MR. J. G. LEATHEM ON THE THEORY OF THE 
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operators, in the case of light vibrations they are algebraical quantities, because 
= — 'p^- 
In theories of this nature it is usual to assume that ( 6 ^, 63 ) are proportional to 
the components, parallel to the axes, of the imposed magnetic force ; the constants 
{9[> 9%' 9%) Hall effect are also usually assumed to vary as the magnetic force; 
and therefore in this case ( 77 ^, 17 ,,, 173 ) would do so also. But in experiments on the 
transmission of light through magnetised metallic films it is found that the rotation 
of the plane of polarisation certainly does not vary as the magnetic force, but verv 
probably varies as the intensity of magnetisation, a quantity very difficult to 
determine. We shall see later that in the mathematical solution of the problem of 
transmission the rotation varies as and hence we are driven to the assumption 
that (771 7^3 7 ^ 3 ) vary as the components of magnetisation. I shall also suppose that 
h^, 63 ) vary as the components of magnetisation, which necessitates the assumption 
that {g^, g. 2 , g^) do so likewise ; the question whether the Hall effect varies as the 
magnetic force or as the magnetisation has not, I think, been put to an experimental 
test ; the latter supposition seems more probable. 
These assumptions can be readily justified from physical considerations. For in 
vacuo there is no magneto-optic rotation, though there is magnetic force; it is there¬ 
fore not the magnetic force, but matter, or some property of matter when under the 
influence of magnetic force, that causes the rotation ; and the property of matter under 
the influence of magnetic force is not force, but magnetisation. 
Denoting the components of the imposed magnetisation by {a^^, y^), we assume 
('’?l5 '’?2 j I'i) — (a^, (Bq, Yq).(37), 
where is the complex magneto-optic constant of the theory. For any particular 
metal the values of Cq and x may be determined by experiment; and if we find that 
the numerical values of these constants, as determined by all the different sorts of 
experiments, are the same, we shall conclude that the theory can account for all the 
observed facts, and therefore constitutes a complete mathematical explanation of the 
phenomena. 
The Optic Constants of Metals. - - 
13. The constants R and a are different for different metals, and also for light of 
different colours. Their values have not been directly tabulated, but they are easily 
obtained from the tabulated values of Drude’s optic constants; these latter are 
denoted by n and h, and are connected with R and a by the relations 
R cos 2a = 2 a ~ — 2 n^k, 
so that ' - - c 
R“ = id (1 -f k~), tan a — — k. 
