Part 5 — NOTES.

NOTE A, Page 7.

In his interesting account of the first Comet of that year, Herschel says, “In every instrument through which I have examined the Comet, I perceived a very faint, or rather darkish interval surrounding the head, wherein the gradually diminishing light of the central brightness was lost. This can only be accounted for, by admitting a transparent elastic atmosphere to envelope the head of the Comet. Its transparency I had an opportunity of ascertaining on the 18th September, when I saw three very small stars, of different magnitudes, within the compass of it: And its elasticity may be inferred from the circular form under which it was always seen; for being surrounded by a certain bright equidistant envelope, we can only account for the equality of the distance, by admitting the interval between the envelope and the head of the Comet, to be filled with an elastic atmospherical fluid.” See likewise Herschel’s Remarks on the Second Comet of the same year.—Philos. Trans. 1812.

NOTE B, Page 8.

According to this comparative view of the lengths of the tails of Comets, it would appear that they depend wholly upon their nearness to the sun at the perihelium. This coincidence, though found to prevail generally, and well exemplifying the action of the sun in producing the tail, cannot be assumed as the exact law: Much evidently depends on the physical constitution of the Comet. But this point will be more fully discussed afterwards.

NOTE C, Page 9.

For the same reason, the top of the hemispherical cap, or that part of the envelope nearest the sun, is generally more brilliant than any other point. In the first Comet of 1811, for example, the line of vision traversed at the top of the cap, was about five times the quantity of luminous matter which it traversed at the side nearest the observer; for, at the latter place, there was no more than the actual thickness of the shell.

NOTE D, Page 14.

On the 14th October Herschel estimated the length of the above Comet’s tail to be 17°; on the following night, he judged it to be 23°. The tail of the Comet of 1759, appeared at Paris to be only 2° or 3° in length; but at Montpellier 25°. The Comet of 1769 at Paris, seemed to have a tail 60° long; but at Boulogne 70°; and at the Isle of Bourbon 97°.—Encycl. Edin. Astron. 675.

These examples prove, how much depends on the constitution of our own atmosphere, in judging of the form and extent of a Comet’s tail. Newton himself entertained the same idea with respect to these appearances in Comets’ tails. His words are, “De caudarum agitationibus subitaneis et incertis, deque earum figuris irregularibus, quas nonnulli quandoque describunt, hic nihil adjicio; propterea quod vel a mutationibus aëris nostri, et motibus nubium caudas aliqua ex parte obscurantium oriantur; vel forte a partibus Viæ Lacteæ, quæ cum caudis prætereuntibus confundi possint, et tanquam earum partes spectari.”

NOTE E, Page 26.

This change of the two angles to opposite sides, evidently indicated a corresponding change in the position of the streams themselves.

Does this circumstance not point out a rotatory motion of the Comet’s tail? Herschel was likewise induced, though on different grounds, to ascribe a rotation to the Comet of 1811: And Mr Dunlop, the assiduous astronomer of Paramatta, has made observations on a Comet, seen there in 1825, which tend to establish a similar result. In a paper, read last session at the Royal Society of Edinburgh, and published in Brewster’s Journal of Science for January 1827, Mr Dunlop has given seventeen drawings of the different appearances which this Comet exhibited from 5th October to the 8th November. These seemed to indicate, plainly, a periodic return of the several branches of the tail to the same form and position; and computing the intervals of time which elapsed between these regularly recurring appearances, Mr Dunlop found the period of rotation to be 20 hours. In the same paper we also find instances of the concavity of the tail on the following side, and its convexity on the preceding, as well as of the formation of smaller tails or branches out of the envelope, and external to the principal tail. It is evident that these branches, or smaller tails, will be the more readily produced if the Comet have a rotatory motion; because, in that case, the centrifugal force greatly diminishes the gravitation of the nebulous particles, and renders them more capable of being acted on by the sun’s rays.

NOTE F, Page 27.

Sturmius also, who observed the great Comet of 1680, remarks, that, on the 20th December, its tail was 20° in length, and that in a short time it attained 60°; afterwards, it rapidly diminished. He also remarks, that, soon after the perihelion passage, the nucleus had the appearance of being enveloped in smoke.

NOTE G, Page 38.

This notion of the ancients, respecting the influence of the constellations upon comets, as they move through them, seems also to have prevailed in the darker ages, in Europe. The author of a romance, the scene of which is laid about that period in Germany, alludes to the belief in these lines:—

“The comet that’s born in the belt of Orion, Whose cradle it gilds, gilds the place they shall die on.”

NOTE H, Page 41.

