322 Mr. Bowditch on the Comet of 1811. 
1038 t — 4198 = 0, whence ¢ = 4°0443, which substituted in the sys- 
tem (E) gives the following values. 
d= 0°78631 
t= «=4°0443 
=—1°61862 
= —0°48012 
= —0'27871 
These substituted in the assumed elements give the corrected val- 
ues, 4 
D + 004d = 10351452 
T +-05-t = September 11d. 972215 mean time at Nantucket. 
P +10 = 75° 07' 49” 
N—10'°n =140 25 48 
I+10% = 70 05 13 
The differences between the geocentric longitudes and latitudes, cal- 
culated directly by these elements, and the observed values, being 
taken for a (*), a (7), (5), &c. give x (1) Fa(?)...4+ 2? = 
456; x(*°)+2x(8!)...4+2(57)=—18"9; x (**) 42x(**) ron 
$x (*)=— 577; v(*7) + (8)... ar(tt4) = — WY 
which vary but very little from the assumed hypothesis, which requit- 
ed that the second members of these equations should be = 9; and 
though these differences were not worthy of notice, I thought it best 
to repeat part of the process for correcting them, with a view of veri- 
fying by this means the preceding calculations; using the elements 
last found instead of D, T, P, N, and I. It is sufficient to state the 
result of these observations, which were ‘004‘d = — 0-0000142; “05% 
= 0°000192; 10°p=0; —10"n=—2"; 10°: =—2", whence the 
s 
Correct elements of the orbit are as follows. 
Perihelion distance 1°035131, the mean distance of the earth from. 
_ the sun being unity. 
