自然哲学的数学原理-53

the tail, lying nearly parallel to the equator, deviated a little from the opposition of the sun towards the north.Nov. 23, O. S. at 5 1. morning, at Nuremberg (that is, at 4^h. at London), Mr. Zimmerman saw the comet in ^t 8 8 , with 2 31 south lat.its place being collected by taking its distances from fixed stars.Nov. 24, before sun-rising, the comet was seen by Montenari in TCI 1?52 on the north side of the right line through Cor Leonis and Spica W,and therefore its latitude was something less than 2 38 ; and since thelatitude, as we said, by the concurring observations of Montenari, A/io- ,and Hook, was continually increasing, therefore, it was now, on the 24th,something greater than 1 58" ; and, taking the mean quantity, may bereckoned 2 18", without any considerable error. Ponthwns and Galletinswill have it that the latitude was now decreasing ; and Cellius, and theobserver in New England, that it continued the same, viz., of about 1,or H. The observations of Ponthceus and Cellius are more rude, especially those which were made by taking the azimuths and altitudes; asare also the observations of Galletins. Those are better which weremade by taking the position of the comet to the fixed stars by Montenari^Hook, Ango, and the observer in New England, and sometimes byBOOK III | O* NATURAL PHILOSOPHY. 4S3Poii t/tfe and Cell lus. The same day, at 5h. morning, at Ballasore, thecomet was observed in "I 11 45 ; and, therefore, at 5h. morning at London, was in "I 13 nearly. And, by the theory, the comet was at thattime in n 13 22 42".Nov. 25, before sunrise. Montenari observed the comet in 1Tl 17|nearly ;and Cellius observed at the same time that the comet was in aright line between the bright star in the right thigh of Virgo and thesouthern scale of Libra; and this right line cuts the comet s way in ^l18 3(5 . And, by the theory, the comet was in ni 18-- 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 madeclear that it was one and the same comet that appeared all the time fromNov. 4 to Mar. 9. The path of this comet did twice cut the plane of theecliptic, and therefore was not a right line. It did cut the ecliptic not inopposite parts of the heavens, but in the end of Virgo and beginning ofCapricorn, including an arc of about 98 : and therefore the way of thecomet did very much deviate from the path of a great circle ;for in themonth 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 descendedtowards the sun, and ascended again from the sun, declining one from theother by an apparent angle of above 30, as observed by Montenari. Thiscomet travelled over 9 signs, to wit, from the last dcg. of 1 to the beginning of n, beside the sign of 1, through wrhich it passed before it beganto be seen ; and there is no other theory by which a comet can go over sogreat a part of the heavens with a regular motion. The motion of thiscomet was very unequable ;for about the 20th of Nov. it described about5 a day. Then its motion being retarded between Nov. 26 and Dec.12, to wit, in the space of 15^ days, it described only 40 But the motion thereof being afterwards accelerated, it described near 5 a day, tillits motion began to be again retarded. And the theory which justly corresponds with a motion so unequable, and through so great a part of theheavens, which observes the same laws with the theory of the planets, andwhich accurately agrees with accurate astronomical observations, cannotbe otherwise than true.And, thinking it would not be improper, 1 have given a true representation of the orbit which this comet described, and of the tail which itemitted in several places, in the annexed figure; protracted in the plane ofthe 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, GHthe intersection of the sphere of the orbis magnus with the plane of thetrajectory. I the place of the comet Nov. 4, Ann. 1680; K the place of thesame AT/r. 11 ; L the place of the same Nov. 19; M its place Dec. 12; IS484 THE MATHEMATICAL PRINCIPLES |BOOK 111.its place Dec. 21 ; O its place Dec. 29 ; P its place Jan. 5 following ; Q,its place Jan. 25 ; R its place Feb. 5 ; S its place Feb. 25 ; T its placeMarch 5 ; and V its place March 9. In determining the length of thetail, I made the following observations.Nov. 4 and 6, the tail did not appear ; Nov. 1 1, the tail just begun toshew itself, but did not appear above | deg. long through a 10 feet telescope ; Nov. 17, the tail was seen by Ponthc&us more than 15 long ; Nov.18, in New-England, the tail appeared 30 long, and directly opposite tothe sun, expending itself to the planet Mars, which was then in njZ, 9 54 ;Nov. 19. in Manjltnd, the tail was found 15 or 20 Ions:; Dec. 10 (byBOOK III.] OF NATURAL PHILOSOPHY. 