Chapter 23

Herschel applied some of his fine instruments to the study of the physical constitution of a comet discovered by Mr. Pigott, on the 28th September, 1807.

The nucleus was round and well determined. Some measures taken on the day when the nucleus subtended only an angle of a single second, gave as its real angle 6/100 of the diameter of the earth.

Herschel saw no phase at an epoch when only 7/10 of the nucleus could be illuminated by the sun. The nucleus then must shine by its own light.

This is a legitimate inference in the opinion of every one who will allow, on one hand, that the nucleus is a solid body, and on the other, that it would have been possible to observe a phase of 8/10 on a disk whose apparent total diameter did not exceed one or two seconds of a degree.

Very small stars seemed to grow much paler when they were seen through the coma or through the tail of the comet.

This faintness may have only been apparent, and might arise from the circumstance of the stars being then projected on a luminous background. Such is, indeed, the explanation adopted by Herschel. A gaseous medium, capable of reflecting sufficient solar light to efface that of some stars, would appear to him to possess in each stratum a sensible quantity of matter, and to be, for that reason, a cause of real diminution of the light transmitted, though nothing reveals the existence of such a cause.

This argument, offered by Herschel in favour of the system which transforms comets into self-luminous bodies, has not, as we may perceive, much force. I might venture to say as much of many other remarks by this great observer. He tells us that the comet was very visible in the telescope on the 21st of February, 1808; now, on that day, its distance from the sun amounted to 2.7 times the mean radius of the terrestrial orbit; its distance from the observer was 2.9: "What probability would there be that rays going to such distances, from the sun to the comet, could, after their reflection, be seen by an eye nearly three times more distant from the comet than from the sun?"

It is only numerical determinations that could give value to such an argument. By satisfying himself with vague reasoning, Herschel did not even perceive that he was committing a great mistake by making the comet's distance from the observer appear to be an element of visibility. If the comet be self-luminous, its intrinsic splendour (its brightness for unity of surface) will remain constant at any distance, as long as the subtended angle remains sensible. If the body shines by borrowed light, its brightness will vary only according to its change of distance from the sun; nor will the distance of the observer occasion any change in the visibility; always, let it be understood, with the restriction that the apparent diameter shall not be diminished below certain limits.

Herschel finished his observations of a comet that was visible in January, 1807, with the following remark:--

"Of the sixteen telescopic comets that I have examined, fourteen had no solid body visible at their centre; the other two exhibited a central light, very ill defined, that might be termed a nucleus, but a light that certainly could not deserve the name of a disk."

The beautiful comet of 1811 became the object of that celebrated astronomer's conscientious labour. Large telescopes showed him, in the midst of the gazeous head, a rather reddish body of planetary appearance, which bore strong magnifying powers, and showed no sign of phase. Hence Herschel concluded that it was self-luminous. Yet if we reflect that the planetary body under consideration was not a second in diameter, the absence of a phase does not appear a demonstrative argument.

The light of the head had a blueish-green tint. Was this a real tint, or did the central reddish body, only through contrast, make the surrounding vapour appear to be coloured? Herschel did not examine the question in this point of view.

The head of the comet appeared to be enveloped at a certain distance, on the side towards the sun, by a brilliant narrow zone, embracing about a semicircle, and of a yellowish colour. From the two extremities of the semicircle there arose, towards the region away from the sun, two long luminous streaks which limited the tail. Between the brilliant circular semi-ring and the head, the cometary substance seemed dark, very rare, and very diaphanous.

The luminous semi-ring always presented similar appearances in all the positions of the comet; it was not then possible to attribute to it really the annular form, the shape of Saturn's ring, for example. Herschel sought whether a spherical demi-envelop of luminous matter, and yet diaphanous, would not lead to a natural explanation of the phenomenon. In this hypothesis, the visual rays, which on the 6th of October, 1811, made a section of the envelop, or bore almost tangentially, traversed a thickness of matter of about 399,000 kilometres, (248,000 English miles,) whilst the visual rays near the head of the comet did not meet above 80,000 kilometres (50,000 miles) of it. As the brightness must be proportional to the quantity of matter traversed, there could not fail to be an appearance around the comet, of a semi-ring five times more luminous than the central regions. This semi-ring, then, was an effect of projection, and it has revealed a circumstance to us truly remarkable in the physical constitution of comets.

