IN the former of the two preceding chapters the powers have been explained, which keep in motion those celestial bodies, whose courses had been well determined by the astronomers. In the last chapter we have shewn, how those powers have been applied by our author to the making a more perfect discovery of the motion of those bodies, the courses of which were but imperfectly understood; for some of the inequalities, which we have been describing in the moon’s motion, were unknown to the astronomers. In this chapter we are to treat of a third species of the heavenly bodies, the true motion of which was not at all apprehended before our author writ; in so much, that here Sir Isaac Newton has not only explained the causes of the motion of these bodies, but has performed also the part of an astronomer, by discovering what their motions are.2. That these bodies are not meteors in our air, is manifest; because they rise and set in the same manner, as the sun and stars. The astronomers had gone so far in their inquiries concerning them, as to prove by their observations, that they moved in the etherial spaces far beyond the moon; but they had no true notion at all of the path, which they described. The most prevailing opinion before our author was, that they moved in straight lines; but in what part of the heavens was not determined. DesCartes[205] removed them far beyond the sphere of Saturn, as finding the straight motion attributed to them, inconsistent with the vortical fluid, by which he explains the motions of the planets, as we have above related[206]. But Sir Isaac Newton distinctly proves from astronomical observation, that the comets pass through the region of the planets, and are mostly invisible at a less distance, than that of Jupiter[207].3. And from hence finding the comets to be evidently within the sphere of the sun’s action, he concludes they must, necessarily move about the sun, as the planets do[208]. The planets move in ellipsis’s; but it is not necessary that every body, which is influenced by the sun, should move in that particular kind of line. However our author proves, that the power of the sun being reciprocally in the duplicate proportion of the distance, every body acted on by the sun must either fall directly down, or move in some conic section; of which lines I have above observed, that there are three species, the ellipsis, parabola, and hyperbola[209]. If a body, which descends toward the sun as low as the orbit of any planet, move with a swifter motion than the planet does, that body will describe an orbit of a more oblong figure, than that of the planet, and have a longer axis at least. The velocity of the body may be so great, that it shall move in a parabola, and having once passed about the sun, shall ascend for ever without returning any more: but the sun will be placed in the focus of this parabola. With a velocity still greater the body will move in an hyperbola. But it is most probable, that the comets move in elliptical orbits, though of a very oblong, or in the phrase of astronomers, of a very eccentric form, such as is represented in fig. 107, where S is the sun, C the comet, and ABDE its orbit, wherein the distance of S and D far exceeds that of S and A. Whence it is, that they sometimes are found at a moderate distance from the sun, and appear within the planetary regions; at other times they ascend to vast distances, far beyond the very orbit of Saturn, and so become invisible. That the comets do move in this manner is proved by our author, from computations built upon the observations, which astronomers had made on many comets. These computations were performed by Sir Isaac Newton himself upon the comet, which appeared toward the latter end of the year 1680, and at the beginning of the year following[210]; but the learned Dr. Halley prosecuted the like computations more at large in this, and also in many other comets[211]. Which computations are made upon propositions highly worthy of our author’s unparallel’d genius, such as could scarce have been discovered by any one not possessed of the utmost force of invention;4. Those computations depend upon this principle, that the eccentricity of the orbits of the comets is so great, that if they are really elliptical, yet they approach so near to parabolas in that part of them, where they come under our view, that they may be taken for such without sensible error[212]: as in the preceding figure the parabola FAG differs in the lower part of it about A very little from the ellipsis DEAB. Upon which ground our great author teaches a method of finding by three observations made upon any comet the parabola, which nearest agrees with its orbit[213].

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.

9. It is therefore to prevent too great disturbances in their motions from these causes, as our author observes, that while the planets revolve all of them nearly in the same plane, the comets are disposed in very different ones; and distributed over all parts of the heavens; that, when in their greatest distance from the sun, and moving slowest, they might be removed as far as possible out of the reach of each other’s action[220]. The same end is likewise farther answered in those comets, which by moving slowest in the aphelion, or remotest distance from the sun, descend nearest to it, by placing the aphelion of these at the greatest height from the sun[221].

