836 MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
Thus, we have finally 
1 = Wo - i 8 (uo + Ui) + lvB {v^ - t’o) [ - 8no [' 
J Q //t' J Q III/ 
(n)| = i = Ho + ivVq. 1 — Sh|j^/x277(l — ^'q)ctrj — ^ 
— ivl\ 
^(Iv \ 
+ Vi 
1~S^.|[ /M^(l — ‘r]Y dr) ^ 
-'0 
1 
J J 
1 4- 8^. j p?r) {I — rj) dr) — \ v' 
-i«^no.83 
1 J /f?y \ 
viwA., 
(A') L = _ Siv 
— 8up 
rj d^rj 
Tt^? 
-|- . IV 6^Ma . 
[ )jdr) dr) — v^ -{• v^ { 
Jo Jo 
[ IX^.{1 — r)) dr) —\v- 
UO 
[\y v~^ 
-f 
+ iv 8nQ 
clrj 
0 
^ • (TII). 
§ 4. Summary. 
The conditions determining r, r', . . . are 
Vibrations y)e7'pendicular to plane of incidence, when 
cho 27rwo ■ /-, X 1 ^ ^TTWi 
a? = 0, -J- =. I —— cos ^0 (1 — when x — a, — — 6 —— cos ^|. s. 
" K ' dx K 
dx 
dx 
Vibrations parallel to plane of incidence 
Electromagnetic Theory, when 
X = 0, 
dv _ ^ __ when x = d, ^ = ' 
dx 
- — t -cos-' .s. 
dx \ ‘■ 
Elastic Solid Theory, when 
dv 2 iTt /Xa f c) ‘ / -t \i •* 
aj = 0, T- = t [cos^^o (1 ~ '^1 + “o I J 
(EC A 
when 
iTT fJi 
\ 
{cos- fpS — sin fis'}, u — — (sin iyi + af), 11^ = yf 
