a first Approximation to the Oihit of a Comet, 177 
and therefore the terms of the higher orders, which are omitted, 
may be supposed to affect the errors in the fourth and fifth 
places of figures, beyond w'hich degree of exactness the ap- 
proximation is already carried. To compute the elements of 
the orbit, we have 
rb 
cos. (p (J5 = 38® 38' 
r—r' 
— cos. ip = 130 8 
6 " 
Anomaly u = 4 ^ — <p == 91 30 
= cos. (p' *.• (p 116® 42' 6 ^" 
l^^ = -cos.iI;'*.-4/'= 49 51 
Anomaly u' = (p' — 66 50 28. 
Then, D = r cos."* — = 9‘57%^35 logarithms 
\ 
/ 
D = r'cos.» = 9 ‘d 7 %^ 35 - 
The times corresponding to tlie anomalies, taken from the 
table, are 
days 114*048 days 62*1248 
log. ^ 2*0570877 log. 17932^0 
log. D^, 9-3648453 log. D^, 9*3^48453 
1*421933^ 1*1581103 
Num. 26*4200 Num. 14*3916: 
tlie difference of these two intervals is 12 0284 ; but it should 
be 12*0360: I therefore add 0*0038 to the first, and subtract it 
from the second interval ; then they are 26 4238 and 14*3878: 
and by adding these corrected intervals, to the times of the 
observations, the time of the comet's passing the perihelion 
will come out, Nov. 18*1087. 
A a 
MDCCCXIV. 
