THE DYNAMICAL THEORY OF GASES. 49 



SF 2 f K \ 

 i \ Pigi^ i / Jx i \ MW A Q / p-2_]7 



*' 80 \2J.f7 ^ Zi'i 



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. 



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, pro- 

 ducing equal acceleration on all the molecules. Let the components of the force 

 in the three coordinate directions be X, Y, Z. Then we have by dynamics for 

 the variations of 2 , and F 2 due to this cause, 



.(44); 

 .(45); 



^ = r,X+tY (46); 



(47); 



v " St 

 where S 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 mole- 

 cules 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 



S,<? S a <? W 



8* ' & ' ' 8t ' 



the quantities already found. We shall find it, however, most convenient in 

 the remainder of this investigation to introduce a change in the notation, and 

 to substitute for 



17, and , + v + rj, and w + (48), 



VOL. II. 7 



