Mr. J. C. Maxwell on the Dynamical Theory of Gases. 189 



molecules, as are all the other results relating to the final distri- 

 bution of velocities. We shall find that it leads to the law of 

 gases known as that of Equivalent Volumes. 



Variation of Functions of the Velocity due to encounters between 

 the Molecules. 



"We may now proceed to write down the values of -~— m the 



different cases. We shall indicate the mean value of any quantity 

 for all the molecules of one kind by placing a bar over the sym- 

 bol which represents that quantity for any particular molecule ; 

 but in expressions where all such quantities are to be taken at 

 their mean values, we shall, for convenience, omit the bar. We 

 shall use the symbols B 1 and 8 2 to indicate the effect produced by 

 molecules of the first kind and second kind respectively, and S 3 

 to indicate the effect of external forces. We shall also confine 

 ourselves to the case in which n=5, since it is not only free from 

 mathematical difficulty, but is the only case which is consistent 

 with the laws of viscosity of gases. 



In this case V disappears, and we have for the effect of the 

 second system or the first, 



where the functions of J, rj, ? in f (Q!—Q)d(p must be put 

 equal to their mean values for all the molecules, and A 1 or A 2 

 must be put for A according as sin 2 6 or sin 2 20 occurs in the 

 expressions in equations (4), (5), (6), (7). We thus obtain: — 



W ¥ 1 = ( M 1 M 2 (M, + M 2 ) )X M A(^-g 1 ) ; • • (36) 

 w St -\M l M !l (M 1 + M il )/ M,+ 



M„ 



{SA^-^M^+M^+AAfe-^ + f,-^ ■' ' 



N 3 M 2 x 



St ~ \M 1 M,(M 1 + M 2 ) / M, + M 2 



f 



(38) 



