situation, the nicest observations do not enable us to distinguish the real orbit from the parabola with which it intimately coincides. 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 observations 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 laws 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 apparent 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 with 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,
