August 28, 18S4J 



NA TURE 



417 



Old World and in the New, recruits must be enlisted to fill the 

 place of those whose work is done. Happy should I be if, 

 through this visit of the Association, or by any words of mine, a 

 larger measure of the youthful activity of the West could be 

 drawn into this service. The work may be hard, and the 

 discipline severe, but the interest never fails, and great is the 

 privilege of achievement. 



SECTION A 

 MATHEMATICAL AND PHYSICAL SCIENCE 



Opening Address by Prof. Sir William Thomson, M.A., 

 LL.D., D.C.L., F.R.SS.L. & E., F.R.A.S., President 

 of the Section 



Steps towards a Kinetic Theory of Matter 

 The now well-known kinetic theory of gases is a step so 

 important in the way of explaining seemingly static properties of 

 matter by motion, that it is scarcely possible to help antici- 

 pating in idea the arrival at a complete theory of matter, in 

 which all its properties will be seen to be merely attributes of 

 motion. If we are to look for the origin of this idea, we must 

 go back to Democritus, Epicurus, and Lucretius. We may 

 then, I believe, without missing a single step, skip 1800 years. 

 Early last century we find in Malebranche's " Recherche de la 

 Verite," the statement that " La durete de corps " depends on 

 " petits tourbillons. " * These words, embedded in a hopeless 

 mass of unintelligible statements of the physical, metaphysical, 

 and theological philosophies of the day, and unsupported by any 

 explanation, elucidation, or illustration throughout the rest of 

 the three volumes, and only marred by any other single sentence 

 or word to be found in the great book, still do express a distinct 

 conception, which forms a most remarkable step towards the 

 kinetic theory of matter. A little later we have Daniel 

 Bernoulli's promulgation of what we now accept as a surest 

 article of scientific faith — the kinetic theory of gases. He, so 

 far as I know, thought only of the Boyle's and Marriot's law of 

 the "spring of air," as Boyle called it, without reference to 

 change of temperature or the augmentation of its pressure if not 

 allowed to expand for elevation of temperature, a phenomenon 

 which perhaps he scarcely knew, still less the elevation of tem- 

 perature produced by compression, and the lowering of tempera- 

 ture by dilatation, and the consequent necessity of waiting for a 

 fraction of a second or a few seconds of time (with apparatus of 

 ordinary experimental magnitude), to see a subsidence from a 

 larger change of pressure, down to the amount of change that 

 verifies Boyle's law. The consideration of these phenomena 

 forty years ago by Joule, in connection with Bernoulli's original 

 conception, formed the foundation of the kinetic theory of gases 

 as we now have it. But what a splendid and useful building has 

 been placed on this foundation by Clausius and Maxwell, and 

 what a beautiful ornament we see on the top of it in the radio- 

 meter of Crookes, securely attached to it by the happy discovery 

 of Tait and Dewar," that the length of the free path of the 

 residual molecules of air in a good modern vacuum may amount 

 to several inches. Clausius' and Maxwell's explanations of the 

 diffusion of gases, and of thermal conduction in gases, their 

 charmingly intelligible conclusion that in gases the diffusion of 

 heat is just a little more rapid than the diffusion of molecules, 

 because of the interchange of energy in collisions between mole- 

 cules, 3 while the chief transference of heat is by actual transport 



1 ■' Preuve de la supposition que j'ay faite : Que la matiere subtile ou ethe're'e 

 estnecessairement composee de petits tourbillons ; et qu'ilssont les causes 

 naturelles de tous les changements qui arrivent a la matiere ; ce que je con- 

 firme par ['explication des effets le plus gerieVaux de la Physique, tels que 

 sont la durete' des corps, leur fluidite", leur pesanteur, leur legerete, la lumiere 

 et la refraction et reflexion de ses rayons." — Malebranche, " Recherche de 

 la Verite," 1712. 



2 Proc. R. S. E., March 2, 1874, and July 5, 1875. 



3 On the other hand, in liquids, on account of the crowdedness of the mole- 

 cules, the diffusion of heat must be chiefly by interchange of energies between 

 the molecules, and should be, as experiment proves it is, enormously more rapid 

 than the diffusion of the molecules themselves, and this again ought to be 

 much less rapid than either the material or thermal diffusivities of gases. 

 Thus the diffusivity of common salt through water was found by Fick to be 

 as smaU as '0000112 square centimetres per second ; nearly 200 times as great 

 as this is the diffusivity of heat through water, which was found by J. T. 

