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?

Lexell's comet, and the calculations of Laplace–The smallness of cometary masses deduced from the fact that comets exercise no disturbing influence upon the earth, the planets, or their satellites.

The educated have long since ceased to believe in the mysterious influence of comets upon human events ; such a belief, in fact, would imply a degree of superstition very little in accordance with the spirit of modern times, and would denote complete ignorance of astronomical phenomena. But if comets, by their unexpected apparitions, no longer announce to the world some great event or terrible catastrophe, are they not capable of acting yet more directly for the overthrow of our planet, either by disturbing it in its movement or by striking against it in a rencontre which might prove fatal to its inhabitants? We will further on consider the probability of such a rencontre, and the effect it would produce upon our globe and its inhabitants. But it is easy to understand that these effects would very greatly depend upon two elements of which we have not yet spoken, viz. the mass and density of the comet.

I have elsewhere endeavoured to give an elementary idea of the methods which astronomers have recourse to in order to calculate the mass of any celestial body; that is to say, the quantity of matter it contains as compared with the mass of the earth or of the sun; in short, to weigh it.

Of the five comets of 1874 the third, or comet of Coggia, was alone visible to the naked eye–Telescopic aspect and spectrum of the comet during the early part of its apparition, according to Messrs. Wolf and Rayet–Observations of Secchi, Bredichin, Tacchini, and Wright; polarisation of the light of the nucleus and tail– Transformations in the head of the comet between the 10th of June and the 14th of July, according to Messrs. Eayet and Wolf.

The comets, and not the comet, of 1874 should form the title, strictly speaking, of the present section of our work. Indeed, at the time of adding these lines to this chapter– that is to say, in the last few days of the month of August of this year [1874]–five new comets have been discovered and observed. But one only, the third in order of date, has attracted the attention of the public, for the simple reason that it alone became bright enough during the time of its apparition to be visible to the naked eye. The other four continued to remain telescopic comets, accessible only to professional astronomers. Although its visibility in Europe was of brief duration, the comet of 1874, III., or comet of Coggia, presented in its physical aspect, and in the changes of form in its head and tail, sufficiently curious phenomena to merit special mention and some detailed description.

Apparent and real dimensions of the largest tails on record–Formation and development of cometary appendages; their disappearance–Variations of length in the tail of Halley's comet at its different apparitions–Great comet of 1858, or comet of Donati.

Since we have entered upon the statistics of various cometary elements, let us here give a few particulars respecting the real and apparent dimensions of cometary tails. We will first confine ourselves to the maximum dimensions under which they have been viewed from the earth, dimensions measured in degrees, according to the apparent extent occupied by the train itself in the celestial vault. Passing, then, from the apparent lengths, we will proceed to the actual measures expressed in miles. Under the first head the scale of magnitude will be found to include an enormous range, varying from the tail of 2½°, belonging to the comet of 1851, to the immense tail of 100°, possessed by the comet of 1264, and to the still greater tail of the comet of 1861, which attained a length of 118°, thus exceeding by 28° the apparent distance between the horizon and the zenith. Nor are the differences less considerable when we compare the true dimensions.

Distinction between cometa, nebulæ, and temporary stars–Comets, in their motions, are subject to stationary periods and retrogressions–The apparent complications arise, as in the case of the planets, from the simultaneous movement of these bodies and the earth.

There is nothing in the foregoing section to distinguish comets from the multitude of brilliant stars which nightly illuminate the azure vault of heaven. Comets, it is true, appear in regions where before they had not been visible, and after a time they disappear; but in this respect they resemble those remarkable stars which have been seen to shine out suddenly in the midst of a constellation, to increase in brilliancy for a time, and afterwards to become faint and disappear; such as the famous temporary stars of 1572 (the Pilgrim), 1604, 1670, and 1866, which appeared and became extinct in the constellations of Cassiopeia, Serpens, Vulpecula, and Corona Borealis respectively. These stars, however, have, without exception, been distinguished by this peculiarity, that from the first to the last day of their apparition they continued immovable in the spot where they first appeared; or, more correctly, that their only motion was that due to the diurnal revolution of the heavens. Situated, like the fixed stars, at immense distances from our system, they had no appreciable movement of their own during the whole time of their visibility–in some instances of considerable duration. The same is true of the nebulæ, which are distinguished from comets by the fact of their immobility.

Is this penetration physically possible?–Oometary influences, according to Dr. Foxster –Were the dry fogs of 1783,1831, and 1834, due to the tails of comets?–Volcanic phenomena and burning turf-beds; their probable coincidence with fogs–Probable hypothesis of Franklin–Dry fogs, atmospheric duat, and bolides.

We perceive, then, that the influence of comets upon living beings by the action of heat is a hypothesis which, for the present, must be abandoned ; in so far, at least, as the action of heat by radiation from a distance is concerned. We have throughout reserved the questions of a collision between the two bodies, and of the penetration of the earth to the heart of a mass in a state of incandescence.

Apart from the action of calorific radiation, what influence of any other kind could a comet exercise upon the meterological conditions of the earth? We know of absolutely none.

It remains, then, to consider the immediate physical or chemical influence of the cometary substance. It is not forbidden to our globe, as we have seen, to traverse the gigantic trains which form the tails of certain comets, nor to penetrate to a certain depth the vaporous atmosphere of some amongst them. Apart from these rencontres, we may suppose that cometary matter may be introduced into our atmosphere by the power of attraction.

Researches of M. E. Roche upon the form and equilibrium of the atmospheres of celestial bodies under the combined influence of gravitation, solar heat, and a repulsive force–Figure of equilibrium of a solid mass submitted to gravitation and the heat of the sun–Comets should have two opposite tails–Completion of the theory of cometary tides by the admission of a repulsive force, real or apparent–Accordance of the theory so completed with observation.

M. Edouard Roche has devoted a series of highly interesting memoirs to the discussion of the figure assumed by the atmosphere of celestial bodies under the action of the forces of the solar system. He has more particularly given his attention to the study of cometary atmospheres, and to all the phenomena which take place in and around cometary masses.

M. Roche begins by reducing the question to its simplest form. He assimilates a comet to ‘ an entirely fluid mass, sensibly homogeneous, and having no movement of rotation. ’ The forces which act upon it are the mutual attraction of its own particles and gravitation towards the sun. For such a mass to be in equilibrium under the action of these forces it must have the figure of a prolate spheroid with its centre at the centre of gravity, and its axis of revolution coincident with the radius vector from the sun.

Hypothesis of Maupertuis : the planetary satellites originally comets, which have been retained by the attractions of the planets–The Arcadians and the moon–Refutation of this hypothesis by Dionys du Séjour.

In the same spirit of speculative enquiry, it has likewise been asked if the moon is not an ancient comet which the earth has diverted from its orbit about the sun, and forced to gravitate about itself. ‘ Not only, ’ says Maupertuis, ‘might a comet carry away our moon, but it might itself become our satellite, and be condemned to perform its revolutions about our earth and illuminate our nights. Our moon might have been originally a small comet which, in consequence of having too nearly approached the earth, has been made captive by it. Jupiter and Saturn, bodies much larger than the earth, and whose power extends to a greater distance, and over larger comets, would be more liable than the earth to make such acquisitions ; consequently Jupiter has four moons revolving about him, and Saturn five. ’

Upon what foundation, upon what serious reasoning has Maupertuis erected this ingenious hypothesis? He does not tell us. Pingré, who records it, observes that the partisans of this opinion based it upon an ancient tradition mentioned by Ovid and Lucian.