Comæ and tails–Classification of the ancients according to apparent external form ; the twelve kinds of comets described by Pliny–The ‘ Guest-star ’ of the Chinese–Modern definitions : nucleus, nebulosity or atmosphere; tails.

What is the distinctive sign of a comet by which it is universally known, by which it is distinguished from all other celestial bodies? Everyone answers at once, it is the train of luminous vapour, the nebulosity of more or less length, which accompanies it or at least surrounds it; in other words, the tail and the coma

This is what the etymology implies, the word comet signifying long-haired or hairy. Armed with its tail, which appears brandished in the heavens like an uplifted sword or a flaming torch, the precursor of some untoward event, a comet is everywhere recognised on the instant of its appearance; it needs no passport signed by astronomers to prove its identity. But should the tail be absent, should no appendage or surrounding nebulosity distinguish the celestial visitor on its apparition, for the world at large it is no comet, but simply an ordinary star like any other.

Nevertheless, there are tailless comets. The comet of 1585 was equal to Jupiter in size, but less brilliant; its light was dull. It had neither beard nor tail, and it might have been compared to the nebula in Cancer (Pingré).

Kepler's Laws: ellipses described around the aim; the law of areas – Gravitation, or weight, the force that maintains the planets in their orbits– The law of universal gravitation confirmed by the planetary perturbations – Circular, elliptic, and parabolic velocity explained; the nature of an orbit depends upon this velocity – Parabolic elements of a cometary orbit

What is the nature of a true cometary orbit? In other terms, what is the geometrical form of curve which a comet describes in space–what is its velocity–how does this velocity vary– and what, in short, are the laws governing the movement of a comet?

In order to reply to these questions, and to enable them to be clearly understood, we must first call to mind a few notions of simple geometry, and also the principal laws which govern the motions of the planets.

Kepler, as we have already said, discovered the form of the planetary orbits, hitherto supposed to be circles more or less eccentric to the sun. This great man demonstrated that the form of a planetary orbit is actually an ellipse, that the sun is at one of the foci of the curve, and that the planet makes its complete revolutions in equal periods of time, but with variable velocity ; in fact, that in equal intervals the elliptic sectors described by the radius vector directed from the sun to the planet are of the same area.

Prediction of 1816; the end of the world announced for July 18–Article in the Journal des Débuts–The comet of 1832; its rencontre with the orbit of the earth– Notice by Arago in the Annuaire du Bureau des Longitudes–Probability of a rencontre between a comet and the earth–The end of the world in 1857 and the comet of Charles V

The terrors of the year 1773 create a smile at the present day; but similar fears, it ought not to be forgotten, have been renewed from time to time in our own century; as, for example, in 1816, 1832, and 1857

In 1816 a report was current of the approaching end of the world; July 18 was the date fixed for the fatal event. Some days after there appeared in the Journal dés Debate a satirical article by Hoffmann, in which that critic ridiculed in the following manner the hypothesis of the earth coming into collision with a comet:–

‘A great mathematician (Laplace), to whom we owe the complete exposition of the system of the world, and whose work is law, has been kind enough to reassure us a little concerning the uncivil comets of Lalande ; but that he is far from having banished all cause of alarm we may judge from the following passage, which I will literally transcribe : “ The small probability of such a rencontre may, by accumulating during a long series of years, become very great.”

The universe is formed of an infinity of worlds similar to our own. The thousands of stars which meet our gaze in the azure vault of the heavens when we contemplate it with the naked eye, and which may be reckoned by hundreds of millions when we explore its depths by the aid of the telescope, are suns. These foci of light, these sources of heat, and incontestably of life, are not isolated; they are distributed into groups or clusters; sometimes by twos or threes, sometimes by hundreds, sometimes by myriads; the clouds of vaporous light called nebulse are for the most part thus constituted.

Isolated or in groups, the stars seem to us immovable, so prodigious is the distance by which they are separated from the earth and from our sun. They move nevertheless ; and amongst those whose velocities have as yet been measured may be reckoned some which are moving ten times and even fifty times quicker than a cannon-ball when it leaves the cannon. Movement is, therefore, the most universal law of the stars.

In like manner our sun moves through space and compels the earth to follow. He bears along with him, in this voyage through the boundless ether, the globes which form his cortege and gravitate about his enormous mass.

Book vii. of Seneca's Qucsstiones Naturales relates to comets–Seneca defends in it the system of Apollonius of Myndus ; lie puts forth just views concerning- the nature of comets and their movements–His predictions respecting future discoveries in regard to comets–The astronomers of the future.

