FOUNDATIONS OF THE KINETIC THEORY OF GASES. 75 



Clerk-Maxwell, however, takes it as 



*2,(n v v) 



I.(n v vjp v ) ' 



i.e., the quotient of the average speed by the average number of collisions per 

 particle per second. But those who adopt this divergence from the ordinary 

 usage must, I think, face the question " Why not deviate in a different direction, 

 and define the mean path as the product of the average speed into the average 

 time of describing a free path ? " This would give the expression 



I.(n v v) . l,(n v p v /v) . 



The latter factor involves a definite integral which differs from that above 

 solely by the factor JJifx in the numerator, so that its numerical determination 

 is easy from the calculations already made. It appears thus that the reducing 

 factor would be about 



~X 0-650, =0734 nearly; 



i.e., considerably more in excess of the above value than is that of Clerk- 

 Maxwell. Until this comparatively grave point is settled, it would be idle to 

 discuss the small effect, on the length of the mean free path, of the diameters 

 of the impinging spheres.] 



III. Number of Collisions per Particle per Second. 



12. Here again we may have a diversity of definitions, leading of course 

 to different numerical results. Thus, with the notation of § 11, we may give 

 the mean number of collisions per particle per second as 



This is the definition given by Clerk-Maxwell and adopted by Meyer ; and 

 here the usual definition of a " mean " is employed. The numerical value, by 

 what precedes, is 



Meyer evaluates this by expanding in an infinite series, integrating, and sum- 

 ming. But this circuitous process is unnecessary ; for it is obvious that the 

 two parts of the expression must, from their meaning, be equal ; while the 

 second part is integrable directly. 



13. On account of its bearing (though somewhat indirectly) upon the treat- 



