448 Mr James, The Theoretical Value of Sutherland's \ 



The correct result is not so simple as this, and cannot be ex- 

 pressed so generally. 



In the same way, the coefficient of diffusion for a mixture of 

 two gases satisfies a relation 



Z)i,x T^/(l + S,,IT), 

 where if 0-12 denotes the mean of the two molecular diameters, 



where A is a number depending on the law of force assumed. Prof. 

 Chapman gives A = | for all laws of force. 



Prof, Chapman informs me that Enskog* has already pointed 

 out the necessity for the corrections here referred to, and that his 

 results agree with those found in § 6. The results of the other 

 sections have not, I understand, been given by him. ,1 



§ 2. A note on the a'p'proximations emfloyed. It is necessary to 

 regard the absolute temperature T as large, since the theory gives 

 for the denominators of /x and D^^ series in descending powers of T. 

 We shall also neglect squares and higher powers of </> (o-). Actually 

 it will be seen that all terms involving ^ (ct) to any power are 

 multiphed by 1/T to the same power. Thus the assumption is 

 really that ^ (o-)/T is negligible in higher powers than the first. 



As regards the terms involving {(f){a)/T}^ it will be found that 

 Prof. Chapman's statement, that these are positive in each case, 

 is not affected. 



§3. Statement of the Problem,. The first step is the determination 

 of the deflection of a typical molecule, relative to a selected molecule 

 which is conveniently supposed reduced to rest. In the diffusion 

 problem these molecules will be of opposite kinds. In the viscosity 

 case we will for simplicity consider a single gas only. 



To the order of approximation explained above it is only neces- 

 sary to consider molecules that actually suffer impact with the 

 selected molecule. Let A and B be the centres of the respective 

 molecules at impact, so that in the general case: I 



AB = (T^2 = i {<^1 + 0'2)- 



Let TN, NT' be the asymptotes of the initial and final relative 

 paths; QB, BQ' the directions of motion immediately before and 

 immediately after impact. Let V be the relative velocity at a great 

 distance, f the perpendicular onto the asymptotes. The molecule B 

 is typified by the direction and magnitude of V, by 2^, and by an 

 azimuthal angle e, determining the direction of f, in a plane at 

 right angles to V. The true deflection required is 



2x=T,NT', 



* Inaugural Dissertation, UiDpsala, 1917. 



