180 PHENOMENA DEPENDENT ON MOLECULAR PATHS 76 



heat-motions of the molecules ; consequently, as the formula 

 shows, it must be proportional to the speed G. It, further, 

 is carried out by the molecules themselves, and therefore 

 will be the greater the more there are of them ; hence the 

 formula for the friction contains the density of the gas as 

 a second factor. The transfer can only take place between 

 layers whose distance apart can be traversed by a molecule ; 

 the friction must therefore be the greater the wider the 

 range of effective layers, and it must therefore, in the third 

 place, be proportional to the molecular free path. The 

 fourth factor, the coefficient J, is explained in the same way 

 as in the exactly similar formula for the pressure, namely, 

 by the circumstance that only a third part of the molecules 

 which are moving in all directions, and therefore sym- 

 metrically with respect to the three dimensions of space, 

 come into account in regard to transference in the direction 

 of one of these three dimensions. 



This explanation of the formula we have found contains 

 at the same time a reason for this remarkable law. Of the 

 factors in the formula there are only two, p and L, which 

 are variable with the compression or rarefaction of the gas, 

 and they vary so that, if the density p increases, the free 

 path L of the molecules, which are hindered in their motion 

 by the constriction of the space containing them, becomes 

 smaller and vice versa. In this way it is possible that the 

 product of these two quantities, of which one increases 

 while the other diminishes, may always keep the same 

 value ; and therefore after this consideration the paradoxical 

 law of Maxwell will have lost much of its improbability. 



The coefficient of viscosity is not, however, independent 

 of the temperature, as it is of the pressure. Of its factors 

 only G and L can be variable with the temperature. With 

 respect to the former we know from experiments on the 

 pressure of gases that it is proportional to the square root 

 of the absolute temperature, or that it increases with the 

 temperature $ measured on the usual scale in the ratio 

 \/(l 4- a$) : 1, where a denotes the thermal coefficient of expan- 

 sion of the gas. As to the free path L, the theory leaves it un- 

 decided whether it alters with the temperature or not. The 