From the beginning of his book Seneca fully appreciates the importance of the question, and the connexion that must necessarily exist between the nature of the comets and the system of the universe itself. He is led to ask ‘ if comets are of the same nature as bodies placed higher than themselves. They have points of resemblance with them, ascension and declination, and also outward form, if we except the diffusion and the luminous prolongation; they have likewise the same fire, the same light.’ Here, then, we have comets assimilated to the planetary bodies as regards their movements, the only points of difference being the nebulosities and tails of the former. Seneca is sensible how important it would be ‘ to discover, if possible, whether the world revolves about the motionless earth, or if the world is fixed and the earth revolves ; whether it is not the heavens but our globe which rises and sets.’

Discovery of the identity of the comets of 1682, 1607, and 1531; Halley announces the next return for the year 1758 – Clairaut undertakes the calculation of the disturbing influence exercised by Jupiter and Saturn upon the comet of 1682; collaboration of Lalande and Mdlle. Hortense Lepaute – The return of the comet to its perihelion is fixed for the middle of April 1759; the comet returns on the 13th of March – Return of Halley's comet in 1835; calculation of the perturbations by Damoiseau and Pontécoulant; progress of theory – The comet will return to its perihelion in May 1910

Let us recal the memorable words of Seneca in his Quœstiones Naturales: ‘ Why should we be surprised that comets, phenomena so seldom presented to the world, are for us not yet submitted to fixed laws, and that it is still unknown from whence come and where remain these bodies, whose return takes place only at immense intervals? … An age will come when that which is mysterious for us will have been made clear by time and by the accumulated studies of centuries… Some day there will arise a man who will demonstrate in what region of the heavens the comets take their way, why they journey so far apart from other planets, what their size, their nature.’ Eighteen centuries have elapsed, and not one man, but the accumulated efforts of many men have raised a corner of the veil spoken of by Seneca.

Cometary tails considered as effects of optical refraction–Objections made by Newton and Gregory–New theory of Gergonne : ideas of Saigey on the subject of planetary tails–Difficulties and lacunae in this theory.

Panætius, a philosopher of antiquity, held the belief that comets did not really exist, but were false appearances. ‘They are,’ he says, ‘ images formed by the reflexion, in the heavenly expanse, of the rays of the sun.’ In the opinion of Cardan and some astronomers and physicists, Apian, Tycho Brahe, in the Renaissance, and Gergonne and Saigey, in our time; the tails of comets are simple optical appearances.

The following is the passage in Cardan's work (De Subtilitate) which relates to this question : ‘It is, therefore, evident that a comet is a globe situated in the heavens and rendered visible by the illumination of the sun ; the rays which pass through it form the appearance of a beard or tail.’ The Milanese doctor has entered into no particulars respecting the manner in which these appearances are formed, which, in his opinion, were doubtless analogous to the effects of refraction produced by the convergence of luminous rays passing through a lenticular glass or globe filled with water; such as were formerly employed by artisans for concentrating the light upon their work.

Newton's Principia and the theory of universal gravitation–Why Kepler did not apply to comets the laws of the planetary movements–Newton discovers the true system of cometary orbits–Halley and the comet of 1682; prediction of its return.

Kepler, in 1618, had already discovered the three laws upon which his fame rests, and which will render his name immortal. These laws govern the movements of bodies which, like the planets and the earth, revolve about the sun in regular periods. In virtue of the first law the orbit described about the sun is an ellipse, of which the sun itself occupies one of the foci; the second relates to the velocity of the planet, a velocity which is greater the nearer the planet is to the sun, and less in proportion as it is further removed; or more accurately the velocity is such that the areas of the sectors swept out by the radius vector of the planet are equal in equal times; hence it follows that the maximum of speed takes place at the perihelion, and the minimum at the aphelion. The third law expresses the constant relation which connects the duration of each periodic revolution with the longest diameter, or major axis of the orbit.

Have all the known comets of the solar world always belonged to it?–Probable modification of their original orbits through the planetary perturbations–Cause of the gradual diminution of the periods of certain comets.

The origin of comets is a question equally interesting and difficult.

On comparing all the orbits that have been calculated we find that they pass by almost imperceptible gradations from comets of short period to comets of periods of immense length, and thence to others the major axes of which are of infinite dimensions. If we suppose the latter to be strangers to our solar system, have the former, we may ask, always formed a part of it? In which case why should periodical comets in the elements of their orbits and their physical constitution differ so essentially from planets? Why do they cut the plane of the ecliptic at all inclinations, and why are their movements sometimes direct and sometimes retrograde? Why are their masses so small, and why do they exhibit such vaporous appearances, such rapid changes of aspect, and the phenomenon of tails?

