STEREOISOMERISM AND OPTICAL ACTIVITY 231 



the distance of b from the central carbon ; any pair of a's will 

 contain the same angle, but this angle will be different from 

 the angle contained by b and any of the a's ; the structure will 

 possess only three planes of symmetry ; and so on. 



Finally, when the groups are different, the structure becomes 

 perfectly irregular, devoid of any plane of symmetry, having all 

 distances different, all angles different. 



When a molecule of such a perfectly irregular configuration 

 lies in the path of a ray of plane-polarised light, let us suppose 

 the direction of the ray to lie along one of the carbon-bonds. 

 Then it is easy to see that the other three bonds will not lie 

 symmetrically round the ray, but will be found to be twisted out 

 of shape in such a manner that the line joining the centres of 

 inertia of the three groups attached to them will describe a spiral 

 round the ray, as shown diagrammatically in the figure : 



And it does not seem unreasonable to suppose that this twisting 

 of the bonds will produce the effect of rotating the plane of 

 polarisation, and also that the amount of rotation will be directly 

 proportional to the degree of this twist in the orientation of the 

 bonds round the ray. 



This twist will be present along whichever of the four bonds 

 we imagine the path of the ray to lie. Whether the twisting of 

 the bonds in each case will be the same or not, the writer cannot 

 say for certain. Most probably it will be equal ; but even if it 

 is not, the principle of "least resistance" will come into opera- 

 tion, and as the molecules are perfectly mobile they will take 

 such a position with reference to the path of the ray as will 

 produce minimum rotation. 



Further, even if the path of the ray lies along none of the four 

 bonds, the screw-spiral twisting will still be there ; and whether 

 the molecule will take any such position or not will depend on 

 whether the twisting is the least or not in that position. But 



