COMET

, a heavenly body in the planetary region, appearing suddenly, and again disappearing; and during the time of its appearance moving in a proper, though very eccentric orbit, like a planet.

Comets are vulgarly called Blazing Stars, and have this to distinguish them from other stars, that they are usually attended with a long train of light, tending always opposite to the sun, and being of a fainter lustre the farther it is from the body of the comet. And hence arises a popular division of comets, into three kinds; viz bearded, tailed, and hairy comets; though in reality, this division rather relates to the several circumstances of the same comet, than to the phenomena of several. Thus, when the comet is eastward of the sun, and moves from him, it is said to be bearded, because the light precedes it in the manner of a beard: When the comet is westward of the sun, and sets after him, it is said to be tailed, because the train of light follows it in the manner of a tail: And lastly, when the sun and comet are diametrically opposite, the earth being between them, the train is hid behind the body of the comet, excepting the extremities, which, being broader than the body of the comet, appear as it were around it, like a border of hair, or coma, from which it is called hairy, and a comet.

But there have been comets whose disc was as clear, round, and well desined, as that of Jupiter, without either tail, beard or coma.

Of the Nature of Comets.—Philosophers and Astronomers, of all ages, have been much divided in their opinions as to the nature of comets. Their strange appearance has in all ages been matter of terror to the vulgar, who have uniformly considered them as evil omens, and forerunners of war, pestilence, &c. Diodorus Siculus and Appollinus Myndius, in Seneca, inform us, that many of the Chaldeans held them to be lasting bodies, having stated revolutions as well as the planets, but in orbits vastly more extensive; on which account they are only visible while near the earth, but disappear again when they go into the higher regions. Others of them were of opinion, that the comets were only meteors raised very high in the air, which blaze for a while, and disappear when the matter of which they consist is consumed or dispersed.

Some of the Greeks, before Aristotle, supposed that a comet was a vast heap or assemblage of very small stars meeting together, by reason of the inequality of their motions, and so uniting into a visible mass, by the union of all their small lights; which must again disappear, as those stars separated, and each proceeded in its course. Pythagoras, however, accounted them a kind of planets or wandering stars, disappearing in the superior parts of their orbits, and becoming visible only in the lower parts of them.

But Aristotle held, that comets were only a kind of transient fires, or meteors, consisting of exhalations raised to the upper region of the air, and there set on fire; far below the course of the moon.

Seneca, who lived in the first century, and who had seen two or three comets himself, plainly intimates that he thought them above the moon; and argues strongly against those who supposed them to be meteors, or who held other absurd opinions concerning them; declaring his belief that they were not fires suddenly kindled, but the eternal productions of nature. He points out also the only way to come at a certainty on this subject, viz, by collecting a number of observations concerning their appearance, in order to discover whether they return periodically or not. “For this purpose, says he, one age is not sufficient; but the time will come when the nature of comets and their magnitudes will be demonstrated, and the routes they take, so different from the planets, explained. Posterity will then wonder, that the preceding ages should be ignorant of matters so plain and easy to be known.”

For a long time this prediction of Seneca seemed not likely to be fulfilled; and Tycho Brahe was the first among the moderns, who restored the comets to their true rank in the creation; for after diligently observing the comet of 1577, and finding that it had no sensible diurnal parallax, he assigned it its true place in the planetary regions. See his book De Cometa, anni 1577.

Before this however, there were various opinions concerning them. In the dark and superstitious ages, comets were held to be forerunners of every kind of calamity, and it was supposed they had different degrees of malignity, according to the shape they assumed; from whence also they were differently denominated. Thus, it was said that some were bearded, some hairy; that some represented a beam, sword, or spear; others a target, &c; whereas modern astronomers acknowledge only one species of comets, and account for their different appearances from their different situations with respect to the sun and earth.

Kepler, in other respects a very great genius, indulged the most extravagant conjectures, not only concerning comets, but the whole system of nature in general. The planets he imagined were huge animals swimming round the sun; and the comets monstrous and uncommon animals generated in the celestial spaces.

A still more ridiculous opinion, if possible, was that of John Bodin, a learned Frenchman in the 16th century; who maintained that comets “are spirits, which having lived on the earth innumerable ages, and being at last arrived on the confines of death, celebrate their last triumph, or are recalled to the firmament like shining stars! This is followed by samine, plague, &c, because the cities and people destroy the governors and chiefs who appease the wrath of God.”—Others again have denied even the existence of comets, and maintained that they were only false appearances, occasioned by the refraction or reflection of light.

