MAGNETO-OPTIC PHENOMENA OP IRON, NICKEL, AND COBALT. 
105 
A _ 2cX, cos i!Cfi7o ( — >') 
B cos i (JJX — cos i) + cos i) 
of v/hich complex the vector angle is found in the usual way to lie, for all angles of 
incidence, between the values x -f- 20° 43', corresponding to i = 90°, and x 74° 23', 
corresponding to 7 = 0. 
If a: have any value between 69° 17' and 195° 37', the cosine of this vector angle 
is always negative ; and so 6 has the same sign as Coyo> oi’ fhe opposite sign to yg. 
Hence this experiment of Kerr’s is satisfied if x have any value between 69° 17' and 
195° 37'. 
17. In Kerr’s fourth experiment the magnetisation is normal to the reflecting 
surface, and the incident light is polarised perpendicularly to the plane of incidence. 
Here — 0, — 0, Bq = 0, and 9 is the real part of B cos 7/A where, from (36), 
B cos i _ 2cA cos 7 Co7o (— 0 
Ta A cos i) - cos i) ’ 
of which complex the vector angle lies between the values x — 105° 37', correspond¬ 
ing to i = 0, and x fl- 20° 43', corresponding to i = 90°. 
Now Kerr found that 0 is, for all angles of incidence, of opposite sign to y^, that 
is, of the same sign as Cgyn. Hence the cosine of the vector angle of B cos ijA. is 
always positive. 'This is in accordance with our theory, provided the value of x lie 
between 15° 37' and 69° 17'. 
Obviously this conclusion is at variance with that derived from the preceding 
experiment, unless x happen to have exactly the value 69° 17'. 
But this experiment of Kerr’s was repeated by Kundt, who found that 6 has not 
the same sign for all angles of incidence, but that it vanishes and changes sign for an 
angle of incidence which he estimated at about 82°. 
I have calculated the values of the vector angle of B cos 7/A for several angles of 
incidence in the neighbourhood of 82°; they are as follows : — 
Angle of incidence. 
Vector angle of B cos if A.. 
Angle of incidence. 
Vector angle of B cos f/A. 
^ C 0 
/D 
a: - 47° 37' 
85° 
X + 0° 43' 
GO 
0 
OT 
a; - 29“ .57' 
86° 
a: -1- 5° 20' 
80^ 
a; - 24° 23' 
86° 30' 
a; + 7° 27'. i 
82° 30' 
a* - 11° 32' 
88° 
a: + 13° 31' ' 
i 
bo that if we denote by 7y that angle of incidence for which 6 changes sign, the 
values of x corresponding to various hypothetical values of iy are as follows :— 
VOL. cxc.—A. 
p 
