98 
MR. J. G. LEATHEM UN THE THEORY OF THE 
where Re”" is the quasi-refractive index of the metal (J. J. Thomson, ‘ Recent 
Reseai’ches,’ p. 419). 
11. Let ns now substitute the assumed exponential expressions for {u, v, w) in the 
surface conditions ; we thus get 
— — A|j -j- " A — — ■ A^ — Ao 
m m rn-^ nt.^ 
11(A„+A) = H' (A,+ Ao) 
H (Bo + B) = H' (I A, - t ^ Ao 
^ ' \ ///, ^ tUc, 
CO.2 
Hla 
--A,- -A.3 -r;3(A, +A, 
m 
m.-, 
Vii - -- -^1 ~ 
m. 
nu 
.Ht (??iBo “ ^nB) — IT (— cojA]^ -j- co^A.^ 
— |-)7i (— t/Aj — dAo) — 173 (oyqA| -}■ ^”^'3-^-3) j 
(32). 
We may make the form of the first of these equations analogous with that of the 
others by multiplying it across by Hoj'’ or The four equations may then be 
written as follows : 
11 (A,, + A) = IT (A, + Ao) - HA.773(y^ A^ 
11 "’- (Ao-A) = H'n-(^'- + ^^ 
Ao 
in. 
H'-w (T + T 
m. 
rn 
in 
1 
Ilia 
i- (33). 
Hi,(B,. + B) = H'(^A, 
\ni. 
A.,') - (A, + A,) - ^ 
' \in, m.t 
Hi 
— lL;n(Bo — B) = H'(co^A^ — cooAj) — H''hT73(?iqxAj + xh^-z) ~ H'~t77i/(Aj -|- A 2 ) 
When we substitute in these the values of aq, coo, m. found above, and neglect 
small quantities of the second and higher orders, we get 
U (A„ + A) = H' |l - ^}(A. + A.) - (A, - A.,) 
11 y (A„ - A) = H' |(A, +A,) - + M,s) (A, - A.) 
- Hc(B„ + B) = H' T (A, - A.) - + M,,) (A, + A.) 
- Hmi (B„ - B) = H'n (A, - A,) - . {Ir,, + Mi,,) (Aj + A.,) 
A (34). 
