Letters on Astronomy Part 17

Kepler was a native of Germany. He was born in the Duchy of Wurtemberg, in 1571. As Copernicus, Tycho Brahe, Galileo, Kepler, and Newton, are names that are much a.s.sociated in the history of astronomy, let us see how they stood related to each other in point of time. Copernicus was born in 1473; Tycho, in 1546; Galileo, in 1564; Kepler, in 1571; and Newton, in 1642. Hence, Copernicus was seventy-three years before Tycho, and Tycho ninety-six years before Newton. They all lived to an advanced age, so that Tycho, Galileo, and Kepler, were contemporary for many years; and Newton, as I mentioned in the sketch I gave you of his life, was born the year that Galileo died.

Kepler was born of parents who were then in humble circ.u.mstances, although of n.o.ble descent. Their misfortunes, which had reduced them to poverty, seem to have been aggravated by their own unhappy dispositions; for his biographer informs us, that "his mother was treated with a degree of barbarity by her husband and brother-in-law, that was hardly exceeded by her own perverseness." It is fortunate, therefore, that Kepler, in his childhood, was removed from the immediate society and example of his parents, and educated at a public school at the expense of the Duke of Wurtemberg. He early imbibed a taste for natural philosophy, but had conceived a strong prejudice against astronomy, and even a contempt for it, inspired, probably, by the arrogant and ridiculous pretensions of the astrologers, who const.i.tuted the princ.i.p.al astronomers of his country. A vacant post, however, of teacher of astronomy, occurred when he was of a suitable age to fill it, and he was compelled to take it by the authority of his tutors, though with many protestations, on his part, wis.h.i.+ng to be provided for in some other more brilliant profession.

Happy is genius, when it lights on a profession entirely consonant to its powers, where the objects successively presented to it are so exactly suited to its nature, that it clings to them as the loadstone to its kindred metal among piles of foreign ores. Nothing could have been more congenial to the very mental const.i.tution of Kepler, than the study of astronomy,--a science where the most capacious understanding may find scope in unison with the most fervid imagination.

Much as has been said against hypotheses in philosophy, it is nevertheless a fact, that some of the greatest truths have been discovered in the pursuit of hypotheses, in themselves entirely false; truths, moreover, far more important than those a.s.sumed by the hypotheses; as Columbus, in searching for a northwest pa.s.sage to India, discovered a new world. Thus Kepler groped his way through many false and absurd suppositions, to some of the most sublime discoveries ever made by man. The fundamental principle which guided him was not, however, either false or absurd. It was, that G.o.d, who made the world, had established, throughout all his works, fixed laws,--laws that are often so definite as to be capable of expression in exact numerical terms. In accordance with these views, he sought for numerical relations in the disposition and arrangement of the planets, in respect to their number, the times of their revolution, and their distances from one another. Many, indeed, of the subordinate suppositions which he made, were extremely fanciful; but he tried his own hypotheses by a rigorous mathematical test, wherever he could apply it; and as soon as he discovered that a supposition would not abide this test, he abandoned it without the least hesitation, and adopted others, which he submitted to the same severe trial, to share, perhaps, the same fate. "After many failures," he says, "I was comforted by observing that the motions, in every case, seemed to be connected with the distances; and that, when there was a great gap between the orbits, there was the same between the motions. And I reasoned that, if G.o.d had adapted motions to the orbits in some relation to the distances, he had also arranged the distances themselves in relation to something else."