Hevelius, from a great number of observations, proposed it as his opinion, that the comets, like the solar maculæ or spots, are formed or condensed out of the grosser exhalations of his body; in which he differs but little from the opinion of Kepler.

James Bernoulli, in his Systema Cometarum, imagined that comets were no other than the satellites of | some very distant planet, which was itself invisible to us on account of its distance, as were also the satellites unless when in a certain part of their orbits.

Des Cartes advances another opinion: He conjectures that comets are only stars, formerly fixed, like the rest, in the heavens; but which becoming gradually covered with maculæ or spots, and at length wholly deprived of their light, cannot keep their places, but are carried off by the vortices of the circumjacent stars; and in proportion to their magnitude and solidity, moved in such a manner, as to be brought nearer the orb of Saturn; and thus coming within reach of the sun's light, rendered visible.

But the vanity of all these hypotheses now abundantly appears from the observed phenomena of comets, and from the doctrine of Newton, which is as follows:

The comets, he says, are compact, solid, fixed, and durable bodies; in fact a kind of planets, which move in very oblique and eccentric orbits, every way with the greatest freedom; persevering in their motions, even against the course and direction of the planets: and their tail is a very thin and slender vapour, emitted by the head or nucleus of the comet, ignited or heated by the sun. This theory of the comets at once solves their principal phenomena, which are as below.

1. First then, those comets which move according to the order of the signs, do all, a little before they disappear, either advance slower than usual, or else go retrograde, if the earth be between them and the sun; but more swiftly, if the earth be placed in a contrary part. On the other hand, those which proceed contrary to the order of the signs, move more swiftly than usual, if the earth be between them and the sun; and more slowly, or else retrograde, when the earth is in a contrary part.—For since this course is not among the fixed stars, but among the planets; as the motion of the earth either conspires with them, or goes against them; their appearance, with respect to the earth, mnst be changed; and, like the planets, they must sometimes appear to move swifter, sometimes slower, and sometimes retrograde.

2. So long as their velocity is increased, they nearly move in great circles; but towards the end of their course, they deviate from those circles; and when the earth proceeds one way, they go the contrary way. Because, in the end of their course, when they recede almost directly from the sun, that part of the apparent motion which arises from the parallax, must bear a greater proportion to the whole apparent motion.

3. The comets move in ellipses, having one of their foci in the centre of the sun; and by radii drawn to the sun, describe areas proportional to the times. Because they do not wander precariously from one fictitious vortex to another; but, making a part of the solar system, return perpetually, and run a constant round. Hence, their elliptic orbits being very long and eccentric, they become invisible when in that part which is most remote from the sun. And from the curvity of the paths of comets, Newton concludes, that when they disappear, they are much beyond the orbit of Jupiter; and that in their perihelion they frequently descend within the orbits of Mars and the inferior planets.

4. The light of their nuclei, or bodies, increases as they recede from the earth toward the sun; and on the contrary, it decreases as they recede from the sun. Because, as they are in the regions of the planets, their access towards the sun bears a oonsiderable proportion to their whole distance.

5. Their tails appear the largest and brightest, immediately after their transit through the region of the sun, or after their perihelion. Because then, their heads being the most heated, will emit the most vapours.—From the light of the nucleus we infer their vicinity to the earth, and that they are by no means in the region of the sixed stars, as some have imagined; since, in that case, their heads would be no more illuminated by the sun, than the planets are by the fixed stars.

6. The tails always <*>cline from a just opposition to the sun towards those parts which the nuclei or bodies pass over, in their progress through their orbits. Because all smoke, or vapour, emitted srom a body in motion, tends upwards obliquely, still receding from that part towards which the smoking body proceeds.

7. This declination, cæteris paribus, is the smallest when the nuclei approach nearest the sun; and it is also less near the nucleus, or head, than towards the extremity of the tail. Because the vapour ascends more swiftly near the head of the comet, than in the higher extremity of its tail; and also when the comet is nearer the sun, than when it is farther off.

8. The tails are somewhat brighter, and more distinctly defined in their convex, than in their concave part. Because the vapour in the convex part, which goes first, being somewhat nearer and denser, reflects the light more copiously.

