Prevalence of popular superstitions–Comets announce wars, plagues, the deaths of sovereigns–Terrors of the year 1000; comets and the end of the world–Gian Galeazzo Visconti and the comet of 1402–-Ambrose Paré celestial monsters– Halley's comet and the Turks; origin of the Angelus de Midi–The comet of 1066 and the conquest of England by the Normans ; apostrophe to the comet by a monk of Malmesbury.

If a complete history were desired of all the superstitions which, during the Middle Ages and in modern times, have obtained with respect to comets, it would be necessary to pass in review every apparition of these stars, together with such incidental phenomena as the Aurora Borealis, new and temporary stars, bolides, &c, all of which have been converted by popular credulity into as many prodigies. Interesting in a scientific point of view, this long enumeration derived from the naïve chronicles of the time, the only documents available in the absence of a more complete and intelligent record, would be but a tedious study of human errors; a constant and monotonous repetition of the same absurd beliefs. To this state of things savants have themselves contributed, as at the epoch when these voluminous records were compiled cometary influences were still believed in, and the erudite of the day shared the universal prejudice.

Comets appear in all regions of the heavens–Effects of parallax–Apparent motion of a comet, in opposition and in perihelion, moving in a direction opposite to the earth–Hypothetical comet of Lacaille; calculations of Lacaille and Olbers concerning the maximum relative movement of this hypothetical comet and the earth.

The orbits which the planets describe about the sun are not circles, but oval curves, termed ellipses; these ellipses differ but little from circles; that is to say, their eccentricities are small. Moreover, the planes of the orbits in which they move are inclined at small angles to the plane of the ecliptic. Hence it follows that their apparent paths are confined to a comparatively narrow zone of the heavens, which zone is called the zodiac. If we imagine these curves pressed down, as it were, upon the ecliptic they will appear as nearly concentric circles described about the sun, and so disposed as not to intersect each other. The distances of the earth and of each of the planets vary according to the position occupied by these bodies in their respective orbits; but these variations are confined within very narrow limits, and hence it follows that the velocities of the planets change so slightly that the difference is all but imperceptible. The mean diurnal motion of Mercury, which of all the planets moves the most rapidly, amounts to only 4°5′

Predominance of atmosphere in comets–Luminous sectors; emission of vaporous envelopes from the nucleus in the comets of 1835, 1858, 1860, and 1861–Formation of envelopes in Donati's comet; progressive diminution of the velocity of expansion in emissions from the nucleus.

The planets, as seen through a telescope, are bodies of regular form and definite dimensions, probably invariable, so far as we can judge from observations made in the short period of two centuries and a half that has elapsed since telescopes have been invented. A globular mass, solid or liquid, surrounded on all sides by a light and comparatively thin aëriform envelope, is perhaps, from a physical point of view, the simplest description of a planet. The comparative stability is due, on the one hand, to the preponderance of the central globe, where general phenomena are modified only at long intervals ; and on the other to the trifling depth of the atmosphere, the portion of the planet the most subject to variation and internal change.

In comets, we have seen, this relation is reversed, and the atmosphere or nebulous envelope constitutes the entire body, or at all events greatly preponderates. At the utmost we can only conjecture that in some comets the nucleus is solid or liquid. Certainly its volume is generally but a very insignificant portion of the entire nebulosity, even if we except the tail.

Kepler's remark upon the number of comets–Comets observed–Comets calculated and catalogued–Conjecture as to the number of comets which traverse the solar system or belong to it; calculations and estimates of Lambert and Arago–Calculation of the probable number of comets from the actual data; Kepler's remark verified.

‘ Comets are as numerous in the heavens,’ said Kepler, ‘ as fishes in the ocean, ut pisces in oceano’. In quoting this comparison of the great astronomer we only follow the invariable custom of all the authors who have hitherto treated the question of the number of comets; but we remark that the expression employed by Kepler is only the result of an opinion which is little more than a conjecture, and that the words ought to be taken in their poetical rather than in their literal sense; but, making allowance for some exaggeration in the expression, we shall see that Kepler was justified in considering the numberof comets as very great.

Our inquiry, it is evident, must be confined to comets which are liable temporarily to traverse our system, or to revolve for ever about the sun as an integral part of the solar system. Any attempted estimate of comets situated outside this sphere, beyond our range of vision, and exterior to the planets which belong to our group, could not rest upon any certain data.

