自然哲学的数学原理-60

because they were found to have no diurnal parallax, so their annualparallax is a convincing proof of their descending into the regions of theplanets. For all the comets which move in a direct course, according tothe order of the signs, about the end of their appearance become more thanordinarily slow, or retrograde, if the earth is between them and the sun ;and more than ordinarily swift if the earth is approaching to a heliocentric opposition with them. Whereas, on the other hand, those which moveagainst the order of the signs, towards the end of their appearance, appearswifter than they ought to be if the earth is between them and the sun ;and slower, and perhaps retrograde, if the earth is in the other side of itscrbit. This is occasioned by the motion of the earth in different situations. If the earth go the same way with the comet, with a swiftermotion, the comet becomes retrograde; if with a slower motion, the cometbecomes slower, however ; and if the earth move the contrary way, it becomes swifter ; and by collecting the differences between the slower andswifter motions, and the sums of the more swift and retrograde motions,and comparing them with the situation and motion of the earth from,whence they arise, I found, by means of this parallax, that the distancesof the comets at the time they cease to be visible to the naked eye arealways less than the distance of Saturn, and generally even less than thedistance of Jupiter.The same thing may be collected from the curvature of the way of thecomets (p. 462). These bodies go on nearly in great circles while theirmotion continues swift ; but about the end of their course, when that partTHE SYSTEM OF THE WORLD. 549of their apparent motion which arises from the parallax bears a greaterproportion to their whole apparent motion, they commonly deviate fromthose circles ; and when the earth goes to one side, they deviate to theother ; and this deflection, because of its corresponding with the motionof the earth, must arise chiefly from the parallax ; and the quantity thereof is so considerable, as, by my computation, to place the disappearingcomets a good deal lower than Jupiter. Whence it follows, that, whenthey approach nearer to us in their perigees and perihelions, they often descend below the orbits of Mars and the inferior planets.Moreover, this nearness of the cornets is confirmed by the annual parallax of the orbit, in so far as the same is- pretty nearly collected by thesupposition that the comets move uniformly in right lines. The methodof collecting the distance of a comet according to this hypothesis fromfour observations (first attempted by Kepler, and perfected by Dr. Wallisand Sir Christopher Wren) is well known and the comets reduced tothis regularity generally pass through the middle of the planetary region.So the comets of the year 1607 and 1618, as their motions are defined byKepler, passed between the sun and the earth : that of the year 16 4 below the orbit of Mars; and that in 1680 below the orbit of Mercury, asits motion was defined by Sir Christopher Wren rind others. By a likerectilinear hypothesis, Hevelius placed all the comets about which we haveany observations below the orbit of Jupiter. It is a false notion, therefore, and contrary to astronomical calculation, which some have entertained, who, from the regular motion of the comets, either remove theminto the regions of the fixed stars, or deny the motion of the earth : whereas their motions cannot be reduced to perfect regularity, unless we supposethem to pass through the regions near the earth in motion ; and these arethe arguments drawn from the parallax, so far as it can be determinedwithout an exact knowledge of the orbits and motions of the comets.The near approach of the comets is farther confirmed from the light oftheir heads (p. 463, 465) ;for the light of a celestial body, illuminated bythe sun, and receding to remote parts, is diminished in the quadruplicateproportion of the distance ; to wit, in one duplicate proportion on accountof the increase of the distance from the sun ; and in another duplicateproportion on account of the decrease of the apparent diameter. Hence itmay be inferred, that Saturn being at a double distance, and having itsapparent diameter nearly half of that of Jupiter, must appear about I (5times more obscure ; and that, if its distance were 4 times greater, itslight would be 256 times less ; and therefore would be hardly perceivableto the naked eye. But now the comets often equal Saturn s light, withoutexceeding him in their apparent diameters. So the comet of the year1668, according to Dr. Hooke s observations, equalled in brightness thelight of a fixed star of the first magnitude ; and its head, or the star ID550 THE SYSTEM OF THE WORLD.the middle of the coma, appeared, through a telescope oi 15 feet, as lucidas Saturn near the horizon ; but the diameter of the head was only 25"that is, almost the same with the diameter of a circle equal to Saturnand his ring. The coma or hair surrounding the head was about ten timesas broad; namely, 4 min. Again ; the least diameter of the hair of thecomet of the year 1682, observed by Mr. Flamsted with a tube of 16 feetand measured