9. The tails always appear broader at their upper extremity, than near the centre of the comet. Because the vapour in a free space continually rarefies and dilates.

10. The tails are always transparent, and the smallest stars appear through them. Because they consist of infinitely thin vapour.

The Phases of Comets.—The nuclei, which are also called the heads, and bodies, of comets, viewed through a telescope, shew a face very different from those of the fixed stars or planets. They are liable to apparent changes, which Newton ascribes to changes in the atmosphere of comets: and this opinion was consirmed by observations of the comet in 1744. Hist. Acad. Scienc. 1744. Sturmius says that, observing the comet of 1680 with a telescope, it appeared like a coal dimly glowing, or a rude mass of matter illuminated with a dusky fumid light, less sensible to the extremes than in the middle; whereas a star appears with a round disc, and a vivid light.

Of the comet of 1661, Hevelius observes, that its body was of a yellowish colour, very bright and conspicuous, but without any glittering light: in the middle was a dense ruddy nucleus, almost equal to Jupiter, encompassed by a much fainter, thinner matter. February 5th, its head was somewhat larger and brighter, and of a gold colour; but its light more dusky than the stars: and here the nucleus appeared divided into several parts. Feb. 6th, the disc was lessened; the parts of the nucleus still existed, though | less than before: one of them, on the lower part of the disc, on the left, much denser and brighter than the rest; its body round, and representing a very lucid little star: the nuclei still encompassed with another kind of matter. Feb. 10th, the head somewhat more obscure, and the nuclei more confused, but brighter at top than bottom. Feb. 13th, the head diminished much both in size and splendor. March 2d, its roundness a little impaired, and its edges lacerated, &c. March 28th, very pale, and exceeding thin; its matter much dispersed; and no distinct nucleus at all appearing.

Weigelius, who saw the comet of 1664, as also the moon, and a small cloud in the horizon illuminated by the sun at the same time, observed, that through the telescope the moon appeared of a continued luminous surface: but the comet very different; being exactly like the little cloud. And from these observations it was that Hevelius formed his opinion, that comets are like maculæ or spots formed out of the solar exhalations.

Of the Magnitude of Comets.—The estimates that have been given of the magnitude of comets by Tycho Brahe, Hevelius, and some others, are not very accurate; as it does not appear that they distinguished between the nucleus and the surrounding atmosphere. Thus Tycho computes that the true diameter of the comet in 1577 was in proportion to the diameter of the earth, as 3 is to 14; and Hevelius made the diameter of the comet of 1652 to that of the earth, as 52 to 100. But the diameter of the atmosphere is often 10 or 15 times as great as that of the nucleus: the former, in the comet of 1682, was measured by Flamsteed, and found to be 2′, when the diameter of the nucleus alone was only 11 or 12″. Though some comets, estimated by a comparison of their distance and apparent magnitude, have been judged much larger than the moon, and even equal to some of the primary planets. The diameter of that of 1744, when at the distance of the sun from us, measured about 1′, which makes its diameter about three times that of the earth: at another time the diameter of its nucleus was nearly equal to that of the planet Jupiter.

Of the Tails of Comets.—There have been various conjectures about the nature of the tails of comets, the principal of which are those of Newton, and the others that follow. Newton shews that the atmospheres of comets will furnish vapour sufficient to form their tails. This he argues from that wonderful rarefaction in our air at a distance from the earth; which is such, that a cubic inch of common air, expanded to the rarity of that at the distance of half the earth's diameter, or 4000 miles, would fill a space larger than the whole region of the stars. Since then the coma, or atmosphere of a comet, is 10 times higher than the surface of the nucleus, from the centre; the tail, ascending still much higher, must necessarily be immensely rare: so that it is no wonder the stars are visible through it.

Now the ascent of vapours into the tail of the comet, he supposes occasioned by the rarefaction of the matter of the atmosphere at the time of the perihelion. Smoke, it is observed, ascends the chimney by the impulse of the air in which it floats; and air, rarefied by heat, ascends by the diminution of its specific gravity, carrying up the smoke along with it: in the same manner then it may be supposed that the tail of a comet is raised by the sun.

The tails therefore thus produced in the perihelions of comets, will go off along with their head into remote regions; and either return from thence, together with the comets, after a long series of years; or rather be there lost, and vanish by little and little, and the comet be left bare; till at its return, descending towards the sun, some short tails are again gradually produced from the head; which afterwards, in the perihelion, descending down into the sun's atmosphere, will be immensely increased.

