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



tical tube had its lower tenth part filled with a heavy gas, and 

 the remaining nine-tenths with a lighter gas. After the lapse 

 of a known time the upper tenth part of the tube was shut off, 

 and the gas in it analyzed, so as to determine the quantity of the 

 heavier gas which had ascended into the upper tenth of the 

 tube during the given time. 



In this case we have u=-0, . (82) 



Ptf -- &ygi l»i . (83) 



and, by the equation of continuity, 



$ + 5<M>-* W 



whence 



dt~~ PlPi kA lP dx*' { } 



or, if we put D = ,. — > 

 PiP<Mi P 



3H>& ^ 



The solution of this equation is 



p^C^Cf**™ cos {rue + a) + &c. . (87) 

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



jp-C^C^e-^ cos— +C 3e - 4 ^cos2— +&c, (88) 

 a a 



where C v C 2 , C 3 are to be determined by the condition that 

 when t = 0, p x =p, from x = to %=-i- u a, andjo^Ofrom %= 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 



b . 2a f -252* . irb 



-v, 



{ 



-\ 



P, D t Za \ _!L^t . 7TD . 7TC 



— — - + —et < e « 2 Bin — sin — 



p a ir^c [_ a a I 



, 1 -4^* • 27Tb . 2tH? ■ "I >' ' ^ ) 



+ ^1 e a 2 Bin sin H &c. y , 



2^ a a J J 



where — is the proportion of the first gas to the whole in the 



portion from x — to x — c. 



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



