Observations of the comet of 1807. 7 
In this manner I calculated the equations, resulting from the twenty 
eight observations, made from October 8 to December 17, and obtain- 
ed the following system of equations A, of which the first twenty 
eight were deduced from the observed longitudes and the rest from 
the observed latitudes, the equations being arranged according to the 
times ‘of observation, and the errors'in the observed longitudes count- 
ed in the same order, being denoted by x), a(@).-,. a8), and 
the errors in the observed latitudes by a(29), 2G... a6). 
xe(?) 815+ dp 2+t4129 + P4239 +n—234 +74 38 
w(?) = 317 +d— 1°t4138- pt242 n—248"i-— 88 
x(2) = —319+d— det+145 + p4+244 n—262+i-—- 98 . 
x(4) =—623+d— B64 * PA DAR 2 N29 te BA 
x4) == 214198 $4249 P4249 dia i+ 21 
w(S) = 329" d 414" 24207 -p4246 n—448-i— 76 
oo 7) =—-827 +d $17 + 14208 +p4242 n—467-2+ 16 
w(#) S—324+d426+ 14212 -p4240 n—485 *i—164 
“() =—321° C45t : t3Aa ees N—505* i—116 
By these rules we might calculate the true anomaly and distance of the comet 
from the sun, and thence deduce the geocentric longitude and latitude for each of 
the observations, supposing the elements D, T, P, N; I, to be the same, as in the 
first supposition, and E to be a very small quantity, as for example ;34- Then, 
denoting any one of these longitudes or latitudes by Lvii, and putting L \ a LViie= 
ivi and E=qho) We must add to the above value of 2(*) the term vie. By this 
means the system on equations: A,B, C, etc. would contain terms depending on e, 
and it would be necessary to make another assumption similar to the four first, 
made use of in the above sereeeone, which would furnish another equation, by 
means of which e might b inated, and the equation reduced to the same form 
as the system —— which the alue of pmight be found as above, The observa- 
tions of thiscomet accorded so well with a parabolic. hypothesis, that the differenc- 
es between the calculated and true places were within the limits of the errors of 
the observations ; therefore I did not attempt to calculate the elliptical orbit. 
