5. NOW what confirms this whole theory beyond the least room for doubt is, that the places of the comets computed in the orbits, which the method here mentioned assigns them, agree to the observations of astronomers with the same degree of exactness, as the computations of the primary planets places usually do; and this in comets, whose motions are very extraordinary[214]. 6. OUR author afterwards shews how to make use of any small deviation from the parabola, that shall be observed, to determine whether the orbits of the comets are elliptical or not, and so to discover if the same comet returns at certain periods[215]. And upon examining the comet in 1680, by the rule laid down for this purpose, he finds its orbit to agree more exactly to an ellipsis than to a parabola, though the ellipsis be so very eccentric, that the comet cannot perform its period through it in the space of 500 years[216]. Upon this Dr. HALLEY observed, that mention is made in history of a comet, with the like eminent tail as this, having appeared three several times before; the first of which appearances was at the death of JULIUS CESAR, and each appearance was at the distance of 575 years from the next preceding. He therefore computed the motion of this comet in such an elliptic orbit, as would require this number of years for the body to revolve through it; and these computations agree yet more perfectly with the observations made on this comet, than any parabolical orbit will do[217]. 7. THE comparing together different appearances of the same comet, is the only way to discover certainly the true form of the orbit: for it is impossible to determine with exactness the figure of an orbit so exceedingly eccentric, from single observations taken in one part of it; and therefore Sir ~ISAAC NEWTON~[218] proposes to compare the orbits, upon the supposition that they are parabolical, of such comets as appear at different times; for if the same orbit be found to be described by a comet at different times, in all probability it will be the same comet which describes it. And here he remarks from Dr. HALLEY, that the same orbit very nearly agrees to two appearances of a comet about the space of 75 years distance[219]; so that if those two appearances were really of the same comet, the transverse axis of the orbit of the comet would be near 18 times the axis of the earth’s orbit; and the comet, when at its greatest distance from the sun, will be removed not less than 35 times as far as the middle distance of the earth. 8. AND this seems to be the shortest period of any of the comets. But it will be farther confirmed, if the same comet should return a third time after another period of 75 years. However it is not to be expected, that comets should preserve the same regularity in their periods, as the planets; because the great eccentricity of their orbits makes them liable to suffer very considerable alterations from the action of the planets, and other comets, upon them.