a first Approximation to the Orbit of a Comet, 
^59 
Application to the second Comet^pf 1781. 
The following observations of this comet, which was dis- 
covered by M. Mechain, are taken by Legendre from the 
Mem. de V Acad, des Sciences, for 1780:* they are all reduced 
to the same hour of every day, namely to 8^ 29' 44," mean time 
at Paris. 
Times of 
Observation. 
Longitude. 
North Latitude. 
Longitude of 
Log. of R. 
September. 
14 
307 14 45 
55 17 9 
Ore 
32 54 2 
R, 9-994864 
19 
51 26 
39 H 48 
e°57 57 4 
9 994426 
24 
c/306 42 £0 
V 31 4 52 
c/63 0 41 
R.' 9'994°28 
By applying the directions and formulas of No. 8, I have 
found. 
Log. 4,6*= 9*0732228 
n = 3^'° 19' 5" 
/ =3 89 21 27 
(5' = — 00000970 
" = 39 ° 1 4' 49" 
/i = 5^ 17 28 
3150 
log. /3 = 0-2892147 
cos. 7 = 9-9600258 
With regard to the three principal formulas of the orbit, I 
remark that it is the logarithms of the coefficients, and not 
the coefficients themselves, that are afterwards used : on this 
♦ Nouvelles Methodes, p* 33> § xxxii. 
