284 
[No. 3, 
The great Comet of 1861. 
2 = 0.3010300 
R — 0.0072236 
R" = 0.0070449 
Cos L"— L = 9.9939490 
0.3092495 
Nat No. 2.0382130 
Cos A" — A = 9.854640 
tang /8 = 0.159149 
tang /3" — 0.276013 
0.435162 
Log = 0.5364658 
2 = 0.3010300 
M = 0.2724837 
1.1099795 
Nat No. 12.8818872 
2 = 0.3010300 
M = 0.2724837 
R = 0.0072256 
CosL — a" = 9.4298720 — 
0.0106113 — 
Nat No. — 1.0247343 (1) 
2 = 0.3010300 
R" = 0.0070449 
Cos L" — A = 1.9714841 — 
— 0.2795590 
Nat No. = — 1.9035270 (2) 
Nat No. = — 1.0247343 (1) 
— 2.9282613 5 
Hence c 2 = 
.715550 
2.723717 
3.439267 
r* + r 2 = 2.066810 + 19.0908450 5 2 — 3.3776642 S 
Remr. = 2.038213 + 12.8818872 5 2 — 2.9282613 S 
... c‘ = 0.028597 + 6.2089578 5 2 — 0.4494029 S 
We have now values of r 2 r" 2 and e 2 in terms of the unknown 
quantity 8, viz. 
r 2 = 1.033835 + 3.0811450 5 2 — 1.7597200 S 
,. "2 — 1.032975 + 16.0097000 5 2 — 1.6179442 5 
c 2 = 0.028597 + 6.2089578 5 2 — 0.4494029 8 
— 3 
To findS, we have the formula 6/a T = (V + r"+c) 2 — (r+r ' — c) 2 
where T is the time between the 1st and 3rd observations, and 6/a is 
a constant, of which the logarithm is 9.0137302. 
It is evident that 8 can only he found by successive approxima- 
tions, and by a very tedious and laborious process. Table II. of 
Bowditch gives the corresponding times to any values of r 3 + r'' 2 , 
and c 1 ; or more nearly to r + r" found at the head of the column 
and c at the side. 
If we suppose 8 to be 1, then roughly 
+ r" 2 = 2.0668 c a = 0.0286 
+ 19.090S + 6.2089 
21.1576 
— 3.3776 
6.2375 
— .4494 
18.7800 
5.7881 
