71 MOLECULAK FKEE PATHS 167 



not remain without effect on the molecular free path ; for 

 by such forces as cause approach the probability of a 

 collision is increased, and the mean probable value of the 

 molecular free path is therefore diminished. 



The process by which Sutherland calculates the 

 amount of diminution of the free path is given in 35* ; 

 I prefer here another way of attaining this object without 

 much calculation. 



Whether the attractions will bring about an encounter of 

 two particles that pass close by each other, or not, depends 

 on the amount of the two kinds of energy, one of which 

 furthers the encounter, while the other hinders it. While 

 the kinetic energy which the particles possess by reason of 

 their speed, as they rush close by each other, opposes a 

 deviation from the rectilinear path, and, therefore, also the 

 probability of an encounter, the potential energy of the 

 attractive forces, on the contrary, has the effect of promoting 

 the encounter. The number of collisions will therefore be 

 the more increased by the molecular energy the greater the 

 amount E of potential energy which comes into activity on 

 the approach of one particle from an infinite distance to 

 entrance into the sphere of action of another; but this 

 increase will be so much the smaller the greater the kinetic 

 energy of the particles. Hence we assume that the number 

 of encounters which a particle undergoes in unit time, by 

 reason of the attractive forces, is increased by a magnitude 

 which is proportional to the given potential energy E y 

 and, on the contrary, is inversely proportional to the mean 

 kinetic energy of the gaseous molecules, and thus inversely 

 proportional to the magnitude 



in which m is the molecular weight of the gas and G 

 represents Clausius' mean value of the molecular speed 

 ( 27). 



According to a formula of 70, the number of encounters 

 in unit time without reference to the molecular attraction is 



