160 PHENOMENA DEPENDENT ON MOLECULAR PATHS 66 



upon it as almost infinitely great. If Q were actually in- 

 finitely great, we should have 



(1 _ Q-i)Q = e -i = 1/2-718 . . . = 0-36788, 



where e is the base of natural logarithms. 



Therefore the number of particles which traverse a path 

 at least q times greater than that passed over in the mean 

 is, with this assumption, 



~ lQq = Me~ q . 



According to this formula we have calculated the follow- 

 ing table. Out of every 100 particles 



without collision. 



The table shows that the mean free path is considerably 

 exceeded extremely seldom. The only play of chance, 

 therefore, is to set up in this case too, as well as in that of 

 the distribution of speeds, a uniformity that is maintained 

 with great exactness. 



67. Free Path if all the Molecules have Equal 



Speed 



The value we have found for the mean free path needs 

 still a correction, which the considerations of the last para- 

 graph do not, however, touch. 



The value of the mean free path found in 65, viz. 



L = X 3 / 2 , 



holds only for a simple hypothetical case described fully in 

 63 ; it was supposed that only the one particle whose free 



