Periodical comets exterior to the solar system; the type of this class is Halley's comet, which is tile only comet of mean period whose return has been verified by observation–Enumeration of comets with periods between 69 and 200 years– Periods; aphelion and perihelion distances.

Of the comets belonging to this class Halley's comet is the type; but it is the only one of which we have several undisputed apparitions. When a comet is suspected to be identical with some other comet that has been previously observed, from the similarity of the parabolic elements, its return is probable; but as a rule great uncertainty attaches to the length of the period, even if, assuming the identity of the two comets, the perturbations be left out of the question. A third apparition is, therefore, generally necessary before the identity and real periodicity of a comet can be affirmed. And this third element up to the present time is wanting in the comets we are now engaged upon. But it will evidently suffice to prove a second apparition, when the elliptic elements have been calculated solely from observations of the first apparition.

The following, in the order of their discovery, are the nine comets of mean period which we have to mention:–

The first on the list is the comet of 1532, observed by Apian and by Fracastoro, ‘ whose head,’ says the latter observer, ‘ was three times larger than Jupiter, with a beard two fathoms long.’

Hypothesis of an electric or magnetic action in the formation of tails–Eepulsive action of the sun upon the cometary matter, and of the nucleus upon the nebulosity –Views of Sir John Herschel and-M. Liais–Theory of Bessel–Oscillations of luminous sectors–Magnetic polar force.

Whether the cause which determines the production of cometary tails and their development, at once so immense and so rapid, be a force sui generis, or only an apparent force, it is none the less true that it has all the features of a repulsive action or force. Heat, the impulsion of the solar rays, gravitation, have all been variously combined in order to furnish the desired explanation; it evidently remained to try the intervention of the electric and magnetic forces.

From this point of view Olbers, Herschel, and Bessel have in turn applied themselves to the problem. We will give a brief analysis of the opinions held by these illustrious astronomers.

The comet of 1811 first drew the attention of Olbers to the subject. ‘ This astronomer, ’ says M. Roche, ‘ attributes to the proximity of the comet and the sun a development of electricity in both these bodies; hence arises a repulsive action of the sun and another repulsive action of the comet upon the nebulosity which surrounds it. ’

First comet whose periodicity, without comparison with previous dates, has been determined by calculation and verified by observation–M. Le Verrier demonstrates that it has nothing in common with the comet of Lexell–Slight eccentricity of Faye's comet and great perihelion distance–Dates of its return–Perturbations in the movements of Faye's comet inexplicable by gravitation alone : a problem to be solved

A communication by Arago, published in 1844, in the Comptes Rendus of the Academy of Sciences, gives an account of the first researches relative to the fourth periodical comet, which we here subjoin :–

‘This body was discovered at the Observatory of Paris by M. Faye, on November 22, 1843. This young astronomer hastened to calculate its parabolic elements. But as the number of observations increased M. Faye perceived that a parabola was quite inadequate to represent the series of positions occupied by the comet, and announced that he should determine its elliptic orbit, as soon as the state of the sky should have permitted him to pursue his observations of the new comet in regions so far removed from those in which it had first appeared that no doubt could possibly exist as to the certainty of his results. M. Faye therefore applied himself to the multiplying of observations, which had become extremely difficult to obtain, on account of the indistinctness of the comet. Matters were in this stage when a letter from Schumacher informed him that Dr. Goldschmidt, a pupil ofGauss, had already calculated an elliptic orbit, having used theobservations made at Paris on November 24, and those of December1 and 9, made at Altona.’

The mathematicians and astronomers who have alluded to the effects of a collision between our earth and a comet, have more especially considered the event from a mechanical point of view ; the two bodies were for them simply two projectiles which, both animated with enormous velocities, could not fail to encounter each other with a violence dependent upon their respective masses, velocities, and directions of motion. They foresaw only the dislocation or rupture of two gigantic masses, a catastrophe which would inevitably cause the destruction of the human race, and of all living beings upon the surface of the earth.

Some philosophers, believing a comet to be an incandescent mass, or at least to have become heated to an intense degree during its passage in the near vicinity of the sun, have conceived that it would inevitably set fire to our globe; in which case we should perish both by the shock and by fire

But it was not then possible to view the phenomenon in its true light, since the great principle of the conversion of mechanical energy into heat had not at that time been discovered. Let us therefore continue the same hypothesis of a comet of solid nucleus, of a mass comparable to that of our globe, and coming into collision with the earth from any direction whatever.

The great comet of 1811 ; the comet wire–Prejudices and conjectures–Remarkable comets and telescopic comets –Comets are continually traversing the heavens.