10. Our philosopher being led by his principles to explain the motions of the comets, in the manner now related, takes occasion from thence to give us his thoughts upon their nature and use. For which end he proves in the first place, that they must necessarily be solid and compact bodies, and by no means any sort of vapour or light substance exhaled from the planets or stars: because at the near distance, to which some comets approach the sun, it could not be, but the immense heat, to which they are exposed, should instantaneously disperse and scatter any such light volatile substance[222]. In particular the forementioned comet of 1680 descended so near the sun, as to come within a sixth part of the sun’s diameter from the surface of it. In which situation it must have been exposed, as appears by computation, to a degree of heat exceeding the heat of the sun upon our earth no less than 28000 times; and therefore might have contracted a degree of heat 2000 times greater, than that of red hot iron[223]. Now a substance, which could endure so intense a heat, without being dispersed in vapor, must needs be firm and solid.

11. It is shewn likewise, that the comets are opake substances, shining by a reflected light, borrowed from the sun[224]. This is proved from the observation, that comets, though they are approaching the earth, yet diminish in lustre, if at the same time they recede from the sun; and on the contrary, are found to encrease daily in brightness, when they advance towards the sun, though at the same time they move from the earth[225].

12. The comets therefore in these respects resemble the planets; that both are durable opake bodies, and both revolve about the sun in conic sections. But farther the comets, like our earth, are surrounded by an atmosphere. The air we breath is called the earth’s atmosphere; and it is most probable, that all the other planets are invested with the like fluid. Indeed here a difference is found between the planets and comets. The atmospheres of the planets are of so fine and subtile a substance, as hardly to be discerned at any distance, by reason of the small quantity of light which they reflect, except only in the planet Mars. In him there is some little appearance of such a substance surrounding him, as stars which have been covered by him are said to look somewhat dim a small space before his body comes under them, as if their light, when he is near, were obstructed by his atmosphere. But the atmospheres which surround the comets are so gross and thick, as to reflect light very copiously. They are also much greater in proportion to the body they surround, than those of the planets, if we may judge of the rest from our air; for it has been observed of comets, that the bright light appearing in the middle of them, which is reflected from the solid body, is scarce a ninth or tenth part of the whole comet,13. I speak only of the heads of the comets, the most lucid part of which is surrounded by a fainter light, the most lucid part being usually not above a ninth or tenth part of the whole in breadth[226]. Their tails are an appearance very peculiar, nothing of the same nature appertaining in the least degree to any other of the celestial bodies. Of that appearance there are several opinions; our author reduces them to three[227]. The two first, which he proposes, are rejected by him; but the third he approves. The first is, that they arise from a beam of light transmitted through the head of the comet, in like manner as a stream of light is discerned, when the sun shines into a darkened room through a small hole. This opinion, as Sir Isaac Newton observes, implies the authors of it wholly unskilled in the principles of optics; for that stream of light, seen in a darkened room, arises from the reflection of the sun beams by the dust and motes floating in the air: for the rays of light themselves are not seen, but by their being reflected to the eye from some substance, upon which they fall[228]. The next opinion examined by our author is that of the celebrated DesCartes, who imagins these tails to be the light of the comet refracted in its passage to us, and thence affording an oblong representation; as the light of the sun does, when refracted by the prism in that noted experiment, which will have a great share in the third book of this discourse[229]. But this opinion is at once overturned from this consideration only, that the planets could be no more free from this refraction than the comets; nay ought to have larger or brighter tails, than they, because the light of the planets is strongest. However our author has thought proper to add some farther objections against this opinion: for instance, that these tails are not variegated with colours, as is the image produced by the prism, and which is inseparable from that unequal refraction, which produces that disproportioned length of the image. And besides, when the light in its passage from different comets to the earth describes the same path through the heavens, the refraction of it should of necessity be in all respects the same. But this is contrary to observation; for the comet in 1680, the 28th day of December, and a former comet in the year 1577, the 29th day of December, appear’d in the same place of the heavens, that is, were seen adjacent to the same fixed stars, the earth likewise being in the same place at both times; yet the tail of the latter comet deviated from the opposition to the sun a little to the northward, and the tail of the former comet declined from the opposition of the sun five times as much southward[230].

