730 Sir J. J. Thomson on some Optical Effects 



would be a valid objection if all the electrons were quite 

 free, or even if they were all under similar conditions of 

 restraint. The electrons, however, are not free, they are 

 acted upon by forces which tend to drag them back to the 

 places from which they start. If these forces are different 

 for the different electrons, the behaviour of one electron 

 will be different from that of another, and this may make the 

 system so unsymmetrical that it may be able to produce 

 rotation of the plane of polarization. We may make this 

 clearer by considering a very simple case, that of four 

 electrons a, /3, 7, 8 at the corners of a tetrahedron, and 

 suppose that the restoring forces for two of the electrons, 

 say a and ft, are very large compared with those for 7 and 8. 

 The effect of this will be much the same as if a and /5 were 

 fixed, so thut the tetrahedron would, when acted upon by 

 the electrical forces in a wave of light, rotate about the line 

 a/3, the two electrons 7 and 8 would rotate about this axis. 

 We see from the considerations given above that each 

 tetrahedron will contribute to the expression for the rotation 

 of the plane of polarization a term equal to 

 2tt e* [PQ] 

 3 c 2 A ' 

 where A is the moment of inertia of the two electrons 7 and 8 

 about the axis a.j3, and [PQ] is six times the volume of the 

 tetrahedron whose corners are 7 and 8 and the feet of the 

 perpendiculars let fall from 7 and 8 on u/3. Let us consider 

 the numerical magnitude of this term. If d is a measure of 

 the radius of the molecule, [PQ] will be of the order d B and 

 A of the order md 2 , where m is the mass of an electron. Thus 

 the contribution to the rotation will be of the order 



and if there are N molecules per c.c, the rotation will be 

 of the order 



„— d. 

 c l m 



If M is the mass of the molecule, then when there is one 

 gramme of the active subst-mce per c.c, NM = 1, so that 

 the intrinsic rotation is 



e 2 \ m 



\ c i m i J 



M. d ' 



Now 



e 2 lc 2 m 2 = (1-8 x 10 7 ) 2 , ^=10" 8 , and m/M= 



l-8xl0 3 .W' 

 where W is the molecular weight of the substance. Thus 



