MR. G. A. SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT, 847 
Ls' (a^ sin ig + olq sin i^) 
= r 
{ot-Q COS ig — L sin^ ig) (1 — t cos ig — i S' (C + ^/i„“ — v')} 
-iSfA'- 
7 ) 1 , 
0 J 
2 / H'O ' ^ 
{ag cos + L sin ig sin 7j) {1 + 8‘^. (C — 
-iS.lA'- A). 
Wo" 
1 ^ 0 ^ 
- “1 
+ 
(ag COS ig + t sin^ ig) { 1 + t hfJig COS ig — 4 S- . (C + ^fXg~ 
1 
771 , 
2 I * f ^ 
u^)] 
^ ( 8 ). 
Substituting from (7) and (8) for r^, s' in (5) and rearranging the terms, we tind 
{fjLg (aj cos ig + t sin ig sin ^\) + (ag cos ig — i sin^ ^o)} (1 + 2 
+ S. (1 — t SjjLg cos ig) Aa^ (ag cos ^g — t sin^ fg) — t S/Xg^a^ cos 2ig 
- L S/Xg^^ag COS ig. e-“» - 4 8 (^A' - . (/X^S - ^^3) 
+ i cos ^'o A - I 8 ^ (^ 1 ^ — /Xg^) COS ig — 8 V /Xg sin i^e~ 
— ^ 8^.{/Xg sin cos 2ig + sin ig cos 2^^) (C + i t^o^) 
/Xg (a^ cos — t sin^ h) + /^i + t sin ^g sin 
- s. + 8 (A - /Xg2) ag (a^ cos - t sin* i^) _ i 8 ("a' - (/Xi* - /Xg*) 
+ I 8* (/Xg sin cos 2^Q + /x^ sin ig cos 2^^) (C — -| /Xg*) e~“i 
{/Xg (a^ cos ^g — t sin ig sin ij + /Xj (ag cos ig + t sin* ^g) j (1 + ^ 8*z^*) 
+ 8(1 + 18 /Xg cos ig) Aaj^ (ag cos ig + t sin* ig) + t 8/Xg*a^ cos 2ig 
- + t Vo/^i«o cos ige“» - 4 8 (A' — 1^) (/xi* - /Xg*) €-“■» 
\ / /n 
+ 4 8/Xg/x^ cos ig i S + (/^i^ - f^o^) cos ig ^ 3 - 8*1/* /Xg sin 
— ^ 8*. (/Xg sin i^ cos 2ig + /x^ sin ig cos 2i^) (C + -g/Ag^) e"" 