In two years after he commenced the study of astronomy, he published a book, called the '_Mysterium Cosmographic.u.m_,' a name which implies an explanation of the mysteries involved in the construction of the universe. This work was full of the wildest speculations and most extravagant hypotheses, the most remarkable of which was, that the distances of the planets from the sun are regulated by the relations which subsist between the five regular solids. It is well known to geometers, that there are and can be only five _regular solids_. These are, first, the _tetraedron_, a four-sided figure, all whose sides are equal and similar triangles; secondly, the _cube_, contained by six equal squares; thirdly, an _octaedron_, an eight-sided figure, consisting of two four-sided pyramids joined at their bases; fourthly, a _dodecaedron_, having twelve five-sided or pentagonal faces; and, fifthly, an _icosaedron_, contained by twenty equal and similar triangles. You will be much at a loss, I think, to imagine what relation Kepler could trace between these strange figures and the distances of the several planets from the sun. He thought he discovered a connexion between those distances and the s.p.a.ces which figures of this kind would occupy, if interposed in certain ways between them. Thus, he says the Earth is a circle, the measure of all; round it describe a dodecaedron, and the circle including this will be the orbit of Mars. Round this circle describe a tetraedron, and the circle including this will be the orbit of Jupiter. Describe a cube round this, and the circle including it will be the orbit of Saturn. Now, inscribe in the earth an icosaedron, and the circle included in this will give the orbit of Venus. In this inscribe an octaedron, and the circle included in this will be the orbit of Mercury. On this supposed discovery Kepler exults in the most enthusiastic expressions. "The intense pleasure I have received from this discovery never can be told in words. I regretted no more time wasted; I tired of no labor; I shunned no toil of reckoning; days and nights I spent in calculations, until I could see whether this opinion would agree with the orbits of Copernicus, or whether my joy was to vanish into air. I willingly subjoin that sentiment of Archytas, as given by Cicero; 'If I could mount up into heaven, and thoroughly perceive the nature of the world and the beauty of the stars, that admiration would be without a charm for me, unless I had some one like you, reader, candid, attentive, and eager for knowledge, to whom to describe it.' If you acknowledge this feeling, and are candid, you will refrain from blame, such as, not without cause, I antic.i.p.ate; but if, leaving that to itself, you fear, lest these things be not ascertained, and that I have shouted triumph before victory, at least approach these pages, and learn the matter in consideration: you will not find, as just now, new and unknown planets interposed; that boldness of mine is not approved; but those old ones very little loosened, and so furnished by the interposition (however absurd you may think it) of rectilinear figures, that in future you may give a reason to the rustics, when they ask for the hooks which keep the skies from falling."

When Tycho Brahe, who had then retired from his famous Uraniburg, and was settled in Prague, met with this work of Kepler's, he immediately recognised under this fantastic garb the lineaments of a great astronomer. He needed such an unwearied and patient calculator as he perceived Kepler to be, to aid him in his labors, in order that he might devote himself more unreservedly to the taking of observations,--an employment in which he delighted, and in which, as I mentioned, in giving you a sketch of his history, he excelled all men of that and preceding ages. Kepler, therefore, at the express invitation of Tycho, went to Prague, and joined him in the capacity of a.s.sistant. Had Tycho been of a nature less truly n.o.ble, he might have looked with contempt on one who had made so few observations, and indulged so much in wild speculation; or he might have been jealous of a rising genius, in which he descried so many signs of future eminence as an astronomer; but, superior to all the baser motives, he extends to the young aspirant the hand of encouragement, in the following kind invitation: "Come not as a stranger, but as a very welcome friend; come, and share in my observations, with such instruments as I have with me."

Several years previous to this, Kepler, after one or two unsuccessful trials, had found him a wife, from whom he expected a considerable fortune; but in this he was disappointed; and so poor was he, that, when on his journey to Prague, in company with his wife, being taken sick, he was unable to defray the expenses of the journey, and was forced to cast himself on the bounty of Tycho.

In the course of the following year, while absent from Prague, he fancied that Tycho had injured him, and accordingly addressed to the n.o.ble Dane a letter full of insults and reproaches. A mild reply from Tycho opened the eyes of Kepler to his own ingrat.i.tude. His better feelings soon returned, and he sent to his great patron this humble apology: "Most n.o.ble Tycho! How shall I enumerate, or rightly estimate, your benefits conferred on me! For two months you have liberally and gratuitously maintained me, and my whole family; you have provided for all my wishes; you have done me every possible kindness; you have communicated to me every thing you hold most dear; no one, by word or deed, has intentionally injured me in any thing; in short, not to your own children, your wife, or yourself, have you shown more indulgence than to me. This being so, as I am anxious to put upon record, I cannot reflect, without consternation, that I should have been so given up by G.o.d to my own intemperance, as to shut my eyes on all these benefits; that, instead of modest and respectful grat.i.tude, I should indulge for three weeks in continual moroseness towards all your family, and in headlong pa.s.sion and the utmost insolence towards yourself, who possess so many claims on my veneration, from your n.o.ble family, your extraordinary learning, and distinguished reputation. Whatever I have said or written against the person, the fame, the honor, and the learning, of your Excellency; or whatever, in any other way, I have injuriously spoken or written, (if they admit no other more favorable interpretation,) as to my grief I have spoken and written many things, and more than I can remember; all and every thing I recant, and freely and honestly declare and profess to be groundless, false, and incapable of proof." This was ample satisfaction to the generous Tycho.