The whole of this book De Cometis, is well worthy a perusal. Seneca not only enters into a detailed account of the opinions of the Greek philosophers upon this subject, and, by the most philosophical arguments, demonstrates their absurdity, but he also occasionally enters upon general statements as to the nature of the planetary movements, which show equally the extent and soundness of his views respecting the arrangement of the system. Next to Aristotle’s opinion, which I have endeavoured to explain, the doctrine of Artemidorus, Democritus, and some others, appears to have gained the most general credit; at least Seneca devotes a large portion of this book to its refutation. These philosophers held, that there are wandering through the universe a multitude of bodies, which, from the weakness of their light, are invisible, but which, by their fortuitous junction, become capable of transmitting so many rays, as to be discernible for a time. Respecting this doctrine, Seneca makes the following just observations:—“Hoc ex his quæ mentitur, levissimum est. Tota ejus narratio mundi mendacium impudens est, nam si illi credimus, summa cœli ora solidissima est, in modum tecti durata, et alti crassique corporis, quod atomi congestæ coacervatæque fecerunt. Huic proxima superficies est ignea, ita compacta, ut solvi vitiarique non possit. Habet tamen spiramenta quædam et quasi fenestras, per quas ex parte exteriore mundi influant ignes, non tam magni, ut interiora conturbent. Rursus ex mundo in exteriora labuntur. Itaque hæc quæ præter consuetudinem apparent, influxerunt ex illa ultra mundum jacente materia. Solvere ista,” he adds, “quid aliud est, quam manum exercere, et in ventum jactare brachia?” It is evident, that these remarks are also intended to apply to the well known doctrines of Aristotle, concerning the solidity of the planetary spheres, which may well be styled “mendacium impudens” by every one imbued with juster views of the universe. He then refutes the opposite notion of Apollonius Myndius, who conceived that there was no real difference between comets and the other heavenly bodies. Seneca relates the doctrine of Apollonius in the following terms:—“Non est species falsa, nec duarum stellarum confinio ignis extentus, sed et proprium sidus, cometes est, sicut solis aut lunæ. Talis forma est, non in rotundum restricta, sed procerior, et in longum producta. Ceterum non est illi palam cursus: altiora mundi secat, et tunc demum apparet, quum in imum cursus sui venit. Nec est, quod putemus, eundem visum esse sub Claudio, quem sub Augusto vidimus: nec hunc, qui sub Nerone Cæsare apparuit, et cometis detraxit infamiam, illi similem fuisse, qui post necem divi Julii, Veneris ludis Genetricis, circa undecimam horam diei emersit. Multi variique sunt dispares magnitudine, dissimiles coloere.” In opposition to the doctrine of Apollonius, Seneca refers to the path which comets follow in the firmament, so totally different from the planets, and likewise to the extraordinary circumstance, which, however, is generally considered entirely a modern discovery, that the body of the comet is sometimes so transparent as to permit the stars to be seen through it. “Si erraret cometes, essetque sidus, intra signiferi terminos moveretur, intra quos omne sidus cursus suos colligit. Nunquam apparet stella per stellam. Acies nostra non potest per medium sidus exire, ut per illud superiora prospiciat. Per cometem autem non aliter, quam per nubem alteriora cernuntur, ex quo apparet, illum non esse sidus, sed tenuem ignem ac tumultuarium.” It is unnecessary here to add any farther account of the just and truly philosophical refutation of the Aristotelian doctrines. But I may be permitted here to observe, that the error into which Aristotle fell, and indeed almost all the ancients, was conceiving comets to be of the same nature as the common meteors of the atmosphere. And to this erroneous impression may probably be referred the belief taught by Aristotle, and universally entertained, “Cometas significare tempestatem, et ventorum intemperantiam atque imbrium.” The phenomena of the Aurora Borealis, Coronæ, Falling Stars, and other electrical productions, we know are intimately connected with the state of the atmosphere; and, hence since comets were classed among these appearances, it was not unnatural that they should also be looked upon as the causes or concomitants of great changes in the weather. Accordingly, in reviewing the general opinions held on this subject, Seneca is most anxious to prove how little the supposed connection of comets with the weather is supported by facts. “If,” says he, “wind be prognosticated by comets, then none should appear unless there be wind. But comets are observed in the calmest atmosphere. Finally, if they owed their production to wind, they would disappear when the wind ceased, and burn with the brighter flame when the wind blows with greater violence.” It is quite impossible not to admire the cautious and yet confident manner in which Seneca endeavours to overturn these vulgar prejudices; confident, from the undoubted facts and conclusive arguments which he adduces, but at the same time cautious in a subject as yet so far removed from experience, and so little illumined by the rays of science. The sentiments with which he sets out at the commencement of the book, evince the profoundest knowledge of human nature, and the most astonishing superiority to the general opinions of the times: after reading them, we cannot help expressing our surprise that these sentiments should have been written in the days of ignorance and superstition. “Nemo usque eo tardus, et hebes, et demissus in terram est, ut ad divina non erigatur, ac toto mente consurget, utique ubi novum aliquod e cœlo miraculum fulsit, nam quamdiu solita decurrent, magnitudinem rerum consuetudo subducit. Ita enim compositi sumus, ut nos quotidiana, etiamsi admiratione digna sunt, transeant; contra minimarum quoque rerum, si insolitæ prodierunt, spectaculum dulce fiat. Hic itaque coetus astrorum, quibus immensi corporis pulchritudo distinguitur, populum non convocat. At quum aliquid ex more innovatum est; omnium vultus in cœlo est. Sol spectatorem, nisi quum deficit, non habet. Nemo observat lunam, nisi laborantem. Tunc urbes conclamant, tunc pro se quisque superstitione vana trepidat.”—“Si quid turbatum est, aut præter consuetudinem emicuit, spectamus, interrogamus, ostendimus. Adeo naturale est, magis nova quam magna, mirari. Idem in cometis fit. Si rarus et insolitæ figuræ ignis apparuit, nemo non scire quid sit, cupit, et oblitus aliorum, de adventitio quærit; ignarus, utrum debeat mirari, an timere, non enim desunt qui terreant, qui significationes ejus graves prædicent.”

NOTE I, Page 44.

