190 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



(7) 



-e 



St 

 K 



M I M a (M, + M !! ) 

 + 



S^; (SA.-BA^f -f-XU-V,*) 



>(39) 



J 



using the symbol S 2 to indicate variations arising from the action 

 of molecules of the second system. 



These are the values of the rate of variation of the mean values 

 of f p fj 2 fj rj v and ^Vj 2 , for the molecules of the first kind 

 due to their encounters with molecules of the second kind. In 

 all of them we must multiply up all functions of f, 77, £ and 

 take the mean values of the products so found. As this has to 

 be done for all such functions, I have omitted the bar over each 

 function in these expressions. 



To find the rate of variation due to the encounters among the 

 particles of the same system, we have only to alter the suffix (2 ) 

 into (i; throughout, and to change K, the coefficient of the force 

 between M x and M 2 into K v that of the force between two mole- 

 cules of the first system. We thus find : — 



03) 



^=0; 



St 



¥ = (ai%)VNA{% 3 + ? -a? 



St 



(_5 



V2M 



* 1 /M 1 N 1 A£{&-.*,-fci»}i 



(40) 



(41) 



(42) 



These quantities must be added to those in equations (36) to 

 (39) in order to get the rate of variation in the molecules of the 

 first kind due to their encounters with molecules of both systems. 

 When there is only one kind of molecules, the latter equations 

 give the rates of variation at once. 