"To err is human: to forgive, divine."

On Kepler's return to Prague, he was presented to the Emperor by Tycho, and honored with the t.i.tle of Imperial Mathematician. This was in 1601, when he was thirty years of age. Tycho died shortly after, and Kepler succeeded him as princ.i.p.al mathematician to the Emperor; but his salary was badly paid, and he suffered much from pecuniary embarra.s.sments.

Although he held the astrologers, or those who told fortunes by the stars, in great contempt, yet he entertained notions of his own, on the same subject, quite as extravagant, and practised the art of casting nativities, to eke out a support for his family.

When Galileo began to observe with his telescope, and announced, in rapid succession, his wonderful discoveries, Kepler entered into them with his characteristic enthusiasm, although they subverted many of his favorite hypotheses. But such was his love of truth, that he was among the first to congratulate Galileo, and a most engaging correspondence was carried on between these master-spirits.

The first planet, which occupied the particular attention of Kepler, was Mars, the long and a.s.siduous study of whose motions conducted him at length to the discovery of those great principles called 'Kepler's Laws.' Rarely do we meet with so remarkable a union of a vivid fancy with a profound intellect. The hasty and extravagant suggestions of the former were submitted to the most laborious calculations, some of which, that were of great length, he repeated seventy times. This exuberance of fancy frequently appears in his style of writing, which occasionally a.s.sumes a tone ludicrously figurative. He seems constantly to contemplate Mars as a valiant hero, who had hitherto proved invincible, and who would often elude his own efforts to conquer him, "While thus triumphing over Mars, and preparing for him, as for one altogether vanquished, tabular prisons, and equated, eccentric fetters, it is buzzed here and there, that the victory is vain, and that the war is raging anew as violently as before. For the enemy, left at home a despised captive, has burst all the chains of the equation, and broken forth of the prisons of the tables. Skirmishes routed my forces of physical causes, and, shaking off the yoke, regained their liberty. And now, there was little to prevent the fugitive enemy from effecting a junction with his own rebellious supporters, and reducing me to despair, had I not suddenly sent into the field a reserve of new physical reasonings, on the rout and dispersion of the veterans, and diligently followed, without allowing the slightest respite, in the direction in which he had broken out."

But he pursued this warfare with the planet until he gained a full conquest, by the discovery of the first two of his laws, namely, that _he revolves in an elliptical orbit_, and that _his radius vector pa.s.ses over equal s.p.a.ces in equal times_.

Domestic troubles, however, involved him in the deepest affliction.

Poverty, the loss of a promising and favorite son, the death of his wife, after a long illness;--these were some of the misfortunes that cl.u.s.tered around him. Although his first marriage had been an unhappy one, it was not consonant to his genius to surrender any thing with only a single trial. Accordingly, it was not long before he endeavored to repair his loss by a second alliance. He commissioned a number of his friends to look out for him, and he soon obtained a tabular list of eleven ladies, among whom his affections wavered. The progress of his courts.h.i.+p is thus narrated in the interesting 'Life' contained in the 'Library of Useful Knowledge.' It furnishes so fine a specimen of his eccentricities, that I cannot deny myself the pleasure of transcribing the pa.s.sage for your perusal. It is taken from an account which Kepler himself gave in a letter to a friend.

"The first on the list was a widow, an intimate friend of his first wife and who, on many accounts, appeared a most eligible match. At first, she seemed favorably inclined to the proposal: it is certain that she took time to consider it, but at last she very quietly excused herself.

Finding her afterwards less agreeable in person than he had antic.i.p.ated, he considered it a fortunate escape, mentioning, among other objections, that she had two marriageable daughters, whom, by the way, he had got on his list for examination. He was much troubled to reconcile his astrology with the fact of his having taken so much pains about a negotiation not destined to succeed. He examined the case professionally. 'Have the stars,' says he, 'exercised any influence here? For, just about this time, the direction of the mid-heaven is in hot opposition to Mars, and the pa.s.sage of Saturn through the ascending point of the zodiac, in the scheme of my nativity, will happen again next November and December. But, if these are the causes, how do they act? Is that explanation the true one, which I have elsewhere given? For I can never think of handing over to the stars the office of deities, to produce effects. Let us, therefore, suppose it accounted for by the stars, that at this season I am violent in my temper and affections, in rashness of belief, in a show of pitiful tender-heartedness, in catching at reputation by new and paradoxical notions, and the singularity of my actions; in busily inquiring into, and weighing, and discussing, various reasons; in the uneasiness of my mind, with respect to my choice. I thank G.o.d, that that did not happen which might have happened; that this marriage did not take place. Now for the others.' Of these, one was too old; another, in bad health; another, too proud of her birth and quarterings; a fourth had learned nothing but showy accomplishments, not at all suitable to the kind of life she would have to lead with him.

