832 -hm. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
hence 
and v <'?/.{ I + +...]< - — 
which is finite as long as 
r/ I 
S < --- or — < - • 
fx A, b zo. yU, 
As before we neglect 8“^ and higher powers, and find 
f(M\ cos“^, > fdv^\ cos^fi - . 
(^L .=^&'- "»>’ ^ 
2 _ ^2 
since v = a sin and thus ^— = cos^i 
(hr\ 
COS^^Q 
7r(I) JO 
COS' 
Jo 
.^A=i 
(’’■(I) - 7r(T7)}2.f?77 d-Vi |^/x3.(7r(l) — 7 r{r])} tt {rj) drj 
= — {77(1) — 77(77)] 7 T{ 7 ])dr] + j'^/x 2 .{ 77 (r 7 )] 2 .f /77 
H ence 
/ (h\ 
l^A=o 
=1 
cos- 
77 ( 1 ) 
Vq. 
, COS- ^0 
cos- %, 
77 (1) 
Vq. 
1 - “ '^{iWdri 
1 -'^iv)} 77 ( 77 )c /77 
f { 77 -(l) — 77(77)] 77(77) 
j 0 
1 
(VI.) 
1 + 
( 1 ) 
+ 7(1? L'*'- <k 
Vibrations parallel to the plane of incidence (Elastic Solid Theory). 
The equations to be solved are (III.), p. 829, adding the third multiplied b}7 tSr 
to the second for a new^ second,— 
^/n 
dv 
dh 
d} ^ ^ ~ dJ~ ~ • (1 ~ n + SV (/x2 - 1/2) -u = 0, 
d^ 
d^^ 
+ iSv. V + 8 ^ = 0, 
d^ m~ 