4S5the observation of Mr. Flamsted), the tail passed through the middle ofthe distance intercepted between the tail of the Serpent of Ophiuchus andthe star 6 in the south wing of Aquila, and did terminate near the starsA, w, l>,in Bayer s tables. Therefore the end of the tail was in Y? 19|5;with latitude about 34^ north ; Dec 11, it ascended to the head of Sag-itta(Bayer s a, 0), terminating in V? 26 43 , with latitude 38 34 north;Dec. 12, it passed through the middle of Sa^itta, nor did it reach muchfarther; terminating in ~ 4, with latitude 42^ north nearly. But thesethings are to be understood of the length of the brighter part of the tail;for with a more faint light, observed, too, perhaps, in a serener sky, atRome, Dec. 12, 5h. 40 , by the observation of PcBu.Sj the tail arose to10 above the rump of the Swan, and the side thereof towards the westand towards the north was 45 distant from this star. But about that timethe tail was 3 broad towards the upper end ; and therefore the middlethereof was 2 15 distant from that star towards the south, and the upperend was X in 22, with latitude 61 north; and thence the tail was about70 long; Dec. 21, it extended almost to Cassiopeia s chair, equally distant from j3 and from Schedir, so as its distance from either of the twowas equal to the distance of the one from the other, and therefore did terminate in T 24, with latitude 47^ ; Dec. 29, it reached to a contact withScheal on its left, and exactly filled up the space between the two stars inthe northern foot of Andromeda, being 54 in length; and therefore terminated in & 19, with 35 of latitude; Jan 5, it touched the star -rr inthe breast of Andromeda on its right side, and the star 。i of the girdle onits left; and, according to our observations, was 40 long; but it wascurved, and the convex side thereof lay to the south ;arid near the head ofthe comet it made an angle of 4 with the circle which passed through thesun and the comet s head ; but towards the other end it was inclined tothat circle in an angle of about 10 or 11; and the chord of the tail contained with that circle an angle of 8. Jan. 13, the tail terminated between Alamech and Algol, with a light that was sensible enough : butwith a faint light it ended over against the star K in Perseus s side. Thedistance of the end of the tail from the circle passing through the sun andthe comet was 3 50 ; and the inclination of the chord of the tail to thatcircle was S|. Jan. 25 and 26, it shone with a faint light to the lengthof 6 or 7 ; and for a night or two after, when there was a very clear sky.it extended to the length of 12. or something more, with a light that wasvery faint and very hardly to be seen; but the axis thereof was exactly directed to the bright star in the eastern shoulder of Auriga, and thereforedeviated from the opposition of the sun towards the north by an angle of10. Lastly, Feb. 10, with a telescope I observed the tail 2 long ;for thatfainter light which I spoke of did not appear through the glasses. ButPonthftiis writes, that, on Feb. 7, lie saw the tail 12 lone:. Feb. 25, thefjrnet was without a tail, and so continued till it disappearedTHE MATHEMATICAL PRINCIPLES [BOOK III.Now if one reflects upon the orbit described, and duly considers the otherappearances of this comet, he will be easily satisfied that the bodies ofcomets are solid, compact, fixed, and durable, like the bodies of the planets ;for if they were nothing else but the vapours or exhalations of the earth, ofthe sun, and other planets, this comet, in its passage by the neighbourhoodof the sun, would have been immediately dissipated; for the heat of thesun is as the density of its rays, that is, reciprocally as the square of thedistance of the places from the sun. Therefore, since on Dec. 8, when thecomet was in its perihelion, the distance thereof from the centre of the sunwas to the distance of the earth from the same as about 6 to 1000; thesun s heat on the comet was at that time to the heat of the summer-sunwith us as 1000000 to 36, or as 28000 to 1. But the heat of boilingwater is about 3 times greater than the heat which dry earth acquires fromthe summer-sun, as I have tried : and the heat of red-hot iron (if my conjecture is right) is about three or four times greater than the heat of boiling water. And therefore the heat which dry earth on the comet, while inits perihelion, might have conceived from the rays of the sun, was about2000 times greater than the heat of red-hot iron. But by so fierce a heat,vapours and exhalations, and every volatile matter, must have been immediately consumed and dissipated.This comet, therefore, must have conceived an immense heat from thesun, and retained that heat for an exceeding long- time ;for a globe of ironof an inch in diameter, exposed red-hot to the open air, will scarcely loseall its heat in an hour s time; but a greater globe would retain its heatlonger in the proportion of its diameter, because the surface (in proportionto which it is cooled by the contact of the ambient air) is in that proportionless in respect of the quantity of the included hot matter; and therefore aglobe of red hot iron equal