470 Prof. D. B. Brace on the Resolution of Light into 



the ordinary sine law of refraction which may be used 

 instead, when a change of velocity is produced in the medium. 

 If, however, there is a change in phase, for example, a 

 continual angular acceleration of the rotating vector in a 

 circular vibration, then the result will be to produce an 

 apparent increase in X. Thus if V is the original wave- 

 length, the altered wave-length will be X = X / + X'Se, where 

 £e is the acceleration of phase over a distance X. Thus Ave 

 should have 



sin i _ \i _ X/+A/6>; 



sm r A r X,/ 4- X r '8e r ' 



To find now the deviation 6Y produced after reflexion 

 under the action of the magnetic field, we have, i being 

 constant, since we are dealing with the first reflecting surface, 



6> cos r = SX r 



sm i 



X; ' 



or 



<s ~ N tan i 



A,- 



since i—r approximately. But hX r — X r 'he where X,/ is the 

 original wave-length and Be the change of phase on either 

 supposition. But the acceleration of phase of one circular 

 component over the other, to produce a rotation 6 of the 

 resultant for a unit distance, is 



LIT 



hence over a distance Xr it would b^ 



X r 6 



Ee = 



77 



Therefore 



X r f X r . 6 



— tan i = A,.— tan i 



X-7T TV 



since X r ' = X r =X l very approximately in this experiment. 

 If co is Verdet's constant, and H the intensity of the field, 



and n— — the index of refraction, where X is the wave- 



*" X tan i 



length in vacuo, we have 6> = g>H- — — , which holds on 



either supposition. 



Applying this formula to the experiment in figure 1, we 



may put 



t = 72° nD = 1-903, g> d = 0-1'x cosl8 o = 0-rx —, 



Xe = 6x10- 5 , H = 2xl0 4 , 



