285 
3 SGI.] The great Comet of 1861. 
But c * 2 is never likely to exceed 1, in the parabolic orbit visible from 
the earth, and therefore this value of S is rejected. 
Supposing 8 to he i and 8 2 = then T = 11 days nearly. Tab. II. 
i and S 2 = J T , ~~ T = 9.76 nearly. 
t 2 t and 8 2 = — T = 10.19. 
log of 8=9.0704073 and log of 8 2 =8.1408146. 
Try t 2 t = .1176 = 8 .-. 
r 2 
Sec 2 £ 0.488712 
Log5 2 8. 1408146 
8.6295266 =.04261149 S 2 
0.2454391 
9.0704073 Log S 
9.3158464= .20694108 
1.033835 R 2 Nat No. 
.0426115 8 2 Nat. No. 
1.0764465 
.2069410 5 Nat No. 
.8695055 = r 2 
2) 9.9392723 = log r 2 
9.9696361 = log r 
.-.«• = .9324727 
r" = 1.0315113 
r + r" 1.9639840 
c= .2482249 
r j r r" + c— 2.2122089 
Log 0.3448262 
3 
2) 1.0344786 
log(r+r"+c) g 0.5172393 
Nat No. = 3.290329 
1.2043834 
8.1408146 
9.3451980 = .2214104 
0.2089636 
9.0704073 
9.2793709 = .19027020 
1.032975 
.2214104 
1.2543854 
.1902702 
1.0641152 = r" 2 
2) 0.0269478 
0.0134739 
.-. r" = 1.0315113 
r= .9324727 
1.9639S40 
c = .2482249 
r + r"— c= 1.7157591 
Log = 0.2344564 
3 
2) 0.7033692 
0.3516846 
Nat No. 2.247422 
0.7930186 
8.1408146 
8.9338332 = .085S6S3S 
9.6526360 
9.0704073 
8.7230433 = .05284978 
.0285970 
.08586838 
.11446538 
.0528 4978 
.06161560 = c 2 
2) 8.7896906 = logc 2 
Log of c 9.3948453 
.-. c = .2482249 
(f+f" + c)® = 3.290329 
(r -f — c) 2 = 2.247422 
0.0182430 = 1.042907 
9.0137302 = 6/j. 
1.0045128 =T ,=10.10445 
T =10. 
f 
Error -j- 0.10445 days 
Thus it appears that .1176 is considerably too much ; and we 
must make a 2nd supposition, which, from having no precise data 
for proportioning, must he somewhat of a leap in the dark. Let us sup- 
pose 8 = .1160 : then the whole computation for the 1st supposition 
must he repeated for the 2nd 'and every successive approximation : 
a tedious and most fatiguing process. We shall tabulate only the 
results ; observing that after the 2nd approximation, we can propor- 
tion for the following, and thus slowly hut surely arrive at an 
accurate value of S. 
2 O 2 