Study of the question by Arago–The calorific action of comets upon the earth appears to be inappreciable–Comparison of the meteorological statistics of various years in which comets did and did not appear–The meteorological influence of a comet is not yet proved by any authentic fact.

We have already said how general a consternation was created in 1832 by the announcement that Biela's comet would pass within a very short distance of the orbit of the earth. Arago made it the occasion of one of those brilliant and interesting notices in which he endeavoured to destroy existing prejudices, and to render the simple truths of astronomy better and more generally understood. The heading of one section of this notice was–

‘ Will the future Comet modify in any appreciable degree the Course of the Seasons of the year 1832?’ To this question he replies in the following terms :– ‘ The above title will doubtless call to mind the beautiful comet of 1811, the high temperature of that year, the abundant harvest following, and, above all, the excellent quality of the comet wine. I am therefore well aware that I shall have to contend with many prejudices in order to establish that neither the comet of 1811, nor any other known comet, has ever occasioned the smallest change in the seasons.

Opinions entertained by astronomers of the last century: Gregory, Maupertuis, Lambert–Calculations of Lalande ; comets move too rapidly in the vicinity of the earth for the effects of their attraction to come into play–Opinion of Laplace– The collision of a comet with the earth; its effect according to the mechanical theory of heat.

It is interesting to note the opinions formed by savants a century ago respecting the probable effect of a collision between a comet and the earth. Further on we shall speak of the theological romance invented by Whiston for the scientific explanation of the Deluge. According to Whiston the famous comet of 1680, after having, 4000 years ago, produced the universal deluge, is destined to accomplish the destruction of the world, and our globe will be ultimately set on fire by the same comet which had previously inundated it.

Whiston wrote at the end of the seventeenth century. In the middle of the eighteenth century theological speculations engaged but very slightly the attention of astronomers ; but that a very exaggerated idea continued to prevail respecting the amount of injury which the proximity of a comet or its collision with the earth would be capable of producing is undoubted.

In 1742 Maupertuis, in his Lettre sur la Comète, writes as follows: ‘ With their variety of movements it is clearly possible for a comet to encounter some planet or even our earth upon its way; and it cannot be doubted that terrible results would ensue.

Comets participate in the diurnal motion of the heavens. During the time of their apparition they rise and set like the sun, the moon, the stars, and the planets. In this respect, therefore, they do not differ from other celestial bodies.

Let the observer, when a comet is in sight, note the point in the heavens which it occupies when his attention is first directed to it. This is easily done by referring the nucleus, the brilliant point from which the tail proceeds, to two adjacent stars. Let a certain time elapse–an hour, for example; at the end of that time the three luminous points, the two stars and the comet, will be found to have changed their position with respect to the horizon, each having described an arc of a circle in the heavens. The common centre of these arcs is the celestial pole, a point situated within a very small distance of the pole-star; the lengths of these arcs depend upon the interval of time between the observations, and the angular distance of each body from the pole. The direction is that of the general movement of the heavens and the stars; that is to say, from east to west.

We have here, then, a fact which clearly teaches us that a comet moves in regions beyond the atmosphere of the earth; for the diurnal motion is an apparent motion, foreign to the comet, and belongs in reality to the observer, or, as we may say,to the observatory.

I have great pleasure in introducing to English readers M. Guillemin's valuable and interesting work on comets. When rapid progress has been made in any branch of science, it is generally very difficult for anyone, who has not been actually concerned in the investigations in question, to obtain accurate information of the state of our knowledge; and for this reason a book, such as the present, which gives an account of the new results that we owe to very recent researches, really confers a benefit upon many persons who, though taking a strong interest in the subject, have necessarily been quite unable to follow its development in the periodical publications of English and foreign scientific societies. There is no work that at all occupies the ground covered by that of M. Guillemin; and as the subject is one which, always of high interest, has in the last few years acquired, great importance in consequence of Schiaparelli's discovery of a connexion between comets and shooting-stars, I was anxious that it should appear in our language.

Complexity and extent of the question–The law of gravitation suffices to explain the movements of comets–Lacunse in the theory; acceleration of the motion of the comets of Encke and Faye–Origin of comets; their systems–Questions relative to their physical and chemical constitution–Form of atmospheres; birth and development of tails.

