728 Sir J. J. Thomson on some Optical Effects 



Consider first the value o£ Q : the terms 1/A, 1/B, I/O, 

 will be of the order 1/M6? 2 , where M will not be less than 

 the mass of the smallest atom in the molecule, nor greater 

 than the mass of the molecule itself, d is a length comparable 

 with the radius of the molecule. The terms %ex r y\ %ex ', 

 may for very unsymmetrical molecules be of the order ed 2 

 and ed respectively, hence Q will be of the order e 2 d/M i 

 hence' we see from equation (4) that the angular rotation in 

 circular measure per centimetre will be of the order 



Ne 2 d XT1i/r e 2 d 

 or NM . -^ft7 . 



c 2 M 



When there is one gramme of the substance per cubic centi- 

 metre NM will be less than unity, hence the specific rotation 

 will be less than e 2 d\c 2 W 2 . Now there are many active 

 substances in which the lightest atom is heavier than OH. 

 If we take M to be the mass of this atom, then since e is 

 expressed in electrostatic measure, ^/cM = 10717, so that 

 the specific rotation per cm. will be less than d x 10 8 /289, or 

 taking d = 10~ 8 less than 1/289, i. e. less than 12'. Many 

 optically active substances have specific rotations greater 

 than 10°, so that our expression for the rotation only 

 accounts for a small fraction of that observed. Nor is this 

 all, the expression we have obtained does not depend upon 

 the frequency of the light, whereas the actual rotations are 

 approximately proportional to the square of the frequency. 

 This discrepancy is due to the fact that we have regarded 

 the molecule as a free system, uninfluenced by other 

 molecules. If the influence of the other molecules is such as 

 to make it set in a definite position and vibrate about this 

 position with a frequency n, the displacements and velocities 

 will be less than when the system is free in the proportion 

 of p 2 to p 2 — n 2 , where p is the frequency of the light. Thus 

 when the influence of other molecules is to be taken into 

 account, we must multiply the expression we have obtained 

 by p 2 /p 2 — n 2 . If n were large compared with p, this factor 

 would be p 2 \n 2 , and as this is proportional to the square of 

 the frequency, we should get the correct variation of the 

 rotation with the frequency of the light. There are, how- 

 ever, two very serious objections to the modification of the 

 formula in this way. In the first place, it is very unlikely 

 that the natural frequency of the motion of a heavy molecule 

 as a whole should be large compared with the frequency of 

 the light ; and secondly, even if it were, since the factor p 2 /n 2 

 would then be small, the rotation, as calculated by the 



