and the Magnetic Rotation of Polarized Light. 257 



From the form of the equations we can well suppose that one 

 solution is 



F = ?' cos (nt — qz) cos mt, 



G = ?' cos (nt—qz) sin mt; 



and making the substitution we find 



{K/*(n 2 +m 2 )-g 9 (l + C ? ^)}cos (nt-qz) cos mt 

 — Kn \ 2mfjL — C-j^ r sin (nt — qz) sin mt = 0, 



| Kfi(n 2 + m 2 ) — q 2 fl + C^r^r ) 1 cos ( nt ~ Q z ) sin mi 

 + Kn { 2m/i - C^ > sin (ra£ - qz) cos m* = 0. 



These are satisfied if we make the coefficients zero. 



If Y is the velocity in general of light in the medium, and 

 Y the velocity in vacuo without magnetic action — if i is the 

 index of refraction of the medium, and \ the complete wave- 

 length in the medium, and \ Q in vacuo, we thus find 



n / 1 + c 





/ 1 + 



KyL6 



^/KfA 8tt 2 ; 



These equations indicate that when a ray of plane-polarized 

 light passes in the direction of the lines of magnetic force, the 

 plane of polarization will be rotated in a direction depending 

 on the sign of the quantity c, which is the well-known action 

 of Faraday. But the second expression (which gives the 

 velocity, and consequently the index of refraction) also de- 

 pends on c, and thus indicates an acceleration of the velocity 

 which is unknown. But this action is so very minute that it 

 can probably never be measured. 



If D is the length of the substance, the total angle of ro- 

 tation of the beam will evidently be 



This solution is rigorously exact for all cases where the 

 index of refraction is not a function of the wave-length. To 