Another grew impatient, and married a more decided admirer while he was hesitating. 'The mischief,' says he, 'in all these attachments was, that, whilst I was delaying, comparing, and balancing, conflicting reasons, every day saw me inflamed with a new pa.s.sion.' By the time he reached No. 8, of his list, he found his match in this respect. 'Fortune has avenged herself at length on my doubtful inclinations. At first, she was quite complying, and her friends also. Presently, whether she did or did not consent, not only I, but she herself, did not know. After the lapse of a few days, came a renewed promise, which, however, had to be confirmed a third time: and, four days after that, she again repented her conformation, and begged to be excused from it. Upon this, I gave her up, and this time all my counsellors were of one opinion.' This was the longest courts.h.i.+p in the list, having lasted three whole months; and, quite disheartened by its bad success, Kepler's next attempt was of a more timid complexion. His advances to No. 9 were made by confiding to her the whole story of his recent disappointment, prudently determining to be guided in his behavior, by observing whether the treatment he experienced met with a proper degree of sympathy. Apparently, the experiment did not succeed; and, when almost reduced to despair, Kepler betook himself to the advice of a friend, who had for some time past complained that she was not consulted in this difficult negotiation.

When she produced No. 10, and the first visit was paid, the report upon her was as follows: 'She has, undoubtedly, a good fortune, is of good family, and of economical habits: but her physiognomy is most horribly ugly; she would be stared at in the streets, not to mention the striking disproportion in our figures. I am lank, lean, and spare; she is short and thick. In a family notorious for fatness, she is considered superfluously fat.' The only objection to No. 11 seems to have been, her excessive youth; and when this treaty was broken off, on that account, Kepler turned his back upon all his advisers, and chose for himself one who had figured as No. 5, in his list, to whom he professes to have felt attached throughout, but from whom the representations of his friends had hitherto detained him, probably on account of her humble station."

Having thus settled his domestic affairs, Kepler now betook himself, with his usual industry, to his astronomical studies, and brought before the world the most celebrated of his publications, ent.i.tled 'Harmonics.'

In the fifth book of this work he announced his _Third Law_,--that the squares of the periodical times of the planets are as the cubes of the distances. Kepler's rapture on detecting it was unbounded. "What," says he, "I prophesied two-and-twenty years ago, as soon as I discovered the five solids among the heavenly orbits; what I firmly believed long before I had seen Ptolemy's Harmonics; what I had promised my friends in the t.i.tle of this book, which I named before I was sure of my discovery; what, sixteen years ago, I urged as a thing to be sought; that for which I joined Tycho Brahe, for which I settled in Prague, for which I have devoted the best part of my life to astronomical contemplations;--at length I have brought to light, and have recognised its truth beyond my most sanguine expectations. It is now eighteen months since I got the first glimpse of light, three months since the dawn, very few days since the unveiled sun, most admirable to gaze on, burst out upon me. Nothing holds me: I will indulge in my sacred fury; I will triumph over mankind by the honest confession, that I have stolen the golden vases of the Egyptians to build up a tabernacle for my G.o.d, far from the confines of Egypt. If you forgive me, I rejoice: if you are angry, I can bear it; the die is cast, the book is written, to be read either now or by posterity,--I care not which. I may well wait a century for a reader, as G.o.d has waited six thousand years for an observer." In accordance with the notion he entertained respecting the "music of the spheres," he made Saturn and Jupiter take the ba.s.s, Mars the tenor, the Earth and Venus the counter, and Mercury the treble.