with the micrometer, was 2 ; but the nucleus, or star inthe middle, scarcely possessed the tenth part of this breadth, and wastherefore only 11 or 12" broad; but the light and clearness of its headexceeded that of the year 1680, and was equal to that of the stars of thefirst or second magnitude. Moreover, the comet of the year 1665, in April,as Hevelws informs us, exceeded almost all the fixed stars in splendor, arideven Saturn itself, as being of a much more vivid colour ; for this cometwas more lucid than that which appeared at the end of the foregoing yearand was compared to the stars of the first magnitude. The diameter ofthe coma was about 6; but the nucleus, compared with the planets bymeans of a telescope, was plainly less than Jupiter, and was sometime*?thought less, sometimes equal to the body of Saturn within the ring. Tothis breadth add that of the ring, and the whole face of Saturn will betwice as great as that of the comet, with a light not at all more intense ;and therefore the comet was nearer to the sun than Saturn. From theproportion of the nucleus to the whole head found by these observations,and from its breadth, which seldom exceeds 8 or 12;,it appears that thi-Btars of the comets are most commonly of the same apparent magnitudeas the planets ; but that their light may be compared oftentimes with thatof Saturn, and sometimes exceeds it. And hence it is certain that in theirperihelia their distances can scarcely be greater than that of Saturn. Attwice that distance, the light would be four times less, which besides by itsdim paleness would be as much inferior to the light of Saturn as the lightof Saturn is to the splendor of Jupiter : but this difference would be easilyobserved. At a distance ten times greater, their bodies must be greattrthan that of the sun ; but their light would be 100 times fainter thanthat of Saturn. And at distances still greater, their bodies would farexceed the sun ;. but, being in such dark regions, they must be no longervisible. So impossible is it to place the comets in the middle regions between the sun and fixed stars, accounting the sun as one of the fixed stars:for certainly they would receive no more light there from the sun than w<?do from the greatest of the fixed stars.So far we have gone without considering that obscuration which cometssuffer from that plenty of thick smoke which encompasseth their heads.and through which the heads always shew dull as through a cloud ; forby how much the more a body is obscured by this smoke, by so much th.2more near it must be allowed to come to the sun, that it may vie with theTHE SYSTEM OF THE WORLD. 651planets in the quantity of light which it reflects : whence it is probablethat the comets descend far below the orbit of Saturn, as we proved beforefrom their parallax. But, above all, the thing is evinced from their tails,which must be owing either to the sun s light reflected from a srnokearising from them, and dispersing itself through the aether, or to the lightuf their own headt.In the former case we must shorten the distance of the comets, lest we beobliged to allow that the smoke arising from their heads is propagatedthrough such a vast extent of space, and with such a velocity of expansion,jus will seem altogether incredible; in the latter case the whole light ofboth head and tail must be ascribed to the central nucleus. But, then, ifwe suppose all this light to be united and condensed within the disk of thenucleus, certainly the nucleus will by far exceed Jupiter itself in splendor,especially when it emits a very large and lucid tail. If, therefore, under a lessapparent diameter, it reflects more light, it must be much more illuminatedby the sun, and therefore much nearer to it. So the comet that appearedDec. }2 and 15, O.S. Anno 1679, at the time it emitted a very shiningtail, whose splendor was equal to that of many stars like Jupiter, if theirlight were dilated and spread through so great a space, was, as to the magnitude of its nucleus, less than Jupiter (as Mr. Flawsled observed), andtherefore was much nearer to the sun : nay, it was even less than Mercury.For on the 17th of that month, when it was nearer to the earth, it appeared to Cassini through a telescope of 35 feet a little less than the globeof Saturn. On the 8th of this month, in the morning, Dr. ffalfey saw thetail, appearing broad and very short, and as if it rose from the body of thesun itself, at that time very near its rising. Its form was like that of anextraordinary bright cloud ; nor did it disappear till the sun itself beganto be seen above the horizon. Its splendor, therefore, exceeded the light ofthe clouds till the sun rose, and far surpassed that of all the stars together,as yielding only to the immediate brightness of the sun itself. NeitherMercury, nor Venus, nor the moon itself, are seen so near the rising sun.Imagine all this dilated light collected together, and to be crowded intothe orbit of the comet s nucleus which was less than Mercury ; by itssplendor, thus increased, becoming so much more conspicuous, it will vastlyexceed Mercury, and therefore must be nearer to the sun. On the 12thand 15th of the same month, this tail, extending itself over a much