 
 There is Thermo-electricity, now almost a separate 
 branch of physics : Clerk-Maxwell's production of 
 double refraction in viscous liquids ; the connection 
 between sun spots and terrestrial magnetism ; the ques- 
 tion of tides in the solid earth (whether the earth is 
 plastic enough to have tides produced in its substance 
 by the moon) ; we have the various proofs of the rota- 
 tion of the earth ; the connection between magnetism 
 and light, as shown by Faraday's experiment and 
 W. Thomson's and Clerk-Maxwell's investigations ; the 
 heating of bodies moving in what we call vacuum ; the 
 motion of light bodies produced by radiation ; abnor- 
 mality of dispersion, and so on ; but even to merely 
 enumerate all such would be, as it were, to double the 
 length of this lecture. But such a statement shows, 
 better than any comments, that we are dealing with a 
 branch of science whose characteristic, as I told you at 
 the outset, is persistent and ever more rapid extension. 
 
LECTURE XIV. 
 
 FORCE. 
 
 Evening Lecture before the British Association, Glasgow, 
 September 8, 1876. 
 
 IT was not to be expected that I could, at short notice, 
 produce a Lecture which should commend itself to the 
 Association by its novelty or originality. But in Science 
 there are things of greater value than even these namely, 
 definiteness and accuracy. In fact, without them there 
 could not be any science except the very peculiar smat- 
 tering which is usually (but I hope erroneously) called 
 ' popular.' It is vain to expect that more than the 
 elements of science can ever be made in the true sense 
 of the word popular ; but it is the people's right to de- 
 mand of their teachers that the information given them 
 shall be at least definite and accurate so far as it goes. 
 And as I think that a teacher of science cannot do a 
 greater wrong to his audience than to mystify or confuse 
 them about fundamental principles, so I conceive that 
 wherever there appears to be such confusion, it is the 
 duty of a scientific man to endeavour by all means in his 
 power to remove it. Recent criticisms of works in which 
 I have had at least a share, have shown me that, even 
 among the particularly well educated class who write 
 for the higher literary and scientific Journals, there is 
 
344 FORCE. 
 
 wide-spread ignorance as to some of the most important 
 elementary principles of Physics. I have therefore 
 chosen, as the subject of my lecture to-night, a very 
 elementary but much abused and misunderstood term, 
 which meets us at every turn in our study of Natural 
 Philosophy. 
 
 I may at once admit that I have nothing new to tell 
 you, nothing which (had you all been properly taught, 
 whether by books or by lectures) would not have been 
 familiar to all of you. But if one has a right to judge 
 of the general standard of popular scientific knowledge 
 from the statements made in the average newspaper : 
 or even from those made in some of the most preten- 
 tious among so-called scientific lectures : there can be 
 but few people in this country who have an accurate 
 knowledge of the proper scientific meaning of the little 
 word FORCE. 
 
 We read constantly of the so-called * Physical Forces' 
 Heat, Light, Electricity, etc., of the ' Correlation of 
 the Physical Forces ' of the ' Persistence or Conserva- 
 tion of Force.' To an accurate man of science all this 
 is simply error and confusion. And I have full confi- 
 dence that the inherent vitality of truth will render the 
 attempt to force such confusion upon the non-scientific 
 public, quite as futile as the hopelessly ludicrous 
 endeavour of the ' Times ' to make us spell the word 
 Chemistry with a Y instead of an E. It is true that in 
 matters such as this last a good deal depends (as Sam 
 Weller said) 'on the taste and fancy of the speller:' 
 and sometimes even absolute error is of little or no con- 
 sequence. But it is quite another thing when we deal 
 with the fundamental terms of a science. He who has 
 not exactly caught their meaning is fpretty certain to 
 
FORCE. 345 
 
 pass from chronic mistakes to frequent blunders, and 
 cannot possibly acquire a definite knowledge of the 
 subject. 
 
 In popular language there is no particular objection 
 to multiple meanings for the same word. The context 
 usually shows exactly which of these is intended : and 
 their existence is one of the most fertile sources of really 
 good puns, such as those of Coleridge, 1 Hood, Hook, 
 or Barham. And there is no reason to object to such 
 phrases as the ( force of habit J the 'force of example! the 
 'force of circumstances I or the ' force of public opinion' 
 But when we read (as I did last week) in one newspaper 
 that the 'force' of a projectile from the 8i-ton gun has 
 at last reached the extraordinary amount of 1450 feet : 
 in another that the 'force' of a ball from the great 
 Armstrong gun lately made for the Italian government 
 is expected to average somewhere about 30,000 foot- 
 tons : and in a third that the water in the boiler of the 
 Thunderer 'would in a second of time generate a " force " 
 sufficient to raise 2,000 tons one foot high ' we 
 that there must be, somewhere at least, if not every 
 where, a most reckless abuse of language. In fact we 
 have come to what ought to be scientific statements, 
 and there even the slightest degree of unnecessary 
 vagueness is altogether intolerable. 
 