"The misery in which Kepler lived," says Sir David Brewster, in his 'Life of Newton,' "forms a painful contrast with the services which he performed for science. The pension on which he subsisted was always in arrears; and though the three emperors, whose reigns he adorned, directed their ministers to be more punctual in its payment, the disobedience of their commands was a source of continual vexation to Kepler. When he retired to Silesia, to spend the remainder of his days, his pecuniary difficulties became still more hara.s.sing. Necessity at length compelled him to apply personally for the arrears which were due; and he accordingly set out, in 1630, when nearly sixty years of age, for Ratisbon; but, in consequence of the great fatigue which so long a journey on horseback produced, he was seized with a fever, which put an end to his life."

Professor Whewell (in his interesting work on Astronomy and General Physics considered with reference to Natural Theology) expresses the opinion that Kepler, notwithstanding his const.i.tutional oddities, was a man of strong and lively piety. His 'Commentaries on the Motions of Mars' he opens with the following pa.s.sage: "I beseech my reader, that, not unmindful of the Divine goodness bestowed on man, he do with me praise and celebrate the wisdom and greatness of the Creator, which I open to him from a more inward explication of the form of the world, from a searching of causes, from a detection of the errors of vision; and that thus, not only in the firmness and stability of the earth, he perceive with grat.i.tude the preservation of all living things in Nature as the gift of G.o.d, but also that in its motion, so recondite, so admirable, he acknowledge the wisdom of the Creator. But him who is too dull to receive this science, or too weak to believe the Copernican system without harm to his piety,--him, I say, I advise that, leaving the school of astronomy, and condemning, if he please, any doctrines of the philosophers, he follow his own path, and desist from this wandering through the universe; and, lifting up his natural eyes, with which he alone can see, pour himself out in his own heart, in praise of G.o.d the Creator; being certain that he gives no less wors.h.i.+p to G.o.d than the astronomer, to whom G.o.d has given to see more clearly with his inward eye, and who, for what he has himself discovered, both can and will glorify G.o.d."

In a Life of Kepler, very recently published in his native country, founded on ma.n.u.scripts of his which have lately been brought to light, there are given numerous other examples of a similar devotional spirit.

Kepler thus concludes his Harmonics: "I give Thee thanks, Lord and Creator, that Thou has given me joy through Thy creation; for I have been ravished with the work of Thy hands. I have revealed unto mankind the glory of Thy works, as far as my limited spirit could conceive their infinitude. Should I have brought forward any thing that is unworthy of Thee, or should I have sought my own fame, be graciously pleased to forgive me."

As Galileo experienced the most bitter persecutions from the Church of Rome, so Kepler met with much violent opposition and calumny from the Protestant clergy of his own country, particularly for adopting, in an almanac which, as astronomer royal, he annually published, the reformed calendar, as given by the Pope of Rome. His opinions respecting religious liberty, also, appear to have been greatly in advance of the times in which he lived. In answer to certain calumnies with which he was a.s.sailed, for his boldness in reasoning from the light of Nature, he uttered these memorable words: "The day will soon break, when pious simplicity will be ashamed of its blind superst.i.tion; when men will recognise truth in the book of Nature as well as in the Holy Scriptures, and rejoice in the two revelations."

LETTER XXV.

COMETS.

----"Fancy now no more Wantons on fickle pinions through the skies, But, fixed in aim, and conscious of her power, Sublime from cause to cause exults to rise, Creation's blended stores arranging as she flies."--_Beattie._

NOTHING in astronomy is more truly admirable, than the knowledge which astronomers have acquired of the motions of comets, and the power they have gained of predicting their return. Indeed, every thing appertaining to this cla.s.s of bodies is so wonderful, as to seem rather a tale of romance than a simple recital of facts. Comets are truly the knights-errant of astronomy. Appearing suddenly in the nocturnal sky, and often dragging after them a train of terrific aspect, they were, in the earlier ages of the world, and indeed until a recent period, considered as peculiarly ominous of the wrath of Heaven, and as harbingers of wars and famines, of the dethronement of monarchs, and the dissolution of empires.

Science has, it is true, disarmed them of their terrors, and demonstrated that they are under the guidance of the same Hand, that directs in their courses the other members of the solar system; but she has, at the same time, arrayed them in a garb of majesty peculiarly her own.