Lubienitz was a Polish writer. In his “Theatrum Cometicum, opus mathematicum, physicum, historicum, politicum, theologicum, ethicum, œconomicum, chronologicum,” a ponderous work in three thick folio volumes, he pretends to give a historical account of every comet which ever was observed. But he gives us rather an enumeration of the events which comets were thought to have occasioned, than any satisfactory account of the comets themselves. His chief design seems to have been to prove, that these bodies ought to be a source of comfort to the virtuous, and of terror to the wicked. “Bona bonis, Mala malis,” form the title of his work, and are frequently repeated through the course of it. Where former historians are silent respecting the appearance of a comet immediately preceding so remarkable an event, Lubienitz finds no difficulty in supplying the deficiency.

In a treatise by one Blaise Vigenere, entitled, “Traité des Cometes ou Estoiles chévelues, apparaissantes extraordinairement au ciel, avec leurs causes et leurs effets, Paris 1578,” we have the following description: “Entre tous les signes qui se manifestent au ciel, en horreur et espouvantement des humains, entre tous les prodiges dont Dieu visiblement nous menace, les éclypses et les Comètes sont les plus frequentes et les plus communes. Il est plus facile de dire des Comètes, ce n’est pas ceci ni cela, que d’affermer résolument ce que c’est; neantmoins la plus solide et reçue opinion tient que ce sont estoiles attachés à la huitieme sphere, et leur queue, chevelue ou barbe, une excroissance de lumière qui à certaines revolutions de tems, s’epanouit de leurs globes.”

Milichius, who was Professor of Mathematics at Maidenburgh, observes, that “there are good grounds for the usual behaviour of men as to comets; for they have reason to gaze at them with so much terror and astonishment as they do, because it has been proved, by a large induction of experience and observation, that they denounce great slaughter to the world, sacking of cities, subversion of kingdoms, and other public disasters.”—Commentary on 2d book of Pliny.

“The great Comet of 1680,” observes a late author, “followed by another lesser one in 1682, was evidently the forerunner of all those remarkable and disastrous events that ended in the Revolution in 1688. It also manifestly presaged the revocation of the edict of Nantz, and the cruel persecution of the Protestants by the French King Louis XIV.; and which was afterwards followed by those terrible wars, which, with little intermission, continued to ravage the finest part of Europe for nearly twenty-four years.”

NOTE K, Page 51.

It was the Baron de Zach who first ascertained this fact, unknown before in the history of astronomy, and adding a new star to the constellation of genius, which shone so brightly in England during the 17th century. When the Baron visited this country some years ago, the MSS. of Thomas Harriot, a celebrated, but unjustly obscure, mathematician of that age, were put into his hands; and among them, he discovered a letter to Harriot, written by Henry Percy, Earl of Northumberland, who was then a state prisoner in the Tower of London. This letter was written in the year 1610, and clearly points out not only his own views with respect to the real path of comets, but the discovery by his friend Harriot, of many astronomical facts, long before the period to which they are now generally referred. The following is an extract from this curious fragment:—

“I have received the perspective cylinder that you promised me, and am sorrie that my man gave you not more warning, that I might have had also the 2 or 3 more that you mentioned to chuse for me. Henceforward, he shall have order to attend you better, and to defray the charge of this an others; for he confesseth to me, that he forgot to pay the workeman.

“Accordingly as you wished, I have observed the Moone in all his changes. In the new, I discover manifestlie the earthshine, a little before the dichotomie, that spot which represents unto me the man in the moone, (but without a head), is first to be seen. A little after, near the brimme of the gibbous parts, towards the upper corner, appeare luminous parts like starres, much brighter than the rest; and the whole brimme along looks like unto the description of coasts, in the Dutch bookes of voyages. In the full, she appaers like a tarte that my cooke made me the last weeke. Here a vaine of bright stuffe, and there of darke, and so confusedlie al over; I must confesse I can see none of this without my cylinder. Yet an ingenious younge man that accompanies me here often, and loves you and these studies much, sees manie of these things even without the helpe of the instrument; but with it sees them most plainielie.

“Kepler I read diligentlie, but therein I find what it is to be so far from you. For as himselfe, he hath almost put me out of my wits, his aequants, his sections of excentricities, librations in the diameters of epicycles, revolutions in ellipses, have so throughlie seased upon my imagination, as I do not onlie ever dreame of them, but oftentimes awake lose myself and power of thinkinge with so much wantinge to it, not of his causes, for I cannot phansie those magnetical natures, but about his theorie which me thinks (although I cannot yet overmaster many of his particulars) he establisheth soundlie, and, as you say, overthrows the circular astronomie. Do you not here startle, to see every day some of your inventions taken from you, for I remember, long since, you told me as much, that the motions of the planets were not perfect circles. So you taught me the curious way to observe weight in water, and within a while after Ghetaldi comes out with it in print. A little before Vieta prevented you of the gharland for the greate invention of algebra. Al these were your deues and manie others that I could mention, and yet to great reservednesse hath robd you of these glories.” “Let your countrie and friends injoye the comforts they would have in the true and great honour you would purchase yourselfe by publishing some of your choise workes. But you know best what you have to doe. Onlie I, because I wish you all good, wish this, and sometimes the more longhinglie, because in one of your letters you gave me some kind of hope thereof.

“But again to Kepler, I have read him twice over cursaridlie, I read him now with calculation. Sometimes I find a difference of minutes, sometimes false prints, and sometimes an other confusion in his accounts;” “for his theorie, I am much in love with these particulars,

“1mo, His permutation of the medial to the apparent motions;

“2do, His elliptical iter planetarum; for me thinks it shewes a way to the solving of the unknowne walks of comets.”

