258 Trof. H. A. Rowland on Magnetic Attractions, 



>vt the value where the index varies, we can use the principle 

 of the superposition of small quantities. Every plane-polarized 

 ray can be supposed to be made up of two circularly polarized 

 ravs; and to say that the plane of polarization is rotated 

 simply means that one of the circularly polarized rays travels 

 faster than the other; when one ray gains A, on the other, the 

 plane of polarization is rotated through the angle 2ir. Hence 

 if Y is the velocity of one and V / of the other, we have 



v=v '( 1+ p) 



where D' is the distance in which the plane of polarization is 

 rotated through the angle 2tt. 



But this effect will be augmented by the dispersion of the 

 body, seeing that the velocity affects the wave-length, and 

 hence the index of refraction will be different for the two com- 

 ponents. This further action can be taken into account by 



V i %' 



multiplying ^-by -; and we then have 



y/ •/ T j)// ' 



so that D f has been changed to 



X 



D" = 



K'+*)- 



This can be put into the form 



D" 1 



But 



whence 



and 



i\ \ a j 



X _ D' + X 

 V D' ' 



i f — i_ X f — X cli o 

 i i dX 



Hence, omitting all quantities of the second order of small- 

 ness, we can write 