 Perhaps no scientific English word has been so much 
 abused as the word ' force.' We hear of * Accelerating 
 Force,' 'Moving Force,' 'Centrifugal Force,' 'Living 
 Force,' ' Projectile Force,' ' Centripetal Force,' and what 
 not. Yet, as William Hopkins, the greatest of Cam- 
 bridge teachers, used to tell us 'Force is Force,' i.e. 
 there is but one idea denoted by the word, and all 
 
 1 See The Forked Tongue. 
 
346 FORCE. 
 
 Force is of one kind, whether it be due to gravity, 
 magnetism, or electricity. This, alone, serves to give a 
 preliminary hint that (as I shall presently endeavour to 
 make clear to you) there is probably no such thing as 
 force at all ! That it is, in fact, merely a convenient 
 expression for a certain 'rate.' If any one should 
 imagine that 'three per cent.' is a sum of money, he will 
 soon be grievously undeceived. ' Three per cent.' means 
 nothing more or less than the vulgar fraction T f ^. True, 
 the ' Three Per Cents ' usually means something very 
 substantial but there the term is not a scientific one. 
 Think for a moment how utterly any one of you, 
 supposed altogether ignorant of shipping, would be 
 puzzled by such a newspaper heading as ' The White 
 Star Line? or ' The Red Jacket Clipper : No doubt 
 some of our scientific terms approach as near to slang 
 as do these : but we are doing our best to get rid of 
 them. 
 
 A good deal of the confusion about Force is due to 
 Leibnitz, and to some of his associates and followers 
 who, whatever they may have been as mathematicians, 
 were certainly grossly ignorant of some elementary 
 parts of Dynamics insomuch that Leibnitz himself is 
 known to have considered the fundamental system of 
 the Principia to be erroneous, and to have devised 
 another and different system of his own. This fact is 
 carefully kept back now-a-days, but it is a fact, 1 and (as 
 I have just said) has had a great deal to do with the 
 vagueness of the terms for Force and Energy in some 
 modern languages. In fact, in their modern dress (with 
 Vis everywhere rendered Force], the Vis Viva, Vis 
 Mortua, and Vis Acceleratrix of that time have, in 
 
 1 Leibnitii Opera (Dutens), vol. iii. 1768. 
 
FORCE. 347 
 
 some of their Protean shapes, hooked themselves like 
 entozoa into the great majority of our text-books. 
 
 Before dealing more definitely with the proper 
 meaning of the word ' Force/ I must briefly consider 
 how we become acquainted with the physical world, 
 and how, consequently, it is more than probable that 
 some of our most profound impressions, if uninformed, 
 are completely erroneous and misleading. 
 
 In dealing with physical science it is absolutely 
 necessary to keep well in view the all-important prin- 
 ciple that 
 
 Nothing can be learned as to the physical world save 
 by observation and experiment , or by mathematical deduc- 
 tions from data so obtained. 
 
 On such a text volumes might be written ; but they 
 are unnecessary, for the student of physical science 
 feels at each successive stage of his progress more and 
 more profound conviction of its truth. He must receive 
 it, at starting, as the unanimous conclusion of all who 
 have in a legitimate manner made true physical science 
 the subject of their study ; and, as he gradually gains 
 knowledge by this the only method, he will see more 
 and more clearly the absolute impotence of all so-called 
 metaphysics, or a priori reasoning, to help him to a 
 single step in advance. 
 
 Man has been left entirely to himself as regards the 
 acquirement of physical knowledge. But he has been 
 gifted with various senses (without which he could not 
 even know that the physical world exists) and with 
 reason to enable him to control and understand their 
 indications. 
 
 Reason, unaided by the senses, is totally helpless in 
 such matters. The indications given by the senses, 
 
348 FORCE. 
 
 unless interpreted by reason, are utterly unmeaning. 
 But when reason and the senses work harmoniously 
 together, they open to us an absolutely illimitable 
 prospect of mysteries to be explored. This is the test 
 of true science there is no resting-place each real 
 advance discloses so much that is new and easily 
 accessible, that the investigator has but scant time to 
 co-ordinate and consolidate his knowledge before he 
 has additional materials poured into his store. 
 
 To sight without reason, the universe appears to be 
 filled with light except, of course, in places surrounded 
 by opaque bodies. 
 
 Reason, controlling the indications of sense, shows us 
 that the sensation of sight is our own property ; and 
 that what we understand by brightness, etc., does not 
 exist outside our minds. It shows us also that the 
 sensation of colour is purely subjective, the only differ- 
 ence possible between different so-called rays of light 
 outside the eye being merely in the extent, form, and 
 rapidity of the vibrations of the luminiferous medium. 
 
 To hearing, without reason, the air of a busy town 
 seems to be filled with sounds. Reason, interpreting 
 the indications of sense, tells us that if we could see the 
 particles of air we should observe among them (super- 
 posed upon their rapid motions among one another) 
 simply a comparatively slow undulation of the nature 
 of alternate compressions and dilatations. And our 
 classification of sounds as to loudness, pitch, and 
 quality, is merely the subjective correlative of what, 
 in the air-particles, is objectively the amounts of com- 
 pression, the rapidity of its alternations, and the greater 
 or less complexity of the alternating motion. 
 
 A blow from a stick or a stone produces pain and a 
 
FORCE. 349 
 
 bruise ; but the motion of the stick or stone before it 
 reaches the body is as different from the sensation 
 produced by the blow as is the alternate compression 
 and dilatation of the air from the sensation of sound, 
 or the ethereal wave-motion from the sensation of light. 
 
