﻿296 Prof. A. 0. Rankine on the Molecular Structure 



collision size, with centres separated by the distances already 

 •specified. In COS we take instead of one of the extreme 

 neon spheres an argon collision sphere ; while in CS 2 both 

 the outer spheres are of the argon size. In all three cases 

 the diagram represents all the nuclei in th.Q plane o£ the 

 paper, and the line joining them is evidently an axis of 

 symmetry. 1£ these symmetrical axes are variously oriented, 

 the area presented by the model assumes different values, 

 and our problem is to calculate the mean value o£ this pro- 

 jected area for comparison with that deduced from viscosity 

 data. The author (loc. cit.) has already derived the necessary 

 formulae for this purpose, and has shown that the result 

 obtained by application to the first model in fig. 1, namely 

 00 2 , is very nearly equal to the actual mean collision area of 

 the carbon dioxide molecule. In other words,, a carbon 

 dioxide molecule behaves in collision as though it had the 

 configuration of three neon atoms in a straight line and with 

 outer electron shells contiguous. 



7. Calculation for the COS Model. — In the model which 

 we are taking to represent the COS molecule, the calculation 

 in the strictest sense is greatly complicated by reason o£ the 

 particular distribution of the spheres. The exact formulae 

 which have been obtained {loc. cit.) for equal and unequal 

 spheres only apply rigidly to cases where a special relation 

 exists between the diameters of the spheres and the distances 

 apart of their centres ; and the model under consideration 

 does not fulfil this condition. But by regarding the problem 

 from two different points of view, we can obtain, by means 

 of the comparatively simple formulae already available, upper 

 and lower limits which are so close together as to render 

 unnecessary the laborious exact calculation. This course is 

 all the more justifiable because it is fully recognized that 

 the general treatment of the problem itself can only be taken 

 as a first approximation to the truth. 



8. Let us consider the effect on the area of projection of 

 the model (reproduced in the full lines of fig. 2, a) caused 

 by variations of orientation of the symmetrical axis joining 

 the centres ]5 2 , and 3 of the constituent spheres. It 

 will be convenient to speak of the sphere with centre L 

 simply as sphere 1, and so on, and of the projections of the 

 spheres, which will of course be circles, as projection 1 

 etc. As the axis 0, 3 approaches the line of sight, the 

 projections of the centres approach one another, and the 

 eclipsing of the spheres becomes more and more marked. Up 

 to a certain point the total projected area is equal to the sum 