14. There are some other false opinions, though less regarded than these, which have been advanced upon this argument. These our excellent author passes over, hastening to explain, what he takes to be the true cause of this appearance. He thinks it is certainly owing to steams and vapours exhaled from the body, and gross atmosphere of the comets, by the heat of the sun; because all the appearances agree perfectly to this sentiment. The tails are but small, while the comet is descending to the sun, but enlarge themselves to an immense degree, as soon as ever the comet has passed its perihelion; which shews the tail to depend upon the degree of heat, which the comet receives from the sun. And that the intense heat to which comets, when nearest the sun, are exposed, should exhale from them a very copious vapour, is a most reasonable supposition; especially if we consider, that in those free and empty regions steams will more easily ascend, than here upon the surface of the earth, where they are suppressed and hindered from rising by the weight of the incumbent air: as we find by experiments made in vessels exhausted of the air, where upon removal of the air several substances will fume and discharge steams plentifully, which emit none in the open air. The tails of comets, like such a vapour, are always in the plane of the comet’s orbit, and opposite to the sun, except that the upper part thereof inclines towards the parts, which the comet has left by its motion; resembling perfectly the smoak of a burning coal, which, if the coal remain fixed, ascends from it perpendicularly; but, if the coal be in motion, ascends obliquely, inclining from the motion of the coal. And besides, the tails of comets may be compared to this smoak in another respect, that both of them are denser and more compact on the convex side, than on the concave. The different appearance of the head of the comet, after it has past its perihelion, from what it had before, confirms greatly this opinion of their tails: for smoke raised by a strong heat is blacker and grosser, than when raised by a less; and accordingly the heads of comets, at the same distance from the sun, are observed less bright and shining after the perihelion, than before, as if obscured by such a gross smoke.

15. The observations of Hevelius upon the atmospheres of comets still farther illustrate the same; who relates, that the atmospheres, especially that part of them next the sun, are remarkably contracted when near the sun, and dilated again afterwards.

16. To give a more full idea of these tails, a rule is laid down by our author, whereby to determine at any time, when the vapour in the extremity of the tail first rose from the head of the comet. By this rule it is found, that the tail does not consist of a fleeting vapour, dissipated soon after it is raised, but is of long continuance; that almost all the vapour, which rose about the time of the perihelion from the comet of 1680, continued to accompany it, ascending by degrees, being succeeded constantly by fresh matter, which rendered the tail contiguous to the comet. From this computation the tails are found to participate of another property of ascending vapours, that, when they ascend with the greatest velocity, they are least incurvated.

17. The only objection that can be made against this opinion is the difficulty of explaining, how a sufficient quantity of vapour can be raised from the atmosphere of a comet to fill those vast spaces, through which their tails are sometimes extended. This our author removes by the following computation: our air being an elastic fluid, as has been said before[231], is more dense here near the surface of the earth, where it is pressed upon by the whole air above; than it is at a distance from the earth, where it has a less weight incumbent. I have observed, that the density of the air is reciprocally proportional to the compressing weight. From hence our author computes to what degree of rarity the air must be expanded, according to this rule, at an height equal to a semidiameter of the earth: and he finds, that a globe of such air, as we breath here on the surface of the earth, which shall be one inch only in diameter, if it were expanded to the degree of rarity, which the air must have at the height now mentioned, would fill all the planetary regions even to the very sphere of Saturn, and far beyond. Now since the air at a greater height will be still immensly more rarified, and the surface of the atmospheres of comets is usually about ten times the distance from the center of the comet, as the surface of the comet it self, and the tails are yet vastly farther removed from the center of the comet; the vapour, which composes those tails, may very well be allowed to be so expanded, as that a moderate quantity of matter may fill all that space, they are seen to take up. Though indeed the atmospheres of comets being very gross, they will hardly be rarified in their tails to so great a degree, as our air under the same circumstances; especially since they may be something condensed, as well by their gravitation to the sun, as that the parts will gravitate to one another; which will hereafter be shewn to be the universal property of all matter[232]. The only scruple left is, how so much light can be reflected from a vapour so rare, as this computation implies. For the removal of which our author observes, that the most refulgent of these tails hardly appear brighter, than a beam of the sun’s light transmitted into a darkened room through a hole of a single inch diameter; and that the smallest fixed stars are visible through them without any sensible diminution of their lustre.18. All these considerations put it beyond doubt, what is the true nature of the tails of comets. There has indeed nothing been said, which will account for the irregular figures, in which those tails are sometimes reported to have appeared; but since none of those appearances have ever been recorded by astronomers, who on the contrary ascribe the same likeness to the tails of all comets, our author with great judgment refers all those to accidental refractions by intervening clouds, or to parts of the milky way contiguous to the comets[233].

