no PETER GUTHRIE TAIT 



Tait was how to define the Mean Free Path, in regard to which he differed 

 from Maxwell. He also laid stress on the principle that throughout the 

 investigation each step of the process of averaging should not be performed 

 before the expressions were ripe for it. Some of his views are put very 

 succinctly in a letter to Thomson in 1888, just about the time he was printing 

 the third paper of the series. We may regard it as containing Tail's last 



statement on the question. 



38 GEORGE SQUARE, 



EDINBURGH, 27/2/88. 

 O. T. 



Ponder every word of this and report. , 



Since there is absolute social equality in the community called a simple gas, 

 the average behaviour of any one particle during 3.IO 20 seconds is the same as that 

 of 3.IO 20 particles (the content of a cubic inch) for one second. 



Hence if be the chance that the speed is from v to v + dv, and if p v be then 

 the mean free path; and if C be the number of collisions in 3.IO 20 seconds, we have 



n v C 



as the number of collisions in which the speed is v to v + dv, and the path /. 

 Thus the whole space travelled over in 3.10" seconds (io 13 years nearly) is 



C2 (/). 



This consists of C separate pieces. The average of these, i.e. the Mean Free 

 Path, is therefore 



2 (a. A) .......................................... (0- 



Also the interval between two collisions, when the speed is v, is p v jv. Hence 



the whole time spent on C collisions is C ( ) . This is 3.10" seconds. Thus 

 the average number of collisions per particle per second is 



Both of these results differ from those now universally accepted. Instead of 

 (i) they, Maxwell, Meyer, Boltzmann etc., give 



2 ( v) 



* A) 



and instead of (2) 



Both are, I think, obviously wrong. 



Yrs. 



