488 Mr. J. G. Leathern. On the Theory of the 



2. The notation is nearly the same as Maxwell's, (P, Q, R), (u, v, 

 w), (a, b, c), and K, having their usual significations; <r is specific 

 conductivity, and c the velocity of radiation ; (/", g", h") corresponds 

 to Maxwell's total electric displacement, and has components (/, g, h) 

 and (/', g', h'), of which the former is the displacement involved in 

 the ether strain, and the latter that involved in the polarisation of 

 the matter. It being as usual assumed that for light oscillations 

 the effective magnetic permeability is unity, the fundamental equa- 

 tions of the theory are as follows : — 



(i) The two circuital relations, 



dc db . -, dH dQ da 



— = 47m and ~ = . 



dy dz dy dz dt 



(ii) The equations of the current, 



u = eY+gzQ-gzR+dfldt, 



where the vector (g lt g 2 , g$) represents the Hall effect. 



(iii) The displacement relations, and the elastic relations between 

 electromotive force and the corresponding polarisation, viz., 



/"=/+/', /=p/w, 



and f = ^±V + b 3 §-b^, 



47rC xS dt dt 



the vector (b u b 2 , b 3 ) representing, in transparent matter, the whole 

 magneto-optic effect. 



3. The equations of propagation are found in the usual way, 

 (u, v, w) being taken as independent variables. In them and in the 

 boundary conditions (b lt b 2 , b 3 ) and (g lf g 2 , # 3 ) appear only as the 



vector, j^L-j-^, (b 2 ^- 2 + g^, (bz^L+g^y, which is assumed 



equal to C e LX (a 0) /3 , 70), where (x , #» 70) is the intensity of magnet- 

 isation ; C e tx is thus the single magneto-optic constant of the 

 theory. 



4. The principal experiments which have been used to test the 

 theory are those of Drs. Sissingh and Zeeman on magnetic reflec- 

 tion, their observations being measurements of the phase m and 

 amplitude ^ of the " magneto-optic component " of the reflected 

 light, for various angles of incidence. It is noteworthy that the 

 value of m derived from the theory involves x, but not C ; while the 

 theoretical value of ft is proportional to , but does not involve x : 

 this circumstance makes the test a severe one. 



5. The following table will serve to indicate what sort of agree- 

 ment is found to exist between the theory and the experiments. 



