708 
MR. G. F. FIT2GERALD ON THE ELECTROMAGNETIC THEORY 
Hence we get solving for c : in terms of cq 
87 TV 
c,= — 
sin 2i sin 2 i cos 2 r 
T 1 sin r(sin 2 i + % sin 2?’)(sin i cos r + y sin r cos i) 
which when x —1 reduces to 
47TV 
^1 = rrC 
sin 2i . sin 2 i cos 2 r 
T 1 sin sin 2 (-i + r) cos (i—r) 
Turning now to the case where the magnetisation is in the surface, I shall first 
suppose the incident vibration to be in the plane of incidence, when we evidently 
assume, as before, equations (A) for £ l5 iq, £ 1? £, 77 , £, and these must satisfy the 
equations (II), and in addition 
As before, we evidently get c=c l3 and from the second equation of (II) see that c 
must be small, as v is, and consequently we may omit vrj in the first equation, and so 
the first equation is the same as before, and we have 
(cq-f-Zq) sin i—a^ . sin r 
(cq— 6 X ) cos i=ci cos r 
. . . . 27 TV . „ . 
cq sm 1 cos i= — cqy sm r . cos r —cos r . snr 4 
which when solved for cq in terms of cq gives 
4771/ sin 2 i sin 2 i cos r 
1 T " 1 (sin 2i + x sin 2?') (sin i cos r +% cos i sin r) 
which when x = l reduces to 
2i7tv . cq sin 2i. sin 2 % cos r 
1 T sin 2 (i + r). cos (i—r) 
Finally, supposing the incident vibration to be perpendicular to the plane of 
incidence, we have g 1} iq, £ 1? f, 77 , £ determined by the equation (B), which when 
substituted in equations (II), neglecting v£ as before on account of its smallness, give 
c i = 
47 TV 
T f 1 (sin 2 i + x s hi 2?’) (sin i cos r+ % cos i sin r) 
which when y — 1 reduces to 
sin 2 i sin 2 i cos r 
c \— ip a i • ■ 
7 tv sin 2 i. sin 2 i . cos r 
T 1 ’ sin 2 (i + r ). cos (i—r) 
