for the Theoretical Proof of Avogadro's Law. 325 



•—> ^—j and -=- will vanish. Nevertheless the former two 

 dt ot at 



magnitudes must be given by the equations (19) and (20) 



r7TT 

 (where X=A = 0). Therefore also ~rr must be given by the 



same equation (22) ; and, from the condition that it must 

 vanish at the same time, it follows exactly as before that 



f=Ae~ hmv2 , F = Be~ AMV2 , 



by which Mr. Burbury's proposition is proved. In this it is 

 simply assumed that the number of molecules A is very large. 

 This produces the effect that, so soon as the condition has 

 become stationary, the distribution of velocities in each sepa- 

 rate vessel is scarcely perceptibly influenced by the condition 

 possessed by the molecule B in that vessel. 



It is only necessary to further remark here in passing, that 

 the proof may be obtained in exactly the same way if, instead 

 of regarding the molecules as elastic spheres, we assume any 

 other law of mutual action ; if only, in the first place, the 

 Lagrange-Hamilton equations of motion are applicable, and, 

 in the second place, if the time of perceptible mutual action 

 for each molecule is vanishingly small in comparison with the 

 time of free motion. 



First Appendix. 



I have just received a treatise by H. Stankewitsch*, which 

 has for object to prove an equation which essentially is iden- 

 tical with equation (15) of this paper. I have long ago, in 

 my treatise " Some General Propositions on the Equilibrium 

 of Heat"|, called attention to the connection of a still more 

 general equation with Jacobi's principle of the last multiplier. 

 H. Stankewitsch arrives at the proof of his equation in an 

 altogether different way, which, however, is in every respect 

 similar to Jacobi's proof of the principle of the last multiplier. 

 However ingenious the method employed by Stankewitsch, 

 I hope to show in the following lines that the equation in 

 question may be proved much more simply in the way indi- 

 cated by Maxwell. I will first show that the equation of H. 

 Stankewitsch is only an altered form of our equation (15). 

 If A be the angle between the velocity v and the axis of 

 abscissae, B the angle made by the XZ plane w T ith the plane 

 which is parallel to the directions of v and OX, and, lastly, K 

 the angle made by the last plane with the plane parallel to the 



* Wiedemann's Annalen, Bd. xxix. p. 153 (1886). 

 t Wiener Sitzber. Bd. lviii. May 1871. 



