844 iMFI. G. A. SCHOTT ON THE R,EPLECTION AND REFRACTION OF LIGHT. 
AVhen ^ = 0, we have 
+ fl, 
82 
(f^i TMo)'" 
I H- 482 (A f,,n(A ^1^) + (B ^ C) 
(fly 
_ OO (A - fl,^) (A - fly^) + (B - C) (fly^ - fly^) 
(/^i + /^o-) 
the same as for vibrations per})endicular to the plane of incidence. 
When iy — -Itt, we liave 
R2 = 1 82 (2^ + /^oVl" ~ ~ ^ I 1 _ A §2 (A + G 
/^o" + /^G L "F iii~ 
tan p = dr tfF,n \tt according as 
PG _j„ ^^2 > A + G fiQfXy, tan cr — 
O A + fly^ + fly- — 
Vibrations parallel to 'plome o f incidence {Elastic Solid Th eory). 
The equations (VII'.) p. 8-38, give on substitution for v^, Vy, . . . 
— [cos iyy {I + r) -V L sin Iq .r] [1 — 82 (F — i^ 2 ^j 
+ [cos ?'j. 5 + t sin iy .s'] [1 + 8^ (E — ^2)] — b i-r h-yp-' 
— I 8p.Q {cos2 (1 — r) + ttQ sin iyy , r i 
— sin (1 — r) + ayyv' — lv S . [cos fo (1 + r) + t sin f,j. r'] (1 + B') 
— «/ 8. [cos iyS + (, sin i\s'] {I — B') — 8/aqA' . r = — (sin ly. s + 
py/ + O '. [cos iyy (1 + r) -h t sin q, .r'} [I — 82 (B — ^ D - ^ ^2)] 
— Lv [cos . s + t sin iy .s'] [1 + -g- 82 (D — ^ v'^)] 
+ 8 [ — sin iyy (1 — r) + a„r'] (A — v^) = pys' 
— 8 [cos iyy (I + r) + t sin ^„r'] (C — v^B') — 8. [cos qs t sin ^s'] (B — v' + wB') 
-Vltv Spo (1 — A'). r' + 82. [ — sin ?o (1 — r) + v'l (C “ i r~) 
— LjXy [cos2 qs — ay sin q .s'] — i/Xq [cos2 hyy (I — r) + sin iy ,. r^]. 
where we liave throimhout neglected except in terms of orders 8'\ 8'. 
