706 
MR. Cx. F. FITZGERALD ON THE ELECTROMAGNETIC THEORY 
as it is easy to see that for these to vanish from the equations when s=0we must 
have the sines of the angles of incidence and reflection equal, while the refracted wave 
must be taken to depend upon 
2 7 t 
<j>=~r-(st—z cos r—x sin r) 
and here we must have, as before, an q this involves, as before, the 
ordinary laws of refraction, as s is constant and in general 
s= 
A / /L^i . /L K i _ 2_ 
V ‘ >K - ' S ~ 
sin 2 r 
sin 2 * 
Taking then first the case of the magnetisation being all normal to the surface and the 
incident displacements £ rj, £ in the plane of incidence, we must evidently assume 
£i=a>i cos i cos <£, — h x cos i cos <f>\ cos r . cos <f> 
rj l =c 1 sin cf)\ t)=c sin <f) 
Ci= — cq sin i cos j> ] —b x sin i . sin <f>\ £= —cq sin r . cos <f> 
in order to satisfy the equations 
= K 1 (d^_dJ\ d v 
dz dx K \dz dx) ' dz 
ch h = K 1 ^dr 1 _ / 
dz K dz V \ dz dx) 
(l = ( n=v 
As it leads to inconsistent results I, in accordance with Fresnel, omit the third 
equation, £ 2 = £. It is not easy to justify this omission, I fear, and the result must do 
so, as well as the consideration that probably if we had a better insight into the 
nature of the change from one medium into another our equations would be so modified 
as not to present these anomalies. 
From the last equation it is manifest that 
c = c x 
and as v is very small it is obvious that c will always be small, so that vr, may be 
omitted in the first equation. Putting in the values of £, r,, £, &c., and remembering 
that when z— 0, = these equations evidently reduce to 
f • • (A) 
