170 
TTT Beebe — The Comet of’ 1771. 
second differences neglected in computing differential coefficients, 
but furnishes a proof that the computations are as accurate as 
necessary. The equations 
( r sin v. A> — r cos u sin /' A Q ' — sin n Ad ) . i A Q' = — 8 4'*31 
I r* sin u* \i' — t*ct . m u ~ in i "l i \ sin n "l J" ) -1 ' 1 Af — — 12"*98 
And the equations 
( A id = ±y ~ cos i' a £ ' ) • \ Aid = — 9' 3l'*13 
A v oive - 
{ A 7d — Ax + 2 sin * [ A 71 — — 17 f 35 # *46 
And the corrected elements are : 
T 
log q 
e 
(C) 
Q 
Ref. to equator. Ret to ecliptic. 
April 19*209541 
9*955903 1 
1 *009663 
105° S' 40' *35 104° T 4l'*17 
9 26 3*28 27 50 36 00 
33 48 49*34 11 15 45*03 
Encke’s elements. 
19*21921 
9*9559104 
1*0093698 
104° 3' 16 ff * (D) 
27 51 55* 
11 15 19* 
An ephemeris computed from these elements and compared with 
the observations gives the residuals da and dS. The substitution 
of the adopted values of Ad and Ad’ in the. equations of condition 
gives aO. 
C-0 
A a 
Ad 
AO 
April 6, 
— 5 i 
- 1*8 
0 
14, 
—11*5 
— 5*9 
— 4*5 
30, 
-22*2 
—39*3 
- *9 
May 8, 
-19*5 
+32*7 
— *5 
16, 
— 53*2 
—12*1 
- 29*1 
24, 
— 1 9*4 
-h 0*8 
0 
J une 1 , 
—33*1 
+ 11 
-12*7 
9, 
-15*9 
— 16*5 
+21*7 
25, 
— 5*7 
-36*2 
- 5*1 
July 11, 
— |— 1 7 *5 
+ 9*5 
-31*6 
To ascertain the most probable parabola, the variations of the 
elements are computed as functions of de. The residuals and differ- 
ential coflicients are substituted in the equations 
d0 dO d0 ^ d0 n ^ r 
cos n — Ax -j- cos n — At 4* cos n ^ «T-j- cos n ^Aq=. cos n Ao(O-C) 
dn fin da , dn dn , da 
da ^ ° + dl M + d X + Te &£ + dT * T + ~ “ n ( ) 
giving the following equations of conditions, where the numbers are 
logarithms; and cos a Ad and An in seconds of arc: 