 Hence to speak, as the great majority even of 
 ' educated ' people do, of what we ordinarily mean by 
 light or sound, as existing outside ourselves, is as absurd 
 as to speak of a swiftly-moving stick or stone as pain. 
 But no inconvenience is occasioned if we announce the 
 intention to use the terms light and sound for the 
 objective phenomena, and to speak of their subjective 
 effects as ' luminous impressions/ or * noise/ as the case 
 may be. In this case there is outside us energy of 
 motion of every kind, but in the mind mere correspond- 
 ing impressions of brightness and colour, noise or 
 harmony, pain, etc. etc. 
 
 As another instance, it is obvious that we must be 
 extremely cautious in our interpretation of the immedi- 
 ate evidence of our own senses as to heat. 
 
 Touch, in succession, various objects on the table. 
 A paper-weight, especially if it be metallic, is usually 
 cold to the touch ; books, paper, and especially a 
 woollen table-cover, comparatively warm. Test them, 
 however, by means of a thermometer, not by the sense of 
 touch, and in all probability you will find little or no 
 difference in what we call their temperatures. In fact, 
 any number of bodies of any kind shut up in an 
 enclosure (within which there is no fire or other source 
 of heat), all tend to acquire ultimately the same 
 temperature. Why then do some feel cold, others 
 warm, to the touch ? 
 
 The reason is simply this the sense of touch does 
 
350 FORCE, 
 
 not inform us directly of temperature, but of the rate at 
 which our finger gains or loses heat. As a rule, bodies 
 in a room are colder than the hand, and heat always 
 tends to pass from a warmer to a colder body. Of a 
 number of bodies, all equally colder than the hand, that 
 one will seem coldest to the touch which is able most 
 rapidly to convey away heat from the hand. The 
 question, therefore, is one of conduction of heat. And to 
 assure ourselves that it is so, reverse the process ; let us, 
 in fact, try an experiment, though an exceedingly simple 
 one ; for the essence of experiment is to modify the 
 circumstances of a physical phenomenon so as to 
 increase its value as a test. Put the paper-weight, the 
 books, and the woollen table-cloth into an oven, and 
 raise them all to one and the same temperature, con- 
 siderably above that of the hand. The woollen cloth 
 will still be comparatively cool to the touch, while the 
 metal paper-weight may be much too hot to hold. 
 The order of these bodies, as to warm and cold in the 
 popular sense, is in fact reversed ; and this is so, because 
 the hand is now receiving heat from all the various 
 bodies experimented on, and it receives most rapidly 
 from those bodies which, in their previous condition, 
 were capable of abstracting heat most rapidly. How- 
 ever it may be in the moral world, in the physical 
 universe the giving and taking powers of one and the 
 same body are strictly correlative and equal. 
 
 Thus, the direct indications of sense are in general 
 utterly misleading as to the relative temperatures of 
 different bodies. 
 
 In a baker's oven, at temperatures far above the boil- 
 ing point of water (on one occasion even 320 F.) so 
 high indeed that a beef-steak was cooked in thirteen 
 
FORCE. 351 
 
 minutes Tillet in France, and Blagden and Chantrey 
 in England, remained for nearly an hour in compara- 
 tive comfort. But though their clothes gave them no 
 great inconvenience, they could not hold a metallic 
 pencil-case without being severely burned. 
 
 On the other hand, great care has to be taken to 
 cover with hemp, or woo], or other badly conducting 
 substance, every piece of metal which has to be handled 
 in the intense cold to which an Arctic Expedition is 
 subjected; for contact with very cold metal produces 
 sores almost undistinguishable from burns, though due 
 to a directly opposite cause. Both of these phenomena, 
 however, ultimately depend on the comparative facility 
 with which heat is conducted by metals. 
 
 Even, from the instance just given, you cannot fail to 
 see that there is a profound distinction between heat 
 and temperature. Heat, whatever it may be, is SOME- 
 THING which can be transferred from one portion of 
 matter to another ; the consideration of temperatures 
 is virtually that of the mere CONDITIONS which deter- 
 mine whether or not there shall be a transfer of heat, 
 and in which direction the transfer is to take place. 
 Bear this carefully in mind, because it has most im- 
 portant analogies to the results we meet with in con- 
 sidering the nature of Force. 
 
 It has been definitely established by modern science 
 that heat, though not material, has objective existence in 
 as complete a sense as matter has. 
 
 This may appear, at first sight, paradoxical ; but we 
 must remember that so-called paradoxes are merely 
 facts as yet unexplained, and therefore still apparently 
 inconsistent with others already understood in their 
 full significance. 
 
352 FORCE. 
 
 When we say that matter has objective existence, we 
 mean that it is something which exists altogether inde- 
 pendently of the senses and brain-processes by which 
 alone we are informed of its presence. An exact or 
 adequate conception of it, if it could be formed, would 
 probably be something very different from any concep- 
 tion which our senses will ever enable us to form ; but 
 the object of all pure physical science is to endeavour 
 to grasp more and more perfectly the nature and laws 
 of the external world, using the imperfect means which 
 are at our command reason acting as interpreter as 
 well as judge, while the senses are merely the witnesses, 
 who may be more or less untrustworthy and incom- 
 petent, but are nevertheless of inconceivable value to 
 us, because they are our only available ones. 
 