In former times when a new comet Avas seen to project upon the sky its vaporous star and plume of light, the first question in the mouth of everyone was, What great calamity does God announce?

Even at the present day people may be heard enquiring what the comet signifies ; but the greater number of enquirers are far more occupied with the physical effects likely to accrue, than with the supernatural import of the apparition. Do you think we shall have a warm and dry summer? is the question of some. Are we to anticipate foggy weather, heavy rains and inundations? ask others. It announces an abundant harvest, or a superior quality of the year's wine, is gladly remarked by those who have-not forgotten the comet and the good wine of the vear 1811

In a word, people readily believe that the passage of a comet within sight of the earth must be followed by certain consequences of a nature to influence not only the climate, temperature, and vegetation of the latter, but likewise the health of animals and man, for I have forgotten to say that the influence of comets upon the production of epidemics and other maladies was formerly an article of popular belief.

Views of Newton on the formation of the tails of cornets–Action of heat and rarefaction of the cometary matter–The ethereal medium, losing its specific weight, rises opposite the sun, and carries with it the matter of the tail–Objections which have been made to the hypothesis of a resisting and ponderable medium.

Newton, in order to explain the formation of the tails of comets, had recourse to no other causes than the ordinary action of the calorific rays on the one hand, and that of gravitation on the other. But, although he does not introduce any new force, he is obliged to suppose that the comet during the whole time that its tail is developing is traversing a medium subject to the force of gravitation and tending towards the sun.

The apparition of a comet or a bolide is a warning from the gods: the Iliad' and the Ænid;neid–Supposed physical influences of comets; Earthquakes in Achaia; submersion of Helicèand Bura; comet of the year 371–Comets, presages of happy augury ; Cæsar transported to the heavens under the form of a comet; popular credulity turned to account; opinion of Bayle–Pliny, Virgil, Tacitus, Seneca–The comet of the year 79 and the Emperor espasian–Comet of the year 400 and the siege of Constantinople.

A comet is thought to have appeared in the last year of the siege of Troy. By Pingré and Lalande it is considered an apparition of the famous comet of 1680, and whilst the former cites in support of his opinion a passage from Homer, the latter draws attention to certain lines in the Æneid probably referring to the same comet.

Ancient apparitions of the comet of 1680, on the hypothesis of a revolution of 575 years–Their coincidence with famous events–Whiston 's theory of the earth: our globe is an ancient comet, whose movements and constitution have been modified by comets–The catastrophe of the Deluge caused by the eighth anterior apparition of the comet of 1680–Final catastrophe : burning of the earth–Future return of our globe to the condition of a comet.

The comet of 1680 is one which has been made the subject of considerable discussion. If we adopt the calculations of Halley, confirmed in the first instance by Newton, it would be that which appeared in the years 531 and 1106 of our era, announced in the year B.C. 43. the death of Cæsar, presided at the taking of Troy, and eleven or twelve centuries earlier, was the direct cause of the deluge mentioned in the Mosaic records.

In 1106, the apparition of this celebrated comet did not, it is true, coincide with any great historical event; but, according to the chroniclers, it was of great brilliancy, ‘ resembling a flaming torch, covering with its rays a great portion of the heavens, and filling all minds with terror.’

The inhabitants of comets as depicted in the Plurality des Mondes of Fontenelle– Ideas of Lambert respecting the habitability of comets–That comets are the abode of human beings is a hypothesis incompatible with the received facts of astronomy.

After Newton, and especially in the eighteenth century, by a not unnatural reaction of ideas from the Aristotelian doctrine of transient meteors, comets were regarded as bodies, stable and permanent as the planets ; they were obedient to the same laws of movement, and differed only as regards appearance, by their nebulosities and tails. The astronomers of that time, taken up with the verification and calculation of their positions and orbits, occupied themselves little or not at all with the study of details which were purely physical, such as are now called cometary phenomena. Regarding them as spheroids, solid like the planets, and similar to them in the constituents of their nuclei, to people them with inhabitants followed in the natural sequence of ideas.

Fontenelle, who, as we know, was a believer in the theory of vortices, and who, moreover, regarded the heads and tails of comets as simple optical appearances, thus expresses himself in the Pluralité des Mondes.

‘ Comets,’ he observes, ‘ are planets which belong to a neighbouring vortex ; they move near the boundaries of it ; but this vortex, being unequally pressed upon by those that are adjacent to it, is rounder above and flatter below, and it is the part below that concerns us.

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.