Although the ancients paid little attention to the ordinary phenomena of Nature, hardly deeming them worthy of a reason, yet, when a comet blazed forth, fear and astonishment conspired to make it an object of the most attentive observation. Hence the aspects of remarkable comets, that have appeared at various times, have been handed down to us, often with circ.u.mstantial minuteness, by the historians of different ages. The comet which appeared in the year 130, before the Christian era, at the birth of Mithridates, is said to have had a disk equal in magnitude to that of the sun. Ten years before this, one was seen, which, according to Justin, occupied a fourth part of the sky, that is, extended over forty-five degrees, and surpa.s.sed the sun in splendor. In the year 400, one was seen which resembled a sword in shape, and extended from the zenith to the horizon.

Such are some of the accounts of comets of past ages; but it is probable we must allow much for the exaggerations naturally accompanying the descriptions of objects in themselves so truly wonderful.

A comet, when perfectly formed, consists of three parts, the nucleus, the envelope, and the tail. The nucleus, or body of the comet, is generally distinguished by its forming a bright point in the centre of the head, conveying the idea of a solid, or at least of a very dense, portion of matter. Though it is usually exceedingly small, when compared with the other parts of the comet, and is sometimes wanting altogether, yet it occasionally subtends an angle capable of being measured by the telescope. The envelope (sometimes called the _coma_, from a Latin word signifying hair, in allusion to its hairy appearance) is a dense nebulous covering, which frequently renders the edge of the nucleus so indistinct, that it is extremely difficult to ascertain its diameter with any degree of precision. Many comets have no nucleus, but present only a nebulous ma.s.s, exceedingly attenuated on the confines, but gradually increasing in density towards the centre. Indeed, there is a regular gradation of comets, from such as are composed merely of a gaseous or vapory medium, to those which have a well-defined nucleus. In some instances on record, astronomers have detected with their telescopes small stars through the densest part of a comet. The tail is regarded as an expansion or prolongation of the coma; and presenting, as it sometimes does, a train of appalling magnitude, and of a pale, portentous light, it confers on this cla.s.s of bodies their peculiar celebrity. These several parts are exhibited in Fig. 67, which [Ill.u.s.tration Figures 67, 68. COMETS OF 1680 AND 1811.] represents the appearance of the comet of 1680. Fig. 68 also exhibits that of the comet of 1811.

The _number_ of comets belonging to the solar system, is probably very great. Many no doubt escape observation, by being above the horizon in the day-time. Seneca mentions, that during a total eclipse of the sun, which happened sixty years before the Christian era, a large and splendid comet suddenly made its appearance, being very near the sun.

The leading particulars of at least one hundred and thirty have been computed, and arranged in a table, for future comparison. Of these, _six_ are particularly remarkable; namely, the comets of 1680, 1770, and 1811; and those which bear the names of Halley, Biela, and Encke. The comet of 1680 was remarkable, not only for its astonis.h.i.+ng size and splendor, and its near approach to the sun, but is celebrated for having submitted itself to the observations of Sir Isaac Newton, and for having enjoyed the signal honor of being the first comet whose elements were determined on the sure basis of mathematics. The comet of 1770 is memorable for the changes its...o...b..t has undergone by the action of Jupiter, as I shall explain to you more particularly hereafter. The comet of 1811 was the most remarkable in its appearance of all that have been seen in the present century. It had scarcely any perceptible nucleus, but its train was very long and broad, as is represented in Fig. 68. Halley's comet (the same which reappeared in 1835) is distinguished as that whose return was first successfully predicted, and whose orbit is best determined; and Biela's and Encke's comets are well known for their short periods of revolution, which subject them frequently to the view of astronomers.

In _magnitude and brightness_, comets exhibit great diversity. History informs us of comets so bright, as to be distinctly visible in the day-time, even at noon, and in the brightest suns.h.i.+ne. Such was the comet seen at Rome a little before the a.s.sa.s.sination of Julius Caesar.

The comet of 1680 covered an arc of the heavens of ninety-seven degrees, and its length was estimated at one hundred and twenty-three millions of miles. That of 1811 had a nucleus of only four hundred and twenty-eight miles in diameter, but a tail one hundred and thirty-two millions of miles long. Had it been coiled around the earth like a serpent, it would have reached round more than five thousand times.

Other comets are exceedingly small, the nucleus being in one case estimated at only twenty-five miles; and some, which are dest.i.tute of any perceptible nucleus, appear to the largest telescopes, even when nearest to us, only as a small speck of fog, or as a tuft of down. The majority of comets can be seen only by the aid of the telescope. Indeed, the same comet has very different aspects, at its different returns.