This Earl of Northumberland, who thus shed a lustre upon his high rank and family by applying himself to scientific pursuits, was no less distinguished by having been one of the commanders of the British fleet sent to oppose the Spanish armada. He was made Knight of the Garter by Queen Elizabeth, and by James I. created a member of the Privy Council and Captain of the Company of Pensioners. In 1606, however, he was brought before the Star-Chamber, accused of allowing his own father to become a pensioner without making him take the Test-Oath, though he knew him to be a Catholic. In consequence of this offence, he was sentenced to pay a heavy fine, to be deprived of all his honours, and be confined the rest of his life in the Tower. It was during this latter period that he seems to have prosecuted his astronomical pursuits, most probably as a source of amusement during his weary and cruel confinement. In the year 1621 he again obtained his liberty, but by that time Harriot, with whom he had carried on his scientific studies, was dead. From the little that is as yet known respecting the manuscript works of Harriot, he appears to have been the greatest mathematician of which England could boast at that time. Even from the casual remarks which occur in the extract of the Earl of Northumberland’s letter given above, it appears that he was in the habit of using a telescope in his observations, though the invention of this wonderful instrument, which has made known to mankind the whole system of the universe, has been commonly ascribed to Galileo in the year 1610; likewise that Harriot was acquainted with the specific gravities of bodies before Ghetaldi, and that he may even dispute with Vieta the discovery of algebra itself; it also seems that he was aware of the planetary orbits being not circular but elliptic, long before the observations of Kepler were published, and that the elliptic course of comets was not unknown to him. It was from the observations made by Harriot of Halley’s Comet in 1607, that Bessel was enabled to calculate its orbit with great precision, and confirm the soundness of all the speculations which astronomers had previously entertained respecting its period of revolution. Were these manuscripts published, from the few specimens which we already possess of the hidden treasure, we are warranted in thinking, that much curious and valuable information would undoubtedly be obtained. Even if they could effect little in promoting the advancement of science, they would at least furnish many new facts in the history of human knowledge; and if they should serve no higher purpose than to add another name to the catalogue of great men who have reflected honour upon their age and country, they would be applied to a far nobler use than by being consigned to inglorious oblivion on the shelves of the University of Oxford.

Doerfel, mentioned in the text as the person to whom the merit is generally ascribed of having first started the idea of the cometary orbits being parabolic, was a Protestant clergyman at Wieda, a small village six leagues from Plauen. His work consisted of five leaves in quarto, with a wood cut representing parabolic orbits. It was published at Plauen in 1689.

NOTE L, Page 52.

These results are derived from the formula , demonstrated in all the books of Astronomy, where M, m, represent the masses of the bodies acting on each other (in this case, the Sun and Comet), r their shortest distance from each other, and a the semi-major axis of the curve they describe. In the circle a = r, and the formula becomes : In the parabola, where the axis is infinite, and therefore , ; the velocities in the circle and in the parabola, are therefore or . In the hyperbola a is negative, which renders the velocity greater than in either the circle or the parabola. In the ellipse, a is positive, which occasions velocities smaller than in the parabola.—See also Leslie’s Nat. Phil. p. 122.

NOTE M, Page 90.

This Comet, whose elements we have now computed, was also observed in Europe. The following are the elements deduced by several astronomers:—

Mr Nicolai, Manheim. Mr Del Re, Naples, Mr Santini, Padua.

Perihelion passage, October 1826, 9·02648 9·09138 9·19806

Longitude of perihelion, 57° 58′ 27″ 57° 3′ 53″ 57° 35′ 6″

Longitude of ascending node, 43 5 41 44 46 16 43 9 5

Inclination of the orbit, 26 1 49 25 32 18 25 30 7

Perihelion distance, ·85110 ·85835 ·85169

Motion, Direct. Direct. Direct.

Mr Henderson of Edinburgh has also computed the elements of this comet from the observations made at Paramatta, with a sight of which I have been favoured: By a comparison of the whole observations taken together, he obtained the following elements:—

Mean Time at Greenwich.

Perihelion passage, October 1826, 10.09593

Longitude of perihelion, 60° 20′ 1″

Longitude of ascending node, 43 7 55

Inclination of the orbit, 27 4 23

Perihelion distance, ·838633

Motion, Direct.

From the discrepancy which exists between the elements deduced from the European observations, and the elements obtained by Mr Henderson and myself, we are led to think that the observations made at Paramatta have been by no means very accurate.

NOTE N, Page 102.

Halley’s Comet, according to La Place, (Mec. Celeste), before it completes its next revolution, will undergo a very considerable variation from its course by the disturbing influence of Uranus. To estimate the precise alterations which will thereby be produced on the period of its revolution, as well as to frame some theory for cometary perturbations in general, has been proposed twice by the French Institute as the subject of their prize. I have not entered upon the mathematical theory of cometary perturbations: The subject is one of too much difficulty, and of too much detail, to be discussed within the limits of this Essay. I confine myself to a more popular and intelligible statement of the effects which the disturbing action of the planets is able to produce on the comet’s orbits. The difficulty of this branch of the subject will be the more readily conceived from the fact, that the above annual prize of a gold medal, worth 3000 francs, proposed by the Institute of France, to all the astronomers and mathematicians of Europe, not having been adjudged, was lately renewed for the third time. Astronomers seem to be appalled by the labours required in these investigations.

NOTE O, Page 105.

