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.

Visibility of stars through the atmospheres and tails of cornets; ancient and modern observations upon this point– Are the nuclei of cornets opaque, or transparent like the atmospheres and tails?–Reported eclipses of the sun and moon produced by comets.

The visibility of stars, even of very small ones, through the comæ and tails of comets is a fact which had been observed by the ancients. Aristotle in his meteorology mentions the stars seen by Democritus notwithstanding the interposition of a comet. Seneca says likewise, in his Quæstiones Naturales, ‘that we may see stars through a comet as through a cloud;’ and further on, ‘the stars are not transparent, and we can see them through comets– not through the body of the comet where the flame is dense and solid, but through the thin and scattered rays which form the hair; it is through the intervals of the fire, not through the fire itself, that you see.’ Humboldt, in quoting this last passage, ‘per intervalla ignium, non per ipsos vides,’ adds:‘This last remark was unnecessary, for it is possible to see through a flame the thickness of which is not too great.’ This is true ; but Seneca has merely recorded the fact that up to his time stars had been seen behind the tail or coma, not behind the nucleus itself. The want of the telescope did not, in fact, permit the ancients to distinguish the body or nucleus of a comet, even when the comet had a nucleus.

Conditions of temperature to which the earth would he suhjected if it were compelled by a comet to descrihe the same orbit as the latter–The comets of Halley, and of 1680, examined from this point of view–Extremes of heat and cold: opinion of Arago : impossibility of living beings resisting such changes.

Arago has examined, in an indirect manner, the question of the habitability of comets; that is to say, he has considered how far the enormous distances through which a body passes in describing a very eccentric orbit around the sun, such as that of a cornetary orbit, are compatible with the existence of inhabitants similar to man. Could the earth, he enquires, ever become the satellite of a comet, and, if so, what would be the fate of its inhabitants?

Arago, basing his reasoning upon the comparative smallness of the masses of comets, regards the transformation of the earth into the satellite of a comet, as an event ‘ within the bounds of possibility, but which is very improbable, ’ an opinion no one at the present day will be inclined to dispute. He next supposes our earth successively made tributary to the comet of Halley and to that of 1680, and proceeds to consider the conditions of temperature to which our globe would be subjected whilst travelling in company with each.

With the comet of Halley our year would be sixty-five times longer than at present.

The masses of Encke's comet and the comet of Taurus determined by M. Babinet– Objections to this method of determination.

We have thus a determination of cometary masses deduced from the reciprocal disturbances exercised by comets and the planets on one another. It shows that comets have extremely small masses, since, greatly disturbed themselves in their course when they approach a planet, they appear never to have exercised any disturbing influence upon the movements of the planet itself. But, from the value found for the mass of Lexell's comet–a value which, however, is only a maximum limit–it may be seen how far a comet is from being considered a visible nonentity (rien visible), to make use of the forcible expression of M. Babinet. The 5,000th part of the mass of the terrestrial globe is equivalent to the sixtieth part of the mass of the moon, a quantity, it will be agreed, far from negligible.

For the justification of his expression M. Babinet has relied upon the following optical considerations. He has called attention to the known fact that stars of exceedingly faint light may be seen through cometary nebulosities without their light losing any of its intensity.

Discovery of the comet of five years and a half period by Brorsen in 1846–Its supposed identity with the comet of 1532 gives reason to suspect elliptic elements; calculation of these elements–Returns of the comet in 1851, 1868, and 1873

In the order of their discovery we proceed to pass in review the periodical comets of the solar system–those at least whose return has been confirmed by observation, and which have justified the predictions of calculation

This brings us to a comet which likewise bears the name of the astronomer who discovered it, at Kiel, on February 26, 1846, viz. to Brorsen's comet, whose period is intermediate to those of Encke and Faye. It performs its revolution round the sun in five years and a half, or, more exactly, in five years 176 days, or 2,002 days

As soon as the parabolic elements of the new comet were calculated, two astronomers, Goujon and Petersen, suspected its identity with a comet observed in 1532, and were thus led to the calculation of an elliptic orbit; this orbit was actually determined by Goujon, by Brünnow, and later by Bruhns. The return was predicted for 1851, and the perihelion passage for November 10 of that year.

Theory of M. Faye–Rigorous definition of the repulsion inherent in the solar rays– Its intensity varies with the surfaces of the two bodies; it decreases inversely as the square of the distance–It is not propagated instantaneously–Discussion and accordance of the facts–Experiments in support of a repulsive force.

It was at the suggestion of M. Faye, as we have seen, that M. Roche introduced into his analytical researches upon cometary phenomena the hypothesis of a repulsive force which has, in fact, led to results more in conformity with what is observed. It should be remarked, however, that M. Roche has considered the matter rather from the point of view of a mathematician than of a physical astronomer; whilst, on the contrary, the physical bearing of the problem has more especially occupied the attention of M. Faye. This astronomer, after passing in review the different theories we have mentioned, and rigorously comparing their conclusions with the facts of recorded observations, in short, after the most exhaustive discussion, has finally decided in favour of an actual repulsive force inherent in the solar rays. This is the base of the theory known as Kepler's theory, and which has been distinguished by the adhesion of Euler and Laplace.

At the time when M. Faye made known his views, two great comets–that of Donati (1858) and that of 1861–had recently appeared.