The two luminous streaks that outlined the tail at its two limits, may be explained in a similar manner; the tail was not flat as it appeared to be; it had the form of a conoid, with its sides of a certain thickness. The visual lines which traversed those sides almost tangentially, evidently met much more matter than the visual lines passing across. This maximum of matter could not fail of being represented by a maximum of light.

The luminous semi-ring floated; it appeared one day to be suspended in the diaphanous atmosphere by which the head of the comet was surrounded, at a distance of 518,000 kilometres (322,000 English miles) from the nucleus.

This distance was not constant. The matter of the semi-annular envelop seemed even to be precipitated by slow degrees through the diaphanous atmosphere; finally it reached the nucleus; the earlier appearances vanished; the comet was reduced to a globular nebula.

During its period of dissolution, the ring appeared sometimes to have several branches.

The luminous shreds of the tail seemed to undergo rapid, frequent, and considerable variations of length. Herschel discerned symptoms of a movement of rotation both in the comet and in its tail. This rotatory motion carried unequal shreds from the centre towards the border, and reciprocally. On looking from time to time at the same region of the tail, at the border, for example, sensible changes of length must have been perceptible, which however had no reality in them. Herschel thought, as I have already said, that the beautiful comet of 1811, and that of 1807, were self-luminous. The second comet of 1811 appeared to him to shine only by borrowed light. It must be acknowledged that these conjectures did not rest on any thing demonstrative.

In attentively comparing the comet of 1807 with the beautiful comet of 1811, relative to the changes of distance from the sun, and the modifications resulting thence, Herschel put it beyond doubt that these modifications have something individual in them, something relative to a special state of the nebulous matter. On one celestial body the changes of distance produce an enormous effect, on another the modifications are insignificant.

OPTICAL LABOURS.

I shall say very little on the discoveries that Herschel made in physics. In short, everybody knows them. They have been inserted into special treatises, into elementary works, into verbal instruction; they must be considered as the starting-point of a multitude of important labours with which the sciences have been enriched during several years.

The chief of these is that of the dark radiating heat which is found mixed with light.

In studying the phenomena, no longer with the eye, like Newton, but with a thermometer, Herschel discovered that the solar spectrum is prolonged on the red side far beyond the visible limits. The thermometer sometimes rose higher in that dark region, than in the midst of brilliant zones. The light of the sun then, contains, besides the coloured rays so well characterized by Newton, some invisible rays, still less refrangible than the red, and whose warming power is very considerable. A world of discoveries has arisen from this fundamental fact.

The dark heat emanating from terrestrial objects more or less heated, became also subjects of Herschel's investigations. His work contained the germs of a good number of beautiful experiments since erected upon it in our own day.

By successively placing the same objects in all parts of the solar spectrum Herschel determined the illuminating powers of the various prismatic rays. The general result of these experiments may be thus enunciated:

The illuminating power of the red rays is not very great; that of the orange rays surpasses it, and is in its turn surpassed by the power of the yellow rays. The maximum power of illumination is found between the brightest yellow and the palest green. The yellow and the green possess this power equally. A like assimilation may be laid down between the blue and the red. Finally, the power of illumination in the indigo rays, and above all in the violet, is very weak.

Yet the memoirs of Herschel on Newton's coloured rings, though containing a multitude of exact experiments, have not much contributed to advance the theory of those curious phenomena. I have learnt from good authority, that the great astronomer held the same opinion on this topic. He said that it was the only occasion on which he had reason to regret having, according to his constant method, published his labours immediately, as fast as they were performed.

LAPLACE.

