ILLUSTRATIONS OP THE DYNAMICAL THEORY OF GASES. 401 



Let us suppose the volumes of the two vessels to be a and b, and the 

 length of the tube between them c, and its trans- 

 verse section s. Let be filled with the first gas, 

 and b with the second at the commencement of 

 the experiment, and let the pressure throughout 

 the apparatus be P. 



Let a volume y of the first gas pass from a to b, and a volume y' of the 

 second pass from b to a ; then if p l and j>, represent the pressures in a due 

 to the first and second kinds of gas, and p\ and p\ the same in the vessel b, 



_- p - P n '~.p y> - 



Pl ~ ~a ' Pt ~ a ' Pl ~b ' 2 '~ b 

 Since there is still equilibrium, 



which gives y = y and p l +p t = P =p\ +p'. } ..................... (49). 



The rate of diffusion will be + -^ for the one gas, and -~- for the other, 

 measured in volume of gas at pressure P. 



Now the rate of diffusion of the first gas will be 



and that of the second, 



JL A 



_dy_ * v 'dx 



We have also the equation, derived from Props. XVI. and XVII., 



wMW-V^O ..... (52). 



From these three equations we can eliminate V l and V,, and find -:- in 

 terms of p and -~- , so that we may write 



- 



at \ I ' dx 



VOL. I. 51 



