34 Light Vibrations in a Magnetic Field. 



These enable us to calculate the dispersion of the substance in terms 

 of the difference of velocity of propagation of waves of oppositely 

 circularly polarised light. 



To get approximate formulae in terms of quantities that can be 

 observed, we have the refractive index /* = V /Y, when V is the 

 velocity in vacuo and p = 2:rY/X. Assuming that \Q/\ is small, i.e., 

 that the dispersion is due to an absorption band far up in the ultra- 

 violet, we get, writing p for e/m, 



4 * H 



The second term on the right-hand side of this equation gives the 

 ordinary dispersion, while the third term gives the Faraday rotation. 

 The first term /i is given by 



and is, as Mr. Larmor has pointed out, composed of two parts, the 

 first being essentially refraction and the second dispersion. 



In the case of air, it is possible to compare this equation roughly 

 with observation. The equation is of the form 



We may estimate a from the dispersion in air, and it is approxi- 

 mately 1-8 x 10- 14 . 



The equation gives for the two absorption bands that exist instead 

 of jp =j3 , 



p*pi = ppi - H, p<?pS = pp z H, 



.*. p z PI = p . H. 

 So that, if 8p be the difference of frequency for unit magnetic force, 



Hence, for the difference of refractive index of two circularly 

 polarised rays, we have 



a pH a Sp TT 

 X * ^V = X ' " 



Assuming, what is certainly not accurately true, that p is the same 

 for all lines, and taking that Mr. Preston's estimate for some lines of 

 Zn applies to oxygen, namely, that 1 A.U. change of wave-length is 

 produced by a field of 20,000 C.G.S. units of magnetic force, we get 