Having been appointed to draw up the report of a committee of the Chamber of Deputies which was nominated in 1842, for the purpose of taking into consideration the expediency of a proposal submitted to the Chamber by the Minister of Public Instruction, relative to the publication of a new edition of the works of Laplace at the public expense, I deemed it to be my duty to embody in the report a concise analysis of the works of our illustrious countryman. Several persons, influenced, perhaps, by too indulgent a feeling towards me, having expressed a wish that this analysis should not remain buried amid a heap of legislative documents, but that it should be published in the _Annuaire du Bureau des Longitudes_, I took advantage of this circumstance to develop it more fully so as to render it less unworthy of public attention. The scientific part of the report presented to the Chamber of Deputies will be found here entire. It has been considered desirable to suppress the remainder. I shall merely retain a few sentences containing an explanation of the object of the proposed law, and an announcement of the resolutions which were adopted by the three powers of the State.

"Laplace has endowed France, Europe, the scientific world, with three magnificent compositions: the _Traité de Mécanique Céleste_, the _Exposition du Système du Monde_, and the _Théorie Analytique des Probabilités_. In the present day (1842) there is no longer to be found a single copy of this last work at any bookseller's establishment in Paris. The edition of the _Mécanique Céleste_ itself will soon be exhausted. It was painful then to reflect that the time was close at hand when persons engaged in the study of the higher mathematics would be compelled, for want of the original work, to inquire at Philadelphia, at New York, or at Boston for the English translation of the _chef d'oeuvre_ of our countryman by the excellent geometer Bowditch. These fears, let us hasten to state, were not well founded. To republish the _Mécanique Céleste_ was, on the part of the family of the illustrious geometer, to perform a pious duty. Accordingly, Madame de Laplace, who is so justly, so profoundly attentive to every circumstance calculated to enhance the renown of the name which she bears, did not hesitate about pecuniary considerations. A small property near Pont l'Evêque was about to change hands, and the proceeds were to have been applied so that Frenchmen should not be deprived of the satisfaction of exploring the treasures of the _Mécanique Céleste_ through the medium of the vernacular tongue.

"The republication of the complete works of Laplace rested upon an equally sure guarantee. Yielding at once to filial affection, to a noble feeling of patriotism, and to the enthusiasm for brilliant discoveries which a course of severe study inspired, General Laplace had long since qualified himself for becoming the editor of the seven volumes which are destined to immortalize his father.

"There are glorious achievements of a character too elevated, of a lustre too splendid, that they should continue to exist as objects of private property. Upon the State devolves the duty of preserving them from indifference and oblivion: of continually holding them up to attention, of diffusing a knowledge of them through a thousand channels; in a word, of rendering them subservient to the public interests.

"Doubtless the Minister of Public Instruction was influenced by these considerations, when upon the occasion of a new edition of the works of Laplace having become necessary, he demanded of you to substitute the great French family for the personal family of the illustrious geometer. We give our full and unreserved adhesion to this proposition. It springs from a feeling of patriotism which will not be gainsayed by any one in this assembly."

In fact, the Chamber of Deputies had only to examine and solve this single question: "Are the works of Laplace of such transcendent, such exceptional merit, that their republication ought to form the subject of deliberation of the great powers of the State?" An opinion prevailed, that it was not enough merely to appeal to public notoriety, but that it was necessary to give an exact analysis of the brilliant discoveries of Laplace in order to exhibit more fully the importance of the resolution about to be adopted. Who could hereafter propose on any similar occasion that the Chamber should declare itself without discussion, when a desire was felt, previous to voting in favour of a resolution so honourable to the memory of a great man, to fathom, to measure, to examine minutely and from every point of view monuments such as the _Mécanique Céleste_ and the _Exposition du Système du Monde_? It has appeared to me that the report drawn up in the name of a committee of one of the three great powers of the State might worthily close this series of biographical notices of eminent astronomers.[22]

The Marquis de Laplace, peer of France, one of the forty of the French Academy, member of the Academy of Sciences and of the _Bureau des Longitudes_, an associate of all the great Academies or Scientific Societies of Europe, was born at Beaumont-en-Auge of parents belonging to the class of small farmers, on the 28th of March, 1749; he died on the 5th of March, 1827.

The first and second volumes of the _Mécanique Céleste_ were published in 1799; the third volume appeared in 1802, the fourth volume in 1805; as regards the fifth volume, Books XI. and XII. were published in 1823, Books XIII. XIV. and XV. in 1824, and Book XVI. in 1825. The _Théorie des Probabilités_ was published in 1812. We shall now present the reader with the history of the principal astronomical discoveries contained hi these immortal works.