 Without further discussion we may state once for all, 
 that our conviction of the objective reality of matter is 
 based mainly upon the fact, discovered solely by experi- 
 ment, that we cannot in the slightest degree alter its 
 quantity. We cannot destroy, nor can we produce, even 
 the smallest portion of matter. But reason requires us 
 to be consistent in our logic ; and thus, if we find any- 
 thing else in the physical world whose quantity we 
 cannot alter, we are bound to admit it to have objective 
 reality as truly as matter has, however strongly our 
 senses may predispose us against the concession. Heat 
 therefore, as well as Light, Sound, Electric Currents, 
 etc., though not forms of matter, must be looked upon as 
 being as real as matter, simply because they have been 
 found to be forms of energy which in all its constant 
 mutations satisfies the test which we adopt as con- 
 clusive of the reality of matter. We shall find that this 
 test fails when applied to Force. 
 
FORCE. 353 
 
 But you must again be most carefully warned to dis- 
 tinguish between heat and the mere sensation of warmth ; 
 just as you distinguish between the motion of a cudgel 
 and the pain produced by the blow. The one is the 
 thing to be measured, the other is only the more or less 
 imperfect reading or indication given by the instrument 
 with which we attempt to measure it in terms of some 
 one of its effects. So that when your muscular sense 
 impresses on you the notion that you are exerting force, 
 as in pushing or pulling, you ought to be very cautious 
 in forming a judgment as to what is really going on ; 
 and you ought to demand much further evidence before 
 admitting the objective reality of force. 
 
 Until all physical science is reduced to the deduc- 
 tion of the innumerable mathematical consequences of 
 a few known and simple laws, it will be impossible to 
 altogether avoid some confusion and repetition, whatever 
 be the arrangement of its various parts which we adopt 
 in bringing them before a beginner. But when we 
 confine ourselves to one definite branch of the subject, 
 all of whose fundamental laws can be distinctly formu- 
 lated, there need be no such confusion. Here, in fact, 
 the mathematician (who, be it most carefully observed, 
 does not necessarily deal with algebraic symbols) has 
 it all in his own hands. He is the skilled artificer with 
 his plan and his trowel, and the hodmen have handed 
 up to him all the requisite bricks and mortar. 
 
 * That which is properly called Physical Science is the 
 knowledge of relations between natural phenomena 
 and their physical antecedents, as necessary sequences 
 of cause and effect ; these relations being investigated 
 by the aid of mathematics that is, by a method in 
 which processes of reasoning, on all questions that can 
 
 z 
 
354 FORCE. 
 
 be brought under the categories of quantity and of 
 space-conditions, are rendered perfectly exact, and 
 simplified, and made capable of general application 
 to a degree almost inconceivable by the uninitiated, 
 through the use of conventional symbols. There is 
 no admission for any but a mathematician into this 
 school of philosophy. But there is a lower department 
 of natural science, most valuable as a precursor and 
 auxiliary, which we may call scientific phenomenology ; 
 the office of which is to observe and classify phenomena, 
 and by induction to infer the laws that govern them. 
 As, however, it is unable to determine these laws to be 
 necessary results of the action of physical forces, they 
 remain merely empirical until the higher science in- 
 terprets them. But the inferior and auxiliary science 
 has of late assumed a position to which it is by no 
 means entitled. It gives itself airs, as if it were the 
 mistress instead of the handmaid, and often conceals 
 its own incapacity and want of scientific purity by 
 high-sounding language as to the mysteries of nature. 
 It may even complain of true science, the knowledge 
 of causes, as merely mechanical. It will endue matter 
 with mysterious qualities and occult powers, and 
 imagines that it discerns in the physical atom, "the 
 promise and potency of all terrestrial life.'" l 
 
 Whether there is such a thing as Force or not, I 
 shall consider presently. But in the meanwhile there 
 can be no doubt that it is a convenient term, provided 
 it be employed in one definite sense, and one only. 
 Let us then first see how it is to be correctly used. 
 Here we cannot but consult Newton. The sense in 
 which he uses the term Vis Impressa, the Latin equi- 
 
 1 Church Quarterly , April 1876. 
 
FORCE. 355 
 
 valent of the scientific word ' Force,' and therefore the 
 sense in which we must continue to use it if we desire 
 to avoid intellectual confusion, will appear clearly from 
 a brief consideration of his simple statement of the 
 Laws of Motion. 
 
 The first of these Laws is : Every body continues in its 
 state of rest or of uniform motion in a straight line, except 
 in so far as it is compelled by forces to change that state. 
 