Newton farther observes, that the vapours, when thus dilated, rarefied, and dissused through all the celestial regions, may probably, by means of their own gravity, be gradually attracted down to the planets, and become intermingled with their atmospheres. He adds that this intermixture may be useful and necessary for the conservation of the water and moisture of the planets, dried up or consumed in various ways. And I suspect, adds our author, that the spirit, which makes the finest, subtilest, and best part of our air, and which is absolutely requisite for the life and being of all things, comes principally from the comets.—On this principle there may seem to be some foundation for the popular opinion of presages from comets; since the tail of a comet thus intermingled with our atmosphere, may produce changes very sensible in animal and vegetable bodies.

It may here be added that another use which Newton conjectures comets may be designed to serve, is that of recruiting the sun with fresh fuel, and repairing the consumption of his light by the streams continually sent forth in every direction from that luminary. In support of this conjecture he observes, that comets in their perihelion may suffer a diminution of their projectile force, by the resistance of the solar atmosphere; so that by degrees their gravitation towards the sun may be so far increased, as to precipitate their fall into his body.

Other opinions on the tails of comets, are the following.

Apian, Tycho Brahe, and some others, think they were produced by the sun's rays transmitted through the nucleus of the comet, which they supposed was transparent, and there refracted as in a glass lens, so as to form a beam of light behind the comet. Des Cartes accounted for the phenomenon of the tail by the refraction of light from the head of the comet to the spectator's eye. Mairan supposes that the tails are formed out of the luminous matter composing the sun's atmosphere: and M. De la Lande combines this hypothesis with that of Newton recited above. But Mr. Rowning, not satisfied with Newton's opinion, accounts for the tails of comets in the following manner: It is well known, says he, that when the sun's light passes through the atmosphere of any body, as the earth, that which passes on one side, is by the refraction made to converge towards that which passes on the opposite side; and this convergency is not wholly effected either at the entrance of the light into the atmosphere, or at its exit on going out; but beginning at | its entrance, it increases in every point of its progress: It is also agreed that the atmospheres of the comets are very large and dense: he therefore supposes that by such time as the light of the sun has passed through a considerable part of the atmosphere of the comet, the rays are so far refracted towards each other, that they then begin sensibly to illuminate it, or rather the vapours floating in it; and so render that part they have yet to pass through, visible to us: and that this portion of the atmosphere of a comet thus illuminated, appears to us in form of a beam of the sun's light, and passes under the denomination of a comet's tail. Rowning's Nat. Philos. part 4. chap. 11.

M. Euler, Mem. Berlin tom. 2. pa. 117, thinks there is a great affinity between the tails of comets, the zodiacal light, and the aurora borealis, and that the common cause of all of them, is the action of the sun's light on the atmospheres of the comets, of the sun, and of the earth. He supposes that the impulse of the rays of light on the atmosphere of comets, may drive some of the finer particles of that atmosphere far beyond its limits; and that this force of impulse combined with that of gravity towards the comet, would produce a tail, which would always be in opposition to the sun, if the comet did not move. But the motion of the comet in its orbit, and about an axis, must vary the position and figure of the tail, giving it a curvature, and deviation from a line joining the centres of the sun and comet; and that this deviation will be greater, as the orbit of the comet has the greater curvature, and as the motion of the comet is more rapid. It may even happen, that the velocity of the comet, in its perihelion, may be so great, that the force of the sun's rays may produce a new tail, before the old one can follow; in which case the comet might have two or more tails. The possibility of this is confirmed by the comet of 1744, which was observed to have several tails while it was in its perihelion.

Dr. Hamilton urges several objections against the Newtonian hypothesis; and concludes that the tail of a comet is formed of matter which has not the power of refracting or reflecting the rays of light; but that it is a lucid or self-shining substance: and from its similarity to the Aurora borealis, that it is produced by the same cause, and is properly an electrical phenomenon. Dr. Halley too seemed inclined to this hypothesis, when he said, that the streams of light in an Aurora borealis so much resembled the long tails of comets, that at sirst sight they might well be taken for such: and that this light seems to have a greater affinity to that which the effluvia of electric bodies emit in the dark. Philos. Trans. N° 347. Hamilton's Philos. Essays, pa. 91.