Double tails of comets; comets of 1823, 1850, and 1851–Tails multiple, fan-shaped, rectilinear, curved–Variable number of tails belonging to the same comet; comets of Donati, of 1861 and of Chéseaux.

Generally a comet has but one tail, which varies considerably in form or size, or, at all events, appears to do so. Sometimes these changes take place very rapidly, but still, as a rule, the tail consists of one luminous train. Nevertheless, examples may be adduced of double and even multiple tails. The comets of 1807 and 1843 were furnished with double tails, or, what comes to the same thing, single tails formed of two branches of very unequal length. It was the same with the comet of 1823, about which Arago gives the following details:–

‘On the 23rd of January, 1824, the comet, in addition to its ordinary tail opposite to the sun, had another which was directed towards the sun, so that it resembled somewhat the great nebula of Andromeda. The first tail appeared to include a space of about 5°, but the length of the second was scarcely 4°. Their axes formed between them a very obtuse angle of nearly 180° (fig. 25). In the close vicinity of the comet the new tail was hardly to be seen. Its maximum brightness occurred at a distance of 2° from the nucleus. During the first few days in February the tail opposite to the sun wasalone visible ; the other had disappeared, or had become sofaint that the best telescopes in the clearest weather failed toshow any trace of it.’

Theory of the formation and development of cometary atmospheres under the influence of gravitation and a repulsive force–Calculations of M. Edouard Roche– Masses of the comets of Donati and Encke as determined by this method.

We are now about to see the same question, when investigated by another method, lead to results quite different to those of M. Babinet. Between the opinions–entirely conjectural, be it observed–of the savants of the eighteenth century who held that comets were bodies dense and massive as the planets, and those of some contemporary astronomers who regard them as visible nonentities, there is room for a determination which is removed from both extremes, and is moreover better justified.

For this method of determination we are indebted to M. Edouard Roche, professor in the Faculty of Sciences at Montpellier. In a series of very remarkable researches into the theory of cometary phenomena, which we shall analyse further on, M. Roche shows that there is a determinate relation between the distance of the comet from the sun, its mass, and the diameter of the portion of its nebulosity subject to the attraction of the nucleus, otherwise called the diameter of its true atmosphere. This relation holds at distances so remote from the sun that the repulsive force, either apparent or real which engenders the tail may be neglected.

We have seen what the telescope has taught us of the structure of comets, so complex and wonderfully mobile, so different in this respect from that of the planets or the sun. On the one hand we see solid or liquid bodies, bearing the most striking analogy to the terrestrial globe, surrounded like it by atmospheres of comparatively small extent, stable in every portion ; these are the planets, the moon, and the satellites of the planets. As regards the sun and the stars–which shine, like the sun, by their own light, and are, like him, as everything leads us to suppose, foci of light and heat to other planetary groups–if these bodies are incandescent gaseous masses, their condensation is so enormous and their physical constitution is comparatively so stable, that the changes of which they are perpetually the theatre have no appreciable effect upon their equilibrium. In comparison with comets they are permanent stars ; while comets seem to be nothing more than clouds–wandering nebulae, to employ the expression of Laplace, who has but reproduced in a more happy form the term so happily applied by Xenophanes and Theon of Alexandria.

RETROSPECTION.

As we close the record of Miss Herschel's residence in England, we may pause for a moment to look back over the space she had traversed while following, with unvarying diligence and humility, the path her brother marked out for her, first in blessed hourly companionship, when she was as necessary in his home as in his library, or among his instruments; and latterly, when with saddened heart but unflagging determination she continued to work for him, but saw his domestic happiness pass into other keeping.

While they toiled together through those first ten years of ever-deepening interest and marvellous activity, during which the rapid juxtaposition of mirror-grinding, concerts, oratorios, music lessons, and frequent papers written for philosophical societies, almost takes the breath away as we read,—the brother had “abundant opportunity of learning how far he could trust to his companion's readiness, as well as capability, to accept of duties as utterly remote from all that her previous life had prepared her for as if he had asked her to accompany him on a pilgrimage to Mecca. And thus, of all of whom he had made trial, it was not the brilliant Jacob, nor the gifted Alexander, but the little quiet, home-bred Caroline, of whom nothing had been expected but to be up early and to do the work of the house, and to devote her leisure to knitting and sewing, in whom he found that steady devotion to a fixed purpose which he felt it was possible to link with his own.

Familiar to all as is the name this volume bears, it is not without hesitation that the following pages are given to the world. To subject the memorials of a deeply earnest life to the eyes of a generation overcrowded with books, raises a certain amount of diffidence.

Of Caroline Herschel herself most people will plead ignorance without feeling ashamed, and yet may we not assert that Caroline Herschel is well worth knowing.

Great men and great causes have always some helper of whom the outside world knows but little. There always is, and always has been, some human being in whose life their roots have been nourished. Sometimes these helpers have been men, sometimes they have been women, who have given themselves to help and to strengthen those called upon to be leaders and workers, inspiring them with courage, keeping faith in their own idea alive, in days of darkness,

These helpers and sustainers, men or women, have all the same quality in common—absolute devotion and unwavering faith in the individual or in the cause. Seeking nothing for themselves, thinking nothing of themselves, they have all an intense power of sympathy, a noble love of giving themselves for the service of others, which enables them to transfuse the force of their own personality into the object to which they dedicate their powers.