96 DIFFUSION OF GASES 259 



just given. While the particle traverses this path its sphere 

 of action moves over a cylindrical path of equal length, the 

 section of which is equal to that of the sphere of action, 

 viz. TTcr 2 . In this volume, whose magnitude is 



there are 



molecules of the second kind, if N 2 denotes the number 

 of these molecules in unit volume; and the number of 

 the collisions that ensue is just the same. If we divide the 

 whole path fl, passed over in unit time by the molecule by 

 this number of collisions, we obtain the mean free path of a 

 particle of the first kind amid a crowd of particles of the 

 second kind for which we are looking, viz. 



In the same way the free path of a molecule of the second 

 kind in a medium consisting of molecules of the first kind is 



B' 2 = iytf^VW + IV).. 



In the particular case of the molecules being all of one 

 kind, these expressions turn into the value of the free path 

 already given in 68 on Maxwell's theory, viz. 



L = 



for this assumption gives 



This comparison of the general formula with the special 

 one already known shows the mechanical meaning of the 

 numerical factor \/2, which was not explained before. 



97. Molecular Free Path in a Gaseous Mixture 



By the help of these formulae it is now easy to write 

 down the value of the mean free path for the case first 

 mentioned in 96, where a molecule moves in a mixture of 

 molecules, some of which are of the same and some of a 

 different kind. 



s 2 



