234 Free Path Phenomena [en. xi 



Adding this to expression (544), we obtain as the value of expression (543), 



X/7T 



"4" 



r + 



of which the value, after simplification, is found to be 



VTT m g 2 I 



xisy, 1 





This is the value of the integral which occurs in expression (542). The 

 whole expression is therefore equal to 



m 1 m 



(545). 



This is the mean chance of collision per unit time for a single molecule of 

 the first kind, and every collision terminates a free path of this molecule. 

 The total number of free paths described by all molecules of the first kind 

 per unit time per unit volume is therefore 



(546) - 



This agrees with expression (47), when there is only one kind of gas. The 

 general expression (546) also could have been arrived at by the shorter 

 method of 30. 



The distance described per unit time by the v l molecules of the first kind 

 in a unit volume is, as in 30, equal to 



Hence the mean free path, X x , of all molecules of the first kind is 



(547). 



These formulae are due to Maxwell. 



Dependence of Free Path on Velocity. 



285. The way in which X c depends on the value of c is of some interest. 

 The formula expressing \ c as a function of c is, however, too complex to 

 convey much definite meaning to the mind, and we are therefore compelled 

 to fall back on numerical values. The following table, which is taken from 



