﻿8 Mr. William Sutherland on the 



Wien Ixii. 1871). The theoretical coefficient also varies as 

 the 3/2 power of the absolute temperature, but it has been 

 shown by Loschmidt and Obermayer (Sitz. Akad. Wien, lxi., 

 Ixii., lxxv., lxxxi., Ixxxv., lxxxvii., xcvi.), in experiments 

 on several pairs of gases, that their coefficients of diffusion 

 vary more rapidly with temperature than according to the 

 theoretical law. They found empirically that the coefficients 

 vary as powers of the temperature, ranging from 1*75 to 2 

 instead of the 1*5 of the theory of forceless molecules. Here 

 is where the effect of molecular force comes in, just as in the 

 case of viscosity. 



In connexion with viscosity it was shown that with like 

 molecules the effect of molecular force on the number of 

 collisions of spherical molecules of radius a is to make it the 

 same as for forceless molecules in which (2a) 2 is increased to 

 (2a) 2 {l + 2m/(l/2a)/V 2 }, where m 2 f(l/'2a) is_ the potential 

 energy of two molecules in contact, and V 2 is the mean 

 square of the relative velocity. So for unlike molecules of 

 masses ra x and m 2 and radii a x and a 2 , with potential energy 

 m^m^f \l/a 1 -\-a 2 ) at contact and mean relative squared velocity 

 V 2 , the effect of molecular force on the number of collisions 

 is to make it the same as for a pair of forceless spheres with 

 (a x + a 2 y enlarged in the ratio 



Now v 2 and v 2 q denoting the mean squared velocities of m x 

 and m 2y 



and k x 2 + k 2 2 = k*(1 + k 2 2 /k^) = y^ 2 (1 + mi/m 2 ) , 



so that the ratio becomes 



1 + ??z 1 ??i 2 /(l/a 1 -f- a 2 )/§ m x K x 2 , 



or 1 + m 1 wi 2 /( 1/ai + a 2 ) /m^ 2 , 



which may be written 1 + iC 2 /T, 



and then the expression for the diffusion-coefficient of attracting 

 molecules derived from (6) for forceless molecules is 



V a p U + nhKaL + aJXi+fiJT) * * • (7) 



As the diffusion-coefficients are all referred to a pressure of 

 one atmosphere, we have for the ratio of D 2 at T 2 to Dj at T 1; 



D,_ /TA H + A/T! . 



D 1 ~ \tJ i+a/t 2 w 



