MR. G. A. SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT. 
849 
[ 1 — t S/X,3 COS Iq — \ COS^ -io + 2 • (C* ~ 2 il^O^ • (“l “ *' 
+ (“o cos 4 — I sin^ Iq) + (a^ cos ig + ag cos + 2t sin ig sin i\)} 
— l 8. ((1 — l S/Hg cos Ig) (A — /Xg^) — t 8 (/Xl cos ^l — /Xg cos ?g) (C — ^ /Xg^) } 
[/Xg (cos ?’g + tag) (a^ COS — t sin^ i\) + /Xj (cos + taj) (ag cos ig — t sin" tg)] 
— I 8“. {(A — ixq^) (A — /Xj^) -i- (^ 1 ® — /Xg2) (B — C)] sin ig sin 
- i 8 A' 
«v/ /^1 
(/^i^ - /^o^) (^0^ 
— 2 flQ cos ?g . 
(Mo“i + H-i^o) {1 + i ~ 2 /^o")] 
— 8. (sin ?g sin t\ — aga^) (A — /Ug^) — 8 ^A' 
^0 
7no7 Ml 
il^i' - H-o^) 
We easily find 
/xg2 (a^ cos — t sin^ g)+Mi^(“u cos Iq—l sin^ {q )cos tgd- ag cos -{- 2t sin fg sin 
_ sii^ [(/xgaid-/Xiag)cos ( 2 g— 2 \) —t(Mi sin ^g— /xosini\)sin (^g— ^l)}, 
—/xg^(aj cos ^\ —t sin^ cos tg+t sin^ ig) —/ixo/xi(“ocos —“i cos ^g+2t sin tg sin ij) 
= ^'sin(?g —^J) {(/xoai+/xiao)cos('/g+ti) + t(;ixi sin tg—/Xgsin t'l) sin (/g+ii)}, 
N- 
+ /xi^"" = sin(^g + h).e‘'‘“ ih 
MoMi 
V 
Mo (cos ig + tag) (aj COS fj — t sin‘^ z]) + /Xi (cos z\ -|- taj) (ag cos ?’g — t sin^ tg) 
/ • • \ / I \ f 1 MdMi (^'o ^i) / • ■ • 
= COS (zq - ii). (/Xo“i + /^i“i) 1 1 - ^ i:;TT 2^ .1,, . ci.. ; (®‘“ ^0 sio ^1 - “o«i 
(Mr + M(|“) sin 4 sin tj 
MoMi si'i (i„ + h) 
t sin (tg — t'l) (mi sin Xg — /Xg sin Zj) 11 — ^ “73 
/Ufj^) sin ig sin i 
r (a,, sin — a, sin v,) i 
i,j ^ 1 1 U/ J 
Mo (cos ^g — tttg) (aj cos z] — t sin^ z]) + Mi (cos + t“i) (“0 cos tg + t sin^ ig) 
= cos 
MdMi sin ( tQ ?g) ^ ... . >1 
-sin ti — agaj 
t/Q / / . 
^—:—:—r (Sin Sin 
>1 /I Ol »i -1 ' ^ 
(i« + h) + ^i«o) {1 - - 
I * * “‘xfi MdMi sin ("tg / .. ••\1 
+ I sin (/g + ) (mi sin tg - /Xq sm i^) | 1 - 1 (^^2 _ ^2) sm^gsin^^^ ^“0 ~ J ' 
MDCCCXCIV.—A. 
5 Q 
