W. Beebe — The Comet of 1771. 
169 
o-c 
cos n Ad 
An 
o 
1 
o 
cos n Ad. 
An. 
April 6, 
0 
— 0 
May 24, 
0 
0 
14. 
— 31"-4 
+ 9'-3 
June 1. 
— 90'-9 
— 39 r -8 
30. 
0 
0 
9, 
— 245 6 
+ 4G-7 
May 8, 
+ 33-8 
+ 69.3 
25. 
— 7112 
+ 137-3 
16, 
+ 73‘5 
— 71-3 
July 11. 
— 1192-2 
+ 1003-0 
With these values we form seven equations of condition of the form 
(70 dd 
cos n aO — cos n f—. aA 4- cos n aA", the weights beins those as- 
dA dA 
signed to the observations from which the residuals were obtained, 
and the numbers in parentheses, logarithms. 
(l n -49748) = 9”-06937) aA -f- (8"81491 )a/J # wt. 65 
(1-52910) = (9"-27054) “ +(9-12005) “ “ 16 
(1-85467) = (9 n -01887) “ + (8-91009) “ “ 45 
(1"-95811) = (9-06236) “ + (9 n '03076) “ “ 18 
(2 n "39028) = (9-34955) “ + (9 B -33284) “ “ 12 
(2 n -85199) =(9-57848) “ + (9 n -67132) “ “ 18 
(3 n -07635) = (9-64616) “ + (9"'82493) “ “ 15 
These combined by least squares give 
(4"-139627) = (0-963599)aJ+ (1"-031530)a A" 
(4"-277655) = (1-031530) “ + (l”-110118) “ 
aA = -}- 210l"-2 = -{- -0101871 (units 7th dec. place) 
aJ'= + 3223-5 = -f- -0156284 “ “ 
Substituting these values in equation of the form 
Sx = Tj aJ+ 3J-^'' &c -’S ives 
Aj= - 16' 13'-5 
A£ = -f -0409094 
At = + -087541 
Aq = — -0072416 
Also, from A* = *&+£ a A - A* 
dA 
Av = — 5' 30*-8 Av' = - 17' 35'"6 
The values of v from the elliptic elements are 
v= — 20° 9' 18'"55 v”= + 50° 20' 20'-88. 
Applying these corrections v = — 20° 14' 49'-35 + 50° 2'45' r "28. 
The values found from an ephemeris computed by the corrected 
elements are v= — 20° 14’47 l, -95 v" — + 5o 2'5l'-08. 
The agreement is not complete, owing to the magnitude of the 