It may also be here noticed, that according to Lexell’s calculations, it appeared, that, on the 27th May 1767, the distance of this Comet from Jupiter was th of its distance from the Sun; the attraction of Jupiter was therefore, at this point, three times greater than that of the Sun, and its power of disturbing the motions of so small a body was still more increased, from the inconsiderable velocity of the Comet at this time, and also the concurrence of direction in their motion, which caused it to remain much longer within the sphere of the planet’s attraction.

NOTE P, Page 107.

If the Moon’s inclination to the Equator, instead of being only about five degrees, had been very considerable, then La Place’s theory could not have applied, and there might have been some grounds for conjecturing it to have been a Comet arrested in its course. But though we, therefore, agree with Du Sejour in the opinion that our Moon has not this origin, we can by no means allow the legitimacy of his inference, that there is no possibility of the Earth ever acquiring another moon or satellite. Indeed his own statement contradicts itself. “Il me paroit suivre evidemment de ce qui vient d’être dit, que la Terre ne peut pas espérer de nouveau satellite. Certainement elle ne peut forcer aucune Comète parabolique au hyperbolique à tourner autour d’elle; et quand même on ne regarderoit point comme impossible, l’hypothèse, la Terre ne pourrait espérer de nouveau satellite, qu’autant qu’elle forcerait une Comète elliptique à s’áttacher à elle.”

NOTE Q, Page 109.

George Phranza, who was Master of the Wardrobe to the Emperors of Constantinople, observed and describes this Comet in the following terms: “Durant l’été 1454, une Comète commença à paroitre tous les soirs après le coucher du Soleil; elle avait la figure d’une longue épée. La Lune ayant atteint son plein, la Comète passa devant son disque, et l’éclipsa, conformément au loix qui occasionment les éclipses des corps célestes. Quelques-uns faisant attention à la forme d’épée qu’on remarquait dans cette Comète, la voyant d’ailleurs s’avancer d’occident en orient, approcher de la Lune, et la depouiller de sa lumière, conclurent que les princes Chrétiens, formant ensemble une puissante ligue viendroient de l’occident, attaqueroient le trône Ottoman et le renverseroient. Ce prodige ne causa pas même de petites frayeurs dans l’esprit des Turcs.”—Pingre, i. 456.

NOTE R, Page 110.

Those calculations by La Lande, were contained in a Memoir published by him in 1773. The terror which this Memoir occasioned, not only in Paris but over all France, was equally ludicrous and unfounded. But at this period mankind were scarcely emancipated from the thraldom of superstition, and had not yet freed their minds from that proneness to imaginary fears, which ignorance of nature so easily inspires. This Memoir by La Lande was intended to be read at a meeting of the Academy of Sciences. “Le Memoire,” as MONTUCLA relates, “ne fut pas lû; mais ce que l’on en dit ce jour-la après la séance, passa de bouche en bouche, et s’accrut beaucoup plus rapidement qu’on n’auroit pu le croire. Bientôt on dit qu’il avoit annoncé une Comète, que dans un an, dans un mois ... dans huit jours, alloit causer la fin du monde, &c. Ces bruits populaires vinrent au point d’effrayer; et le lieutenant de police demanda au cit de La Laude une explication prompte capable de rassurer le public; elle parut en peu de mots dans la Gazette de France, du 7 Mai; mais cela ne suffisait pas pour justifier l’auteur de toutes les choses absurdes qu’on lui imputoit presque géneralement à Paris, et meme dans les provinces; la multitude des lettres qu’il reçut, et des questions qu’on lui adressa à ce sujet, lui fit juger qu’il étoit indespensable de publier sans délai cette portion de son memoire.”

NOTE S, Page 111.

I may remark, in passing, that even the mind of the great Newton was not exempt from this absurd notion. He gives it as his opinion, that, for the preservation of humidity in the planets, comets are absolutely requisite, from whose vapours and exhalations all the moisture expended in vegetation may be supplied. His words are, “Ad conservationem marium et humorum in planetis requiri videntur Cometæ, ex quorum exhalationibus et vaporibus condensatis, quicquid liquoris per vegetationem et putrefactionem consumitur, et in terram aridam convertitur, continuo suppleri et refici posset.” And he shortly after adds a conjecture, still more extravagant, in the following terms: “Porro suspicor spiritum illum, qui aëris nostri pars minima est sed subtilissima et optima, et ad rerum omnium vitam requiritur, ex Cometis præcipue venire.” Principia, lib. iii.

This notion, that Comets produce atmospherical changes, resembles another popular prejudice respecting the influence of the Moon upon the weather. If persons, who speak and act upon this belief, are asked, What may be their reasons for attributing such an influence to the Moon? the sole reply, generally obtained, is, that such has always been the common opinion: no other evidence whatsoever is adduced for the assumption. The ordinary manner in which the Moon affects the Earth is by producing the tides; an effect totally unconnected with the existence of atmospherical changes. As this effect of the lunar attraction is periodical, depending on the position of the Moon, in like manner, if any similar influence were exerted upon the atmosphere, it would be followed by such periodical alterations in the state of the weather, as would have been easily detected by long continued observation of the barometer. Unquestionably there is some effect produced on the atmosphere by the Moon’s attraction, as upon the waters of the ocean.—But that it is infinitely too small to alter the state of the weather has been lately proved by La Place, who computed, from a series of 4752 barometrical observations, made between 1815 and 1823, that the magnitude of the lunar atmospherical tide amounts to no more than th of an English inch.—Brewster’s Journal of Science, 1823.

