402 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF OASES. 



Since the capacity of the tube is small compared with that of the vessels, 

 we may consider -3- constant through the whole length of the tube. We may 



then solve the differential equation in p and x ; and then making p =p, when 

 x = 0, ahd p=p\ when x = c, and substituting for p t and p\ their values in 

 terms of y, we shall have a differential equation in y and t, which being solved, 

 will give the amount of gas diffused in a given time. 



The solution of these equations would be difficult unless we assume rela- 

 tions among the quantities A, B, C, D, which are not yet sufficiently estab- 

 lished in the case of gases of different density. Let us suppose that in a 

 particular case the two gases have the same density, and that the four quan- 

 tities A, B, C, D are all equal. 



The volume diffused, owing to the motion of agitation of the particles, is 



then 



.? dp , 



-*pdx vl > 



and that due to the motion of translation, or the interpenetration of the two 



gases in opposite streams, is 



s dp kl 

 ~Pdxv' 



The values of v are distributed according to the law of Prop. IV., so that 



the mean value of v is - , and that of is -p-- , that of k being ia*. The 



Jir V Jva 



diffusions due to these two causes are therefore in the ratio of 2 to 3, and 

 their sum is 



dy_ 4 /2k si dp . } 



dt~ s/s/TPdx" 

 If we suppose -j- constant throughout the tube, or, in other words, if we 



Ct7) 



regard the motion as steady for a short time, then -/ will be constant and 

 equal to ' '; or substituting from (48), 



whence - y.-i-e-*') ........................... (56). 



