316 Mr. Bowditch on the Comet ef 1811. 
10,1; ‘and at the sixth D, T, P, N,1+10'.. Supposing the longitudes 
and latitudes calculated in these different hypotheses to be denoted res- 
pectively by L’, L”, L’”, Liv, Ly, Lvi, the corresponding observed 
longitude or latitude by L; the error of the observation by a); and 
the correct values of the elements of the orbit by D + :004d; T+ 
O5¢; P+10'p; N—10'n; 14107; each of these observed longi- 
tudes or latitudes would furnish an equation of condition of this form 
= (L—L)+(L'— UL") d+(L’— L") ¢ + (LD) — Lv) p + (UL — 
Ly )» +(L’—L" )i; as was more fully explained in my paper on the 
comet of 1807. 
As there were fifty seven observations, they produced one hundred 
and fourteen equations of condition, which are arranged in the follow- 
ing Table, (A) according to the order of the dates. The errors of 
longitude being denoted by a(*), (7), &c. a(*7), those of latitude by 
x(**), (5°) &e. to (24+). The coefficients are expressed in tenths 
of a second ; the calculations being made to that degree of accuracy, 
by Taylor’s logarithms, except in the four first observations, which 
were found to the nearest second. 
x(7) = —1730+ 1700-d— 90:%t— 310+p41820-n—3370% 
x(#) = —22404 1800d— S50°%t— 180:641830—3580% 
«(%) = —2700+ 1840-d— 13+— 120:p-41820-n—3690% 
(4) = —1810+ 1906-d—  4:t— —37-4.1830-n—3797% 
, #(F) = 3764-4 2045-d}. St  136-p41846-n—4031°i 
*(°) = 32704 2125-d4  g3-t4 232*p-+-1857¢n—41 53% 
w(7) = 12354 2211-d4 115-4 339-p-41870-n—4278% 
x(°) = —30414 2308-d4 152-14. 450*P4.1889-n—4405°7 
x(°)= —40634 2410d4 191-24 —569+-41909-n—4535%i 
*O°)S—3756-+ 2523d4 232-44  699-94.1932-n—46681 
#CN)= 2994-4 2654-d4 280-4  846-7-4.1961-n—4810°% 
*(79)=—34914 3490-4 sei-t4. 1773-p42193-n—5507%% 
