Mr. J. C. Maxwell on the Dynamical Theory of Gases. 191 



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 coordinate directions 

 be X, Y, Z. Then we have by dynamics for the variations of 

 f, £ 2 , and fV 2 due to this cause : — 



(«) §f = X; (44) 



(0)%^=3fXj . . . (45) 



^i?=,X + fY; (46) 



(y) ^P = 2^X+^Y-+?Z)+XV 2 ; . . (47) 



where 8 3 refers to variations due to the action of external forces. 



On the Total rate of change of the different functions of the velo- 

 city of the molecules of the first system arising from their encoun- 

 ters with molecules of [both systems and from the action of ex- 

 ternal forces. 



To find the total rate of change arising from these causes, we 

 must add 



&> it' and It' 



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 



f, 7), and f, u + %, v + 7], 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 



MA = Pl , M 2 N 2 =p 2 , .... (49) 



where p x and p 2 are the densities of the two systems of molecules 

 — that is, the mass in unit of volume. We shall also write 



KmfJ^^' (m.m^+m,)/^' and \m*) **** (50) 



