﻿Relative Dimensions of Molecules. 553 



where N is the number of molecules per unit volume and a 

 is the radius of the molecule, gives the connexion between 

 the mean free path and the molecular radius. 



As was pointed out by Sutherland*, however, the calcu- 

 lation of cr by means of these two equations leads to incon- 

 sistencies, because the viscosity of a gas is not, in fact, 

 proportional to the square root of the absolute temperature. 

 Hence the value of a so estimated becomes smaller and 

 smaller as the temperature corresponding to the viscosity 

 datum increases. 



The modification in the theory introduced by Sutherland 

 was to take into account the forces of attraction which the 

 gaseous molecules exert upon one another ; and he showed 

 that this involved that the mean free path was smaller than 



c 



that estimated for forceless molecules in the ratio 1 : 1+ vp 



where is a constant and T is the absolute temperature. 



Upon this basis Sutherland showed that the viscosity of a 



gas, instead of being proportional to the square root of the 



T* 

 absolute temperature, was proportional to p. This 



modified theory has been found to correspond with expe- 

 riment very well, at any rate much more accurately than 

 the simple theory. 



In applying these results to the calculation of molecular 

 dimensions we have, according to Sutherland, to diminish 

 the molecular radius as estimated from the simple theory in 



the proportion (l + =, \ : 1, in order to obtain the true radius, 



for the molecular attractions make the molecules behave 

 from the point of view of frequency of collision as though 

 they were larger than they are in reality. 



For this purpose, therefore, we require to know not merely 

 the viscosity of a gas at one temperature, but also the variation 

 with temperature, so that the constant C can be found. 



The author has recently made such measurements for a 

 considerable number of gases, and the molecular dimensions 

 deduced therefrom exhibit some points of interest. The gases 

 in question are three members of the group of inert gases, 

 viz. argon, krypton, and xenon, and the three corresponding 

 members of the halogen group, viz. chlorine, bromine, and 



* Sutherland, Phil. Mag. vol. xxxvi. p. 507 (1803). 