Let us glance back for a moment at the contents of the preceding chapters.

We there find many facts accumulated, observations both interesting and instructive, phenomena whose variations suggest reflections without limit concerning the nature of the bodies to which they relate. Nevertheless, do these collected facts permit a clear and certain reply to the simple question: What is a comet?

I say a simple question, for so, as a rule, it is thought to be by non-scientific people; but in reality there is no question more complex. In order to attempt to reply to it, or at least to relate what is known for certain about comets, and to pass in review the most probable conjectures on doubtful points, we must proceed methodically, and thus as it were divide the difficulty.

A first natural division of the subject is at once apparent, it seems to us, from the exposition of cometary phenomena which has been made in the preceding chapters.

Comets lost or strayed: the comet of 1743; the comet of Lexell, or 1770; perturbations caused by Jupiter; in 1767 the action of Jupiter shortens the period, and in 1779 produces an opposite effect–Comet of De Vico; short period comets of 1783, 1846, and 1873.

During the month of February 1743 a comet was observed at Paris, Bologna, Vienna, and Berlin whose parabolic elements were calculated by Struyct and Lacaille. A mathematician of our time, M. Clausen, identified it as a comet of short period, performing its revolution in five years and five months. Is this, as has been supposed, the same comet that was seen in November 1819? If so, its period must have greatly changed, since the calculations of Encke assign to the latter a period of about four years and ten months.

The comet of which we are now about to speak is celebrated in the history of astronomy. The following extract from a memoir by M. Le Verrier gives an account of the circumstances of its first apparition:–

‘ Messier perceived, during the night of the 14–15th of June, 1770, a nebulosity situated amongst the stars of Sagittarius, but not discernible by the naked eye ; it was a comet first coming into view. On the 17th of June it appeared surrounded by an atmosphere the diameter of which was about 5′ 23″. In the centre appeared a nucleus; its light was bright, like that of the stars. Messier estimated its diameter at 22 seconds.

First signs of the doubling of Biela's comet, in the month of January 1840–Observations of the twin comets in America and Europe–Gradual separation and approach of the fragments–The two comets return and are observed in 1852; their distances found to have increased–Elements of the orbits of the two comets.

We now come to transformations still more singular in the outward appearance of cometary nebulosities, and more radical in their nature.

The second return of Biela's comet (period 6¾ years) since the epoch of its discovery as a periodical comet in 1826, or the eleventh of its returns since it was first observed in 1772, was marked by a memorable event, viz. its duplication and division into two distinct and separate comets. We here subjoin a few details on the subject of this event.

On December 21, 1845, the comet was observed by Encke at Berlin; on the 25th of the same month it was seen by M. Valz at Marseilles. Neither of these two astronomers perceived the slightest trace of separation. On the 19th, however, Mr. Hind remarked towards the north of the nucleus what appeared to be a kind of protuberance : was this a premonitory sign of the doubling of the comet? However this may be, it appears certain that the comet was first seen to be double on Janunry 13,1846, at Washington.

Variations of length in the tail of Halley's comet at its different apparitions– Similar phenomena exhibited by Donati's comet in 1858–Does the maximum development of the tail always coincide with the perihelion passage of the comet?

It is now desirable to consider a phenomenon of high importance as regards the physical constitution of comets, viz., the development and variation of their tails according to the position which the comet occupies in its orbit; that is to say, according to its greater or less distance from the sun.

It has been already seen that the tails of comets frequently are formed and developed during the period of the comet's visibility, and generally before the perihelion passage. ‘ It has been constantly observed, ’ says Pingré, ‘ that a comet advancing to its perihelion begins to assume a tail only on its near approach to the sun. The fine comet of 1680 had no tail on the 14th of November, thirty-four days before its perihelion passage. The real length of the tail increases day by day, and the head, or rather the coma surrounding the head, seems, on the contrary, to diminish. The tail attains its greatest length shortly after the comet has passed its perihelion; it then diminishes by degrees, but in such wise that at equal distances from the perihelion the tail is longer after the perihelion passage than before. It has been, moreover, observed that comets whose perihelion distance has much exceeded themean distance of the sun from the earth have not developedtails, and that the tails of others, all else being the same, havebeen more magnificent in proportion as the perihelion distanceshave been less.’