greaterspace, appeared more rare; but its light was still so vigorous as to becomevisible when the fixed stars were hardly to be seen, and soon after to appearlike a fiery beam shining in a wonderful manner. From its length, whichwas 40 or 50 degrees, and its breadth of 2 degrees, we may compute whatthe light of the whole must beThis near approach of the comets to the sun is confirmed from the situtionthey are seen in when their tails appear most resplendent; for whenTHE SYSTEM OF THE WORLD.the head passes by the sun, and lies hid under the solar rays, very brightand shining ta Is, like fiery beams, are said to issue from the horizon; butafterwards, when the head begins to appear, and is got farther from thesun, that splendor always decreases, and turns by degrees into a palenesslike to that of the milky way, but much more sensible at first;after thatvanishing gradually. Such was that most resplendent comet described byAristotle, Lib. 1, Meteor. 6. " The head thereof could not be seen, becauseit set before the sun, or at least was hid under the sun s rays ; but the nextday it was seen as well as might be ; for, having left the sun but a verylittle way, it set immediately after it; and the scattered light of the headobscured by the too great splendour (of the tail) did not yet appear. Butafterwards (says Aristotle), when the splendour of the tail was now diminished (the head of), the comet recovered its native brightness. And thesplendour of its tail reached now to a third part of the heavens (that is, to60). It appeared in the winter season, and, rising to Orion s girdle, therevanished away." Two comets of the same kind are described by Justin,Lib. 37, which, according to his account," shined so bright, that the wholeheaven seemed to be on fire; and by their greatness filled up a fourth partof the heavens, and by their splendour exceeded that of the sun." Bywhich last words a near position of these bright comets and the rising orsetting sun is intimated (p. 494, 495). We may add to these the comet ofthe year 1101 or 1106, " the star of which was small and obscure (like thatof ] 6SO) ; but the splendour arising from it extremely bright, reaching likea fiery beam to the east and north," as Hevelius has it from Simeon, themonk of Durham. It appeared at the beginning of February about theevening in the south-west. From this and from the situation of the tailwe may infer that the head was near the sun. Matthew Paris says, "itwas about one cubit from the sun ; from the third [or rather the sixth] tothe ninth hour sending out a long stream of light." The comet of 1264,in July, or about the solstice, preceded the rising sun, sending out its beamswith a great light towards the west as far as the middle of the heavens ;and at the beginning it ascended a little above the horizon : but as the sunwent forwards it retired every day farther from the horizon, till it passedby the very middle of the heavens. It is said to have been at the beginninglarge and bright, having a large coma, which decayed from day to day. Itis described in Append. Matth, Paris, Hist. Aug. after this manner : ^Au.Christi 1265, there appeared a comet so wonderful, that none then livinghad ever seen the like; for, rising from the east with a great brightness, itextended itself 。uth a great light as far as the middle of the hemispheretowards the west." The Latin original being somewhat barbarous and obgcure,it is here subjoined. Ah oriente enim cum tnaguo fulgore sur-" :is, usque ad medium hcmisp]icerii versus occideutcm, omuia per lucid*pertrahcbai.THE SYSTEM OF THE WORLD. 553"In the year 1401 or 1402, the sun being got below the horizon, thereappeared in the west a bright and shining comet, sending out a tail upwards, in splendor like a flame of fire, and in form like a spear, darting itsrays from west to east. When the sun was sunk below the horizon, by thelustre of its own rays it enlightened all the borders of the earth, not permitting the other stars to shew their light, or the shades of night to darkenthe air, because its light exceeded that of the others, and extended itself tothe upper part of the heavens, flaming," &c., Hist. Byzaut. Due. Mich.Nepot. From the situation of the tail of this comet, and the time of itsfirst appearance, we may infer that the head was then near the sun, andwent farther from him every day ; for that comet continued three months.In the year 1527, Aug. 11, about four in the morning, there was seen almost throughout Europe a terrible comet in Leo, which continued flamingan hour and a quarter every day. It rose from the east, and ascended tothe south and west to a prodigious length. It was most conspicuous to thenorth, and its cloud (that is, its tail) was very terrible ; having, accordingto the fancies of the vulgar, the form of an arm a little bent holding asword of a vast magnitude. In the year 1618, in the end of November,there began a rumour, that there appeared about sun-rising a bright beam,which was the tail of a comet whose head was yet concealed within thebrightness of the solar rays. On Nov. 24, and from that time, the cometitself appeared with a bright light, its head and tail being extremely resplendent. The length of the tail, which was at first 