MR. CLERK MAXWELL ON THE DYNAMICAL THEORY OF GASES. 
M \ N 2M 2 |A,(i 2 i,y?4-2i 1 (u v?)) 
M 
+M^t a (2A,-34J2(5,-aU-V!> 
M f ( 89 ) 
+CT;( 2A '+ 2 W° 
+ (n^irJ( 2A .- 2A =) 2 fe-?.)v ! }; 
using the symbol \ 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 x , £ 2 t]„ and 
£ x V,, 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 £, q, £, 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 (1) throughout, and to change K, the 
coefficient of the force between M x and M 2 into K„ that of the force between two mole- 
cules of the first system. We thus find 
(«) $ =»; (I®) 
8 # K»i) 5m,n ‘ As3{4 ~ ; (42) 
( y ) ?i|^=(A-.)VN I A a 3(|;.y[-|V?) • • • • (13) 
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 mole- 
cules of both systems. When there is only one kind of molecules, the latter equations 
give the rates of variation at once. 
On the Action of External Forces on a System of Moving Molecules. 
We shall suppose the external force to be like the force of gravity, producing equal 
acceleration on all the molecules. Let the components of the force in the three coor- 
dinate directions be X, Y, Z. Then We have by dynamics for the variations of £, §' 2 , and 
£y 2 due to this cause, 
M ¥= x ; 
(44) 
