79 VISCOSITY OF GASES 199 



with the molecular weight, and also with the number of 

 atoms which are joined together in the molecule. 



This supposition is also actually justified by the numbers 

 given as values of the free path for diatomic and triatomic 

 molecules ; for on the whole they decrease as the molecular 

 weight increases, and they are on the average smaller for 

 triatomic molecules than for diatomic. 



Yet in each of these two series of values of the free 

 path there occurs about the middle a slightly marked but 

 still plainly recognisable rise. The central section, therefore, 

 of the sphere of action cannot continuously increase as the 

 molecular weight increases, but at mean values of the mole- 

 cular weight the section must decrease when the weight 

 increases. This behaviour is explained the most simply if 

 we assume that the atoms in the molecule can be grouped 

 together differently, and we may indeed assume that they 

 draw the more closely together the heavier their masses. 

 The consequence of this would be that with increase of mass 

 the sphere of action is contracted, although the intensity of 

 the action will perhaps increase. 



After this discussion the relations between the numbers 

 that represent the collision-frequency are easily intelligible. 

 The formula for the collision-frequency is 



this contains a factor fl, which continuously decreases as the 

 molecular weight increases, while the other factor irs 2 for 

 the most part increases with the molecular weight. The 

 collision-frequency may therefore as well decrease as increase 

 with increase of the molecular weight. 



According to the formula a greater value of the collision- 

 frequency may result from two different causes which are, 

 to a certain extent, antagonistic. On the one hand this 

 number is increased by an increase in the speed of the 

 particles, on the other it rises in value with the extent of the 

 sphere of action, and therefore with the mass of the mole- 

 cule. Consequently those molecules collide the oftenest 

 which, firstly, move with the greatest rapidity, that is, the 

 lightest ; and those, secondly, which are in a certain measure 



