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ajirst Approximation to the Orbit of a Comet, 
situation, the nicest observations do not enable us to distinguish 
the real orbit from the parabola with which it intimately co- 
incides. It is only after one or more reappearances of the 
same comet, that we can hope to discover the period of its 
revolution round the sun, and the mean distance of the ellipse 
in which its motions are really performed : unless indeed a 
rare instance may sometimes occur, in which the length of 
time a comet continues visible, and a great number of obser- 
vations extending over a considerable portion of the orbit, 
may mark so great deviations from a parabolic motion as to 
lead to a tolerably exact estimation of the elliptic elements. 
For a single appearance we must be content with supposing 
the orbit to be a parabola; a supposition which, if it be not 
rigorously true, serves important purposes in astronomy: it 
proves that the comets move round the sun by the same law's 
as the planets ; and it enables us to discover the identity of a 
comet with one already observed, when we find that they agree 
in having the same parabolic elements. 
Three geocentric observations of the longitude and latitude 
of a comet are sufficient for determining the parabola which it 
describes. The problem is one of great difficulty. The appa- 
rent motion of a comet is the combined effect of its own motion 
and of that of the earth ; it is therefore extremely irregular 
and intricate ; and on this account it is difficult to deduce the 
heliocentric positions from observations made on the earth's 
surface. We can observe the planets at all times and in all 
situations ; and wnth regard to them we can thus select those 
positions where the heliocentric places are found immediately 
from observation, without any perplexed calculations; but we 
are deprived of this expedient in the case of the comets, 
R 2 
