ions of the comet of 1807. 
eo ee than is necessary for finding the values 
of d, t, p, m, 7, and determining the elements of the orbit. 
Now it is evident that if the comet moved exactly in a parabola, 
and the observations were perfectly correct, all these equations would 
concur in giving nearly* the same values of d, t, p,m, and 7, but as 
errors arising from those sources are unavoidable, the substitution of 
the correct values of d, ¢, p, m, and i, in the equations will not gene- 
rally make the second members equal too ; but will render them 
equal to the combined effect of the errors of the observations and of 
the parabolic hypothesis, and if we denote these errors by x), w@), 
x), etc.f the equations will become of this form.f — 
Oe. ‘ aioe © t41"” — n+lv +ith 
at Ena ay . . s = not 
exdpaetogel to the comvednontiir yareabicod of the claments of the « 
fore the equations will not give exactly the same values of d, t, 1, m, and Z. 
+ It may be necessary to observe, that the figures annexed to x do not signify 
exponents of the powers of 2, as the quantities z(*), x(?), etc. are a inde- 
pendent of each other. 
__ 4 If the comet, during its appearance, had described so great an arch of its or- 
bit, as to render it sensibly different from a parabola, we might calculate the ellip- 
tical elements by introducing another term into the above equation. For if D be 
the perihelion distance of the comet, U its angular distance from the perihelion, 
calculated for the time of any of the observations by the parabolic hypothesis, 
U-+<z the same angular distance calculated in the elliptical hypothesis,. “supposing 
the perihelion distance of the comet, divided by its mean distance from the sun, 
to be E, we should have by the rules, given by La Place i in the abovementioned 
work, 
Sine z = 7, E° tang. 3U- Sa: cox PUIG C08. 5 ‘} 
8 STR RE eS eae would be. 
pees aS ia Sts) Po. 
By 