 In other words, any change whether in the direction 
 or in the rate of motion of a body is attributed to Force. 
 Thus a stone let fall moves quicker and quicker, and we 
 say that a force (viz. the weight of the stone or the earth's 
 attraction for it) is continually acting so as to increase 
 the rate of the motion. If the stone be thrown upwards, 
 the rate of its motion continually diminishes, and we say 
 that the same Force (the stone's weight) is continually 
 acting so as to produce this diminution of speed. So 
 far, none of you probably feels the least difficulty. But 
 we have got only half of the information on this point 
 which Newton's First Law affords. You see the moon 
 revolving about the earth, and the earth and other 
 planets revolving about the sun approximately at 
 least in circles why is this ? Their directions of motion 
 are constantly changing in fact, a curved line is merely a 
 line whose direction changes from point to point, while a 
 straight line is one whose direction does not change but 
 to produce in a body this change of direction of motion 
 Force is required just as much as to produce change of 
 speed. That is supplied by the gravitation attraction of 
 the central body of the system. The old notion was that 
 a centripetal Force was required to balance the so-called 
 centrifugal Force, it being imagined that a body moving 
 in a circle had a tendency to fly outwards from the 
 
356 FORCE. 
 
 centre ! Newton's simple Law exposes fully the ab- 
 surdity of this. If a body is to be made to move in a 
 curved line instead of its natural straight path, you must 
 apply Force to compel it to do so ; certainly not to 
 prevent it from flying outwards from the centre about 
 which it is for the moment revolving. In fact, the Vis 
 Inertiae, now called Inertia (not, mark you, The Force 
 of Inertia), implies, not revolutionary activity, but dogged 
 perseverance; and just as you must apply force in the 
 direction of motion to change the rate of motion, so 
 must you apply force perpendicular to the direction of 
 motion to change that direction. 
 
 Newton's Second Law is now required : Change of 
 motion is proportional to the force, and takes place in the 
 direction of the straight line in which the force acts. 
 
 Mark here most carefully that this simple law (upon 
 which the Parallelogram of Forces depends) holds for all 
 kinds of force alike. There is no special law for gravita- 
 tion-force, and others for electric and magnetic forces. 
 All are defined alike, without reference to their origin. 
 
 Motion, as Newton has previously defined it, is here 
 used as a technical scientific term for what we now call 
 momentum. It is the product of the mass moving into 
 the velocity with which it moves. * Change of motion/ 
 therefore, is change of momentum or the product of the 
 mass of the moving body into its change of velocity. 
 Now, a change of velocity is itself a velocity, as we see 
 by the science of mere motion kinematics, the purely 
 mathematical science of mixed space and time. 
 
 Newton's words, however, imply more than this. Of 
 course, the longer a given force acts the greater will be 
 the change of momentum which it produces ; so that to 
 compare forces, which is the essence of the process of 
 
FORCE. 357 
 
 measuring them, we must give them equal times to act, 
 or, in scientific language, we must measure a force by 
 the rate at which it produces change of momentum. 
 Rate of change of velocity is called in kinematics Ac- 
 celeration. Thus the measure of a force is the product 
 of the mass of the body moved into the acceleration 
 which the force produces in it. This is the so-called 
 Vis Matrix Impressa y the 'moving force' of the 
 Cambridge text-books the Vis Acceleratrix or so- 
 called ' accelerating force ' being really no force at all, 
 but another name for the kinematical quantity Ac- 
 celeration which I have just defined. 
 
 Unit force is thus that force which, whatever be its 
 source^ produces unit momentum in unit of time. If we 
 employ British units unit of force is that which, in one 
 second, gives to one pound of matter a velocity of one 
 foot per second. Here you must carefully notice that 
 a pound of matter is a certain mass or quantity of matter. 
 When you buy a pound of tea you buy a quantity of 
 the matter called tea equal in mass to the standard 
 pound of platinum. The idea of weight does not enter 
 primarily into the process. In fact, the use of an ordinary 
 balance depends upon one clause of Newton's Law of 
 Gravitation, which tells us that in any locality whatever 
 the weights of bodies are equal if their masses are equal. 
 The weight of a pound of matter varies from place to 
 place on the earth's surface ; it depends on the attracting 
 as well as the attracted body. The mass of a body is 
 its own property. The earth's attraction for a body, or 
 the weight of the body, is a force which produces in it 
 in one second a velocity which (in this latitude, and at 
 the sea-level) is about 32-2 feet per second. So that in 
 Glasgow the weight of a pound, which we take as our 
 
358 FORCE. 
 
 standard of mass, is rather more than 32 units of force 
 or, what comes to the same thing, the British unit of 
 force is about the former limit of weight of a penny 
 letter that of half an ounce. 
 
 Some people are in the habit of confounding force 
 with momentum. No one having sound ideas of even 
 elementary mathematics could be guilty of this or any 
 similar monstrosity. He would as soon, as Hopkins 
 used to say, measure heights in acres, or arable land in 
 cubic miles. But to show to a non-mathematician that 
 it is really monstrous to confound force and momentum, 
 it suffices to change the system of units employed in 
 measuring them, when it will be found that, if numeri- 
 cally equal for any one system of units, they are neces- 
 sarily rendered unequal by a mere change of the unit 
 employed for time. Now two things which are really 
 equal to one another must necessarily be expressed by 
 the same numerical quantity whatever system of units 
 be adopted. Let us try, then, unit of force and unit of 
 momentum, as defined by pound, foot, second, units, 
 and see what alterations a common change of these 
 fundamental units will make in their numerical ex- 
 pression. 
 
 Unit momentum is that of one pound of matter moving 
 with a velocity of one foot per second. Unit force is 
 that force which, acting for one second, produces in 
 unit of mass a velocity of one foot per second. In each 
 of these statements you may put an ounce or a ton 
 instead of a pound, and an inch or a mile in place of a 
 foot, and their relative value will not be altered. But 
 suppose we take a minute instead of a second as the 
 unit of time. One foot per second is 60 feet per minute, 
 so this change of the time unit increases sixty-fold the 
 
FORCE. 359 
 
 nominal value of the momentum considered. But in 
 the case of the force our statement would stand thus : 
 What we formerly called unit of force is that which, 
 acting for one-sixtieth only of our new unit of time, 
 produces in a mass of one pound sixty-fold the new unit 
 of velocity. In other words, the number expressing the 
 momentum is increased sixty-fold, while that represent- 
 ing the force is increased three thousand six hundred 
 fold. 
 