to our earth, that is, about 40000000 feet indiameter, would scarcely cool in an equal number of days, or in above50000 years. But I suspect that the duration of heat may, on account ofsome latent causes, increase in a yet less proportion than that of thediameter ; and I should be glad that the true proportion was investigatedby experiments.It is farther to be observed, that the comet in the month of December.just after it had been heated by the sun, did emit a much longer tail, andmuch more splendid, than in the month of November before, when it hadnot yet arrived .it its perihelion; and, universally, the greatest and mostfulgent tails always arise from comets immediately , fter their passing bythe neighbourhood of the sun. Therefore the heat received by the cometconduces to the greatness of the tail: from whence, I thiufc I may infer,that the tail is nothing else but a very fine vapour, which the head ornucleus of the comet emits by its heat.Jbut we have had three several opinions about the tails of comets; forBOOK III.] OF NATURAL PHILOSOPHY. 48?some will have it that they are nothing else but the beams of the sun slight transmitted through the comets heads, which they suppose to betransparent ; others, that they proceed from the refraction which light suffers in passing from the comet s head to the earth : and, lastly, others, thacthey are a sort of clouds or vapour constantly rising from the comets7 heads.and tending towards the parts opposite to the sun. The first is the opinion of such as are yet unacquainted with optics : for the beams of the sunare seen in a darkened room only in consequence of the light that is reflected from them by the little particles of dust and smoke which arealways flying about in the air; and, for that reason, in air impregnatedwith thick smoke, those beams appear with great brightness, and move thesense vigorously ;in a yet finer air they appear more faint, and are lesseasily discerned ; but in the heavens, where there is no matter to reflectthe light they can never be seen at all. Light is not seen as it is in thebeam, but as it is thence reflected to our eyes ; for vision can be no otherwise produced than by rays falling upon the eyes ; and. therefore, theremust be some reflecting matter in those parts where the tails of the cometsare seen : for otherwise, since all the celestial spaces are equally illuminated by the sun s light, no part of the heavens could appear with moresplendor than another. The second opinion is liable to many difficulties.The tails of comets are never seen variegated with those colours whichcommonly are inseparable from refraction; and the distinct transmissionof the light of the fixed stars and planets to us is a demonstration thatthe aether or celestial medium is not endowed with any refractive power :for as to what is alleged, that the fixed stars have been sometimes seen bythe Egyptians environed with a Coma or Capit/itinm, because that hasbut rarely happened, it is rather to be ascribed to a casual refraction ofclouds; and so the radiation and scintillation of the fixed stars to tinrefractions both of the eyes and air; for upon laying a telescope to theeye, those radiations and scintillations immediately disappear. By the tremulous agitation of the air and ascending vapours, it happens that the rays oflight are alternately turned aside from the narrow space of the pupil of theeye; but no such thing can have place in the much wider aperture of the object-glass of a telescope ; and hence it is that a scintillation is occasioned ir,the former case, wrhich ceases in the latter; and this cessation in the lattercase is a demonstration of the regular transmission of light through theheavens, without any sensible refraction. But, to obviate an objectionthat may be made from the appearing of no tail in such comets as shinebut with a faint light, as if the secondary rays were then too weak to affect the eyes, and for that reason it is that the tails of the fixed stars donot appear, we are to consider, that by the means of telescopes the light ofthe fixed stars may be augmented above an hundred fold, and yet no tailsare seen ; that the light of the planets is yet more copious without any488 THE MATHEMATICAL PRINCIPLES [BOOK 111.tail; but that comets are seen sometimes with huge tails, when the lightof their heads is but faint and dull. For so it happened in the comet ofthe year 1680, when in the month of December it was scarcely equal inlight to the stars of the second magnitude, and yet emitted a notable tail,extending to the length of 40, 50, 60, or 703, and upwards ; and afterwards, on the 27th and 28th of January, when the head appeared but usa star of the 7th magnitude, yet the tail (as we said above), with a lightthat was sensible enough, though faint, was stretched out to 6 or 7 degreesin length, and with a languishing light that was more difficultly seen, evento .12, and upwards. But on the 9th and 10th