The Motion of Comets.—If it be supposed that the paths of comets are perfectly parabolical, as some have imagined, it will follow that, being impelled towards the sun by a ceatripetal force, they descend as from spaces infinitely distant; and that by their falls they acquire such a velocity as will carry them off again into the remotest regions, never more to return. But the frequency of their appearance, and their degree of velocity, which does not exceed what they might acquire by their gravity towards the sun, seem to put it past doubt that they move like the planets, in elliptic orbits, though exceedingly eccentric; and so return again after very long periods.

The apparent velocity of the comet of 1472, as observed by Regiomontanus, was such as to carry it through 40° of a great circle in 24 hours: and it was observed that the comet of 1770 moved through more than 45° in the last 25 hours.

About the return of comets there have been different opinions. Newton, Flamsteed, Halley, and other English astronomers, seem satisfied of the return of comets: Cassini and some of the French think it highly probable; but De la Hire and others oppose it. Those on the affirmative side suppose that the comets describe orbits prodigiously eccentric, insomuch that we can see them only in a very small part of their revolution: out of this, they are lost in the immensity of space; hid not only from our eyes, but our telescopes: that little part of their orbit next us passing sometimes within those of all the inferior planets.

M. Cassini gives the following reasons in favour of the return of comets. 1. It is found that they move a considerable time in the arch of a great circle, when referred to the fixed stars, that is a circle whose plane passes through the centre of the earth; deviating but a little from it chiefly towards the end of their appearance; a deviation however common to them with the planets.—2. Comets, as well as planets, appear to move so much the faster as they are nearer the earth; and when they are at equal distances from their perigee, their velocities are nearly the same. By subtracting from their motion the apparent inequality of velocity occasioned by their different distance from the earth, their equal motion might be found: but we should not still be certain that this is their true motion; because they might have considerable inequalities, not distinguishable in that small part of their orbit visible to us. It is rather probable that their real motion, as well as that of the planets, is unequal in itself; and hence we have a reason why the observations made during the appearance of a comet, cannot give the just period of their revolution.—3. There are no two different planets whose orbits cut the ecliptic in the same angle, whose nodes are in the same points of the ecliptic, and having the same apparent velocity in their perigee: consequently, two comets seen at different times, yet agreeing in all those three circumstances, can only be one and the same comet. Not that this exact agreement, in these circumstances, is absolutely necessary to determine their identity: for the moon herself is irregular in all of them, so that it seems there may be cases in which the same comet, at different periods of revolution, may disagree in these points.

As to the objections against the return of comets, the principal is that of the rarity of their appearance, with regard to the number of revolutions assigned to them. In 1702 there was a comet, or rather the tail of one, seen at Rome, which M. Cassini takes to be the same with that observed by Aristotle, and again lately in the year 1668; which would imply a period of 34 years: Now, it may seem strange that a star which has so short a revolution, and of consequence such frequent returns, should be so seldom seen. Again, in April of the same year 1702, a comet was observed by Messrs. Bianchini and Maraldi, which the latter sup- | posed was the same with that of 1664, both on account of its motion, velocity, and direction. M. de la Hire thought it had some relation to another he had observed in 1698, which Cassini refers to that of 1652; which would make it a period of 43 months, and the number of revolutions between 1652 and 1692, 14: now, it is hard to suppose, that in this age, when the heavens are so narrowly watched, a star should make 14 revolutions unperceived; especially such a star as this, which might appear above a month together; and consequently be often disengaged from the crepuscula. For this reason M. Cassini is very reserved in maintaining the hypothesis of the return of comets, and only proposes those for planets where the motions are easy and simple, and are solved without straining, or allowing any irregularities.

M. de la Hire proposes one general difficulty against the whole system of the return of comets, which would seem to prevent any comet from returning as a planet: which is this; that by the disposition necessarily given to their courses, they ought to appear as small at first as at last; and always increase till they arrive at their nearest proximity to the earth; or if they should chance not to be observed, as soon as they are capable of being seen, it is yet hardly possible but they must often shew themselves before they have arrived at their full magnitude and brightness: but, adds he, none were ever yet observed till they had arrived at it. However, the appearance of a comet in the month of October 1723, while at a great distance, so as to be too small and dim to be viewed without a telescope, as well as the observations of several others since, may serve to remove this obstacle, and set the comets still on the same footing with the planets.