 In fact, whatever be the system of units you employ, 
 if you increase in any proportion the unit of time, the 
 measure of a momentum is increased in that proportion 
 simply, while that of a force is increased in the duplicate 
 ratio. The two things are, therefore, of quite dissimilar 
 nature, and cannot lawfully be equated to one another 
 under any circumstances whatever. The mathematician 
 expresses this distinction at once by saying that Momen- 
 tum is the Time-Integral of Force, because force is the 
 rate of change of Momentum. 
 
 But what I have already said as to the meaning of 
 Newton's two first laws leaves absolutely no doubt as to 
 the only definite and correct meaning of the word Force. 
 It is obviously to be applied to any pull, push, pressure, 
 tension, attraction or repulsion, etc., whether applied by 
 a stick or a string, a chain or a girder, or by means of 
 an invisible medium such as that whose existence is 
 made certain by the phenomena of light and radiant 
 heat, and which has been shown with great probability 
 to be capable of explaining the phenomena of electricity 
 and magnetism. 
 
 I have already mentioned to you that the notion of 
 force is suggested to us by the so-called muscular sense, 
 which gives us a peculiar feeling of pressure when we 
 
360 FORCE, 
 
 attempt to move a piece of matter. To get a notion of 
 what it really means we must again have recourse to 
 physical facts, instead of the uncontrolled evidence of 
 the senses. Almost all that is required for this purpose 
 is summed up for us in the remaining law of Motion. 
 Before we take it up, however, let us briefly consider 
 the position at which we have arrived. 
 
 We have seen how to get rid of two gratuitous 
 absurdities : the so-called Centrifugal Force, and 
 Accelerating Force ; and we must proceed to exter- 
 minate Living Force. Cormoran and Blunderbore 
 have been disposed of, but a more dangerous giant 
 remains. More dangerous, because he is a reality, 
 not a phantom like the other two. Whatever force 
 may be, there is no such thing as Centrifugal Force ; 
 and Accelerating Force is not a physical idea at all. 
 But that which is denoted by the term Living Force, 
 though it has absolutely no right to be called force, is 
 something as real as matter itself. To understand its 
 nature we must have recourse to another quotation 
 from the Principia. 
 
 Newton's Third Law of Motion is to the effect that 
 To every action there is always an equal and contrary 
 reaction ; or, the mutual actions of any two bodies are 
 always equal and oppositely directed. 
 
 This law Newton first shows to hold for ordinary 
 pressures, tensions, attractions, impacts, etc., that is for 
 forces exerted on one another by two bodies ; or their 
 time-integrals. And when he says If any one presses 
 a stone with his finger, his finger is pressed with an 
 equal and opposite force by the stone, we begin to 
 suspect that force is a mere name a convenient abs- 
 traction not an objective reality. 
 
FORCE. 361 
 
 Pull one end of a long rope, the other being fixed. 
 You can produce a practically infinite amount of force, 
 for there is stress across every section throughout the 
 whole length of the rope. Press upon a moveable piston 
 in the side of a vessel full of fluid. You produce a 
 practically infinite amount of force, for across every ideal 
 section of the liquid a pressure per square inch is pro- 
 duced equal to that which you applied to the piston. 
 Let go the rope, or cease to press on the piston, and all 
 this practically infinite amount of force is gone ! 
 
 The only man who, to my knowledge, ever tried to 
 discover experimentally what might be correctly called 
 Conservation of Force was Faraday. He was not 
 satisfied with the mode of statement of Newton's law 
 of gravitation, in which the mutual attraction between 
 two bodies is said to VARY inversely as the square of 
 their distance from one another. When the distance 
 between two bodies is doubled their mutual attraction 
 falls off to one-fourth of what it formerly was. Faraday 
 seriously set to work to determine what became of the 
 three-fourths which have disappeared, but all his skill 
 was insufficient to give him any result. Faraday's 
 insight was so profound that we cannot assert that some- 
 thing may not yet be discovered by such experiments ; 
 but it will assuredly not be a conservation of force. 
 
 But Newton proceeds to point out that there is an- 
 other and much higher sense in which his statement is 
 true. He says : 
 
 1 If the action of an agent be measured by the product 
 of its force into its velocity ; and if, similarly, the reaction 
 of the resistance be measured by the velocities of its several 
 parts into their several forces, whether these arise from 
 friction, cohesion, weight, or acceleration; action and 
 
362 FORCE. 
 
 reaction, in all combinations of machines, will be equal 
 and opposite' 
 
 The actions and reactions which are here stated to 
 be equal and opposite, are no longer simple forces, but 
 the products of forces into their velocities, i.e. they are 
 what are now called Rates of doing Work ; the time- 
 rate of increase, or the increase per second of a very 
 tangible and real SOMETHING : for the measurement of 
 which rate Watt introduced the practical unit of a 
 horse-power, or the rate at which an agent works when 
 it lifts 33,000 pounds one foot high per minute against 
 the earth's attraction. 
 
