37 



MOLECULAR FREE PATHS 



429 



and these I subjoin in the following table 1 : 



The first, third, and fourth columns contain the ratios of the 

 actual speed o> to the mean speed i, of the probable collision- 

 frequency B to its mean value F, and of the probable free path I 

 to the mean free path L. The values of these ratios all increase 

 together, as is shown by the curves on p. 430, which are 

 plotted from the given numbers, the first representing the collision- 

 frequencies, the second the free paths, as functions of the speed. 



It is worth while to notice that the equalities w = O, B = F, 

 and I = L do not occur simultaneously ; but the mean collision- 

 frequency is that of a particle which moves with a speed some- 

 what greater than the mean speed, and the mean free path is 

 attained by a particle whose speed is rather less than the mean 

 speed. 



38*. Different Mean Values of the Free Path. 



In addition to the mean value of the molecular free path 

 already calculated in 33*, we can, by a slightly different calcula- 

 tion founded on these last considerations, deduce another mean 

 value which is important for the development of our theory. 



1 [Here fcwH 2 = 4/ir = 1-27324. TB.]. 



