MR. CLERK MAXWELL ON THE DYNAMICAL THEORY OF GASES. 67 
( 0 ) Hr («) 
^=„X+|Y; (46) 
M 4 f^=2|(|X+,Y+?Z)+XV ! ; (47) 
where & 3 refers to variations due to the action of external forces. 
On the Total rate of change of the different functions of the velocity of the molecules 
of the first system arising from their encounters with molecules of both systems and 
from the action of external forces. 
To find the total rate of change arising from these causes, we must add 
?£, 8 #>and«, 
8t ’ 8t It 
the quantities already found. We shall find it, however, most convenient in the re- 
mainder of this investigation to introduce a change in the notation, and to substitute for 
£, y\, and £, w-f£, and w+£, (48) 
where u , v, and w are so chosen that they are the mean values of the components of the 
velocity of all molecules of the same system in the immediate neighbourhood of a given 
point. We shall also write 
M 2 N 2 =f 2 , (49) 
where ^ and g> 2 are the densities of the two systems of molecules, that is, the mass in 
unit of volume. We shall also write 
K 
i 
=k, and 
(50) 
§ 2 , k 2 , and k are quantities the absolute values of which can be deduced from expe- 
riment. We have not as yet experimental data for determining M, N, or K. 
We thus find for the rate of change of the various functions of the velocity, 
(«) ^=*A , ? ,( % -«,)+X; 
( 0 ) 
M 0 
also 
+ ^ 2 M7Aq 2Ai ( M2 — ' +^2 — —2 U 2 —U, 
+Mrfts s { 2A '( M ^i- M 'S)+ A « M *'+?’- 2 ^+ > <+^- 2 S)} : 
4= - +% (2A, - 3A ,)(«,-«.)(«,- v, 
+M^% 3 { 2A '( M ^A- M ^^')-3A s M a (f li)l +| A )]. 
K 2 
(51) 
(52) 
( 53 ) 