 Now, think of the difference between raising a 
 hundredweight and endeavouring to raise a ton. With 
 a moderate exertion you can raise the hundredweight 
 a few feet, and in its descent it might be employed to drive 
 machinery, or to do some other species of work ; but tug 
 as you please you will not be able to lift the ton, and 
 therefore after all your exertion it will not be capable 
 of doing any work by descending again. 
 
 Thus it appears that force is a mere name ; and that 
 fat product of a force into the displacement of its point of 
 application has an objective existence. [Even those who 
 are so metaphysical as not to see that the product of a 
 mere name into a displacement can have objective exist- 
 ence, may perhaps see that the quotient of a horse- 
 power by a velocity is not likely to be more than a mere 
 name.] In fact, modern science shows us that force is 
 merely a convenient term employed for the present (very 
 usefully), to shorten what would otherwise be cumbrous 
 expressions ; but it is not to be regarded as a thing any 
 more than the bank rate of interest (be it two, two and a 
 half, or three per cent.) is to be looked upon as a sum of 
 
FORCE. 363 
 
 money, or than the birth-rate of a country is to be looked 
 upon as the actual group of children born in a year. 
 Another excellent instance is to be had from the rain- 
 fall. We say rain fell on such a day at the rate of an 
 inch in twenty-four hours. What can be an inch of 
 rain ? especially when we mean a linear not a cubic 
 inch. But there is no confusion or absurdity here. 
 What is implied is, that, if it had gone on raining at 
 that rate for twenty-four hours, and if the rain (like 
 snow) remained where it fell, the ground would have 
 been coated to the depth of an inch. 
 
 In fact, a simple mathematical operation shows us 
 that it is precisely the same thing to say : 
 
 The horse-power of an agent, or amount of work done 
 by the agent in each second, is the product of the force into 
 the average velocity of the agent, 1 
 and to say : 
 
 Force is the rate at which an agent does work per 
 unit of length. 
 
 In the special illustration of Newton's words which I 
 have just given, the resistance was a weight, that of a 
 hundredweight or of a ton. When the resistance was 
 overcome, work was done, and it was stored up for 
 use in the raised mass in a form which could be 
 made use of at any future time. 
 
 Following a hint given by Young, we now employ 
 the term ENERGY to signify the power of doing work, 
 in whatever that power may consist. The raised mass, 
 
 1 [I have slightly altered this sentence so as to meet the preposterous 
 charge, made by some of my critics, that I spoke here of the * horse-power 
 done in a second ' ! The preternatural acumen, required to make this 
 discovery, ought to have been carefully reserved for some altogether 
 illegible inscription in some unknown language.] 
 
364 FORCE. 
 
 then, we say possesses in virtue of its elevation an 
 amount of energy precisely equal to the work spent 
 in raising it This dormant, or passive, form, is called 
 Potential Energy. Excellent instances of potential 
 energy are supplied by water at a high level, or with a 
 ' head/ as it is technically called, in virtue of which it 
 can in its descent drive machinery by the wound-up 
 'weights' of a clock, which in their descent keep it 
 going for a week by gunpowder, the chemical affini- 
 ties of whose constituents are called into play by a 
 spark, etc., etc. 
 
 Another example of it is suggested by the word 
 ' Cohesion ' employed in Newton's statement, and which 
 must be taken to include what are called molecular 
 forces in general, such as, for instance, those upon which 
 the elasticity of a solid depends. 
 
 When we draw a bow we do work, because the place 
 of application of the force exerted has a velocity ; but 
 the drawn bow (like the raised weight) has, in potential 
 energy, the equivalent of the work so spent. That can 
 in turn be expended upon the arrow ; and what then ? 
 
 Turn again to Newton's words, and we see that he 
 speaksijpf one of the forms of resistance as arising from 
 * acceleration.' In fact, the arrow, by its inertia, resists 
 being set in motion ; work has to be spent in propelling 
 it ; but the moving arrow has that work in store in 
 virtue of its motion. It appears from Newton's 
 previous statements that the measure of the rate at 
 which work is spent in producing acceleration is the 
 product of the momentum into the acceleration in tJte 
 direction of motion, and the energy produced is measured 
 by half the product of the mass into the square of the 
 velocity produced in it. This active form is called 
 
FORCE. 365 
 
 Kinetic Energy, and it is the double of this to which 
 the term Vis Viva, erroneously translated Living Force, 
 has been applied. 
 
 As instances of ordinary Kinetic Energy, or of mixed 
 kinetic and potential energies, take the energy of 
 a current of water, capable of driving an undershot 
 wheel ; of winds which also are used for driving ma- 
 chinery ; the energy of water-waves or of sound-waves ; 
 the radiant energy which comes to us from the sun, 
 whether it affect our nerves of touch or of sight (and 
 therefore be called radiant heat or light) or produce 
 chemical decomposition, as of carbonic acid and water 
 in the leaves of plants, or of silver salts in photography 
 (and be therefore called actinism) ; the energy of 
 motion of the particles of a gas, upon which its pressure 
 depends, etc. [When the motion is vibratory the 
 energy is generally half potential, half kinetic.] 
 
