May 12, 1892] 



NATURE 



31 



^^Introduction by Lord Rayleigh, Sec.R.S. 

 " The publication of this paper after nearly half a 

 century demands a word of explanation ; and the oppor- 

 tunity may be taken to point out in what respects the 

 received theory of gases had been anticipated by Water- 

 ston, and to offer some suggestions as to the origin of 

 certain errors and deficiencies in his views. 



" So far as I am aware, the paper, though always acces- 

 sible in the Archives of the Royal Society, has remained 

 absolutely unnoticed. Most unfortunately the abstract 

 printed at the time (Roy. Soc. Proc, 1846, vol. v. p. 604 ; 

 . . . ) gave no adequate idea of the scope of the memoir, 

 and still less cf the nature of the results arrived at. The 

 deficiency was in some degree supplied by a short account 

 in the Report of the British Association for 1851 ( . . . ), 

 where is distinctly stated the law, which was afterwards 

 to become so famous, of the equality of the kinetic energies 

 of different molecules at the same temperature. 



" My own attention was attracted in the first instance to 

 Waterston's work upon the connection between molecular 

 forces and the latent heat of evaporation, and thence to a 

 paper in the Philosophical Magazine for 1858, 'On the 

 Theory of Sound.' He there alludes to the theory of 

 gases under consideration as having been started by 

 Herapath in 1821, and he proceeds: — 



" ' Mr. Herapath unfortunately assumed heat or tempera- 

 ture to be represented by the simple ratio of the velocity 

 instead of the square of the velocity — being in this 

 apparently led astray by the definition of motion generally 

 received — and thus was baffled in his attempts to recon- 

 cile his theory with observation. If we make this change 

 in Mr. Herapath's definition of heat or temperature, viz. 

 that it is proportional to the vis viva, or square velocity 

 of the moving particle, not to the momentum, or simple 

 ratio of the velocity, we can without much difficulty 

 deduce, not only the primary laws of elastic fluids, but 

 also the other physical properties of gases enumerated 

 above in the third objection to Newton's hypothesis. In 

 the Archives of the Royal Society for 1845-46, there is a 

 paper " On the Physics of Media that consist of Perfectly 

 Elastic Molecules m a State of Motion," which contains 

 the synthetical reasoning upon which the demonstration 

 of these matters rests. The velocity of sound is therein 

 deduced to be equal to the velocity acquired in falling 

 through three-fourths of a uniform atmosphere. This 

 theory does not take account of the size of the molecules. 

 It assumes that no time is lost at the impact, and that if 

 the impact produce rotatory motion, the vis viva thus 

 invested bears a constant ratio to the rectilineal vis 

 viva, so as not to require separate consideration. It 

 also does not take account of the probable internal 

 motion of composite molecules ; yet the results so 

 closely accord with observation in every part of the 

 subject as to leave no doubt that Mr. Herapath's 

 idea of the physical constitution of gases appproxi- 

 mates closely to the truth. M. Kronig appears to have 

 entered upon the subject in an independent manner, and 

 arrives at the same result ; M. Clausius, too, as we learn 

 from his paper " On the Nature of the Motion we call 

 Heat " {Phil. Mag., vol. xiv., 1857, p. 108).' 



" Impressed with the above passage and with the 

 general ingenuity and soundness of Waterston's views, I 

 took the first opportunity of consulting the Archives, and 

 saw at once that the memoir justified the large claims 

 made for it, and that it marks an immense advance in the 

 direction of the now generally received theory. The 

 omission to publish it at the time was a misfortune, which 

 probably retarded the development of the subject by ten 

 or fifteen years. It is singular that Waterston appears 

 to have advanced no claim for subsequent publication, 

 whether in the Transactions of the Society, or through 

 some other channel. At any time since i860 reference 

 would naturally have been made to Maxwell, and it cannot 

 be doubted that he would have at once recommended 



NO. I 176, VOL. 46] 



that everything possible should be done to atone for the 

 original failure of appreciation. 



"It is difficult to put oneself in imagination into the 

 position of the reader of 1845, and one can understand 

 that the substance of the memoir should have appeared 

 speculative, and that its mathematical style should have 

 failed to attract. But it is startling to find a referee 

 expressing the opinion that ' the paper is nothing but 

 nonsense, unfit even for reading before the Society.' 

 Another remarks ' that the whole investigation is con- 

 fessedly founded on a principle entirely hypothetical, from 

 which it is the object to deduce a mathematical representa- 

 tion of the phenomena of elastic media. It exhibits 

 much skill and many remarkable accordances with the 

 general facts, as well as numerical values furnished by 

 observation. . . . The original principle itself involves an 

 assumption which seems to me very difficult to admit, 

 and by no means a satisfactory basis for a mathematical 

 theory, viz. that the elasticity of a medium is to be 

 measured by supposing its molecules m vertical motion, 

 and making a succession of impacts against an elastic 

 gravitating plane.' These remarks are not here quoted 

 with the idea of reflecting upon the judgment of the 

 referee, who was one of the best qualified authorities of 

 the day, and evidently devoted to a most difficult task his 

 careful attention ; but rather with the view of throwing 

 light upon the attitude then assumed by men of science 

 in regard to this question, and in order to point a moral. 

 The history of this paper suggests that highly speculative 

 investigations, especially by an unknown author, are best 

 brought before the world through some other channel 

 than a scientific Society,which naturally hesitates to admit 

 into its printed records matter of uncertain value. Per- 

 haps one may go further, and say that a young author who 

 believes himself capable of great things would usually do 

 well to secure the favourable recognition of the scientific 

 world by work whose scope is limited, and whose value 

 is easily judged, before embarking upon higher flights. 



" One circumstance which may have told unfavourably 

 upon the reception of Waterston's] paper is that he men- 

 tions no predecessors. Had he put forward his investi- 

 gation as a development of the theory of D. Bernoulli, a 

 referee might have hesitated to call it nonsense. It is 

 probable, however, that Waterston was unacquainted with 

 Bernoulli's work, and doubtful whether at that time he 

 knew that Herapath had to some extent foreshadowed 

 similar views. 



" At the present time the interest of Waterston's paper 

 can, of course, be little more than historical. What 

 strikes one most is the marvellous courage with which 

 he attacked questions, some of which even now present 

 serious difficulties. To say that he was not always 

 successful is only to deny his claim to rank among the 

 very foremost theorists of all ages. The character of 

 the advance to be dated from this paper will be at once 

 understood when it is realized that Waterston was the 

 first to introduce into the theory the conception that heat 

 and temperature are to be measured by vis viva. This 

 enabled him at a stroke to complete BernouUi's explana- 

 tion of pressure by showing the accordance of the hypo- 

 thetical medium with the law of Dalton and Gay-Lussac. 

 In the second section the great feature is the statement 

 (VII.), that 'in mixed media the mean square molecular 

 velocity is inversely proportional to the specific weight of 

 the molecules.' The proof which Waterston gave is 

 doubtless not satisfactory ; but the same may be said of 

 that advanced by Maxwell fifteen years later. The law 

 of Avogadro follows at once, as well as that of Graham 

 relative to diffusion. Since the law of equal energies 

 was actually published in 1851, there can be no hesita- 

 tion, I think, in attaching Waterston's name to it. The 

 attainment of correct results in the third section, dealing 

 with adiabatic expansion, was only prevented by a slip of 

 calculation. 



