283 
1861.] The great Comet of 1861. 
For denominator. 
m = 0.358099 
Sin V — A ''=9.9718945 
0.3299935 Nat no. 2.137935 
tang, f} 1 ' = 0.2760130 Nat no. 1.888018 
Denr. .249887 
Numr. = .467980 Log 9.6702273 
Denr. = .219887 Log 9.3977436 
Diff = 0.2724-837 
Log L= 0.0000000 
t 
11 = 0.2724837 
and 
M 2 = 0.5449674 
This may be cheeked by the formula 
tang. /3 sin L' — A' — tang ft sin L' — A t’ 
M = 
tang. ft sin L' — A" — tang ft sin L' — A' t 
Having thus found M we proceed to find the values of r\ 
and e 3 . The formulae are 
; 
,79 
r 3 = R 3 + Sec 3 /3 S 3 + 2 8 R cos L — A 
F' 3 = R" 3 + Sec 3 ft' M 3 S 3 -f 2 S R" M cos L" — A" 
Leaving 8 to be afterwards determined, we find — 
For r 2 Nat No. 
See 2 0 — 0.488712 = 3.081145 5 2 
2 = 0.3010300 
E = 0.0072256 
Cos L — A = 9.9371835 — 
— 0.2454391 = 1.759720 5- 
E 2 = 0.0144512 = 1.033835 
For r>’ 2 Nat No. 
Sec 2 0" = 0.6594160 
M 2 = 0.5449674 
1.2043834= 16.00970 
2 =0.3010300 
K" =0.0070449 
M =0.2724837 
Cos L''- A"= 9.6284050 — 
— 0.2089636 = — 1 .6179442 
E" 2 = 0.0140898 = 1.032975" 
r 2 = 1.033835 + 3.0811450 5 2 — 1.7597200 5 
r" 2 — 1.032975 + 16.0097000 5 2 — 1.6179442 5 
r i + ,."2 _ 2.066810 + 19.0908450 5 2 — 3.3776642 5 
The formula for c 2 is 
e 3 — r 2 + r " 2 ~ 2S 3 (cos A"’ — A -j- tan g/3 tang ft ) M — 2SRM 
cos. L — A" — 23 R" cos L" - A — 2 R R" cos L" — L. 
2 o 
