1907-8.] Sunset and Twilight Curves, and Related Phenomena. 327 
XIII. e>72° 
1. 
a< tan 
1 \ cot e 
a 
a 
d 
f 
e 
2. 
<90°- 
- e 
c 
a 
d 
f 
e 
3. 
< sin - 
1 cot e 
b 
a 
d 
f 
e 
4. 
<180° 
-2 e 
b 
d 
a 
f 
e 
5. 
<t e 
d 
b 
a 
f 
e 
6. 
< 2 sin 
-1 \ cosec e 
d 
b 
a 
e 
f 
7. 
<120° 
~h 
d 
b 
e 
a 
f 
8. 
< e 
d 
e 
b 
a 
f 
9. 
>£ 
d 
e 
b 
a 
9 
§ 22. We are now in a position to tabulate the sequences of phenomena 
that appear for any values of e and a and for values of <p varying from 
0° to 90°. 
It will be seen from an inspection of the results of the last section that 
there are only 22 distinct cases. These are tabulated as follows. It is to 
be noted that the sequence which holds for each number which is mentioned, 
holds also for the corresponding arabic numeral under each of the follow- 
ing roman numerals up to the next mentioned. Thus the sequences for 
I 6, II 6, ... V 6 are the same, and those for VIII 3, . . . XIII 3 are the 
same. 
I b 
12, 
V 2, 
13, 
IV 3, 
VIII 3, 
I 4, 
II 4, 
VI 4, 
15, 
III 5, 
VII 5, 
16, 
VI 6, 
X 6, 
VI 7, 
XI 7, 
VI 8, 
XIII 8, 
VI 9. 
§ 23. We have then the following table of sequences of phenomena. 
The figures in heavy type refer to the diagrams in Plate I. 
I. e< 24° 6' 
1. a<fe <£<sin -1 (sin e sin a) 2 
< 90° — e — a 1 
< 90° - e 4 
< 90° — e + a 7 
< 90° - ® 14 
>9°°- I 
15 
