104 
ME. J. G. LEATHEM ON THE THEORY OF THE 
The experiment will also tell us the sign of Cq ; for, in accordance with Kerr’s 
observations, when the incidence is very nearly normal, 9 is of the same sign as ; 
and when the angle of incidence is nearly 90°, 9 is of the opposite sign to a^. Now 
the table of values given above indicates that as i passes through that value (be it 
75° or 80°) for which 9 vanishes, from a less to a greater value, the cosine of the 
vector angle from being negative becomes positive, so that for very great angles of 
incidence 9 is of the same sign as Coao- Hence Cq is negative. 
15. In Kerr’s first experiment the magnetisation is parallel to the reflecting 
surface and the incident light is polarised in the plane of incidence. If 9 be the 
rotation of the major axis of the ellipse of polarisation in the same sense as before, 
Kerr found that 9 has the same sign for all angles of incidence, and that this sign 
is opposite to that of «q. 
In this case = 0, = 0, Ay = 0, and 9 = real part of (— A/B cos i). 
From result (36) we readily deduce that 
— 2cX sill i cos i Co«ot. 
\]~^i ~ (M - cos i) ( + cos ’ 
of which the vector angle (including the minus sign) is x ~ 90° — 2a — sum of 
vector angles of i«, im — cos i), cos ^). 
If = 0, vector angle of A/B cos i is 
a; 4- 128° 3'. 
If i =; 61° 30' vector angle is 
a: + 115° 42'. 
If i = 90°, vector angle is 
a: + 76° 4'. 
x4nd evidently for all angles of incidence the vector angle lies between a: 4" 1^6° 
f^nd a- + 128°. So that if x have any value between 14° and 142°, the cosine of 
the vector angle of A/B cos i is negative for all angles of incidence. Thus 9 has 
always the same sign as Cyay, that is, the opposite sign to ay. 
Hence any value of x lying between 14° and 142° satisfies all the conditions of 
Kerr’s first experiment. 
16. In another of Kerr’s experiments the magnetisation is normal to the i-eflecting 
surface, and the incident light is polarised in the plane of incidence. 
Here 
rji = 0, y).2 — 0, A-y = 0 , 
9, liaving the same meaning as before, is found by Kerr to be of opposite sign to yy 
for all angles of incidence. Now 9 is the real part of — A/B cos i, and we readil}' 
deduce from formula (36) that 
