Dynamical Theory of Heat and Liglit. 11 



"motion, will, sooner or later, pass [infinitely nearly*] 

 "through every phase which is consistent with the equation 

 u of energy " (p. 714) and, again (p. 716). 



" It appears from the theorem, that in the ultimate state of 

 " the system the average t kinetic energy of two portions 

 u of the system must be in the ratio of the number of degrees 

 " of freedom of those portions. 



" This, therefore, must be the condition of the equality of 

 " temperature of the two portions of the system." 



I have never seen validity in the demonstration % on which 

 Maxwell founds this statement, and it has always seemed to 

 me exceedingly improbable that it can be true. If true, it 

 would be very wonderful, and most interesting in pure 

 mathematical dynamics. Having been published by Boltz- 

 mann and Maxwell it would be worthy of most serious 

 attention, even without consideration of its bearing on 

 thermo-dynamics. But, when we consider its bearing 

 on thermo-dynamics, and in its first and most obvious appli- 

 cation we find it destructive of the kinetic theory of gases, of 

 which Maxwell was one of the chief founders, we cannot sec 

 it otherwise than as a cloud on the dynamical theory of heat 

 and light. 



§ 19. For the kinetic theory of gases, let each molecule be 

 a cluster of Boscovich atoms. This includes every possibility 

 ("dynamical," or "electrical," or "physical," or " chemical") 

 regarding the nature and qualities of a molecule and of all its 

 parts. The mutual forces between the constituent atoms 

 must be such that the cluster is in stable equilibrium if given 

 at rest ; which means, that if started from equilibrium with 



* I have inserted these two words as certainly belonging* to Maxwell's 

 meaning. — K. 



t The average here meant is a time-average through a sufficiently long 

 time. 



\ The mode of proof followed by Maxwell, and its connection with 

 antecedent considerations of his own and of Boltzmann, imply, as in- 

 cluded in the general theorem, that the average kinetic energy of any 

 one of three rectangular components of the motion of the centre of inertia 

 of an isolated system, acted upon only by mutual forces between its parts, 

 is equal to the average kinetic energy of each generalized component of 

 motion relatively to the centre of inertia. Consider, for example, as 

 hi parts of the system " two particles of masses m and »»' free to move 

 only in a fixed straight line, and connected to one another by a massless 

 spring. The Boltzmann-Maxwell doctrine asserts that the average 

 kinetic energy of the motion of the inertial centre is equal to the average 

 kinetic energy of the motion relative to the inertial centre. This is 

 included in the wording of Maxwell's statement in the text if, but not 

 unless, m = ?7i'. See footnote on § 7 of my paper " On some Test-Cases 

 for the Boltzmann-Maxwell Dc ctrine regarding Distribution of Energy.' r 

 Proc. Roy. Soc, June 11, 1891. 



