Comets which have or seem, to have a common origin–Double comets–Systems of comets according to M. Hoek–Distribution of aphelia over the celestial vault; region of the heavens particularly rich in aphelia.

When, in accordance with the actual facts of science, we endeavour to form an idea of the constitution of the visible universe, we see that the celestial bodies which compose this whole are everywhere distributed into groups and associations united by the common bond of universal gravitation.

There are the planetary systems. In the centre of each group is a star or central sun, whose preponderating mass retains near him, circulating in regular orbits, other stars or planets, to which this central sun distributes heat and light. Our planetary system is the type of associations of this kind.

There are the stellar systems, groups of two, three, or more suns gravitating about one another, probably in accordance with the same laws. These systems are themselves the elements of greater associations, which, like the resolvable nebulas known under the name of stellar masses, are composed of myriads of suns. The Milky Way is one of the most splendid examples of these immense agglomerations.

In certain regions of the heavens the nebulae are themselves to all appearance grouped into systems, so that the general plan of the universe is one vast synthesis of associations of different orders encompassing each other without end.

Differences of inclination, eccentricity, and direction of motion.

If, then, periodical comets, calculated as such, and known to be periodical by their return, are governed by the same laws as the planets, why is a distinction made between these two kinds of celestial bodies? This is a question of high importance, and one which we cannot completely answer at the present moment. A full reply would necessitate some definite knowledge concerning the origin of the bodies which compose the solar world. It would be necessary to have studied and compared the physical constitution of comets with that of planets. Both in origin and constitution we shall see farther on that they appear to be essentially different. Surveying the question, however, from a single point of view, regarding it as a question of movement only, we can already show differences which separate these two classes of celestial bodies, and justify the double denomination by which they are distinguished.

Comets, as we have already seen, appear in any quarter of the heavens, instead of moving, like the planets, in the narrow zone of the zodiac. This difference arises from the inclinations of their orbits to the plane of the ecliptic Among the principal planets Mercury alone has an inclination as great as 7 degrees; and among 115 telescopic planets 29 only have an inclination greater than 10 degrees, and very few exceed 30 degrees; but we see, on the contrary, the planes of cometary orbits admit of all inclinations.

Calculation of the elliptic elements of the second comet of 1867, discovered by Tempel–Perturbations due to Jupiter, and corsequent delay in the return of the comet to its perihelion in 1873–Remarkable agreement of observation and calculation.

The second comet of 1867, discovered by M. Tempel, was found by several astronomers to have elliptic elements. It passed its perihelion on May 23, 1867, and its period had been calculated at 2,064 days. But Dr. Söllinger, taking into account the perturbations its passage in the vicinity of Jupiter would produce in the elements of its orbit, assigned a retardation of 117 days in the date of its return to perihelion in 1873. It was, in fact, seen again in the course of that year, and its perihelion passage took place on May 9, which gives for the duration of the revolution performed in the interval between the two apparitions a value of very nearly six years, or 2,178 days, three days less than the number determined by calculation.

Tempel's comet of short period is, therefore, the ninth periodical comet whose return has been verified by observation; that is to say, which really forms an integral part of our solar system. Observed in May 1873, at Greenwich, by Messrs. Christie and Carpenter, it appeared in the telescope like an elongated nebulosity, about 40″ in diameter, with a central nucleus, which shone like a star of the twelfth or thirteenth magnitude.

Had the Egyptians and Chaldeans any positive knowledge concerning cornets?– Apollonius of Myndus; the Pythagoreans considered comets to be true stars– According to Aristotle they are transient meteors ; fatal influence of the authority of this great philosopher upon the development of Cometary Astronomy.

Such is a very brief history of the errors into which the human mind–we should rather say the human imagination–. has fallen with respect to comets. We have now to show how little by little, and by very slow degrees, truth disengaged itself from error, and to supplement the history of superstitions and prejudices by that of science. Both are instructive and throw light upon each other at all stages of their mutual velopment. Thus, for example, we may readily conceive that the irregular movements of comets, their sudden and unforeseen apparition, to say nothing of the singularity of their aspect, for a long time precluded the idea of their being true stars, subjected to fixed laws, like the planets. Centuries of work, observation, and research were required for the discovery of the true system of the world as far as the sun, the planets, and the earth were concerned; but a difficulty of another kind stood in the way of the discovery of the true movements and nature of comets, since no trouble was taken to make exact and continuous observations of them.

Direction of the tail opposite to the sun; discovered by Apian; the Chinese astronomers were acquainted with this law–Deviations in some comets–Variable aspect of the tail according to the relative positions of the comet, the earth, and the sun.

