428 Mr. W. Sutherland on the 



collides with 1 and with 2 ; and we have now to obtain ex- 

 pressions for these momenta. I have not succeeded in doing 

 this from first principles, but by the study of Graham's ex- 

 perimental data have been led to a simple result allowing of 

 very simple interpretation, namely, that if in expression (9) 

 the coefficients a x and a 2 are multiplied respectively by 



{2m 2 /(mi + m 2 )}* and {2m 1 /(m 1 -\-m 2 )}*, 



all the experimental results can be represented by the formula 

 so derived, namely, 



77= = 77^ — ; r- ; 77^ — 7— , where B 2 is similar to 6 V 



and 

 £, = * J 



Kit) 



f 1 + / Wq+i(VT) \»\Y 2m 2 \ n+A/T | 



I \ V2 mf(l + 2 C 2 /T)/ i Kmi + mJ 1 + iC/Ty 



Thus the ratio i/t^/iAh is represented by { 2m 2 /(m 1 + m 2 )}*, 

 and we can easily trace the origin of the form of this ; for 

 the momentum exchanged in an average collision between an 

 m x and an m 2 with velocities a x and a 2 being 



2 («! + a 2 )ni 1 m 2 /S (m 1 + m 2 ) , 



and between an m x and an m l being 2m 1 a 1 /3, the ratio of the 

 two is {2m 2 /(m 1 + m 2 )}{(a 1 -\-a 2 )/2a 1 } ; and if this is equal to 

 {2m 2 /(m 1 + w 2 )}*, then (a 1 + a 3 )/2a| = {2w2 2 /(m 1 + m 2 )}^, but 

 if X V 2 2 and xVx 2 are the average squared relative velocities of 

 a 1 and a 2, and of a 1 and a 1, then 



7V?/rvV)= (*i 2 + *2 2 )/2ki 2 = K+™ 2 )/2m 2 , 



so that if («i + « 2 ) 2 and (2«i) 2 are regarded as quantities which 

 are being carried across the mixed gas with average velocities 

 proportional to X Y 2 and {Vi, then the final meaning of our 

 result is that they are carried at the same rate. 



We have now to show how closely (11) represents the 

 experimental facts, and with that view Graham's results are 

 reproduced in the following tables from the Phil. Trans. 1846, 

 or his collected Chemical and Physical papers, along with the 

 necessary data for use in equation (11) and the results given 

 by that equation. The necessary data are the viscosities of 

 the two pure gases which are measured by Graham at tem- 

 peratures near 15° C, and were given by him in terms of 

 that for oxygen at the same temperature as unity, also the 

 molecular masses referred to that of H 2 as 2, and finally the 