But in the same manner as with Comets, the Moon’s influence upon the earth has not been limited to the production of physical changes. It was long imagined, and by many even at the present day it is still believed, to exert a moral or some other mysterious agency. I allude here to the opinion, that lunatics, as the term imports, are liable to be affected by the Moon; and I am informed, that at one of the late meetings of the Royal Medical Society of Edinburgh, a paper was read and discussed concerning the influence of the Moon upon the human constitution. Such prejudices, however, if they yet linger in some places among the shattered remnants of that ignorance and superstition which once overspread Europe, are now rapidly disappearing before the advancement of science: they resemble the shadows of the night that flit for a while amid ruins, though the general darkness has passed away; but which, ere long, also vanish, by the progressive and brightening influence of the sun.

NOTE T, Page 112.

“The comet of 1807,” says a late author, “which appeared towards the south in September, presaged the troubles in Spain, the dethroning of its king, and the subsequent usurpation of his son Ferdinand, with those remarkable events that almost immediately succeeded its appearance. But the great comet of 1811, which appeared near the constellation Ursa Major, and whose orbit crossed the ecliptic in the 16th degree of Leo and Aquarius, was the most remarkable that has appeared in modern times, when about the time of its greatest northern declination, and when its appearance was in consequence most conspicuous, it daily passed over the midst of Europe. Neither were the nightly changes, of which it was the forerunner, less conspicuous in their quick and rapid succession. A few months afterwards, the late French emperor, guided by his evil star, commenced his unfortunate march against Russia. The burning of Moscow, the destruction of his armies, and the stupendous events which almost immediately followed the appearance of that celestial omen, are subjects of history never to be forgotten. And he who would deny the possibility of comets being sent as special tokens to forewarn mankind, after considering such facts as the above, offers a most pointed insult to the divine wisdom of the Most High, the Almighty Ruler of the Universe.” It is added in farther evidence of comets being sent as signs to the human race of the will of Heaven, “that the greatest of them, and the most remarkable, have uniformly appeared in the northern hemisphere; thus passing over those nations which have been the most convulsed by great political events.”

Will it be credited, that the work from which this extraordinary statement is extracted, was published in England in the present year? That such a pitiful combination of superstition and ignorance should have been exposed to the world, is disgraceful to the country, and insulting to the spirit of the times. Josephus, in relating the blindness and obstinacy of his countrymen who shut their eyes even to the direct forewarnings of Providence of the approaching destruction of their city, expressed by various prodigies in the firmament, mentions, as one of these premonitory signs, the appearance “of a Comet, in the form of a sword, which hung over Jerusalem for a whole year together.”—Josephus V. v. 3. We may not perhaps feel much surprise at the pious credulity of the Jewish historian; those events in the natural world, which are beyond the understanding of men, have in all ages been deemed miraculous; but we were certainly little prepared to expect that these absurd prejudices should be again revived in the 19th century.

NOTE U, Page 115.

The agency of the Comet of 1680, here employed by Whitson to produce both a deluge and a conflagration, has also been resorted to by M. Freret, to account for another great catastrophe of a similar nature, the deluge of Oxyges. The historians, who relate this event, mention a fact, upon which, as it would seem, M. Freret’s theory has been wholly grounded, viz. that forty years before the deluge the planet Venus was observed to abandon its ordinary situation, and shrouding itself in a long train of light, to commence a course towards the north. From the relation of this one fact (the date of which deserves to be noted) M. Freret draws the following remarkable conclusions: 1st, That this was not the planet Venus at all, but a Comet emerging from behind the Sun! 2d, That this Comet could be no other than the great Comet of 1680! 3d, That this Comet occasioned the deluge of Oxyges! Will it be credited that these notions were made the subject of serious philosophical discussion, and deemed worthy of a place in the Memoirs of the Academy?

NOTE V, Page 116.

The case in which these several conditions are combined, may be represented by an equation. According to the notation formerly employed in equat. (2.) and (3.) of the parabolic method, let the planet’s radius vector be R, that of the Comet r, and call the distance between the planet and comet ; then we obtain from the ordinary property of triangles, combined with equation (10.) : But since , where D is the perihelium distance and the anomaly, in the supposed case equal to , we have . In order that a shock shall take place, it is evident that should not exceed the semidiameter of the planet and comet.

NOTE W, Page 123.

This conclusion, which is derived from geological data, is strikingly confirmed by astronomical considerations. If the earth had been originally a fluid of uniform density, it would have followed, from the mutual attraction of its parts, and the rotation on its axis, that the increase of the length of the seconds pendulum would be nearly as the square of the sine of latitude: Also, if the earth had been a fluid of unequal density, the denser parts would so arrange themselves towards the centre, that the same law would still be preserved. Now we know, from various experiments, that the interior of the earth is much denser than the parts nearer the surface, and that in both hemispheres the length of the pendulum is proportional to the square of the latitude; whence it follows, that our globe must originally have existed in a fluid state. The above deduction, therefore, which the appearance of our Earth suggests, is strikingly confirmed by this test, the combined result of experiment and theory; and, according to La Place, may be marked as one among the few certainties known in geology.

NOTE X, Page 125.

As an instance of these boulders, Playfair, from whose well known work this passage is taken, mentions a block of granite on the east side of the lake of Geneva, called Pierre de Gauté, about 10 feet in height, with a horizontal section of 15 by 20. “From the present situation, to the place whence it must have been transported, the distance,” says he, “is about 30 English miles, with many mountains and valleys at present interposed.”

NOTE Y, Page 126.

