MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 843 
Hence 
H-i 
Mo 
E2 = 
cos COS 
Ml _|_Mo^ 
1 + 282 
Mo K M 
Mo 
K 
Ml 
M 
\COS I 
1 
cos 
cos Zq a cos \ a 
Ml ^ Mo 
+ 28 
3 cos a cos a 
cos ^ 
cos tn 
Ml 
cos t 
1 
Ml 
cost, 
0 
H- 82 
J^iMo 
a 
0 \ cos cos to 
-A 
+ A 
Mo 
/ Mj_ 
\COS tj cos t, 
_ 5V3 \ COS t^ cos to 
2 ® 7 ij \2 
/ Mo 
\COS t\ cos tf 
tan® (to — tj) 
tan® (to + h) _ 
1 + 48V.,.„ cos i. cos 
^ ^ /t^-COS® to — /io^ COS-tj 
+ cos !„cosii Gyo«)sm'‘U{A (A G^,0sin-»i} 
^ (/Ltj-COS® tg — ^0 COS®ti)- 
2mo 
i2 _ 
COS t 
_Mi_|_ Mo 
'cos tj cos to 
Mo K Ml M 
1 _|_ 2 S® — + 2 82 
COS tn a cos ti a 
Mo 
Ml 
r + 
COS tj cos to 
a_Jhl^ + A 
\ 2 - 
g3 \ COS tj COS tg 
4 sin® t\ cos® t'o 
sin® (to + ti)cos®(to—tj) 
\cos tj cos tf 
] —82.(B —C —J sin Iq sin tj) 
(IX.). 
/ij cos tg - /tg '*'1 
yu-i COS t'o + /to COS if 
_ g 2 {A - /tp® - (A - G /tp^) sin®tp} {A - /t,® - (A - G /t^^) sin®t\} 
(/tj cos t’o + /tp cos tj)® 
28 
Mo Mi- 
tan p = 
COS tp \ cos® tj 
- A 
Ml' 
Mo" 
cos® t’l cos® tp 
" /tj® COS® tp — /tp® cos® tj 
since a = 1 — v-Q (p. 837), where v — Mq sin % = pi sin t,. 
8 . 
tan cr = 
a 
MiMo 
cos tf cos tp 
r +A 
Ml 
r + 
Mo 
COS tf COS tp 
_ S + A cos tp cos tf — G /t.o®/tf® sin tp sin tf) 
/tj cos t’o + /tp cos tf 
5 P 2 
