1907-8.] Sunset and Twilight Curves, and Related Phenomena. 325 
V. 42° 41'<e< 45° 
1. 
a < tan 1 \ cot e 
a 
c 
d f e 
2. 
c 
a 
d f e 
3. 
< € 
c 
a 
d e f 
4. 
< 90° - € 
c 
a 
deg 
5. 
<2e 
b 
a 
deg 
6. 
>2e 
b 
a 
g d 
YI. 45° <e<51° 50' 
1. 
a<tan 1 \ cot e 
a 
c 
d f e 
2. 
<h 
c 
a 
d f e 
3. 
<90° -e 
c 
a 
d ef 
4. 
< e 
b 
a 
d ef 
5. 
< sin -1 cot c 
b 
a 
deg 
6. 
< 180° — 2e 
b 
d 
a e g 
7. 
< 2 sin -1 \ cosec e 
d 
b 
a e g 
8. 
< 120° — fe 
d 
b 
e a g 
9. 
>120°-|e 
d 
e 
bag 
VII. 51° 50'<e<54° 
1. 
a < tan 1 ^ cot e 
a 
c 
d f e 
2. 
< § e 
c 
a 
dfe 
3. 
vu 
1 
0 
o 
05 
V 
c 
a 
def 
4. 
< sin 1 cot c 
b 
a 
d e f 
5. 
<e 
b 
d 
a e f 
6. 
A 
I—* 
00 
© 
l 
to 
b 
d 
a e g 
7. 
< 2 sin 1 J cosec € 
d 
b 
a e g 
8. 
< 120° - ft 
d 
b 
e a g 
9. 
>120° - |c 
d 
e 
bag 
VIII. 54° <e<58° 
1. 
a < tan 1 \ cot e 
a 
c 
df e 
2. 
<90° -e 
c 
a 
d f e 
3. 
< l e 
b 
a 
dfe 
4. 
< sin -1 cot e 
b 
a 
def 
5. 
<€ 
b 
d 
a e f 
6. 
< 180° - 2e 
b 
d 
a e g 
7. 
< 2 sin -1 1 cosec e 
d 
b 
a e g 
8. 
< 120° - |e 
d 
b 
e a g 
9. 
> 120° — §€ 
d 
e 
bag 