In respect to the direction of cometary tails let us call attention to an important point–to a general phenomenon which was remarked by the ancients, in the very earliest times. Seneca refers to it in the following line:–

The comæ of comets fly the ray a of the sun. According to Edward Biot the Chinese astronomers had observed, since the year 837. this constant direction of cometary tails from the sun. ‘ In Europe, ’ says Lalande, ‘ Apian was the first to perceive that the tails of comets were always opposite to the sun; this rule was afterwards confirmed by Gemma Frisius, Cornelius Gemma, Fracastoro. and Cardan. Nevertheless, Tycho Brahe did not believe it to be very general or well demonstrated; but the fact itself is beyond a doubt. ’

Pingré observes with truth that the direction of the tail is not always strictly opposite to the sun. He instances the comet of 1577, whose tail was deflected as much as 21° towards the south, and the great comet of 1680, when the deflection was about 4 ½°. On both these occasions, however, the comet and the earth occupied the same relative positions in the heavens.

Periodicity of the meteor-swarms; radiant points; number of swarms recognised at the present day–Periodical maxima and minima in certain meteoric currents; thirty years period of the November swarm–Parabolic velocity of shooting stars ; the swarms of shooting stars come from the sidereal depths.

These considerations bring us to the theory recently elaborated by the learned Italian astronomer M. G. V. Schiaparelli, Director of the Observatory of Brera, at Milan.

According to this theory there exists between comets and shooting stars a connexion and community of origin, which henceforth we may regard as certain, as it is supported both by logical deduction and observation. We shall now explain by what train of ideas this assimilation between phenomena which at first sight appear so foreign to each other has passed from the phase of simple hypothesis into that of a theory which observations of great value permit us at the present time to consider demonstrated.

Let us first of all pass in review the facts upon which the theory is based.

The shooting stars which may be observed on any clear night throughout the year are notably more numerous at certain times, the dates of which are nearly fixed, as, for example, August 10, November 13 or 14, and April 20.

Three observations are necessary for the calculation of a parabolic orbit – Cometary ephemerides; what is meant by an ephemeris; control afforded by the ulterior observations –Elements of an elliptic orbit – Can the apparition or return of a comet be predicted?– State of the question – Refutation by Arago of a current prejudice

Three observations of a comet–that is to say, three different positions (in right ascension and declination) of the nucleus of a comet, or, in a word, three points of its trajectory or apparent orbit sufficiently distant from each other–are required, as we have said, for the calculation of the parabolic elements of the true orbit.

In the last century this determination was not only a long and laborious operation, but involved much tentative and uncertain work. Before engaging in the difficult calculation of the elements of an orbit, astronomers made trial graphically and even mechanically of different parabolas, and only began the calculation after satisfying themselves that one of these curves nearly represented the positions furnished by observation. Great improvements were introduced into these methods during the last century by Lalande, Laplace, and Gauss. But the calculation of a cometary orbit is always a sufficiently complex operation, even if it be simply parabolic, and it still takes a skilful computer accustomed to this kind of work, several hours to find approximate values of the different elements. This is not the place for us, of course, to attempt an explanation of the work itself.

WHAT is meant by the physical or chemical constitution of a celestial body, or of any luminary whatever, whether star or sun, planet or moon; or, aswe are treating of comets only, what is meant by the physical or chemical constitution of a comet?

We have presented for our consideration a question the nature of which is easily explained and not less easily understood; but it is one that the best-informed of astronomers would find it difficult to answer in its full integrity.

By comparison with the bodies that we see on the surface of the earth and with the terrestrial globe itself, considered as a whole, we shall proceed to explainwhat is meant by the physico-chemical constitution of a comet.

The earth is a globe, more accurately, a spheroid, whose form and dimensions are perfectly defined and well known, at all events as far as concerns its solidcrust, the atmosphere that surrounds it, and the rocks and strata near its surface.

Comets are, from all these points of view, their movements alone excepted, conspicuously different from the earth and the rest of the planets.

The memoir of Lalande and the panic of the year 1773–Letter of Voltaire upon the Comet–Announcement in the Gazette de France and the Memoirs of Bachaumont– Catalogue given by Lalande of comets which up to that time had approached nearest to our globe.

In the spring of the year 1773 a singular rumour, soon followed by a strange panic, obtained in Paris and rapidly spread throughout France. A comet was shortly to appear upon the earth's track, to come into collision with our planet, and thus infallibly bring about the end of the world. The origin of this rumour was a memoir which Lalande was to have read before the Academy of Sciences on April 21; it was, however, not read, but the title alone was sufficient to create a popular ferment. The work of the learned astronomer was entitled Reflexions sur les Comètes qui peuvent approcher de la Terre. It was speedily imagined, and without the smallest foundation–for nothing of the kind was to be found in the memoir–that a comet predicted by the author was about to dissolve the earth on May 20 or 21, 1773.

Rapid undulations occasionally observed in the light of cometary tails ; observations of Kepler, Hevelius, Oysatus, and Pingre; comets of 1607, 1618, 1652, 1661, and 1769–Undulations in the tails of the comets of 1843 and 1860; do these undulations arise from a cause peculiar to the comet itself, or do they depend upon the state of the atmosphere?–Objection made by Olbers to the first of these hypotheses ; refutation by M. Liais.

