CHAPTER XI. 



FREE PATH PHENOMENA. 



CALCULATION OF THE FREE PATH. 



278. IN the problems which have so far been discussed, it has hardly 

 been necessary to consider the dynamics of individual collisions at all. We 

 now approach a class of problems of which the treatment must be made to 

 depend mainly upon the occurrences at individual collisions. It is obvious 

 that we cannot hope to get results of the same degree of accuracy as before, 

 for the results will depend upon the details of occurrences at collisions, and 

 of these we know almost nothing. The present chapter deals with some 

 problems connected with collisions and free paths in a gas, the molecules 

 being assumed for this purpose to be elastic spheres. 



Length of mean Free Path. 



279. In 30 we gave a calculation of the mean free path in a gas. We 

 shall now give a more detailed investigation applicable to the free paths of 

 molecules in a mixture of gases, the molecules of the different gases being of 

 different sizes, and shall at the same time examine the correlation between 

 the velocity of a molecule and its probable free path. ~ 



We shall suppose the constants of the molecules of different types to be 

 distinguished by suffixes, those of the first type having a suffix unity 

 (vi, m ly o-j ...), and so on. 



We shall also require a system of symbols to denote the distance apart 

 at collisions of the centres of two molecules of different kinds. Let these be 

 $11, $12 > $23 > etc., Spg being the distance of the centres of two molecules of 

 types p, q when in collision. Obviously, then, 



$12 = i ("i + "2), $n = <TI - 



280. Consider a molecule of the first kind, having a velocity c of which 

 the components are u, v, w. The chance of collision per unit time with a 

 molecule of the second kind having a specified velocity is equal to the 