Ideas of Kepler concerning the formation of tails–Galileo, Hooke, and Euler–Hypnthesis of Kepler formulated by Laplace–Where does the impulsion come from in the theory of undulations?

Kepler, who for a moment suffered himself to be led away by the idea of Cardan, soon abandoned it, and substituted in its place that of the action of the solar rays. According to this theory cometary tails have substance and are formed of materials borrowed from the comet, its nucleus, or at least its nebulosity. ‘The sun,’ says Kepler, ‘strikes upon the spherical mass of the comet with direct rays, which penetrate its substance, and carrying with them a portion of this matter, issue thence to form that trace of light which we call the tail of the comet. This action of the solar rays rarefies the particles which compose the body of the comet; it drives them away and dissipates them.’

Hooke, a contemporary of Newton, in order to explain the ascent of the light and tenuous matters which, emanating from the nucleus and flowing back in a direction opposite the sun, contribute to form the tail, assumes that these volatile matters are imponderable : to gravitation he opposes their levitation; according to him they have a tendency to fly from the sun. This amounts to assuming a repulsive force without explaining where this force resides. The opinion of Kepler has been completed, extended, and modified.

Apian observes that the tails of comets are invariably directed from the sun - Observations of Tycho Braihé his views and hypotheses concerning the nature of comets–Kepler regards them as transient meteors, moving in straight lines through space–Galileo shares the opinion of Kepler–Systems of Oassini and Hevelius.

Sixteen centuries passed away between the prediction of Seneca and its full realisation through the accumulated researches of many astronomers and the publication of the Principia, in which Newton demonstrated the law of cometary movements. There is nothing to tell of the history of comets and of systems during this long and dreary period in which the doctrine of Aristotle prevailed, except that it is entirely filled with astrological predictions. Our first chapter contains a résumé of all that the learned have found of interest concerning the apparition of comets and their formidable signification.

Towards the middle of the sixteenth century the movementof the Renaissance, so favourable to letters and the arts, extended its beneficent influence to the science of observation. At the end of the fifteenth century, we find Regiomontanus describing with care the movements of comets, Apian observing that cometary tails are always turned in a direction from the sun; Cardan remarking that comets are situated in a region far beyond the moon, founding his opinion upon the smallness or absence of parallax.

Accelerated motion of Encke's comet; its periods continually diminish–It describes a spiral, and will ultimately fall into the sun–Hypothesis of a resisting medium; how does the resistance of a medium increase the rapidity of motion?–The nature of this supposed medium, according to Arago, Encke, and Plana–Objections of M. Faye; the acceleration of motion explained by the tangential component of the repulsive force.

In our account of the periodic comet of Encke we gave, together with the dates of its successive apparitions, the durations of the revolutions comprised between these dates. If the reader will turn back to the table on p. III he will readily perceive that these durations are unequal, and that the period is continually decreasing, and has suffered a diminution of a little more than two days, or exactly of 2.06 days. As the table includes twenty-two revolutions of the comet it is at most a diminution in each revolution of two hours twenty-two minutes, a quantity small in itself, but which, incessantly accumulating, is capable of producing changes of very great importance in the course of time.

The discovery of this acceleration is due to the astronomer whose name the comet bears.

Different colours of the heads and tails of comets–Examples of colour taken from the observations of the ancients : red, blood-red, and yellow comets–Difference of colour between the nucleus and the nebulosity–Blue comets–The diversity of colour exhibited by comets is doubtless connected with cometary physics, and with the temperature and chemical nature of cometary matter.

The light of many comets has been sensibly coloured. The comet of B.C. 146 exhibited a reddish tinge, according to Seneca: ‘A comet as large as the sun appeared. Its disc was at first red and like fire.’ A little further on Seneca again observes: ‘ Comets are in great number, and of more than one kind; their dimensions are unequal, their colours are different; some are red, without lustre ; others are white and shine with a pure liquid light.… Some are blood-red, sinister presage of that which will soon be shed.’ The ancients had, therefore, observed the difference of colour in the light of comets. And we shall mention a number of similar examples taken from the chronicles of the Middle Ages and from modern observers.

The comets of 662 and 1526 are cited by Arago as having been ‘of a beautiful red;’ and we have seen that Pliny in his classification speaks of comets whose ‘ mane is the colour of blood.’ Such was the comet which appeared in November 1457; according to an ancient chronicle ‘its coma or tail resembled the colour of flame.’