310 On Boltzmann's Theorem on the average Distribution 



-ingle body — that, for example, the mean kinetic energy of a 

 momentum should be greater in one body than that calculated 

 above, in which case it must of course be smaller again in other 

 bodies, so that we may have the true mean value for all bodies. 



But it is to be remembered that all our bodies are found, 

 similarly constituted, of equal temperature, and under similar 

 external conditions. In the case just spoken of, therefore, the 

 behaviour of bodies of that kind would be different according 

 to the initial condition from which they started. But this is 

 not confirmed by experience. As often as one and the same 

 body is left to itself with the same energy of motion and under 

 the same external conditions, it assumes with time the same 

 thermal condition, the stationary condition corresponding to 

 that temperature and those external conditions. We are 

 therefore justified in maintaining that our equations hold not 

 simply for the above-defined conceptions of bodies, but also 

 for the stationary final condition of each single warm body. 

 That the condition of equality of temperature between warm 

 bodies has a very simple mechanical meaning independent 

 of their initial conditions, follows also from the fact that 

 it is not influenced by the compression, turning, or displace- 

 ment of particular parts. 



If we substitute for the system S two different gases sepa- 

 rated by a solid division-wall permeable to heat, then there 

 follows the equality of the mean kinetic energy of progressive 

 motion of the molecules of both gases, or Avogadro's law ; 

 the proof of which, hitherto resting on the equality of this 

 mean kinetic energy in mixtures of gases, is unreliable, since 

 we are not able to show that the mean kinetic energy of pro- 

 gressive motion is the same in mixtures as in separate gases 

 at the same temperature. 



The second case discussed by Maxwell is very interesting, 



but cannot be here reproduced in full. In this q 1 . , . q n are 



the rectangular coordinates ;i\...z n , therefore p x .. ,p u the 



velocity-components multiplied by the masses m^a x . . . m n ic„ of 



a free system of atoms S' with any internal forces but without 



external forces. Maxwell introduces into equation (5), instead of 



du x dvi du\ du 2 dv 2 div 2 du 3 , the product dJJ dV dW dF dGdH. dE ; 



where U, V, and W are the velocity-components of the centre 



of gravity, F, G, and H the constant sums of angular momenta 



of the elements of motion of the system S'. Equation (5) 



+ i o ,, ,. .,. , dJJ dY ( fW dF dG dR dE 

 therefore, after dividing by — a«umes 



the form " ™» 8 



d>%\ . . . dz' n dv'z . • . cho'n _ dx x .. . dz n dv 3 . . . dw n 