19. The discussion of this appearance in comets has led Sir Isaac Newton into some speculations relating to their use, which I cannot but extreamly admire, as representing in the strongest light imaginable the extensive providence of the great author of nature, who, besides the furnishing this globe of earth, and without doubt the rest of the planets, so abundantly with every thing necessary for the support and continuance of the numerous races of plants and animals, they are stocked with, has over and above provided a numerous train of comets, far exceeding the number of the planets, to rectify continually, and restore their gradual decay, which is our author’s opinion concerning them[234]. For since the comets are subject to such unequal degrees of heat, being sometimes burnt with the most intense degree of it, at other times scarce receiving any sensible influence from the sun; it can hardly be supposed, they are designed for any such constant use, as the planets. Now the tails, which they emit, like all other kinds of vapour, dilate themselves as they ascend, and by consequence are gradually dispersed and scattered through all the planetary regions, and thence cannot but be gathered up by the planets, as they pass through their orbs: for the planets having a power to cause all bodies to gravitate towards them, as will in the sequel of this discourse be shewn[235]; these vapours will be drawn in process of time into this or the other planet, which happens to act strongest upon them. And by entering the atmospheres of the earth and other planets, they may well be supposed to contribute to the renovation of the face of things, in particular to supply the diminution caused in the humid parts by vegetation and putrefaction. For vegetables are nourished by moisture, and by putrefaction are turned in great part into dry earth; and an earthy substance always subsides in fermenting liquors; by which means the dry parts of the planets must continually increase, and the fluids diminish, nay in a sufficient length of time be exhausted, if not supplied by some such means. It is farther our great author’s opinion, that the most subtile and active parts of our air, upon which the life of things chiefly depends, is derived to us, and supplied by the comets. So far are they from portending any hurt or mischief to us, which the natural fears of men are so apt to suggest from the appearance of any thing uncommon and astonishing.20. That the tails of comets have some such important use seems reasonable, if we consider, that those bodies do not send out those fumes merely by their near approach to the sun; but are framed of a texture, which disposes them in a particular manner to fume in that sort: for the earth, without emitting any such steam, is more than half the year at a less distance from the sun, than the comet of 1664 and 1665 approached it, when nearest; likewise the comets of 1682 and 1683 never approached the sun much above a seventh part nearer than Venus, and were more than half as far again from the sun as Mercury; yet all these emitted tails.

21. From the very near approach of the comet of 1680 our author draws another speculation; for if the sun have an atmosphere about it, the comet mentioned seems to have descended near enough to the sun to enter within it. If so, it must have been something retarded by the resistance it would meet with, and consequently in its next descent to the sun will fall nearer than now; by which means it will meet with a greater resistance, and be again more retarded. The event of which must be, that at length it will impinge upon the sun’s surface, and thereby supply any decrease, which may have happened by so long an emission of light, or otherwise. And something like this our author conjectures may be the case of those fixed stars which by an additional increase of their lustre have for a certain time become visible to us, though usually they are out of sight. There is indeed a kind of fixed stars, which appear and disappear at regular and equal intervals: here some more steady cause must be sought for; perhaps these stars turn round their own axis’s, as our sun does[236], and have some part of their body more luminous than the other, whereby they are seen, when the most lucid part is next to us, and when the darker part is turned toward us, they vanish out of sight.

22. Whether the sun does really diminish, as has been here suggested, is difficult to prove; yet that it either does so, or that the earth increases, if not both, is rendered probable from Dr. Halley’s observation[237], that by comparing the proportion, which the periodical time of the moon bore to that of the sun in former times, with the proportion between them at present, the moon is found to be something accelerated in respect of the sun. But if the sun diminish, the periods of the primary planets will be lengthened; and if the earth be encreased, the period of the moon will be shortened: as will appear by the next chapter, wherein it shall be shewn, that the power of the sun and earth is the result of the same power being lodg’d in all their parts, and that this principle of producing gravitation in other bodies is proportional to the solid matter in each body.