 These explanations and definitions being premised, 
 we can now translate Newton's words (without altera- 
 tion of their meaning) into the language of modern 
 science, as follows : 
 
 Work done on any system of bodies (in Newton's state- 
 ment, the parts of any machine) has its equivalent in 
 work done against friction, molecular forces, or gravity, 
 if there be no acceleration ; but if there be acceleration, 
 part of the work is expended in overcoming the resistance 
 to acceleration, and the additional kinetic energy developed 
 is equivalent to the work so spent. 
 
 But we have just seen that when work is spent against 
 molecular forces, as in drawing a bow or winding up a 
 spring, it is stored up as potential energy. Also it is 
 stored up in a similar form when done against gravity, 
 as in raising a weight 
 
3 66 FORCE. 
 
 Hence it appears that, according- to Newton, when- 
 ever work is spent, it is stored up either as potential or 
 as kinetic energy except possibly in the case of work 
 done against friction, about whose fate he gives us no 
 information. Thus Newton expressly tells us that 
 (except possibly when there is friction) energy is inde- 
 structible it is changed from one form to another, and 
 so on, but never altered in quantity. To make this 
 beautiful statement complete, all that is requisite is to 
 know wJiat becomes of work done against friction. 
 
 Here, of course, experiment is requisite. Newton, 
 unfortunately, seems to have forgotten that savage men 
 had long since been in the habit of making it whenever 
 they wished to procure fire. The patient rubbing of 
 two dry sticks together, or (still better) the drilling of a 
 soft piece of wood with the slightly blunted point of a 
 hard piece, is known to all tribes of savages as a means 
 of setting both pieces of wood on fire. Here, then, 
 heat is undoubtedly produced, but it is produced by the 
 expenditure of work. In fact, work done against friction 
 has its equivalent in the heat produced. This Newton 
 failed to see, and thus his grand generalisation was left, 
 though on one point only, incomplete. The converse 
 transformation, that of heat into work, dates back to 
 the time of Hero at least. But the knowledge that a 
 certain process will produce a certain result does not 
 necessarily imply even a notion of the ' why ; ' and Hero 
 as little imagined that in his aeolipile heat was converted 
 into work, as do savages that work can be converted into 
 heat. 
 
 But whenever any such conversion or transference 
 takes place, there is necessarily motion ; and the mere 
 rate of conversion or transference of energy per unit 
 
FORCE. 367 
 
 length of that motion is in the present state of science 
 very conveniently called Force. No confusion can arise 
 from using such a word in such a sense. On the contrary, 
 there is always a gain in clearness, when compactness 
 can lawfully be introduced. 
 
 Rumford and Davy, at the very end of last century, 
 by totally different experimental processes, showed con- 
 clusively that the materiality of heat could not be 
 maintained ; and thus gave the means of completing 
 Newton's statement, which, still further extended and 
 generalised, rather more than thirty years ago, by the 
 magnificent experimental work of Colding and Joule, 
 now stands as one massive pillar of the fast-rising temple 
 of Science known as the law of the Conservation of 
 Energy. 
 
 The conception of kinetic energy is a very simple one, 
 at least when visible motion alone is involved. And 
 from motion of visible masses to those motions of the 
 particles of bodies whose energy we call Heat, is by no 
 means a very difficult mental transition. Mark, how- 
 ever, that heat is not the mere motions, but the energy 
 of these motions a very different thing, for heat and 
 kinetic energy in general are no more ' modes of motion ' 
 than potential energy of every kind (including that of 
 unfired gunpowder) is a ' mode of rest /' In fact, a 
 * mode of motion ' is, if the word motion be used in its 
 ordinary sense, purely kinematical, not physical : and, 
 if motion be used in Newton's sense, it refers to momen- 
 tum, riot to energy. 
 
 The conception of potential energy, however, is not 
 by any means so easy or direct. In fact, the apparently 
 direct testimony of our muscular sense to the existence 
 of force, makes it at first much easier for us to conceive 
 
368 FORCE. 
 
 of force than of potential energy. Why two masses of 
 matter possess potential energy when separated in 
 virtue of which they are conveniently said to attract one 
 another is still one of the most obscure problems in 
 physics. I have not now time to enter on a discussion 
 of/the very ingenious idea of the ultramundane Cor- 
 puscles, the outcome of the lifework of Le Sage, and the 
 only even apparently hopeful attempt which has yet 
 been made to explain the mechanism of Gravitation. 
 The. most singular jthing about it is thatjifjt be true, it 
 will probably lead us to regard all kinds of energy as 
 ultimately Kinetic. 
 
 And a curious quasi-metaphysical argument may be 
 raised on this point, of which [ can give only the 
 barest outline. The mutual convertibility of Kinetic and 
 Potential energy shows that relations of equality (though 
 not necessarily of identity) can exist between the two ; 
 and thus that their proper expressions involve the same 
 fundamental units and in the same way. Thus, as we 
 have already seen that kinetic energy involves the unit 
 of mass and the square of the linear unit directly, 
 together with the square of the time unit inversely ; the 
 same must be the case with potential energy. And it 
 seems very singular that potential energy should thus 
 essentially involve the unit of time if it do not ultimately 
 depend in some way on energy of motion. 
 
 THOMAS AND ARCHIBALD CONSTABLE, PRINTERS TO HER MAJESTY. 
 
Tilt 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
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