20 or 30 dog., increased till December 9, when it arose to 75 deg,, but with a light muchmore faint and dilute than at the beginning. In the year 1668, March 5,N. S., about 7 in the evening, P. Volent. Estaucius, being in Brazil, sawa comet near the horizon in the south-west. Its head was small, andscarcely discernible, but its tail extremely bright and refulgent, so that thereflection of it from the sea was easily seen by those who stood upon theshore. This great splendor lasted but three days, decreasing very remarkably from that time. The tail at the beginning extended itself from westto south, and in a situation almost parallel to the horizon, appearing likea shining beam 23 deg. in length. Afterwards, the light decreasing, itsmagnitude increased till the comet ceased to be visible; so that Cassiid,at Bologna^ saw it (Mar. 10, 11, 12) rising from the horizon 32 deg. inlength. In Portugal it is said to have taken up a fourth part of theheavens (that is, 45 deg.), extending itself from west to east with a notablebrightness ; though the whole of it was not seen, because the head in thispart of the world always lay hid below the horizon. From the increase ofthe tail it is plain that the head receded from the sun. and was nearest toit at the beginning, when the tail appeared brightest.To all these we may add the comet of 1680, whose wonderful splendorat the conjunction of the head with the sun was above described. Hut so554 THE SYSTEM OF THE WORLD.great a splendor argues the comets of this kind to have really passed nearthe fountain of light, especially since the tails never shine so much intheir opposition to the sun jnor do we read that fiery beams have ever appeared there.Lastly, the same thing is inferred (p. 466; 407) from the light of theheads increasing in the recess of the comets from the earth towards thesun, and decreasing in their return from the sun towards the earth ; for sothe last comet of the year 1 665 (by the observation of Hevelius]^ from thetime that it was first seen, was always losing of its apparent motion, andtherefore had already passed its perigee : yet the splendor of its head wasdaily increasing, till, being hid by the sun?s rays, the comet ceased to appear. The comet of the year (683 (by the observation of the same Hejelius),about the end of July, when it first appeared, moved at a veryslow rate, advancing only about 40 or 45 minutes in its orbit in a day stime. I3ut from that time its diurnal motion was continually upon theincrease till Septe/uber 4, when it arose to about 5 degrees ; and thereforein all this interval of time the comet was approaching to the earth. Whichis likewise proved from the diameter of its head measured with a micrometer ; for, August the 6th, Hevelius found it only 6 5", including thecoma ; which, September 2, he observed 9 7". And therefore its headappeared far less about the beginning than towards the end of its motion,though about the beginning, because nearer to the sun, it appeared farmore lucid than towards the end, as the same Hevelius declares. Wherefore in all this interval of time, on account of its recess from the sun,it decreased in splendor, notwithstanding its access towards the earth. Thecomet of the year 1618, about the middle of December, and that of theyear 1680, about the end of the same month, did both move with theirgreatest velocity, and were therefore then in their perigees : but the greatestsplendor of their heads was seen two weeks before, when they had just gotclear of the sun s rays : and the greatest splendor of their tuild a littlemore early, when yet nearer to the sun. The head of the former comet,according to the observations of Cysattis, Dec. 1, appeared greater thanthe stars of the first magnitude: and, Dec. 16 (being then in its perigee),)i a small magnitude, and the splendor or clearness was much diminished.Jan. 7, Kepler, being uncertain about the head ? left off observing. Dec.12, the head of the last comet was seen and observed by Flamxted at thedistance of 9 degrees from the sun, which a star of the third magnitudecould hardly have been. December 15 and 17, the same appeared like astar of the third magnitude, its splendor being diminished by the brightclouds near the setting sun. Dec. 26, when it moved with the greatestswiftness, and was almost in its perigee, it was inferior to Os Pegasi, astar of the third magnitude. Jait. 3, it appeared like a star of the fourth :fan. 9, like a star of the fifth. Jan. 13. it disappeared, by reason of tb<~THE SYSTEM OF THE WORLD. 