848 MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
In the same way we get from (6) 
r. 
/Xq- («! sin {q + sin g) (1 — t S/x^ cos g) — t S sin g («u cos — l sin^ (A — 
— S®/Xq cos if) sin sin g cos ^o + (B — C) e~‘^] 
+ 6-. 
fi) (a^ sin + a^, sin g) — t S sin {q (a^ cos g — <- siiA g) (A — Go') 
+ 2 lS^v sin G sin g (C — ^ /Xq^) e“‘*^ 
1 
J 
/Xq (aj sin G + ttQ sin g) (1 + t o^o cos g ) + sin g. (a^ cos g + t sin® g) (A — /Xq®) 
— S®/Xq cos g sin G sin g {)a,/ cos g + (B — C) e““}. 
Solving these two equations for r, s, we get, after some algebraic transformations, 
using the values sin g == sin® g — “i sin g = sin®G — neglecting in 
terms of order 8®, and finally discarding a common factor, ag sin g + sin g— 
{1 — t S/xq cos G “ i S®/xo^ cos® G + i (C — /Xg®)} {/xq'^•(«! cos g “ t sin® g) 
+ /x^®. («() cos G — <- sin® g) + /Xq/^i (“i cos g + cos g + 2x sin g sin g)} 
- 18 . ((1 — 18 /xo cos g) (A — /xq®) — 18 (/x^ cos g — /ao cos g) (C — -g-G o^)) 
{Go (cos g + cos G — <- sin® g) + /Xj (cos g + taj (ag cos g — ^ sin® g)} 
- t 8®. {(A - /xq®) (A - /x^®) + (/xi^ - /Xq®) (B - C)] sin G sin g.€-‘C»+''^> 
- 4 8 ^A' - (/xi® - Go®) (Goe"“‘ + 
{1 + t 8 go cos g — i S'Vo® cos® G + 2 (C — i /ao®)} [ — /^q® (a^ cos g — i sin® g) 
+ Gi^. (“o cos G + t sin® g) — GuGi (^o cos g — “i cos g + 2t sin g sin g)] 
— 18 . {(1 + t 8 go cos g) (A — Go®) — t S (gi cos g + Go cos g) (C — | go~)} 
(Go (cos g — (“i cos G “ <- sin® g) -f- Gi (cos g + ^“i) (“o cos G+ sin® g)} 
— 18 ®. {(A — Go®) (A — Gi®) + (gi® — Go®) (B — C)} sin g sin Ge‘Co-*>) 
— I 8 (^A' - (gi® - Go®) (Gi^"“" - Goe““0 ; 
and, in the same way. 
