'8 Lord Kelvin on the 



rescued from oblivion by Lord Rayleigh and published, with 

 an introductory notice of great interest and importance, in 

 the Transactions of the Royal Society for 1892), enunciated 

 the following proposition: " In mixed media the mean square 

 " molecular velocity is inversely proportional to the specific 

 a weight of the molecule. This is the law of the equilibrium 

 " of vis viva/' Of this proposition Lord Rayleigh in a 

 footnote * says, " This is the first statement of a very 

 " important theorem (see also Brit. Assoc. Rep., 1851). 

 u The demonstration, however, of § 10 can hardly be de- 

 a fended. It bears some resemblance to an argument 

 " indicated and exposed by Professor Tait (Edinburgh 

 "Trans., vol. 33, p. 79, 1886). There is reason to think 

 " that this law is intimately connected with the Maxwellian 

 u distribution of velocities of which Waterston had no know- 

 " ledge." 



§ 13. In Waterston's statement, the " specific weight of 

 a molecule" means what we now call simply the mass of a 

 molecule ; and u molecular velocity" means the translational 

 velocity of a molecule. Writing on the theory of sound in 

 the Phil. Mag. for 1858, and referring to the theory de- 

 veloped in his buried paper t, Waterston said, " The theory 

 " . . . . assumes .... that if the impacts produce rotatory 

 *' motion the vis viva thus invested bears a constant ratio to 

 u the rectilineal vis viva." This agrees with the very 

 important principle or truism given independently about the 

 same time by Clausius to the effect that the mean energy, 

 kinetic and potential, due to the relative motion of all the 

 parts of any molecule of a gas, bears a constant ratio to 

 the mean energy of the motion of its centre of inertia when 

 the density and pressure are constant. 



§ 14. Without any knowledge of what was to be found in 

 Waterston's buried paper. Maxwell, at the meeting of the 

 British Association at Aberdeen, in 1859 J gave the following 

 proposition regarding the motion and collisions of perfectly 

 elastic spheres : " Two systems of particles move in the same 

 *' vessel ; to prove that the mean vis viva of each particle 

 " will become the same in the two systems." This is pre- 

 cisely Waterston's proposition regarding the law of partition 

 of energy, quoted in § 12 above ; but Maxwell's 1860 proof 

 was certainly not more successful than Waterston's. Max- 



* Phil. Trans. A, 1892, p. 16. 



t " On the Physics of Media that are composed of Porce and Perfectly 

 Elastic Molecules in a State of Motion." Phil. Trans., A, 1892, p. 13. 



J ■" Illustrations of the Dynamical Theory of Gases," Phil. Mag., 

 January arid July 1860, and collected works, vol. i. p. 378. 