Halley's comet, in 1305, was described by the historians of that age as the comet of terrific magnitude; (_cometa horrendae magnitudinis_;) in 1456 its tail reached from the horizon to the zenith, and inspired such terror, that, by a decree of the Pope of Rome, public prayers were offered up at noonday in all the Catholic churches, to deprecate the wrath of heaven; while in 1682 its tail was only thirty degrees in length; and in 1759 it was visible only to the telescope until after it had pa.s.sed its perihelion. At its recent return, in 1835, the greatest length of the tail was about twelve degrees. These changes in the appearance of the same comet are partly owing to the different positions of the earth with respect to them, being sometimes much nearer to them when they cross its track than at others; also, one spectator, so situated as to see the comet at a higher angle of elevation, or in a purer sky, than another, will see the train longer than it appears to another less favorably situated; but the extent of the changes are such as indicate also a real change in magnitude and brightness.

The _periods_ of comets in their revolutions around the sun are equally various. Encke's comet, which has the shortest known period, completes its revolution in three and one third years; or, more accurately, in twelve hundred and eight days; while that of 1811 is estimated to have a period of thirty-three hundred and eighty three years.

The _distances_ to which different comets recede from the sun are equally various. While Encke's comet performs its entire revolution within the orbit of Jupiter, Halley's comet recedes from the sun to twice the distance of Ura.n.u.s; or nearly thirty-six hundred millions of miles. Some comets, indeed, are thought to go a much greater distance from the sun than this, while some are supposed to pa.s.s into curves which do not, like the ellipse, return into themselves; and in this case they never come back to the sun. (See Fig. 34, page 153.)

Comets s.h.i.+ne _by reflecting the light of the sun_. In one or two instances, they have been thought to exhibit distinct _phases_, like the moon, although the nebulous matter with which the nucleus is surrounded would commonly prevent such phases from being distinctly visible, even when they would otherwise be apparent. Moreover, certain qualities of _polarized_ light,--an affection by which a ray of light seems to have different properties on different sides,--enable opticians to decide whether the light of a given body is direct or reflected; and M. Arago, of Paris, by experiments of this kind on the light of the comet of 1819, ascertained it to be reflected light.

The tail of a comet usually increases very much as it approaches the sun; and it frequently does not reach its maximum until after the perihelion pa.s.sage. In receding from the sun, the tail again contracts, and nearly or quite disappears before the body of the comet is entirely out of sight. The tail is frequently divided into two portions, the central parts, in the direction of the axis, being less bright than the marginal parts. In 1744 a comet appeared which had six tails spread out like a fan.

The tails of comets extend in a direct line from the sun, although more or less curved, like a long quill or feather, being convex on the side next to the direction in which they are moving,--a figure which may result from the less velocity of the portion most remote from the sun.

Expansions of the envelope have also been at times observed on the side next the sun; but these seldom attain any considerable length.

The _quant.i.ty of matter_ in comets is exceedingly small. Their tails consist of matter of such tenuity, that the smallest stars are visible through them. They can only be regarded as ma.s.ses of thin vapor, susceptible of being penetrated through their whole substance by the sunbeams, and reflecting them alike from their interior parts and from their surfaces. It appears perhaps incredible, that so thin a substance should be visible by reflected light, and some astronomers have held that the matter of comets is self-luminous; but it requires but very little light to render an object visible in the night, and a light vapor may be visible when illuminated throughout an immense stratum, which could not be seen if spread over the face of the sky like a thin cloud.

"The highest clouds that float in our atmosphere," says Sir John Herschel, "must be looked upon as dense and ma.s.sive bodies, compared with the filmy and all but spiritual texture of a comet."

The small quant.i.ty of matter in comets is proved by the fact, that they have at times pa.s.sed very near to some of the planets, without disturbing their motions in any appreciable degree. Thus the comet of 1770, in its way to the sun, got entangled among the satellites of Jupiter, and remained near them four months; yet it did not perceptibly change their motions. The same comet, also, came very near the earth; so that, had its quant.i.ty of matter been equal to that of the earth, it would, by its attraction, have caused the earth to revolve in an orbit so much larger than at present, as to have increased the length of the year two hours and forty-seven minutes. Yet it produced no sensible effect on the length of the year, and therefore its ma.s.s, as is shown by La Place, could not have exceeded 1/5000 of that of the earth, and might have been less than this to any extent. It may indeed be asked, what proof we have that comets have any matter, and are not mere reflections of light. The answer is, that, although they are not able by their own force of attraction to disturb the motions of the planets, yet they are themselves exceedingly disturbed by the action of the planets, and in exact conformity with the laws of universal gravitation. A delicate compa.s.s may be greatly agitated by the vicinity of a ma.s.s of iron, while the iron is not sensibly affected by the attraction of the needle.

