124 
MR. J. G. LEATHEM OR THE THEORY OP THE 
Now 
6 = — cm^h = — + it) 
(jj = — vmji = — tMA (1 -- \t) 
aiicl therefore, if the modulus of iM/;. be not exceedingly great, 
e® = {I ~U. iM/O e-^ = {I + . lWi) 
(1 + • ^M/0 c-^ = e‘“ {I - hj . tWi). 
Substituting; these expressions, we readily find that, to the first order in t, 
X = (1 + a;) 12 (1 + a;) - (1 - a;) - . tMA (1 + x) j 
— {I — a:) 12 (1 — x) — t{l x) *f ^. lMJi (1 — a-) j, 
Z = (1 + x) |2 (1 + a:) -h i (1 - a;) -h ^ t.M/i (1 + a;) j 
— (1 — a;) |2 (L — £c) + i (1 x) ~~ t. iM/i (1 — a:)|, 
and so 
F ' 
(1 + a;) ■ 
1 - Jj ( 1 -f* tA') 
■ - -‘'d ■ 
1 + a- — lWi (1 — x) 
“ 
L 
^ E “ 
aA - - 
.oj 
whence 
{1A + ‘"‘h 
[-{ 
' - - i' - 'h .MA ’ 
1 + ai \ 1 + I'l’/ 
I 1 
I 
1 — 
A AA-2iM/i 
and if 6 be the angle through which the major axis of the ellipse of polarisation of 
the transmitted lioht is rotated from the axis of x towards the axis of v, 6 is the real 
partofF/E. For a given metal, and given values of Ji and this angle can be 
calculated exactly from the above formula, but such calculation would be very 
tedious. It is well therefore to examine the relative magnitudes of the difi’erent 
terms in cases corresponding to the known experiments on this subject, in order to 
see whether there is any approximate formula of a simpler character. It will be 
sufficient to consider some of the experiments on transmission through films of iron 
described by Lobach (‘ Wied. Ann.’ vol. 39, p. 356) and by Drude (‘Wied. Ann.’ 
vol. 46, p. 416). 
Now 
1 — X R — cos a. + t sill « 
1 + a; R + cos a — t sin « 
_ / IF + 1 — 2 cos 
\lk + 1 -I- 2 cos a/ 
