55 
Captain Hall's comet seen at Valparaiso. 
In this case, comet's hel. long. =earth's long. — TSP. Also 
dhz\. lat. (7r)=x tan SCT cot CST tan 7 r. - - (3) 
d hel. long. [f 3 ) = — x cot TSP tan SCT (tan CST" — cot CST 
tan 9 tt) — ( 4 ) 
These angles SCT, &c. are found in the course of the cal- 
culation. 
If ( 3 , 1 G' 13 " represent three hel. longitudes, and 7r, 7/ tt" re- 
present three hel. latitudes, and V, V' represent the bases of 
two spherical triangles of which the sides are 90 0 — tt, 90° — 7/ , 
and 90° — 7 r, 90 — tt", and the vertical angles ( 3 — ( 3 1 and ( 3 —‘f 3 " 
respectively, 
cos V= cos ( 7 r — 7 r') — 2 sin*£ (jQ— ( 3 r ) cos 7 r cos 7 r (5) 
cos V= cos (tt — 7r") — 2sin 1 -±- [( 3 — jG") cos 7 r" cos tt (6) 
Taking the observations of April 8,21, and May 3, and the 
above values of p and t, 
Anomalies. 
Hel. Long. 
Hel. Lat. S. 
April 8 
Zl 
May 3 
O / !/ 
I 39 4-6 38* — v 
146 38 6 —v 
150 12 IO —v" 
s * 0 1 « 
2 5 17 1-0 
2 3 47 4 °=^' 
2 2 35 30—0' 
O t // 
48 55 1 9 — ’T 
42 43 42 = ^ 
39 22 30— n" 
If \J=v'— v and U 
The observations of April 8 and April 21, give 
U==6° 51' 28" Yz= 6 °i 6 ' 44" 
Those of April 8, and May 3, give 
U'=io°2 5 ' 3 2" V'= 9 0 44' 12" 
Therefore because U + t/U =V -{- dV 
and U'+^U'^V'+^V' 
* 1 he results are put down to seconds ; but as only five places in the logarithms 
were used in this part of the process, they may sometimes err by several seconds. 