of February, when to thenaked eye the head appeared no more, through a telescope I viewed thetail of 2 in length. But farther; if the tail was owing to the refraction of the celestial matter, and did deviate from the opposition of thesun, according to the figure of the heavens, that deviation in the sameplaces of the heavens should be always directed towards the same parts.Bu n e comet of the year 1680, December 28d. S^h. P. M. at London, wasseen in X 8 41 , with la itude north 28 6 ; while the sun was in V? 1826 . And the cornet of the year 1577, December 29d. was in X 8 41 ,with latitude north 28 40 , and the sin, as before, in about V^ 18 26 .In both cases the situation of the earth was the same, and the comet appeared in the same place of the heavens ; yet in the former case the tailof the comet (as well by my observations as by the observations of others)deviated from the opposition of the sun towards the north by an angle of4|- degrees ; whereas in the latter there was (according to the observationsof Tychfi) a deviation of 21 degrees towards the south. The refraction,therefore, of the heavens being thus disproved, it remains that the phatiomenaof the tails of comets must be derived from some reflecting matter.And that the tails of comets do arise from their heads, and tend towardsthe parts opposite to the sun, is. farther confirmed from the laws whichthe tails observe. As that, lying in the planes of the comets orbitswhich pass tl trough the sun, they constantly deviate from the oppositionof the sun towards the parts which the comets heads in their progressalong these orbits have left. That to a spectator, placed in those planes,they appear in the parts directly opposite to the sun ; but, as the spectatorrecedes from th >se planes, their deviation begins to appear, and daily becomes greater. That the deviation, cceteris paribus, appears less whenthe tail is more oblique to the orbit of the comet, as well as when thehead of the comet approaches nearer to the sun, especially if the angle ofdeviation is estimated near the head of the comet. That the tails whichhave no deviation appear straight, but the tails which deviate are likewise bended into a certain curvature. That this curvature is greater whenthe deviation is greater ; and is more sensible when the tail, cceteris paribusis longer ;for in the shorter tails the curvature is hardly to be p-jrHOOK HI.] or NATURAL PHILOSOPHY. 489ccived. That the angle of deviation is less near the comet s head, butgreater towards the other end of the tail; and that because the convexside of the tail regards the parts from which the deviation is made, andwhich lie in a right line drawn out infinitely from the sun through thecomet s head. And that the tails that are long and broad, and shine witha stronger light, appear more resplendent and more exactly defined on theconvex than on the concave side. Upon which accounts it is plain thatthe phenomena of the tails of comets depend upon the motions of theirheads, and by no means upon the places of the heavens in which theirheads are seen ; and that, therefore, the tails of comets do not proceed fromthe refraction of the heavens, but from their own heads, which furnish thematter that forms the tail. For, as in our air, the smoke of a heated bodyascends either perpendicularly if the body is at rest, or obliquely if thebody is moved obliquely, so in the heavens, where all bodies gravitate towards the sun, smoke and vapour must (as we have already said) ascendfrom the sun, and either rise perpendicularly if the smoking body is atrest, or obliquely if the body, in all the progress of its motion, is alwaysleaving those places from which the upper or higher parts of the vapourhad risen before ; and that obliquity will be least where the vapour ascendswith most velocity, to wit, near the smoking body, when that is near thesun. But, because the obliquity varies, the column of vapour will be incurvated; and because the vapour in the preceding sides is something morerecent, that is, has ascended something more late from the body, it willtherefore be something more dense on that side, and must on that accountreflect more light, as well as be better defined. I add nothing concerningthe sudden uncertain agitation of the tails of comets, and their irregularfigures, which authors sometimes describe, because they may arise from themutations of our air, and the motions of our clouds, in part obscuringthose tails ; or, perhaps, from parts of the Via Laclea, which might havebeen confounded with and mistaken for parts of the tails of the comets JIBthey passed by.But that the atmospheres of comets may furnish a supply of vapourgreat enough to fill so immense spaces, we may easily understand from therari ty of our own air; for the air near the surface of our earth possessesa space 850 times greater than water of the same weight ; arid thereforea cylinder of air 850 feet high is of equal weight with