168 PHENOMENA DEPENDENT ON MOLECULAR PATHS 71 



this is increased in consequence of the attractive forces, 

 and, in accordance with the hypothesis just mentioned, may 

 be put as 



where k denotes a numerical factor. But now JmG 2 + E is. 

 the total amount of energy of a gaseous particle ; if then 

 we were to put Jc = 1, the formula 



would indicate that, owing to forces of i cohesion, the number 

 of encounters is increased in the ratio in which the whole 

 energy stands to the kinetic energy. But this would be an 

 assumption which, by its very simplicity, may convince us 

 of its truth, and there is scarcely any need of the mathe- 

 matical proof of it contained in Sutherland's calculation, 

 which is given in 35*. 



For the application of the theory-to the calculation of 

 observations we do not need the assumption k = 1, since 

 we can express the result of our considerations even more 

 simply without it. Considering that, according to 14 

 and 15, the magnitude G 2 is proportional to the absolute 

 temperature , while k, m, and J*do not depend upon it, 

 we see that the ratio in which the collision-frequency is 

 increased by the cohesion, viz. 



1 + ZkE/mG 2 : 1, 



may also be brought into the form 



1 + (7/6:1, 



where C denotes a constant depending on the nature of the 

 gas but not on its temperature. 



Hence the collision-frequency appears as a magnitude 



which depends in a twofold manner on the temperature; 