555brightness of the moon, which was then in its increase. Jan. 25, it wasscarcely equal to the stars of the seventh magnitude. If we take equaltimes on each hand of the perigee, the heads placed at remote distanceswould have shined equally before and after, because of their equal distancesfrjin the earth. That in one case they shined very bright, and in theother vanished, is to be ascribed to the nearness cf the sun in the first case,and his distance in the other; and from the great difference of the lightin these two cases we infer its great nearness in the first of them : forthe light of the comets uses to be regular, and to appear greatest whentheir heads move the swiftest, and are therefore in their perigees ; excepting in so fur as it is increased by their nearness to the sun.From thee things I at last discovered why the comets frequent so muchthe region of the sun. If they were to be seen in the regions a great waybeyond Saturn, they must appear oftener in these parts of the heavensthat are opposite to the sun ; for those which are in that situation wouldbe nearer to the earth, and the interposition of the sun would obscure theothers: but, looking over the history of comets, I find that four or fivetimes more have been seen in the hemisphere towards the sun than in th-3opposite hemisphere ; besides, without doubt, not a few which have beenhid by the light of the sun ; fur comets descending into our parts neitheremit tails, nor are so well illuminated by the sun, as to discover themselves to our naked eyes, till they are come nearer to us than Jupiter. Butthe far greater part of that spherical space, which is described about thesun with so small an interval, lies en that side of the earth which regardsthe sun, and the comets in that greater part are more strongly illuminated,as being for the most part nearer to the sun : besides, from the remarkable eccentricity of their orbits, it comes to pass that their lower apsidesare much nearer to the sun than if their revolutions were performed incircles concentric to the sun.Hence also we understand why the tails of the comets, while their headsare descending towards the sun, always appear short and rare, and are seldom said to have exceeded 15 or 20 deg. in length ;but in the recess ofthe heads from the sun often shine like fiery beams, and soon after reachto 40, 50, 60, 70 deg. in length, or more. This great splendor and lengthof the tails arises from the heat which the sun communicates to the cometas it passes near it. And thence, I think, it may be concluded, that all thecomets that have had such tails have passed very near the sun.Hence also we may collect that the tails arise from the atmospheres ofthe heads (p. 487 to 488) : but we have had three several opinions aboutthe tails of comets ; for some will have it that they are nothing else butthe beams of the sun s light transmitted through the comets heads, whichthey suppose to be transparent ; others, that they proceed from the refraction which light suffers in passing from the comet s head to the earth ;55fi THE SYSTEM OF THE WORLD.and, lastly, others, that they are a sort of clouds or vapour constantlyrising from the cornets heads, and tending towards the parts opposite tothe sun. The first is the opinion of such as are yet unacquainted withoptics ; for the beams of the sun are not seen in a darkened room, but inconsequence of the light that is reflected from them by the little particlesof dust and smoke which are always flying about in the air; and hence itis that in air impregnated with thick smoke they appear with greaterbrightness, and are more faintly and more difficultly seen in a finer air;but in the heavens, where there is no matter to reflect the light, they arenot to be seen at all. Light is not seen as it is in the beams, but as it isthence reflected to our eyes ;for vision is not made but by rays fallingupon the eyes, and therefore there must be some reflecting matter in thoseparts where the tails of comets are seen; and so the argument turns uponthe third opinion ;for that reflecting matter can be no where found but inthe place of the tail, because otherwise, since all the celestial spaces areequally illuminated by the sun s light, no part of the heavens could appearwith more splendor than another. The second opinion is liable to manydifficulties. The tails of comets are never seen variegated with thos-ecolours which ever use to be inseparable from refraction ; and the distincttransmission of the light of the fixed stars and planets to us is a demonstration that the aether or celestial medium is not endowed with any refractive power. For as to what is alledged that the fixed stars have beensometimes seen by the Egyptians environed with a coma or capillitiumbecause that has but rarely happened, it is rather to be ascribed to a casualrefraction of clouds, as well as the radiation and scintillation of the fixedstars to the refractions both of the eyes and air; for upon applying a telescope to the eye, those radiations and scintillations immediately disappear.By the tremulous agitation of the air and ascending vapours, it happensthat the rays of light are alternately turned aside from the narrow spaceof the pupil of the eye ; but no such thing can have place in the muchwider aperture of the object-glass of a telescope ; and hence it is that ascintillation is occasioned in the former case which ceases in the latter;and this cessation in the latter case is a demonstration of the regular transmission of light through the heavens without any sensible refraction.But, to obviate an objection that may be made from the appearing of notail in such comets as shine but with a faint light, as if the secondaryrays were then too weak to affect the eyes, and for this reason it is thatthe tails of the fixed stars do not appear, we are to consider that by themeans of telescopes the light of the fixed stars may be augmented above