290 Free Path Phenomena 



then this equation becomes 



e = 2n- a =00 



I I [Q]advde 



[CH. xv 



(686). 



a=0 



Calculations of AQ. 



347. We begin by putting Q = u. The value of [Q], or of u u, is now 



given at once by equation (683), and we have, by equation (686) 







K 



e = 2?r a=oo 



r r i ft' ) 



M 2 (w' - u) cos 2 5- - V F 2 - (M' - uj sin 0' cos e [ adacfe 

 / / ( J 



e=0 a=0 



The integration with respect to e can be effected at once, resulting in the 

 disappearance of the last term, and leaving 



A 12 u = 



_ 



/ K r 



., A / - I (u! u) 



- V TO! + ra 2 J 



ft' 



cos 2 -ado. 

 2 



cos 2 ado.. 



a = 



Maxwell writes 



(687). 



Tables for the calculation of A^ by quadrature are given in Maxwell's 

 original paper. He finds for its value 



A, = 2-6595 ............. -. ................ (688) 



and we accordingly have _ 



(689). 



To calculate A u , we notice that u ' and u now become identical, so that 

 A u w = 0. This could have been foreseen : the value of u averaged through a 

 system of equal molecules cannot be changed by collisions with one another. 



Thus the expression on the right-hand of equation (689) contains the 

 whole value of Aw, so that 



/ ~K 

 Aw = i^i/sm, A / - -A 1 (u 'u ) .................. (690). 



V 7/lj ~r TTZo 



