1907-8.] Sunset and Twilight Curves, and Related Phenomena. 321 
§ 16. There are fifteen different forms of yearly phenomena, and they 
are represented in Plate I. The following is a description of the diagrams, 
using the notation explained above : — 
1, 2 DTN 
always. 
4, 5 DTN 
8< 90° - a — 
DT 
8> 90° — a — cf>. 
3 DT 
always. 
7, 8 TN 
8<<£ - 90°, 
6 DT 
8 < a — cf) — 90°, 
DTN 
<£ - 90° < 8 < 90° - a - 
DTN 
a — cf> — 90°< S< 90° — a - <f>, 
DT 
90° — a — </> < 8< 90° — <£, 
DT 
8 > 90° — a — </>• 
D 
8 > 90° — </>. 
9 T 
8<<£ - 90°, 
10, 11 TN 
8 < 90° — a — cf), 
DT 
cf> - 90°<8<90° - <f>, 
T 
90° — a — cf)<B<cf) — 90°, 
D 
8 >90° - cf>. 
DT 
cf) - 90°<8<90° - cf>, 
D 
8>90° - cf). 
12 T 
8<a - <f> - 90°, 
13 T 
8< a — cf> — 90°, 
TN 
a- cf>- 90°<8< </> - 90°, 
TN 
a — cf) — 90° < 8< 90° — a — 
DTN 
cf> — 90° < 8< 90° — a — cf), 
T 
90 u — a — cf) <1 8 <C cf) — 90°, 
DT 
90° - a - </><8<90° - cf>, 
DT 
eft — 90 <8<90° - </>, 
D 
8>90°-c f>. 
D 
8 >90° - <£. 
14 N 
8< cf> — 90° - a, 
15 N 
8<^> - 90° — a, 
TN 
cf> — 90° — a < 8< <f> — 90°, 
TN 
<£ — 90° — a< 8 < 90° — a — 
DTN 
<f> - 90°<8< 90° - a — <f>, 
T 
90° - a — cf)<$<cj) - 90°, 
DT 
90° — a — <f> < 8< 90° — cf >, 
DT 
cj)-99°<8<90°-cf), 
D 
8 >90° - </>. 
D 
8 > 90° — <£. 
§ 17. The following criteria which follow from the subsequent investi- 
gations (see p. 334) are here tabulated for convenience. 
6 
) 
< 
^ a 
- e, <90 - -~T. 
12 
r </><€ + a - 90°, 
>90° 
13 
) 
> 2 
[0<9O’-e-a, 
^sin 
< 
_1 (sin e sin a). 
y 
) 
< 
7 
/ > € + a — 90° 1 
> > 
> 
< 
10 I 
5 
1 ) >90° -6- 
| h< < 90° + c - 
■a ( 1 
■“ 1 ) 
sin -1 (sin e sin 
a), 90° - 
< 
> 
■ e , 
8 
V < 90° — e + a ; - 
> < 
> 
< 
11 J 
) 
> 
g j ’ </> > 90° + e - a, 
< 90° 
> 
— e. 
14 i 
15 j 
|- cf) > 90° — e + a, 
<90° 
a 
- ~2‘ 
VOL. XXVIII. 
21 
