gained during the Mixing of Gases. 317 



and P 2 is (since Q 2 and Q 2 log Q 2 vanish) 



W=(P, + P,)t, log?I±-^; .... (5) 



and hence the value of W for the interdiffusion of the quantities 

 v l and Vq is 



W=«, (P, + P.) log ^i±^i +i> 2 (P, + P,) log ?i± Ps 



or, since by hypothesis 



P 2 :P,=v 2 : v v 



<2 



W = (P, •+ P 2 ) f », log "j-t^ + „, log ^J 



(P, + P 2 )lo g ^T a (6) 



1 2 



This equation agrees with the rule enunciated at the beginning 



of this paper, inasmuch as (P^P^^log L 2 represents the 



v \ 

 work gained in the expansion of the first gas from volume v x to 



volume v 1 + v 2 , and (P l +Yc l )v 2 \og— represents the corre- 



sponding quantity for the second gas. 



The significance of equation (5) may perhaps be more fully 

 brought out by the following investigation of it. Whatever the 

 relative proportions of the two gases in the reservoir may be, it 

 will always be possible by going high enough to obtain a small 

 quantity of the lighter gas in any required degree of purity. 

 The removal of this at the top of the tube, its condensation to 

 the pressure in the reservoir, the fall to the level of the reservoir, 

 and the introduction into the reservoir would, on the whole, re- 

 quire no work to be done if this kind of gas had alone been pre- 

 sent. The only effect of the heavier gas is to render necessary 

 a greater condensation in the third operation ; and thus W is the 

 work that is required to condense the gas from the partial pres- 

 sure Pj to the total pressure in the reservoir Pj + P 2 , whence 

 equation (5) follows at once. If it is desired to isolate a small 

 quantity of the heavier gas, the tube must be taken downwards. 



It is to be observed that the work required to force a given 

 quantity of gas into a large reservoir containing gas at the same 

 pressure is independent of this pressure, since, according to 

 Boyle's law, v is diminished in the same proportion that p is 

 increased. 



The principle of dissipation may be employed to prove that 

 the pressure in a vertical column of mixed gases is greater 