 Bottomley to be about "002 square centimetres per second. The material 

 diffusivities of gases, according to Loschmidt's experiments, range from '098 

 (the interdiffusivity of carbonic acid and nitrous oxide) to '642 (the inter- 

 diffusivity of carbonic oxide and hydrogen), while the thermal diffusivities of 

 gases, calculated according to Clausius' and Maxwell's kinetic theory of 

 gases, are '089 for carbonic acid, "16 for common air or other gases of nearly 

 the same density, and i"i2 for hydrogen (all, both material and thermal, 

 being reckoned in square centimetres per second). 



of the molecules themselves, and Maxwell's explanation of the 

 viscosity of gases, with the absolute numerical relations which 

 the work of those two great discoverers found among the three 

 properties of diffusion, thermal conduction, and viscosity, have 

 annexed to the domain of science a vast and ever-growing 

 province. 



Rich as it is in practical results, the kinetic theory of gases, as 

 hitherto developed, stops absolutely short at the atom or mole- 

 cule, and gives not even a suggestion towards explaining the 

 properties in virtue of which the atoms or molecules mutually 

 influence one another. For some guidance towards a deeper 

 and more comprehensive theory of matter, we may look back 

 with advantage to the end of last century, and the beginning of 

 this century, and find Rumford's conclusion regarding the heat 

 generated in boring a brass gun: "It appears to me to be 

 extremely difficult, if not quite impossible, to form any distinct 

 idea of anything capable of being excited and communicated in 

 the manner the heat was excited and communicated in these 

 experiments, except it be motion," and Davy's still more 

 suggestive statements : "The phenomena of repulsion are not 

 dependent on a peculiar elastic fluid for their existence. . . . 

 " Heat may be defined as a peculiar motion, probably a vibration, 

 of the corpuscles of bodies, tending to separate them. ..." 

 "To distinguish this motion from others, and to signify the 

 causes of our sensations of heat, &c, the name repulsive motion 

 has been adopted." Here we have a most important idea. It 

 would be somewhat a bold figure of speech to say the earth and 

 moon are kept apart by a repulsive motion ; and yet, after all, 

 what is centrifugal force but a repulsive motion, and may it not 

 be that there is no such thing as repulsion, and that it is solely 

 by inertia that what seems to be repulsion is produced ? Two 

 bodies fly together, and, accelerated by mutual attraction, if they 

 do not precisely hit one another, they cannot but separate in 

 virtue of the inertia of their masses. So, after dashing past one 

 another in sharply concave curves round their common centre of 

 gravity, they fly asunder again. A careless onlooker might 

 imagine they had repelled one another, and might not notice the 

 difference between what he actually sees and what he would see if 

 the two bodies had been projected with great velocity towards 

 one another, and either colliding and rebounding, or repelling 

 one another into sharply convex continuous curves, fly asunder 

 again. 



Joule, Clausius, and Maxwell, and no doubt Daniel Bernoulli 

 himself, and I believe every one who has hitherto written or 

 done anything very explicit in the kinetic theory of gases, has 

 taken the mutual action of molecules in collision as repulsive. 

 May it not after all be attractive ? This idea has never left my 

 mind since I first read Davy's " Repulsive Motion," about 

 thirty-five years ago, but I never made anything of it, at all 

 events have not done so until to-day (June 16, 18S4) — if this can 

 be said to be making anything of it — when, in endeavouring to 

 prepare the present address, I notice that Joule's and my own 

 old experiments 1 on the thermal effect of gases expanding from 

 a high-pressure vessel through a porous plug, proves the less 

 dense gas to have greater intrinsic potential energy than the 

 denser gas, if we assume the ordinary hypothesis regarding the 

 temperature of a gas, according to which two gases are of equal 

 temperatures - when the kinetic energies of their constituent 

 molecules are of equal average amounts per molecule. 



Think of the thing thus. Imagine a great multitude of 

 particles inclosed by a boundary which may be pushed inwards 

 in any part all round at pleasure. Now station an engineer 

 corps of Maxwell's army of sorting demons all round the in- 

 closure, with orders to push in the boundary diligently every- 

 where, when none of the besieged troops are near, and to do 

 nothing when any of them are seen approaching, and until after 

 they have turned again inwards. The result will be that, with 

 exactly the same sum of kinetic and potential energies of the 

 same inclosed multitude of particles, the throng has been caused 

 to be denser. Now Joule's and my own old experiments on 

 the efflux of air prove that if the crowd be common air, or 



1 Republished in Sir W. Thomson's " Mathematical and Physical Papers," 

 vol. i. Article xlix. p. 381. 



* That this is a mere hypothesis has been scarcely remarked by the 

 founders themselves, nor by almost any writer on the kinetic theory of 

 gases. No one has yet examined the question : What is the condition as 

 regards average distribution of kinetic energy, which is ultimately fulfilled by 

 two portions of gaseous matter, separated by a thin elastic septum which 

 absolutely prevents interdiffusion of matter, while it allows interchange of 

 kinetic energy by collisions against itself? Indeed I do not know but that 

 the present is the very first statement which has ever been published of this 

 condition of the problem of equal temperatures between two gaseous masses. 



