THE DYNAMICAL THEORY OF GASES. 59 



and by the equation of continuity, 



dp, d , 



3? + sfc*>- ( 84 )> 



whence 1 



dt p 1 pJcA l p da? 



or if we put D = ,\ . 



p 



dt ' 



The solution of this equation is 



If the length of the tube is a, and if it is closed at both ends, 



- t TTX t irx 



** a "a -\ )' 



where C lt C v (7, are to be determined by the condition that when t = Q, p l =p, 

 from x = to x = -foci, and p 1 = from x = -faa to x = a. The general expression 

 for the case in which the first gas originally extends from x = to x = b, and 

 in which after a time t the gas from x = to x = c is collected, is 



, 6 2a f -*?t . irb . ire 1 - t '-^t . 2nb . 2irc } 



-*-=-+- \e ' sin sin +.e a " sm sin- +&C.V (89), 



p a ir*c { a a 2' aa j 



tn 



where ' is the proportion of the first gas to the whole in the portion from 

 x = Q to x = c. 



In Mr Graham's experiments, in which one-tenth of the tube was filled 

 with the first gas, and the proportion of the first gas in the tenth of the tube 

 at the other end ascertained after a time t, this proportion will be 



We find for a series of values of taken at equal intervals of time T, 



P 



m log, 10 a" 

 where 7 = . . . -^ . 



82 



