700 
MR. G. F. FITZGERALD ON THE ELECTROMAGNETIC THEORY 
vanishes, or at least may be supposed to do so, the medium being isotropic and s=s', 
so that the two refracted waves coincide. Also /3,,=0 and y8 / 0 =^8 1 =0 likewise, as can 
easily be seen by assuming that the reflected and refracted waves have components out 
of the plane of incidence and then trying to satisfy the equations. Hence our equa¬ 
tions reduce to 
T„+T'o=4t i 
r 
and £ q =£' 0 becomes 
(T 0 —T' 0 ) sin cos r 
i being the angle of incidence and r of reflection. The first of these is 
(Tq+T'q) sin ^’=T 1 sin r 
and solving them we get 
„ sin (i—r) „ _„ sin 2i 
0 0 sin (i+r) 1 0 ' sin (i -f r) 
If r) 0 be perpendicular to the plane of incidence we obtain a 0 = i, /3 0 = 0, and 
equations become 
T 0 +T' 0 =T 1 
and 
which give 
(T 0 —T' 0 ) sin i cos t=T\ sin r cos r 
rjv tan (i /) _rj, sin 
0 ’ tan (i + r) 1 0 sin (i + r) cos (i — r) 
our 
Having now deduced the already known laws of reflection and refraction of light at 
crystalline and ordinary surfaces, I shall proceed to consider the case that Mr Kerr’s 
wonderfully beautiful experiments have made so interesting—namely, the case of 
reflection from magnetic surfaces. In order to do this I shall assume, with Professor 
J. Clerk Maxwell (see ‘ Electricity and Magnetism,’ vol. ii., § 824), that the kinetic 
energy of the medium contains a term depending on the displacement of certain 
supposed vortices, and that it may be expressed by an equation of the form (§ 826) 
T = - c .(ii s (^ ■ Vv *)^=-cfn(|-/ + l -9+f e h)dxdydz 
where 
- = a- + B-+-A 
cie d^ rp d^ rr dz 
and a, /3, y are now the components of the vortex 50?. 
4r7T • 
I shall assume the medium to be isotropic, so that taking 4 >= ^ electrostatic 
energy of the medium may be expressed as 
* When [> is the refractive index. 
