u134March 7, 7h. 30' at Paris (that is, March 7, 8h. 37' at Dantzick), from the observations of M. Auzout, the distance of the comet from the second star in Aries was equal to the distance of that star from the star[Pg 499] 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 comets 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° 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.

[Pg 500]

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:—

This theory is yet farther confirmed by the motion of that retrograde comet which appeared in the year 1682. The ascending node of this (by Dr. Halley's computation) was in ♉ 21° 16' 30''; the inclination of its orbit to the plane of the ecliptic 17° 56' 00''; its perihelion in ♒ 2° 52' 50''; its perihelion distance from the sun 58328 parts, of which the radius of the orbis magnus contains 100000; the equal time of the comet's being in its perihelion Sept. 4d. 7h. 39'. And its places, collected from Mr. Flamsted's observations, are compared with its places computed from our theory in the following table:—

This theory is also confirmed by the retrograde motion of the comet that appeared in the year 1723. The ascending node of this comet (according to the computation of Mr. Bradley, Savilian Professor of Astronomy at Oxford) was in ♈ 14° 16'. The inclination of the orbit to the plane of the ecliptic 49° 59'. Its perihelion was in ♉ 12° 15' 20''. Its perihelion distance from the sun 998651 parts, of which the radius of the orbis magnus contains 1000000, and the equal [Pg 501]time of its perihelion September 16d 16h. 10'. The places of this comet computed in this orbit by Mr. Bradley, and compared with the places observed by himself, his uncle Mr. Pound, and Dr. Halley, may be seen in the following table.

From these examples it is abundantly evident that the motions of comets are no less accurately represented by our theory than the motions of the planets commonly are by the theories of them; and, therefore, by means of this theory, we may enumerate the orbits of comets, and so discover the periodic time of a comet's revolution in any orbit; whence, at last, we shall have the transverse diameters of their elliptic orbits and their aphelion distances.

That retrograde comet which appeared in the year 1607 described an orbit whose ascending node (according to Dr. Halley's computation) was in ♉ 20° 21'; and the inclination of the plane of the orbit to the plane of the ecliptic 17° 2'; whose perihelion was in ♒ 2° 16'; and its perihelion distance from the sun 58680 of such parts as the radius of the orbis magnus contains 100000; and the comet was in its perihelion October 16d. 3h. 50'; which orbit agrees very nearly with the orbit of the comet which was seen in 1682. If these were not two different comets, but one and the same, that comet will finish one revolution in the space of 75 years; and the greater axis of its orbit will be to the greater axis of the orbis magnus as to 1, or as 1778 to 100, nearly. And the aphelion distance of this comet from the sun will be to the mean distance of the earth from the sun as about 35 to 1; from which data it will be no hard matter to determine the elliptic orbit of this comet. But these things are to be supposed on condition, that, after the space of 75 years, the same comet shall return again in the same orbit. The other comets seem to ascend to greater heights, and to require a longer time to perform their revolutions.

But, because of the great number of comets, of the great distance of their[Pg 502] aphelions from the sun, and of the slowness of their motions in the aphelions, they will, by their mutual gravitations, disturb each other; so that their eccentricities and the times of their revolutions will be sometimes a little increased, and sometimes diminished. Therefore we are not to expect that the same comet will return exactly in the same orbit, and in the same periodic times: it will be sufficient if we find the changes no greater than may arise from the causes just spoken of.

And hence a reason may be assigned why comets are not comprehended within the limits of a zodiac, as the planets are; but, being confined to no bounds, are with various motions dispersed all over the heavens; namely, to this purpose, that in their aphelions, where their motions are exceedingly slow, receding to greater distances one from another, they may suffer less disturbance from their mutual gravitations: and hence it is that the comets which descend the lowest, and therefore move the slowest in their aphelions, ought also to ascend the highest.

The comet which appeared in the year 1680 was in its perihelion less distant from the sun than by a sixth part of the sun's diameter; and because of its extreme velocity in that proximity to the sun, and some density of the sun's atmosphere, it must have suffered some resistance and retardation; and therefore, being attracted something nearer to the sun in every revolution, will at last fall down upon the body of the sun. Nay, in its aphelion, where it moves the slowest, it may sometimes happen to be yet farther retarded by the attractions of other comets, and in consequence of this retardation descend to the sun. So fixed stars, that have been gradually wasted by the light and vapours emitted from them for a long time, may be recruited by comets that fall upon them; and from this fresh supply of new fuel those old stars, acquiring new splendor, may pass for new stars. Of this kind are such fixed stars as appear on a sudden, and shine with a wonderful brightness at first, and afterwards vanish by little and little. Such was that star which appeared in Cassiopeia's chair; which Cornelius Gemma did not see upon the 8th of November, 1572, though he was observing that part of the heavens upon that very night, and the sky was perfectly serene; but the next night (November 9) he saw it shining much brighter than any of the fixed stars, and scarcely inferior to Venus in splendor. Tycho Brahe saw it upon the 11th of the same month, when it shone with the greatest lustre; and from that time he observed it to decay by little and little; and in 16 months' time it entirely disappeared. In the month of November, when it first appeared, its light was equal to that of Venus. In the month of December its light was a little diminished, and was now become equal to that of Jupiter. In January 1573 it was less than Jupiter, and greater than Sirius; and about the end of February and the beginning of March became equal to that star. In the months of April and May it was equal to a star of the second magnitude;[Pg 503] in June, July, and August, to a star of the third magnitude; in September, October, and November, to those of the fourth magnitude; in December and January 1574 to those of the fifth; in February to those of the sixth magnitude; and in March it entirely vanished. Its colour at the beginning was clear, bright, and inclining to white; afterwards it turned a little yellow; and in March 1573 it became ruddy, like Mars or Aldebaran: in May it turned to a kind of dusky whiteness, like that we observe in Saturn; and that colour it retained ever after, but growing always more and more obscure. Such also was the star in the right foot of Serpentarius, which Kepler's scholars first observed September 30, O.S. 1604, with a light exceeding that of Jupiter, though the night before it was not to be seen; and from that time it decreased by little and little, and in 15 or 16 months entirely disappeared. Such a new star appearing with an unusual splendor is said to have moved Hipparchus to observe, and make a catalogue of, the fixed stars. As to those fixed stars that appear and disappear by turns, and increase slowly and by degrees, and scarcely ever exceed the stars of the third magnitude, they seem to be of another kind, which revolve about their axes, and, having a light and a dark side, shew those two different sides by turns. The vapours which arise from the sun, the fixed stars, and the tails of the comets, may meet at last with, and fall into, the atmospheres of the planets by their gravity, and there be condensed and turned into water and humid spirits; and from thence, by a slow heat, pass gradually into the form of salts, and sulphurs, and tinctures, and mud, and clay, and sand, and stones, and coral, and other terrestrial substances.