a cylinder of waterof the same breadth, and but one foot high. But a cylinder of air reaching to the top of the atmosphere is of equal weight with a cylinder ofwater about 33 feet high : and, therefore, if from the whole cylinder ofair the lower part of 850 feet high is taken away, the remaining upperpart will be of equal weight with a cylinder of water 32 feet high : andfrom thence (and by the hypothesis, confirmed by many experiments, thatthe compression of air is as the weight of the incumbent atmosphere, and400 THE MATHEMATICAL PRINCIPLES [BOOK IIIthat the force of gravity is reciprocally as the square of the distance fromthe centre of the earth) raising a calculus, by Cor. Prop. XXII, Book II,I found, that, at the height of one semi-diameter of the earth, reckonedfrom the earth s surface, the air is more rare than with us in u far greaterproportion than of the whole space within the orb of Saturn to a sphericalspace of one inch in diameter ; and therefore if a sphere of our air of butone inch in thickness was equally rarefied with the air at the height ofone semi-diameter of the earth from the earth s surface, it would rill allthe regions of the planets to the orb of Saturn, and far beyond it. Wherefore since the air at greater distances is immensely rarefied, and the comaor atmosphere of comets is ordinarily about ten times higher, reckoningfrom their centres, than the surface of the nucleus, and the tails rise yethigher, they must therefore be exceedingly rare ; and though, on accountof the much thicker atmospheres of comets, and the great gravitation oftheir bodies towards the sun, as well as of the particles of their air andvapours mutually one towards another, it may happen that the air in thecelestial spaces and in the tails of comets is not so vastly rarefied, yetfrom this computation it is plain that a very small quantity of air andvapour is abundantly sufficient to produce all the appearances of the tailsof comets : for that they are, indeed, of a very notable rarity appears fromthe shining of the stars through them. The atmosphere of the earth,illuminated by the sun s light, though but of a few miles in thickness,quite obscures and extinguishes the light not only of all the stars, buteven of the moon itself; whereas the smallest stars are seen to shinethrough the immense thickness of the tails of comets, likewise illuminatedby the sun, without the least diminution of their splendor. Nor is thebrightness of the tails of most comets ordinarily greater than that of ourair, an inch or two in thickness, reflecting in a darkened room the light ofthe sun-beams let in by a hole of the window-shutter.And we may pretty nearly determine the time spent during the ascentof the vapour from the comet s head to the extremity of the tail, by drawing a right line from the extremity of the tail to the sun, and markingthe place where that right line intersects the comet s orbit : for the vapourthat is now in the extremity of the tail, if it has ascended in a right linefrom the sun, must have begun to rise from the head at the time when thehead was in the point of intersection. It is true, the vapour does not risein a right line from the sun, but, retaining the motion Avhich it had fromthe comet before its ascent, and compounding that motion witli its motionof ascent, arises obliquely ; and, therefore, the solution of the Problem willbe more exact, if we draw the line which intersects the orbit parallel tothe length of the tail; or rather (because of the curvilinear motion of thecomet) diverging a little from the line or length of the tail. And bymeans of this principle I found that the vapour which, Ja/iutiry 25, wasBOOK III.] OF NATURAL PHILOSOPHY. 491in the extremity of the tail, had begun to rise from the head before December 11, and therefore had spent in its whole ascent 45 days ; but thatthe whole tail which appeared on December 10 had finished its ascent inthe space of the two days then elapsed from the time of the comet s beingin its perihelion. The vapour, therefore, about the beginning and in theneighbourhood of the sun rose with the greatest velocity, and afterwardscontinued to ascend with a motion constantly retarded by its own gravity ;and the higher it ascended, the more it added to the length of the tail;and while the tail continued to be seen, it was made up of almost all thatvapour which had risen since the time of the comet s being in its perihelion; nor did that part of the vapour which had risen first, and whichfunned the extremity of the tail, cease to appear, till its too great distance, as well from the sun, from which it received its li^it, as from oureyes, rendered it invisible. Whence also it is that the tails of other cometswhich are short do riot rise from their heads with a swift and continuedmotion, and soon after disappear, but are permanent and lasting columnsof vapours and exhalations, which, ascending from the heads with a slowmotion