It is a conjecture of Newton, that as those planets which are nearest to the sun, and revolve in the least orbits, are the smallest; so among the comets, such as in their perihelion come nearest the sun, are the smallest, and revolve in the least orbits.

There have been many writings upon the subject of comets, beside the notices of historians as to the appearance of certain particular ones.

Regiomontanus first shewed how to find the magnitudes of comets, their distance from the earth, and their true place in the heavens. His 16 problems De Co- metæ Magnitudine, Longitudine, ac Loco, are to be found in a book published in the year 1544, with the title of Scripta Joannis Regiomontani.

Peter Apian observed and wrote upon the comets of 1631, 1632, &c. Other writers are Tycho Brahe, in his Progymnasmata Astronomiæ Instauratæ.—Kepler, of the comet in the year 1607, and de Cometis Libelli tres.—Ricciolus, in his Almagestum Novum, published 1651, enumerates 154 comets cited by historians down to the year 1618.—Hevelius's Prodromus Cometicus, containing the history of the comet of the year 1664. Also his Cometographia.—Lubienietz, in a large folio work expressly on this subject, published 1667, extracts, with immense labour, from the passages of all historians, an account of 415 comets, ending with that of 1665.— Dr. Hook, in his Posthumous works.—M. Cassini's little Tract of Comets.—Sturmius's Dissertatio de Cometarum Natura.—Newton, in his Principia, lib. 3; who first assigned their proper orbits, and by calculations compared the observations of the great comet of 1680 with his theory.—Dr. Halley, his Synopsis Cometica, in the Philos. Trans. number 218, &c; who computed the elements and orbits of 24 comets, and who first ventured to predict the return of one in 1759, which happened accordingly.—De la Lande, Théorie des Comètes, 1759; also, in his Astronomie, vol. 3.—Clairaut, Théorie du mouvement des Comètes, 1760—D'Alembert, Opuscules Mathématiques, vol. 2 pa. 97.—M. Albert Euler, 1762.—Séjour, Essai sur les Comètes, 1775.— Besides Boscovich, De la Grange, De la Place, Frisi, Lexel, Barker, Hancocks, Cole, with many others.— And M. Pingré's Cométographie, in 2 vols. 4to, 1784; in which is contained the most ample list of such comets as have been well observed, and their elements computed, to the number of 67. And accounts of a very few more that have been observed since that time, may be seen in the Mem. de l'Acad. and in the Philos. Trans.—And while this work is printing, there has just come out a very ingenious and ample work upon comets, by Sir Henry Englefield, entitled, “On the Determination of the Orbits of Comets.”

The whole list of comets that have been noticed, on record, amount to upwards of 500, but the following is a complete list of all that have been properly observed, and their elements computed, the mean distance of the earth from the sun being 100000.

M. Facio has suggested, that some of the comets have their nodes so very near the annual orbit of the earth, that if the earth should happen to be found in that part next the node at the time of a comet's passing by; as the apparent motion of the comet will be immensely swift, so its parallax will become very sensible; and its proportion to that of the sun will be given: whence, such transits of comets will afford the best means of determining the distance between the earth and sun.

The comet of 1472, for instance, had a parallax above 20 times greater than the sun's: and if that of 1618 had come down in the beginning of March to its descending node, it would have been much nearer the earth, and its parallax much more notable. But hitherto none has threatened the earth with a nearer appulse than that of 1680: for, Dr. Halley finds, by calculation, that Nov. 11th, at 1 h. 6 min. afternoon, that comet was not more than one semidiameter of the earth to the northward of the earth's path; at which time had the earth been in that part of its orbit, the comet would have had a parallax equal to that of the moon.— What might have been the consequence of so near an appulse, a contact, or lastly, a shock of these bodies? Mr. Whiston says, a deluge!

To determine the Place and Course of a Comet.—Observe the distance of the comet from two fixed stars, whose longitudes and latitudes are known: then from the distances thus known, calculate the place of the comet by spherical trigonometry.

Longomontanus shews an easy method of finding and tracing out the places of a comet mechanically, which is, to find two stars in the same line with the comet, by stretching a thread before the eye over all the three; then do the same by two other stars and the comet: this done, take a celestial globe, or a planisphere, and draw a line upon it first through the former two stars, and then through the latter two; so shall the intersection of the two lines be the place of the comet at that time. If this be repeated from time to time, and all the points of intersection connected, it will shew the path of the comet in the heavens.