a first Approximation to the Orbit of a Comet, 16*3 
By a table of the motion in a parabola I have found the in- 
tervals corresponding to l» and u' 
i6* 1316 days, 
log. 1*2076773 
log. Di = 9'97 4,3123 
as follows, viz. 
and 5-5198 days 
07419233 
9-9742123 
0*7161356 
Num. 5*20 16. 
1*1818896 
Num. 15*2016 
These are the intervals between the two extreme observa- 
tions and the passage of the, perihelion, which according to 
the rule in No. 10, will be posterior to both the observations: 
therefore the comet will be in the perihelion, Nov. 29*5556, or 
Nov. 29, 13^^ 20' 4." 
M. Mechain has applied the method of Laplace to this 
comet, using as the basis of his calculations, five observations 
between the 24th and 25th of November.* Laplace's method 
gives rules for finding two elements only, viz. the perihelion 
distance, and the time of arriving at the perihelion *. for the 
sake of comparison, I now subjoin the results of M. Mechain; 
the same elements calculated by Legendre from the obser- 
vations used here ; and the more exact elements corrected by 
distant observations. 
Perihelion 
Time of Pas- 
Distance. 
sage Nov. 29. 
M. Mechain by Laplace's method 
0'9583509 
h 
18 10 34 
Legendre - - - 
0-96044,9 
0^ 
00 
In this paper > _ . 
0*961188 
13 20 4 
Corrected elements 
o' 96 'o 995 
12 42 46 
* These calculations are giren in Biot’s Astron. zd Edit. Vo). III. 
