850 MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
Writing '^’ ^ — M, the equations become, dividing out common factors, 
such as 1 — cos^ ^ (C — and neglecting S^, . . . as before, 
(cot. (^o — 'ii) “ tM] (I — tS/Ao cos 4 ) 
I _ (A /^o~) _ go sin (tg q) /q _ ^ 2\ 
y^u/^ sill (i:„ + h) sill (io + h) ^ 
t8' 
{(A - /^Q-) (A - + (yu-d" - /^u~) (B - C)} . sill ^ sin q . 
(yud + gill ^ q) |cos (io - h) - tM sin (lo - q)} 
_ S / A _ 3\ MoAt'i . COS (iq h) (sin tq sin ^'l t sin (i^ q) (stg sin q u-y sin ^'Q) 
^ ^ yu-f _i_ ^^2 y . {cos (iy — h) — tM sin (ty — q)} 
P.(A' 
1 \ /ty 
M 
(<o—ii) 
Sill 
cos ('iy — h) — tAI sin (ly — q) 
= — (cot (iy + ii) + tM) (1 + 1 8 / 1,0 cos iy) 
I __ 1 8i^ (A /ly") _ g2 sin (iy + h) /q _ g. 
/iy/ii sin - h) sin (4 - q) ^ 
— t 83 {(A - /t,/) (A - /td) + (/ti^ - /t ,, -) (B - C)} sin 4sing. 6‘(^'<>-0 
(/id + /ty-) sin (4 — 4) {cos (4 + 4) + iM sin (4 + 4)} 
- S (A - /X, 
- iS^A' - 
2 /iy/ti cos (4 + 4) 4 i^hi 4 — «yoei) + t sill (4 + 4) (ttp sin 4 — «i sin 4) 
O I f 
/t] + /ty' 
I \ /ty 
M 
1 ^. {cos (4 4- 4 ) + AI sin (4 + 4 )} 
7»i// siiiiy cos (4 + 4) + tM sin (4 + 4) 
and 
.<. [cot (4 — ij) — tM} (I — t8/ty cos 4 — ^SVo^ COS' 4 ) 
2 cos 4) sin 4 
Bracket 
of r 
sin(4-4)sin (4 + 4) 
1 _ 8 (A - /tyg)--^^^ • Sin4siivq «y«i _ 13 
Vi“ + /to" \ my-/sin iy J 
Now r = Re‘4 A' = Se“"; hence changing t into — i, multiplying and dividing- 
corresponding equations, and, as before, neglecting 8®, 8'^ ^ (and, thei’efore, 
8' (sin 4 sin 4 “ “u°^i))> '''c ^*oid 
