Constant in the Kinetic Theory of Gases 453 



= V2^3COsecx, 

 in the limit e -^ 0. Approximately 



Aa"(7) = -877a2 0(a)/F [ (2^2_i)^3^^ 



.'0 



= - 2a2 0((T)/37, 

 whence Ai2 = - ^^^ |-^ 



and it will be seen that this leads to *S = 0. The approximation 

 consists only in the neglect of higher terms in the expansion of 

 sin^ 2 (x'— 4)- These terms will not disappear. 



§ 9. The Second Order Terms. It will be sufficiently typical to 

 consider only the inverse power law. These terms arise in five ways. 



I. From the second term in the expansion of «/» {a). 



II. From the first term in the expansion of i/r (a) ; and the second 



term in the expansion OM t- ) 



III. From the first term in if} (a) arising from the approximate 

 value of the upper hmit p^ . This is conveniently dealt with simul- 

 taneously with the last. 



IV. From the j/f^ term in the expansion of sin^ '^{x— "A)' 



V. From the deflection of molecules, which do not actually 

 suffer collision. 



These and these only lead to terms of type l/T^ in the denomi- 

 nator of the expression for /x. I have verified by actual calculation 

 that taken together they give a term of the type K {</> {a)jRT}^, 

 where K is a positive number. 



§ 10. Diffusion of a Mixture of Two Gases. We have to calculate* 



p„ 



Q.'{V) = inV sin^ xpdP' 



and sin^ x = sin^ x'— -^ sin x cos x, so that 



AQ.' ( F) - SttF ]" iff sin x cos x V ^h- 



.'o 



For the inverse power law we find 



AQ'(F) = -87rA;^„/F<,'«-3, 



* fi'(F) is Prof. Chapman's ^\i{V^). 



