MAGNETO-OPTIC PHENOMENA. OP IRON, NICKEL, AND COBALT. 
93 
and 
so that equations ( 7 ) become 
K d _ 1 
^ Tttc^ di — H ' 
w = ~ P -b — rj.^R 
V = ^ Q + Tj^U — T^gP 
^ — ’?iQ 
( 9 )> 
(10). 
Now {gi, g^, g^) and b^, 63) are supposed to be exceedingly small quantities, so 
that (r)^, 172, 173) are also extremely small. If we neglect squares and products of 
(771, 772, 773) and solve equations (10) for P, Q, R, we get 
P = H (w — H7737; + }lrj^iv) 
Q = H (y — H 77 ^iy + 
> 
R = H {w — II772W H 772 'y) 
( 11 ). 
To get the equations of propagation difterentiate with respect to the time the first 
of equations (l) 
^ du d I db 
^ dt ” il ' ^“ 
d^/ d^ 
dt j dy \ dt 
dz \ dz 
dx 
dy \dx dy 
by (2) 
^ V^p - 'V— -L ^ -L 
dx \d.x ■*" dy dz 
— HV^ {u — H773'U -{- H 7722 y) 
- h4 b: (y '7) + .S 
d.i 
dv dw 
'dio dn' 
d 
dy/ 
\dx 
dz 
du 
dy 
and hence, if for brevity we put 
,_ /die dv\ (du du;\ (dv du 
^ \dy ~ Iz) dx) \(y^ — ((y 
dv\ 
dx 
( 12 ). 
our equations of propagation become 
rhi dVl' "A 
477 ^ = HV 2 {u - H773U + H7727y) + W ^ 
4,7 ^ = HV^ (*; - H,,«, + H,,«) + . 
477'^“ = HV^ {m - + Hi,,);) + ^ 
(13). 