Regarding the celebrated Kirkdale cave, we are told that “on its sides there are seen spines of sea-urchins and other marine remains, incrusted in the mass of the rock; but it is on the bottom, and there only, that there is found the stratum of mud, of about a foot thick, stuck full of bones, as at Gaylenreuth.”—“The greatest number of these bones, without comparison, belong to hyenas of the same species as those of the caverns of Germany; but there are also many of other large and small animals, which Mr Buckland supposes to form twenty-one species. From the pieces which I have under my eye, says Cuvier, there indisputably occur bones of the elephant, hippopotamus, horse, an ox of the size of the common deer, rabbits, field-rats; also bones of some other carnivora, viz. tiger, wolf, fox, weasel.” The cave of Gaylenreuth in Germany, presents a still more striking aggregation of various species. According to Cuvier, the bones of carnivorous animals found there, are those of the bear, the hyena, tiger, wolf, fox, glutton, and polecat. According to Rosenmuller’s recent examinations, there are also found in the same cavern bones of men, horses, oxen, sheep, deer, roes, mules, badgers, dogs, but which, in his opinion, must have been deposited at a period subsequent to those of the bear, tigers, and hyenas‍‍149. In order to account for these extraordinary accumulations of animal remains, Cuvier thinks that only three general causes can be imagined, which could have brought these bones into their present situation. Either, 1st, They are the remains of animals which tenanted the caverns, and died peaceably in them; or, 2d, They have been carried there by inundations, or some other violent agent; or, 3dly, They have been enveloped in the strata, by the dissolution of which these caves have been formed, and the bones have been left by the water which carried off the matter of the strata. The last supposition is allowed on all hands to be quite untenable, from the single fact, that the strata in which the caves occur never contain any bones. Some have also strong objections to the second supposition, on account of the entireness of the bones themselves, which seem to warrant the conclusion, that the bones cannot have been rolled from a distance. “We are therefore obliged to have recourse to the first supposition, whatever difficulties it presents on its part, and to say that these caves served as a retreat to carnivorous animals, and that these carried there, for the purposes of devouring them, the animals which formed their prey.”‍‍150 But it is exceedingly difficult to reconcile this theory with several points. For, 1st, If it be said that the bones of the herbivorous races have been dragged into these caves by carnivorous animals, how is it that the remains of the former seem, in many instances, to have been deposited at a much more recent date? 2d, Is it possible to imagine that so many different animals of the carnivorous tribe would have lived in the same cave, or that the habits of the tiger in these days would have led him to choose a subterranean retreat? 3d, It has been found that the aperture leading into those caverns is often much too small to have admitted its supposed inhabitants.‍‍151 The second supposition, therefore, does humbly appear to me to be the least objectionable. That the bones are yet entire and unbroken, is not really a circumstance which excludes the possibility of their having been brought into their present situation by an inundation. For if it be supposed that, when this event took place, the animals themselves were transported by the rush of waters, then no injury could have been sustained by the bones, which would not be deposited till the bodies decayed. And it is worthy of remark, that, in the cave of Gaylenreuth above mentioned, “there are found, confusedly mixed with the bones, pieces of a bluish marble, of which all the corners are rounded and blunted, and which appear to have been rolled‍‍152.” Accordingly, Cuvier himself seems to have adopted this idea. When speaking of the remains in the cavern near Besançon, he says that “these remains must have been accumulated for a long time, and at last were buried in the mud which has been thrown there by some great inundation‍‍153.”

NOTE Z, Page 126.

Mr Buckland, in his Reliquiæ Diluvianæ, relates the same fact. “The occurrence of these bones,” he says, “at such an enormous elevation in the regions of eternal snow, and consequently in a spot now unfrequented by such animals as the horse and deer, can, I think, be explained only by supposing them to be of antediluvian origin, and that the carcasses of the animals were drifted to their present place, and lodged in sand, by the diluvial waters. This appears to me the most probable solution that can be suggested; and, should it prove the true one, will add a still more decisive fact to those of the granite blocks drifted from the heights of Mont Blanc to the Jura, and the bones of diluvial animals found by Humboldt on the elevated plains of South America, to show that all the high hills and mountains under the heavens were covered at the time when the last great physical change by an inundation of water took place over the surface of the whole earth.

NOTE AA, Page 128.

“The Hymalaya mountains,” observes a late author, “the loftiest in the world, are extremely precipitous on the side of Hindostan; while they decline, with a very gradual descent, towards the elevated plains of Thibet. In like manner, the Alps, which rise abruptly on the side next Italy, present a more easy ascent on the side of Switzerland. A similar remark is applicable to the Andes, which, though extremely steep on their western flanks, gradually sink away on the eastern sides, into the immense basins of the Amazon and Oroonoko.”—“The most abrupt sides,” it is added, “of all the principal mountains, seem to face the south and west, though occasionally they look to the opposite points of the horizon.”—Encyc. Edin. Physical Geography.

