35* MOLECULAR FREE PATHS 427 



If these gases had no cohesion, then F(p) would be zero for 

 every value of p, and the condition for the occurrence of a collision 

 would be 6 2 <s 2 , as is obvious from the meaning of b, viz. the 

 distance of the particle encountered from the path of the striking 

 particle. The influence of the forces of cohesion on the frequency 

 of the collisions and on the length of the free path therefore con- 

 sists in the replacement in all calculations of the actual section ?rs 2 

 of the sphere of action by a larger area 



The magnitude by which the section has to be augmented depends 

 on the temperature, and is, indeed, inversely proportional to the 

 absolute temperature, as is shown by the occurrence in the deno- 

 minator of the square of the molecular velocity r. This ratio was 

 given in 71, and its value was estimated in 85 for the explana- 

 tion of the observations on internal friction. 1 



In the next following investigations we shall for simplicity 

 leave out of account both this correction and that given in 34*. 



36*. Free Path in Mixed Gases 



In the case of a mixture of gases composed of molecules of 

 two different kinds, we find the free path L\ of a particle of the 

 first kind and the free path L 2 of a particle of the second kind 

 from the formulae of 30*, viz. 



taking account of the meaning of the magnitudes 1 we may write 

 these 



+ inrWj-N/fL + k 2 m 2 /k l m l )}L. 2 = 1, 

 and, in case the temperature of both components of the mixture is 



the same, 



These equations were first established by Maxwell. 2 



1 Compare the account of the observations on the friction of vapours in 87. 



2 Phil Mag. [4] xix. p. 29, 1860 ; Scientific Papers, i. p. 388. 



