1900.] on the Dynamical Theory of Heat and Light. 369 



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

 " molecular velocity " means the translational velocity of a moleculo. 

 Writing on the theory of sound in the Phil. Mag. for 1858, and 

 referring to the theory developed in his buried paper,* Waterston 

 said, " The theory .... assumes .... that if the impacts produce 

 " rotatory motion the vis viva thus invested bears a constant ratio to 

 " the rectilineal vis viva." This agrees with the very important prin- 

 ciple 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 Water- 

 ston's buried paper, Maxwell, at the meeting of the British Association 

 at Aberdeen, in 1859 | 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 

 precisely 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. Maxwell's 1860 proof has 

 always seemed to me quite inconclusive, and many times I urged my 

 colleague, Professor Tait, to enter on the subject. This he did, and 

 in 1886 ho communicated to the Royal Society of Edinburgh a paper J 

 on the foundations of the kinetic theory of gases, which contained a 

 critical examination of Maxwell's 1860 paper, highly appreciative 

 of the great originality and splendid value, for the kinetic theory of 

 gases, of the ideas and principles set forth in it ; but showing that the 

 demonstration of the theorem of the partition of energy in a mixed 

 assemblage of particles of different masses was inconclusive, and 

 successfully substituting for it a conclusive demonstration. 



§ 15. Waterston, Maxwell, and Tait, all assume that the particles 

 of the two systems are thoroughly mixed (Tait, § 18), and their 

 theorem is of fundamental importance in respect to the specific heats 

 of mixed gases. But they do not, in any of the papers already referred 

 to, give any indication of a proof of the corresponding theorem, 

 regarding the partition of energy between two sets of equal particles 

 separated by a membrane impermeable to the molecules, while permit- 

 ting forces to act across it between the molecules on its two sides, || 



* ' On the Physics of Media that are Composed of Force and Perfectly 

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



t ' Illustrations of the Dynamical Theory of Gases.' Phil. Mag., January and 

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



J Phil. Trans. R.S.E., 'On the Foundations of the Kinetic Theory of Gases,' 

 May 14 and December 6, 1886, and January 7, 1887. 



|| A very interesting statement is given by Maxwell regarding this subject in 

 his latest paper regarding the Boltzmann-Maxwell doctrine. ' On Boltzmann's 

 Theorem on the Average Distribution of Energy in a System of Material Points,' 

 Camb. Phil. Trans., May 6, 1878 ; Collected Works, vol ii. pp. 713-741. 



