84B MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
Similarly, from (2) and (4) 
r . {jX(^ — tS cos L^ (C + — H'd sin® Iq (C — -gv®)] + s . {/x^ — 18 cos i-^ (B — ^i^)} 
-|- S^-' sin {q. [C + — /Xq® — Sy (C — ^y^)} + 8s' sin . (B — -^y^) 
= /Xq + 18 cos ^Q (C + ^y'^) — /Xq 8® sin® ^Q. (C — ^y^) .(6). 
Multiply (l)by «, |l — 8(|jp,a, + i-B' — 
(2) by + 
and add, using the relations otg = 
+ i S^ (F - E - if.,/+ 
whence 
«i) , sin 4 
sin ?■„ 
sin ^ 
v-f 
sin Zj o I X • 
- - = 2 + terms in —: . . . . 
?/?■* 
and neglecting’ terms of order 8^, 8® —, 
. we have 
tr'. («! sin sin t\) 
r 
(a, COS i], + t sin if, sin ^J) {I — t 8/Xye "» — ^ 8® (C + ^/x,/) e ®“"} 
-hiSA'.^. €“» 
/V 
+ .s (aj coszj — tsin®t\) [1 — 8i/d-:|8®. (C — ^/X|®+i^®)} d- ^8A'. ” . e 
L 
(«! cos ff) — I sin if, sin ^l) {1 + i 8/Xf)e‘''’ — ^ 8® (C + ^/u,q®) 
O 1> (7)- 
+ 1 SA' . e-.. 
Again, multiplying 
(1) by «„ {1 - S - .B' + J A' + t S^ (F - E - ip/ + } . 
(2) by . Bin {1 + i S (a' - A) _ i §=. (C - ip/)} , 
and subtracting, we find 
