﻿of Carbon Oay sulphide and Carbon Bisulphide, 297 



o£ the areas of the whole of projection 3, the crescent formed 

 by the overlapping of projection 3 over projection 2, and the 

 crescent formed similarly by the eclipse of projection 1 by 

 projection 2. Before the eclipsing of 2 by 3 is complete, 

 however, projection 3 begins to encroach upon regions of 

 projection 1 which are not already covered by projection 2. 

 Tt is this fact that introduces into the exact treatment of the 

 problem the complications to which reference has already 

 been made. Thus in fig. 2, b, which shows the projected 

 area for that orientation of the axis for which the eclipse of 

 2 by 3 is just complete, the crescent formed by 2 and 1 still 



Fiff. 2. 



•survives, but parts of it (as indicated by the shading) are 

 covered by projection 3. The projected centres are 0/, 2 ', 

 and (V respectively, and this particular state of affairs occurs 

 when the angle between C^ 3 and the direction of projection 

 is 9° 47' for the spheres having the dimensions and distribu- 

 tion already specified. 



9. Overlapping of the type just indicated, like all 

 overlapping, has the effect of reducing the projected area ; 

 it is therefore clear that if w r e neglect it we shall obtain too 

 large a value for the mean area of projection — that is, an 

 upper limit will be obtained by taking the mean collision 

 area as the sum of the three parts : (a) the area of the circle 

 3, (It) the mean value of the area of the crescent formed by 

 ^cireles 3 and 2 (c) the mean value of the area of the crescent 



