MR. G. A. SCHOTT ON THE REFLECTION AND REE'RACTION OF LIGHT. 845 
We get, collecting the terms, 
cos 4^. [1 — t S/jto — 8 ® (F — ^ — cos {1 + (E — 
+ L sin 4 . r' (I + S/j-oCiQ + 8 ". (^ — F + ^ v~)} — t sin ..§'.{ I + 8 ^ (E — l 
= — cos i'o . (1 + t Sfj.Q cos — S® (E — i i'®)] .(1), 
sin . r. (1 — t 8 /Xq cos Iq . (I- -f B')] + sin . {1 — t 8 / 4 ^ cos (4 — B')l 
+ r . {ao + 8 ^ 0 . (sin2 . A + B' — A')} + s'. [«! + 8/^1 siiA (i 
= sin 4 . {1 + t 8 / 4 o cos (-1 + E') }. 
-B')} 
( 2 ), 
gQ Sin ?o cos ^o 
. r . 11 - 4 8 ^ - 8MB - 1 D - 14.2 
L A^o cos 
— /x^ sin cos ^\ . s . {1 + ^ 82 (D — ■§■ 4 ^“)} 
— tixo cos2 A. r . 1 1 + 8 ao “— ^ tan2 1 ,.. (B — i D 
+ t/X] cos 2 s'. {1 ~ 2 tan 2 (D — -I v ^)} 
= - /xo sin ^ cos to. {1 + t S MVosT “ i D - 14 . 2 ) 
I UUo t-Q 
1 2 
3 •' 
(3), 
/Xo cos2 to. ?■. «! 1 - 4 8 - S'^ taii2 to (C - 1 4.2 
+ /Xj COs 2 tj . S . ^ 1 — 4 8 
B - 4.- + 4.-B^ 
/4j cos 
• • . 1 C — — A^oMI — A') , 5,0 
H-O sm ^o . r \ ao “ o-+ §““0 (E 
A^o 
B - 4 .- + 4.-B^ 
A^i 
= /xo cos2 to. 11 + 4 8 ^— 82 tan2 to (C — i 
L A^o cos io 
— tv 
— /Xj sin tj. s'. 1 C 4 ^ — 8 
(4). 
In working wdth these equations we shall throughout neglect 8'^, 8^, 82A', A'2. 8, 
&c., &c. 
We may thus in terms of order 82 , interchange ^qj sin to and a^, sin t^. 
Multiplying (l) by 4 . = p-o sin to = ju.^ sin t^ and subtracting (3) we have 
4 8 sin to . r {A — — 4 8 p,o cos to (B — -|D — F — ^4.2)} 
— 82, sin tj cos t^. s . (E — -^D — ■g-4'2) 
+ t’’' • {/^o d- S^qA + A^oS® sin2to (B — ID — F + f/xo^ — -^ 4 . 2 )} 
— 4S' . [/Xi + /x^ 82 siiA tj. (E — — ^4.2)} 
= 4 8 sin tg. IA — jXQ^ A 1 8/xo cos tg (B — — F — ^v'^) ] . . 
( 5 ). 
