96 
MR. J. G. LEATHEM OR THE THEORY OP THE 
Corresponding to the two values of m there are two sets of constants (A, B, C); 
these we distinguish by the suffixes (j) and ( 3 ). 
Equation (17) shews that 
C, =-^ Ai and Co = —^ A,.(26). 
This taken in conjunction with the second of equations (16) gives 
(Hco® + 47712^) B = — ^2 ^ 
whether the suffix be ( 1 ) or ( 2 ). 
Hence in virtue of equations (19) 
. = - 
H o o 
A 
7H, 
D 
-n-o H-Wj- . 
— L . H^w.,B) = —-A.1 
' ' r/l:, 
or 
B, = + i.-’-Aj, Ao . . . 
(27). 
8 . In the case of air (or any medium in which there is no magneto-optic rotation) 
7 ^ 1 , 7 ^. 3 , 773 are zero. For air also o- = 0, K = 1 , H = AttC^Il'P = — l. inC-jp. The 
substitution of the exponential forms of u, v, iv in the equations of pi’opagation gives 
— t . 47rc"/2J . + 4771^ = 0, 
or C'oj” = py as was to be expected. 
Problem of lieflection. 
9 . We are now in a position to attack the problem of the reflection of light at the 
surface of a magnetised metal. Let the interface between the two media be the 
plane z — 0 •, the air occupying the space 2 positive, and the metal the space 2 nega¬ 
tive. The plane of incidence is taken as the plane y — 0 . 
We assume that, in the air, 
u= Aq& + Ae‘ 
{lx + VIZ + 7)0 _|_ ggi {lx - mz + pi) 
A Ac‘ ~ ''' 
■m 1)1 
where A^j, B^ represent the incident wave, and A, B the reflected wave. 
