/* =1 +. 



720 Sir J. J. Thomson on some Optical Effects 



If fx is the refractive index, 



2ire 2 a 

 m(n 2 —p' 2 ) 



hence the angle through which the plane of polarization is 

 twisted is equal to 



eri.'-J^H.D, (6) 



c in ir — p z y 



this can be written as 



f~t H - D > (7) 



2 c ??i ap v J 



which agrees with the expression given by Becquerel. 



Ke/m is the angular velocity witli which an electron 

 would describe a spiral round the line of magnetic force H; 

 let this be denoted by &>, then if t is the time the light takes 

 to pass across the slab D, the angle through which the plane 

 of polarization is rotated in this time is 



■ n 2 —p 2 



Thus when the atoms have only one intrinsic frequency 

 the rotation is given by a very simple expression. If n is 

 large compared with p, the rotation is proportional to 

 (jj,— l)p 2 /n 2 , and is thus proportional to the square of the 

 frequency : a result which is a rough approximation to the 

 truth in a considerable number of cases. 



If, as indicated by equation (7), the rotation can be 

 expressed as a function of the dispersion, it follows that no 

 information as to the structure of molecules can be obtained 

 by experiments on magnetic rotation which cannot be 

 obtained by experiments on dispersion. 



Rotation of the Plane of Polarization by substances such as 

 quartz or sugar solution. 



We cannot explain this rotation if we consider isolated 

 electrons in an atom, but we shall see that we could account 

 for it by a system of electrons held so firmly in position that 

 they act somewhat as a rigid body, a force acting on one 

 electron displacing the whole system of electrons. 



We shall suppose as before that the primary beam is 

 travelling along the axis of x, that it is plane polarized, and 

 that the electrical force in it is parallel to z. Let the co- 

 ordinates of an electrical charge, electron or positive particle, 

 be a?*, y s , z s . If Z s is the electrical force in the primary 

 wave at this point, the moment about the axis of x of the 

 forces acting on the electrical charges in the atom is %eZ s y s . 



