320 Mr. Bowditch on the Comet of 1811. 
x(113)= 1005—6645-d— 526%— 4619:p—3844:n— 397% 
x(218)=— 708—6438-d— 492:t— 4535-p—3867-n— 424+i 
aw(214)=— 502—6247-d— 461t— 4458:p—3884en— 4440. - 
To deduce from these equations the values of the unknown quanti- 
ties d, t, ~, n, 7, I divided them into four nearly equal portions, and 
supposed that in each the sum of the errors of longitude or latitude 
was equal to 0; due regard being had to the signs. This hypothesis 
gave x (2) +r (*). +6400 (8°) =0, ar (2°) 4 (21)... 00 (57) =0, 
w(F8) +xe(F9)o.. +(**)=0, x (87) +x (88) .0. +e (114) =0, 
These substituted in the sums of the corresponding equations (A) 
give the system of equations (C), 
O= —86097+ 150823-d-+4 34887-t+ 106305-p-+ 91396-n—15198% 
O= 358614 92103-d+ 41788-t+ 107728:p-+ 158553°n-+ 96120% 
O= 69935— 58772-d+ 37980%%+ 86569°'p+ 66916°n-+ 24015% 
o= 7005 —202553*d—17489-t—122408-p— 72168°n-+ 35116% 
(C) 
Which by the usual rules of elimination give 
d= 0°2814729+ 0°1248260.t 
p=—0'9198046—0°1727901+t (E) 
m= 0°5858239—0-2635675:¢ 
i= —0°5782452+4 0-0740628-t 
These values substituted in the equations (A) give 
2(1)=2048—354+t 
x(*)=1574—542+¢ (F) 
2(*)=1128—516:t . 
: a(*)=2028—523+ 
: &e, &e. 
To render the sum of the errors x(*), x(?), 2(2), &c. taken posi- 
tively as little as possible, I made use of the method of La Place in 
Vol. II. page 135 of his Mécanique Céleste. First. by changing the 
Signs of the terms of those equations where the coefficients of ¢ were 