The tails of certain comets have exhibited variations of brilliancy, sudden changes of intensity, analogous to the phenomena of the same kind which are observed in the aurora borealis, and which, it is believed, have been remarked in the zodiacal light. This fact was unknown to the ancients ; and when Seneca speaks of the augmented or diminished brilliancy of comets, it is evident that he alludes to the changes produced, in the course of their apparition, by the variations of their distance from the earth. He compares them ‘to other stars which throw out more light and appear larger and more luminous in proportion as they descend and come nearer to us, and are smaller and less luminous as they are returning and increasing their distance from us.’ (Quæstiones Naturales, vii. 17.)

Kepler is the first observer who has made mention of these singular changes.

Introduction of poisonous vapours into the terrestrial atmosphere–The end of the world and the imaginary comet of Edgar Poe; Conversation of Eiros and Charmion –Poetry and Science; impossibilities and contradictions.

We now come to that other cometary influence which we have already alluded to, an influence capable of changing the air we breathe by the introduction of foreign effluvia.

Nothing within the range of fact and observation, up to the present time, affords ground for belief in such an influence. But this hypothesis has had the fortune to be presented in a striking and practical form by a modern writer of powerful imagination. The American poet Edgar Poe, whose Extraordinary Histories are known to everyone, has placed in the mouth of a being who has suffered death, an account of the destruction of the world by the near approach of a comet. We subjoin the principal portion of this wonderful dream, in which Eiros relates to Charmion the circumstances which put an end to the world.

‘ The individual calamity was, as you say, entirely unanticipated, but analogous misfortunes had been long a subject of discussion with astronomers. I need scarce tell you, my friend, that, even when you left us, men had agreed to understand those passages in the most holy writings which speak of the final destruction of all things by fire as having reference to the orb of the earth alone.

If we arrange in the order of date the various apparitions of comets (hat have been recorded, and note how these bodies appear in different regions of the heavens, and how some pursue a direct and others a retrograde course; or, better, if we study their elements in a catalogue, our attention is at once arrested by the diversity of these elements, which seem connected by no relation.

It may, however, be instructive to examine, by comparing these materials, whether any law presides over the distribution of comets in time and space. We shall, therefore, give a rapid résumé of the analysis we have made with this object. We have taken the catalogue published by Mr. Watson at the end of his work on Theoretical Astronomy as the basis of our investigation.

In this catalogue, which we reproduce at the end of this work, we find 279 comets arranged in the order of their successive apparitions, from the most ancient times to the commencement of the year 1867; we have ourselves completed it for the seven following years, including also the first half of the year 1874; so that the total number of comets in the catalogue is by this means increased to 311, a number very inferior, not only to the actual number of comets, but to the number of those which have received mention in history.

Do the nuclei of comets exhibit phases?–Polarisation of cometary light–Experiments of Arago and of several contemporary astronomers–The light of nebulosities and atmospheres is partly light reflected from the sun.

In the last century astronomers were almost entirely preoccupied with the study of cometary movements, the nature of cometary orbits, the periodicity of comets, and with every question, in fact, that tended to prove that, like the planets, these bodies are subjected to the universal law of gravitation. Astronomical physics was then hardly recognised, and conjecture filled the place of modern analytical research. It was doubtless owing to this preoccupation that comets were at that time looked upon as bodies of kindred nature to the planets. There was a kind of reaction against the ancient hypothesis of terrestrial meteors and transient fires. ‘Planets are opaque bodies,’ says Pingré; ‘they only send back the light which they receive from the sun. We ought not, perhaps, to conclude definitively that comets are also opaque bodies ; it is not absolutely proved that a luminous body may not circulate around some other body. But the light of comets is feeble and dull; its intensity varies; we can perceive in it sensible inequalities and even gaps. It does not appear that these phenomena can be explained otherwise than by supposing comets to be opaque bodies, possessed of no other light than that which they receive from the sun, and surrounded by an atmosphere similar to that of the earth. Clouds are formed within this atmosphere, just as in our ownatmosphere; these clouds weaken or totally intercept the rays ofthe sun, and successively deprive us of the sight of a portionof the comet. This hypothesis would explain everything. . .’

Transformation of a nebula which has entered into the sphere of the sun's attraction; continuous parabolic rings of nebulous matter–Similarity between the elements of the orbits of meteor streams and cometary orbits–The August stream; identity of the Leonides and the comet of 1862–Identity of the Perseids and the comet of 1866 (Tempel)–The shooting stars of April 20 and the comet of 1861–Biela's comet and the December stream–Did the earth encounter Biela's comet on November 27,1872?

It still remains to explain the origin of meteor swarms or streams, and the reason of their annual periodicity and the maxima which appear at dates separated by intervals of several years. For this purpose it will be necessary for a moment to quit the domain of fact and consider some theoretical speculations.

The swarms of shooting stars appear to be constituted, as it were, of aggregations of particles separated from one another by some distance. But if, instead of seeing them on their arrival in the proximity of the earth, in contact with its atmosphere, it were possible to contemplate them from a distance in the heavens, the whole of these myriads of particles, whether illuminated by the sun's rays or shining by their own light, would appear to the observer like a cloud or nebulosity.