Ponthæus and Cellius. The same day, at 5h. morning, at Ballasore, the comet was observed in ♏ 11° 45′; and, therefore, at 5h. morning at London, was in ♏ 13° nearly. And, by the theory, the comet was at that time in ♏ 13° 22′ 2″.
Nov. 25, before sunrise, Montenari observed the comet in ♏ 17¾′ nearly; and Cellius observed at the same time that the comet was in a right line between the bright star in the right thigh of Virgo and the southern scale of Libra; and this right line cuts the comet's way in ♏ 18° 36′. And, by the theory, the comet was in ♏ 18⅓° nearly.
From all this it is plain that these observations agree with the theory, so far as they agree with one another; and by this agreement it is made clear that it was one and the same comet that appeared all the time from Nov. 4 to Mar. 9. The path of this comet did twice cut the plane of the ecliptic, and therefore was not a right line. It did cut the ecliptic not in opposite parts of the heavens, but in the end of Virgo and beginning of Capricorn, including an arc of about 98°; and therefore the way of the comet did very much deviate from the path of a great circle; for in the month of Nov. it declined at least 3° from the ecliptic towards the south; and in the month of Dec. following it declined 29° from the ecliptic towards the north; the two parts of the orbit in which the comet descended towards the sun, and ascended again from the sun, declining one from the other by an apparent angle of above 30°, as observed by Montenari. This comet travelled over 9 signs, to wit, from the last deg. of ♌ to the beginning of ♊, beside the sign of ♌, through which it passed before it began to be seen; and there is no other theory by which a comet can go over so great a part of the heavens with a regular motion. The motion of this comet was very unequable; for about the 20th of Nov. it described about 5° a day. Then its motion being retarded between Nov. 26 and Dec. 12, to wit, in the space of 15½ days, it described only 40°. But the motion thereof being afterwards accelerated, it described near 5° a day, till its motion began to be again retarded. And the theory which justly corresponds with a motion so unequable, and through so great a part of the heavens, which observes the same laws with the theory of the planets, and which accurately agrees with accurate astronomical observations, cannot be otherwise than true.
And, thinking it would not be improper, I have given a true representation of the orbit which this comet described, and of the tail which it emitted in several places, in the annexed figure; protracted in the plane of the trajectory. In this scheme ABC represents the trajectory of the comet, D the sun DE the axis of the trajectory, DF the line of the nodes, GH the intersection of the sphere of the orbis magnus with the plane of the trajectory, I the place of the comet Nov. 4, Ann. 1680; K the place of the same Nov. 11; L the place of the same Nov. 19; M its place Dec. 12; N
