46 SCIENCE PROGRESS 



This method must be regarded as giving a lower limit to the 

 diameter of the molecule, since it has been assumed to be a 

 perfect conductor. If the distortion of the atomic structure in 

 the electrical field is not so great as to justify this assumption, 

 the diameters of the molecules must be larger than those given 

 above. 



The expressions for the viscosity, thermal conductivity, and 

 diffusion coefficient of a gas, which are deduced by the Kinetic 

 Theory, depend on the free path of the molecule, and so involve 

 the molecular radius or. The experimental data can be satis- 

 factorily explained by supposing, for purposes of mathematical 

 treatment, that the molecules are hard spheres, which rebound 

 on collision, and which exert an attractive influence when in 

 close proximity to each other. The average length of the free 

 path depends both on the size of the spheres, being inversely 

 proportional to the area tto-* of the target which each molecule 

 presents to other molecules, and on the attractive force between 

 the molecules, which tends to bring molecules into collision 

 which would otherwise pass each other. If the attraction were 

 non-existent, the viscosity t], free path X, and molecular radius o- 

 would be connected by the equations 



7? = 0-499 pX V ^ (2) 



(3) 



V2 N' 



TTO-' 



where p is the pressure of the gas, p its density. 



The attractive force between molecules increases the number 

 of collisions, and Sutherland has shown that its influence may 

 be allowed for by supposing the effective diameter of the mole- 

 cule to be increased by an amount which depends on the tem- 

 perature. The Sutherland correction may be stated in the form 



o-o = o- (i + 7) (4) 



where o-^ is the true radius of the spheres, a the apparent radius 

 at a temperature T. This may be interpreted physically as 

 meaning that, the higher the temperature and consequent 

 average velocity of the molecules, the less important is the part 

 played by the attractive force in increasing the number of 

 collisions. The constant S can be calculated from the variation 

 of viscosity with temperature. From equations (2), (3), and (4) 

 the value of tto-^* may be determined by measuring the viscosity 

 of a gas 7) and its temperature coefficient. 



An estimate of the molecular diameter may also be obtained 



