8 

 the passing molecules and from the (not central) colliding molecules) : 



1 — 6M 



a^ =a, + (a,), =:to X -7^ -j-jr» .... (12) 



According to the above this part comprises the almost totality of 



the angles of incidence, from 90° to near to 0^ at hi(//i temperatures ; and 



onlj a very small part, from 90° to near to 90° at loiv temperatures; i. e. 



in the limiting cases n^ 1 and n ^ 0. But also in intermediate cases 



this continues to hold, because at high temperatures /^' always lies in 



cr a^ — s" 



the neigbourhood of ^X — r- = 1, and at low temperatures 



a' 

 always in the neighbourhood of X = 0. 



a"^ — s^ 



Hence the region left for the part of a that is dependent on the 

 temperature, is the greater as the temperature becomes smaller. 



1—n 



Now the quantity a^ in (12) lies between to X i^' = 



v{l — n^) 



1 1 



= <^X ,., , ■ i-i' = w X ^i' ïovn — 1 , and w X — X i^' = «^ for 



§ XVIII. Calculation of (a,),. 



We finally come to the calculation of the part that is dependent 



on the temperature, and corresponds with the more central collisions 



of the second stage of I^. We now have for the integration with 



respect to /■ (cf ^ XVII) : 





dr 



r\/p^r^-\-a'{cos' ff—p^y 



in which cos^ — />^ remains positive between the limits (9 = 0' and 

 & = Bg cos p. The integral yields : 



w 



hen cos is put again ^ x, and cos 0^ = x^, ,i;„^ being = 



= //(l — "^j (Cf. § XVI). Hence we have 



