in the Kinetic Theory of Gases. 317 



powers of V and E in the differentiation, we should assume 

 <f>(kco 2 ) to consist of even powers of co\/k. 



As the result when all the integrations are effected, -j- 



will be a function of k of dimension KAj J . And ^— of 

 dimensions %(&)• 



So we should obtain 



(%W) 2 = %W or X (*)= •£. 



v k 



But the excess of momentum carried in the positive 

 direction through unit area of the plane of xz y on which the 

 viscosity depends, varies as 



m 



dcoe- k " 2 co 4 X {k)<l>(kG>z) ; 



that is varies as — -=, or as the square root of the absolute 

 vk 



temperature. 



24. The above results are obtained on the hypothesis that 



7T5 2 is independent of p or E, and therefore only on the 



hypothesis that the molecules may be treated as elastic 



spheres. On any other hypothesis its 2 is a function of E, and 



as such will affect the integration according to E, and the 



degree in h or k which -r- assumes as the result of that inte- 

 gration. For instance, if the molecules be centres of force 

 repelling one another with a force varying as -^,7rs 20c -. 

 In this case, in dealing with diffusion -7— will be proportional 



to (y(A)) 2 ; instead of - - as in the case of elastic spheres, 



v h 1 



and the rate of diffusion would vary as j> that is as the 



absolute temperature, instead of as the square root of the abso- 

 lute temperature. 



If the experiments from which it appeared that the rate of 

 diffusion varies as the square root of the temperature can be 

 relied on as giving exact, and not merely approximate, 

 results, they afford ground for the inference that molecules 

 of gases may, as regards their mutual encounters, be treated 

 as elastic spheres. 



Phil. Mag. S. 5. Yol. 30. No. 185. Oct. 1890. Z 