By approaching very near to a large planet, a comet may have its...o...b..t entirely changed. This fact is strikingly exemplified in the history of the comet of 1770. At its appearance in 1770, its...o...b..t was found to be an ellipse, requiring for a complete revolution only five and a half years; and the wonder was, that it had not been seen before, since it was a very large and bright comet. Astronomers suspected that its path had been changed, and that it had been recently compelled to move in this short ellipse, by the disturbing force of Jupiter and his satellites. The French Inst.i.tute, therefore, offered a high prize for the most complete investigation of the elements of this comet, taking into account any circ.u.mstances which could possibly have produced an alteration in its course. By tracing back the movements of this comet, for some years previous to 1770, it was found that, at the beginning of 1767, it had entered considerably within the sphere of Jupiter's attraction. Calculating the amount of this attraction from the known proximity of the two bodies, it was found what must have been its...o...b..t previous to the time when it became subject to the disturbing action of Jupiter. It was therefore evident why, as long as it continued to circulate in an orbit so far from the centre of the system, it was never visible from the earth. In January, 1767, Jupiter and the comet happened to be very near to one another, and as both were moving in the same direction, and nearly in the same plane, they remained in the neighborhood of each other for several months, the planet being between the comet and the sun. The consequence was, that the comet's...o...b..t was changed into a smaller ellipse, in which its revolution was accomplished in five and a half years. But as it approached the sun, in 1779, it happened again to fall in with Jupiter. It was in the month of June that the attraction of the planet began to have a sensible effect; and it was not until the month of October following, that they were finally separated.

At the time of their nearest approach, in August, Jupiter was distant from the comet only 1/491 of its distance from the sun, and exerted an attraction upon it two hundred and twenty-five times greater than that of the sun. By reason of this powerful attraction, Jupiter being further from the sun than the comet, the latter was drawn out into a new orbit, which even at its perihelion came no nearer to the sun than the planet Ceres. In this third orbit, the comet requires about twenty years to accomplish its revolution; and being at so great a distance from the earth, it is invisible, and will for ever remain so unless, in the course of ages, it may undergo new perturbations, and move again in some smaller orbit, as before.

With the foregoing leading facts respecting comets in view, I will now explain to you a few things equally remarkable respecting their _motions_.

The paths of the planets around the sun being nearly circular, we are able to see a planet in every part of its...o...b..t. But the case is very different with comets. For the greater part of their course, they are wholly out of sight, and come into view only while just in the neighborhood of the sun. This you will readily see must be the case, by inspecting the frontispiece, which represents the orbit of Biela's comet, in 1832. Sometimes, the orbit is so eccentric, that the place of the focus occupied by the sun appears almost at the extremity of the orbit. This was the case with the orbit of the comet of 1680. Indeed, this comet, at its perihelion, came in fact nearer to the sun than the sixth part of the sun's diameter, being only one hundred and forty-six thousand miles from the surface of the sun, which, you will remark, is only a little more than half the distance of the moon from the earth; while, at its aphelion, it was estimated to be thirteen thousand millions of miles from the sun,--more than eleven thousand millions of miles beyond the planet Ura.n.u.s. Its _velocity_, when nearest the sun, exceeded a million of miles an hour. To describe such an orbit as was a.s.signed to it by Sir Isaac Newton, would require five hundred and seventy-five years. During all this period, it was entirely out of view to the inhabitants of the earth, except the few months, while it was running down to the sun from such a distance as the orbit of Jupiter and back. The velocity of bodies moving in such eccentric orbits differs widely in different parts of their orbits. In the remotest parts it is so slow, that years would be required to pa.s.s over a s.p.a.ce equal to that which it would run over in a single day, when near the sun.

The appearances of the same comet at different periods of its return are so various, that we can never p.r.o.nounce a given comet to be the same with one that has appeared before, from any peculiarities in its physical aspect, as from its color, magnitude, or shape; since, in all these respects, it is very different at different returns; but it is judged to be the same if its _path_ through the heavens, as traced among the stars, is the same.