14 Observations of the comet of 1807.» 
D-+0:002 ».d = 064969 
T-+0-2 + t = Sep. 18d. 6074 
P+10'* p = 98 19 0 11" 
a cis *2=8 26 24 57 
I—10'- =63. 942 
These would be i true elements depending on the ecto laid 
down if the variations of the calculated geocentric longitudes and lati- 
tudes were strictly proportional to the variations of the elements 
0°002d, 0°2°t, &c. but as this is not the case, it was necessary to re- 
peat in part the operation to make the calculations agree exactly with 
those principles, _ For this purpose I made use of the approximate 
values of the elements last found, instead of D, T, P, N, and I, and 
recalculated the values of / as in the first Suppose and thus obtain- 
ed new values of the constant terms of the equatio A, instead of 
438, —88, etc. These new terms arranged i in the oir of the equa- 
tions are 126, 0, —10, 1, 93, —12, 76, —108, —66, —28, 122, —248, 
—137, —490, 261, 25, —466, 860, 507, —102, —251, 316,356, 
—346, 14, —607, 960, —643, 4, —48, —112, 46, —77, —20, —212, 
—11, 68, 35, 62, 224, 37, 346,—206,—-114, 495,—727,—-127,—101, 
369, 510, 683, 224, —9, —426, —907, —115, and by substituting 
them in the equations A, and making the cor pondir 
the constant terms of the equations B, C, D, ‘etc. a new system of 
equations G was obtained, and by operating on them in the same man- 
ner as before I found that the value of ps which would render the sum 
of the errors x(*), a(*), &e. a minimum, would be had by putting 
75°p+2=0, whence p=—0-027, which, substituted in the equations 
(4), (3), (2), (1), deduced from these last calculations, will give n=—_ 
0011, d=—0-036, i=—0°025, t=0°0013. Consequently the cor- 
rections of the fast found, elements are 0-002'd-—=—0'00007, 0,2t= - 