On the other hand, if comets are all of extra-solar origin, why have not all cometary orbits a major axis equal at least to the radius of the sphere of the sun's activity?

The reply to the first questions would be difficult on the hypothesis of comets having the same origin as the planets.

The ancients were unacquainted with the physical nature of comets–False ideas entertained by astronomers of the eighteenth century respecting the physical constitution of comets; comets regarded by them as globes, nearly similar to the planetary spheroids–Views of Laplace upon comets, compared by him to nebulae–Contemporary astronomers have confirmed these views and rectified the errors of the ancient hypotheses–Desideratum of science ; the rencontre of the earth with a comet or the fragment of a comet.

The question, What is a comet? examined in the preceding chapter, and which we reproduce as the heading of this Section, has been the subject of numerous hypotheses. It cannot, however, yet be considered as answered. But it has lately been attempted in an entirely new manner, and by a method least of all to be expected–that of direct investigation. The exposition of this method, and the considerations which have led to it, will be the object of this new chapter.

Let us commence by recapitulating the substance of what our previous enquiries and researches have already taught us.

The ancients, as we have seen at the commencement and in the course of this work, held notions concerning the nature of comets that were entirely hypothetical, and moreover contradictory. On passing their conjectures in review it is surprising, no doubt, to meet with ideas, to some extent, in conformity with the accepted facts of modern science.

Real dimensions of the nuclei and atmospheres of various comets–Uncertainty of these elements; variations of the nucleus of Lonali's comet–Observations of Hevelius upon the variations of the comet of 1652–Do cometary nebulosities diminish in size when their distance from the sun decreases?–Encke's comet considered in regard to this question at its apparitions in 1828 and 1838.

The observations that we have just recorded give an idea of the brightness of cometary light, and the intensity to which that brightness may attain ; but they afford no certain indication concerning the dimensions of cometary nuclei or atmospheres. Upon this point we are about to give the result of a few measurements ; but these measurements, it must be understood, are not so exact as those of the bodies of the solar system, the planets, the moon, and sun. The uncertainty we speak of does not arise from the difficulties experienced in the determination of the measures themselves, although they contribute to it, cometary nuclei being often as deficient in a clear and well-defined outline as the nebulosities; but what more especially prevents us from regarding the numbers we now give as constant, and therefore characteristic elements of the comets to which they belong, is the continual variation to which the different parts of the head are subject during the time of the comet's apparition.

Periodical comets which have not been seen again; long periods; circumstances unfavourable to observation ; motions possibly disturbed by perturbations–Elliptic orbits determined by calculation–Uncertainty of return under these different hypotheses.

The nine comets of which we have just given an account are up to the present time the only comets which can be considered as certainly belonging to our system. But they are not the only comets which regularly perform their revolutions round the sun. Of the numerous comets moving in apparently elliptic orbits some, we shall now see, have been regarded as new apparitions of comets previously observed, the great resemblance of their parabolic elements having caused their periodicity to be suspected. But either their return to perihelion has not yet taken place, or circumstances favourable to observation have not occurred; or, an equally likely hypothesis, they may have been disturbed in their courses by the vicinity of the planetary masses, producing perturbations powerful enough to change their periods, or even to cast them out of the sphere of the sun's attraction, of which perhaps until then they had formed for a time a part.

Other comets, which have not been assimilated to comets already observed, have elliptic orbits determined by calculation; but for the reasons that we have just enumerated they have not been seen again ; that is to say, they have periods much too long, or they have been subjected to disturbing causes.

Comets have been considered in all times and in all countries as signs, precursors of fatal events –Antiquity and universality of this belief; its probable origin- Opinion of Seneca ; habitual and regular phenomena fail to attract the attention of the multitude; meteors and comets, on the contrary, make a profound impression – The moderns in this respect resemble the ancients contemporary with Seneca –The incorruptible heavens of the ancients, in contradistinction to the sublunary or atmospheric regions; stars and meteors –Inevitable confusion of certain celestial or cosmical phenomena with atmospheric meteors.

In all countries and in all times the apparition of a comet has been onsidered as a presage: a presage fortunate or unfortunate according to the circumstances, the popular state of mind, the prevailing degree of superstition, the imbecility of princes or the calculation of courtiers. Science itself has helped to confirm the formidable and terrible signification most frequently accorded by common belief to the sudden and unexpected arrival of one of these remarkable stars. Not two centuries ago, as we shall shortly see, learned men and astronomers of undoubted merit continued to believe in the influence of comets over human events. What wonder, then, if we should find existing in our own time, in the midst of the nineteenth century, numerous vestiges of a superstition as old as the world?