426 Mr. W. Sutherland on the 



shown (Phil. Mag., Dec. 1893) that the effect of molecular 

 attraction in the viscosities of gases and allied phenomena is 

 important, we must take account of it here. It was also 

 shown (Phil. Mag., Dec. 1893, and July 1894) that molecular 

 attraction can be taken account of by replacing (a x + a 2 ) 2 and 

 (% + a x ) 2 in such equations as (3) and (4) by 



(a 1 + a 2 ) 2 (l + 1 C 2 /T) and (a 1 + a i y(l + 1 C 1 /T), 

 where X C 2 depends only on the mutual potential energy of a 1 

 and a 2 in contact, and xCx on the potential energy of a 1 and 

 a 1, and T is the absolute temperature. On introducing the 

 factors 1+iC/T, H-A/T, and 1 + 2 C 2 /T into equations (3) 

 and (4) and eliminating as before, we obtain the equations 



7i=z - - — ; \-- — — , where a x is similar to ««, 



l-f«l™2/ n l l + ^2 n l/ n 2 



and >■ (9) 



- 1 f 1 1 /' WO- + iQi /T) \* \ 2 / ™i + ™ 2 Y 1 + iC 2 /T | 

 " l ±\ ~ Jr \r ]2 m 1 $(l + 2 C 2 /f)J J V 2m s /1+^/TJ 



to replace (8) when molecular attraction is taken account of 

 If #! and a 2 were each unity this equation would reduce to 

 (n 1 + w 2 ) ? ? = n i , 7i + ?V7 2 , which Graham found empirically to 

 be true within the limits of experimental error for mixtures 

 of N 2 and 2 , CO and 2 , and CH 4 and 2 , but not for mix- 

 tures containing H 2 . Thus we see that the simplicity of 

 Graham's result for these pairs of gases is the result of what 

 may be called an accidental simplification of the true relation, 

 brought about by a certain accidental approximate relation 

 between certain physical constants of the two gases of each 

 pair. 



Let us write the last formula in the form 



V= l + 1 v,/ 1 v 1 + 1 + Jj 2 v 2 '' • • • • ( 10 > 



and we can see that, as regards the general case of any two 

 gases, its defect consists in making each of the x v 2 encounters 

 just as effective in producing viscosity as each of the x v x or 2 v 2 . 

 According to the ordinary mode of presenting the theory of 

 viscosity of a single gas, which has already been sketched, it 

 is not easy to see exactly how serious the defect may be or 

 how it is to be remedied. But there is another method of 

 regarding viscosity according to which we get more at the 

 heart of the process. 



In a single gas the average distance normal to the solid 

 planes travelled by a molecule is \/2, so that the molecules 

 which collide in any thin layer may be considered as coming 



