32* MOLECULAR FREE PATHS . 421 



which can be put into another form 

 B = 



I arrived at this last expression in 1866 in a Latin disserta- 

 tion, 1 in which, starting with Clausius' formula, I deduced 

 Maxwell's. From this value of B I calculated, by integration, 

 the value of the mean collision-frequency 



r = 47r-i 



and, by developing this in a series, obtained the same value 



which we have already found in a simple way. 



The magnitude B denotes the number of collisions which a- 

 particle moving with speed w experiences in unit time from an 

 assemblage of N other particles whose mean speed is li. Closely 

 allied to this expression is that of another magnitude 



which we deduced in 30* ; this represents the number of 

 collisions that occur in unit time between a particle of a group 

 whose mean speed is ^ and the N 2 particles of another group 

 with mean speed Ii 2 - The chief difference between the two 

 expressions is that w denotes a speed of arbitrary amount, while 

 Q! represents a mean value ; but otherwise they are so similar 

 that we might expect the formula 



which we have formed from that last given, to represent the 

 number B with at least approximate accuracy. 



This expectation is fairly well justified by the comparison of a 

 few values of the exact ratio 



with those of the approximate expression 



1 Dissertatio de Gasorum Theoria, Vratislavise 1866. Also in the first 

 edition of this book, 1877, p. 294. 