In the 7th volume of the Transactions of the Royal Society of Edinburgh, there is a very elaborate and instructive paper by Sir James Hall of Dunglass, upon the proofs of diluvial action occurring in the neighbourhood of Edinburgh. From the abundant proofs which he brings forward, in the subversion of the strata, in the occurrence of boulders, in the excavation of valleys, and in singular but well-marked ruts or scratches on the faces of the rocks, which were exposed to the action of the torrent of waters, the operation of the deluge in this quarter of the world has been completely established. Describing the small sandstone hills which are so numerous round Edinburgh, Sir James Hall observes, that “from each of them a tail or prolongation extends to the eastward, formed chiefly of the blue clay already mentioned, together with beds of sand and gravel. These decline very gently, and maintain to a considerable distance the individual character given to each by the firm mass producing it.” Thus it is that the various ridges have been formed which may be observed every where in the Lothians; and, to use the words of this distinguished geologist,—“It is an important circumstance, that these ridges maintain a very correct parallelism with each other with the tail of the Castle Rock, and of the Calton Hill, and with the alluvial prolongations that extend to the eastward, from all the eminences of this neighbourhood.” After enumerating those various striking geological facts, Sir James Hall states, that “the direction of the stream in the neighbourhood of Edinburgh, as indicated by the medium result of a number of observations, appears to have been from 10° S. of West to 10° N. of East, by true bearings taken with a needle, and allowing 27 degrees West of North for variation.”

NOTE BB, Page 133.

By the same rule we may calculate the probability of a comet approaching this Earth so near as the Moon, which, if Phranza’s relation be true, has actually happened. The Moon is distant from us about 60 semidiameters of the Earth, therefore expresses the probability; or, in other words, that in about 88,000 years this event will again take place. The Comet of 1770, so often already mentioned, approached the Earth about six times the distance of the Moon; this event may happen, therefore, in the space of 2336 years. This interesting paper of Olbers was first published in Monat. Corresp. II. p. 409.

The following are some of the comets whose elliptic orbits have been computed, together with their respective periods of revolution, and aphelion distances. The aphelion distances are reckoned in millions of geographical miles, and the periods of revolution in sidereal years.

Years. Aph. Dist. Periods.

1680 2898 575

1759 363 75 or 76

1763 15500 7334

1769 3967 929

1770 117 5

1772 415 6

1805 98

1807 5943 1713

1st 1811 8747 3383

2d 1811 1873 875

1815 700 74 or 75

It may here perhaps be proper to make some remarks upon the probable number of comets traversing the system. Historical records give intimation of about 400 comets; but there are not more than 130 whose orbits, up to the present year (1827), have been computed. We are not to imagine, however, that we thus obtain any information with respect to the actual number; for the discoveries of these bodies, as well as of new facts in every other branch of astronomy, have been increasing with every succeeding year, depending wholly on the improvement of instruments and the assiduity of observers. There are several circumstances which prevent the more frequent discovery of these bodies. Many comets which, even at their nearest approach to the Sun, are still too far distant to be discovered from the earth; many which, requiring, as the above list shows, thousands of years to accomplish a single revolution, have seldom or never yet reached their perihelion within the recorded experience of mankind; many which, on account of their diminutive size, may be invisible to the naked eye, and are only discovered by an accidental position of the telescope; many which are to be seen only on the south side of the equator, where there are as yet but few means of observation; many which, though on the north side of the equator, rise above the horizon only during the day, when the Sun’s light prevents them from being discerned; many, finally, which pass the Earth unnoticed, owing to cloudy weather, or other unfavourable circumstances,—many such must be traversing the system, of which we have no possible intelligence.

But from the number of comets which have been observed, we may attempt to form some conjecture concerning the probable amount. In examining a catalogue of comets where the perihelion distances are given, it will be found, that about 70 have been observed within the orbit of the earth, during the last century. Considering, however, the multitude of comets which, for some of the reasons above assigned, have not been perceived, we may assume 140 as the number which, within the last 100 years, have passed between the sun and the earth. If we reckon, therefore, 1000 years to be the average period of the revolutions of comets, which is certainly not too great; and reflect, that if astronomers had always been as assiduous in their observations as during the last century, an equal number might have been seen, it follows, that (1000/100 =) ten times the number of comets would have been recorded that there actually are; and hence we have 140 × 10 or 1400, the whole amount of comets in the system, which come nearer the Sun than the Earth. In order now to estimate the number, whose perihelia are situated within Uranus, we must farther multiply this number by the cube of 20, which is the distance of Uranus from the Sun, calling the Earth’s radius unity. Hence (1400 × 20³ =) 11,200,000 of comets, may be considered as an approximate estimate of the number of these bodies, which, in their approach to the Sun, pass within the orbit of Uranus. But may there not also be Comets, whose perihelia are situated even beyond the orbit of this planet?

NOTE CC, Page 139.

This theory, concerning the consolidation of comets, is strikingly supported by the analogy of the planets. It is well known that their densities diminish pretty regularly with their distance from the Sun. Is it not possible that this law may depend on the actual influence of the solar heat? A general view of the case renders the hypothesis extremely probable; and if we take the product of their respective distances and periods of revolution, as I have now done with respect to comets, their densities will be found to follow very nearly the same proportion. It is true, however, that La Place’s theory, as to the origin of the planets, may also explain this circumstance with respect to their density. He supposes the planetary bodies to have been formed out of a nebulous medium surrounding the Sun like an atmosphere; and if the density of this circumambient medium, like any other atmosphere, diminished in proportion to the distance from the Sun, the bodies themselves, formed out of this medium, must be affected by the same law.

NOTE DD, Page 141.

When a receiver begins to be exhausted of its air, a thermometer placed inside will indicate a sudden decrease of temperature; whilst if the air be compressed, an opposite effect is produced. It is in an ingenious application of this principle of rarefaction, as promoting evaporation, that Professor Leslie’s well known method of freezing chiefly consists: and on the opposite principle of condensation, that a little instrument has been constructed, in which, by the sudden stroke of a piston to compress the air, fire is instantaneously generated.