Page:Newton's Principia (1846).djvu/505

 A, that is, 52,′ 29″; and the difference of the longitude of the comet and the second star in Aries was 45′ or 46′, or, taking a mean quantity, 45′ 30″; and therefore the comet was in ♉ 0° 2′ 48″. From the scheme of the observations of M. Auzout, constructed by M. Petit, Hevelius collected the latitude of the comet 8° 54′. But the engraver did not rightly trace the curvature of the comet's way towards the end of the motion; and Hevelius, in the scheme of M. Auzout's observations which he constructed himself, corrected this irregular curvature, and so made the latitude of the comet 8° 55′ 30″. And, by farther correcting this irregularity, the latitude may become 8° 56, or 8° 57′.

This comet was also seen March 9, and at that time its place must have been in ♉ 0° 18′, with 9° 3½' north lat. nearly.

This comet appeared three months together, in which space of time it travelled over almost six signs, and in one of the days thereof described almost 20 deg. Its course did very much deviate from a great circle, bending towards the north, and its motion towards the end from retrograde became direct; and, notwithstanding its course was so uncommon, yet by the table it appears that the theory, from beginning to end, agrees with the observations no less accurately than the theories of the planets usually do with the observations of them: but we are to subduct about 2′ when the comet was swiftest, which we may effect by taking off 12″ from the angle between the ascending node and the perihelion, or by making that angle 49° 27′ 18″. The annual parallax of both these comets (this and the preceding) was very conspicuous, and by its quantity demonstrates the annual motion of the earth in the orbis magnus.

This theory is likewise confirmed by the motion of that comet, which in the year 1683 appeared retrograde, in an orbit whose plane contained almost a right angle with the plane of the ecliptic, and whose ascending node (by the computation of Dr. Halley) was in ♍ 23° 23′; the inclination of its orbit to the ecliptic 83° 11′; its perihelion in ♊ 25° 29′ 30″; its perihelion distance from the sun 56020 of such parts as the radius of the orbis magnus contains 100000; and the time of its perihelion July 2d.3h.50′. And the places thereof, computed by Dr. Halley in this orbit, are compared with the places of the same observed by Mr. Flamsted, in the following table:—