OF THE REFLECTION AND REFRACTION OF LIGHT. 
705 
-^=90?y-, and hence we get Mr. Kerr’s result (‘Phil. Mag.,’ March, 1878, p. 174) that 
when the plane of incidence is normal to the lines of magnetic force the magnetising 
of the mirror produces no change in the reflected light. 
Assuming, then, first that the magnetisation is normal to the surface, we have 
cl cL 
a=/3= 0 , y=9)?, and —=9Jso that calling 47 tCK 1 3 L )?=v our equations become 
dz dx Iv dx) dz‘ 
dv.^dX- f 9 4_dj\ 
dz K 'dz V \ dz dx) _ 
(I) 
while if it be all in x — i.e., in the intersection of the plane of incidence and the 
d_ 
dli '"dx 
surface, a= 9 D?, ^> — y— 0 , and -jj = SD?-. -, so that our equations are 
in ~| 
dz tlx K\& th:P V dx 
dr) l K x dr] dj- 
Y 
(II) 
dz K " dz dx _J 
I shall now proceed to solve these two systems of equations each for the two cases 
of waves whose magnetic forces 77 , £ are first in the plane of incidence, and secondly 
at right angles to it. From the forms of the equations it is evident that we cannot 
assume either the reflected or refracted rays to be similarly polarised, but it is easy to 
convince oneself that there can be no difference of phase introduced in this case any 
more than in the former one of ordinary reflection, and, as I then remarked, it is 
evidently a question of greater complication than to be capable of being deduced from 
the simple assumption that the alteration of the nature of the medium in going from 
one into another is abrupt. Until more is known of the nature and extent of this 
change I fear we must be content with theories which only partially represents 
the facts. 
As before, I shall assume £ 1} rj x , to be due to the incident and reflected rays, while 
£ f], £ are due to the refracted ray. The incident ray may be taken to depend upon 
the angle 
,27 T , . .. 
ip x — --(i—z cos i—x sm i) 
calling the velocity in this medium unity and the reflected wave on 
/ 27T, 
(t-\-z cos i—x sin i). 