Astronomy is the science of which the human mind may most justly boast. It owes this indisputable preëminence to the elevated nature of its object, to the grandeur of its means of investigation, to the certainty, the utility, and the unparalleled magnificence of its results.

From the earliest period of the social existence of mankind, the study of the movements of the heavenly bodies has attracted the attention of governments and peoples. To several great captains, illustrious statesmen, philosophers, and eminent orators of Greece and Rome it formed a subject of delight. Yet, let us be permitted to state, astronomy truly worthy of the name is quite a modern science. It dates only from the sixteenth century.

Three great, three brilliant phases, have marked its progress.

In 1543 Copernicus overthrew with a firm and bold hand, the greater part of the antique and venerable scaffolding with which the illusions of the senses and the pride of successive generations had filled the universe. The earth ceased to be the centre, the pivot of the celestial movements; it henceforward modestly ranged itself among the planets; its material importance, amid the totality of the bodies of which our solar system is composed, found itself reduced almost to that of a grain of sand.

Twenty-eight years had elapsed from the day when the Canon of Thorn expired while holding in his faltering hands the first copy of the work which was to diffuse so bright and pure a flood of glory upon Poland, when Würtemberg witnessed the birth of a man who was destined to achieve a revolution in science not less fertile in consequences, and still more difficult of execution. This man was Kepler. Endowed with two qualities which seemed incompatible with each other, a volcanic imagination, and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expressions, by _harmonic_ laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely towards the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labour to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of any one, "The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his works?"[23]

To investigate a physical cause capable of making the planets revolve in closed curves; to place the principle of the stability of the universe in mechanical forces and not in solid supports such as the spheres of crystal which our ancestors had dreamed of; to extend to the revolutions of the heavenly bodies the general principles of the mechanics of terrestrial bodies,--such were the questions which remained to be solved after Kepler had announced his discoveries to the world.

Very distinct traces of these great problems are perceived here and there among the ancients as well as the moderns, from Lucretius and Plutarch down to Kepler, Bouillaud, and Borelli. It is to Newton, however, that we must award the merit of their solution. This great man, like several of his predecessors, conceived the celestial bodies to have a tendency to approach towards each other in virtue of an attractive force, deduced the mathematical characteristics of this force from the laws of Kepler, extended it to all the material molecules of the solar system, and developed his brilliant discovery in a work which, even in the present day, is regarded as the most eminent production of the human intellect.

The heart aches when, upon studying the history of the sciences, we perceive so magnificent an intellectual movement effected without the coöperation of France. Practical astronomy increased our inferiority. The means of investigation were at first inconsiderately entrusted to foreigners, to the prejudice of Frenchmen abounding in intelligence and zeal. Subsequently, intellects of a superior order struggled with courage, but in vain, against the unskilfulness of our artists. During this period, Bradley, more fortunate on the other side of the Channel, immortalized himself by the discovery of aberration and nutation.

The contribution of France to these admirable revolutions in astronomical science, consisted, in 1740, of the experimental determination of the spheroidal figure of the earth, and of the discovery of the variation of gravity upon the surface of our planet. These were two great results; our country, however, had a right to demand more: when France is not in the first rank she has lost her place.[24]

This rank, which was lost for a moment, was brilliantly regained, an achievement for which we are indebted to four geometers.

When Newton, giving to his discoveries a generality which the laws of Kepler did not imply, imagined that the different planets were not only attracted by the sun, but that they also attract each other, he introduced into the heavens a cause of universal disturbance. Astronomers could then see at the first glance that in no part of the universe whether near or distant would the Keplerian laws suffice for the exact representation of the phenomena; that the simple, regular movements with which the imaginations of the ancients were pleased to endue the heavenly bodies would experience numerous, considerable, perpetually changing perturbations.

To discover several of these perturbations, to assign their nature, and in a few rare cases their numerical values, such was the object which Newton proposed to himself in writing the _Principia Mathematica Philosophiæ Naturalis_.

Notwithstanding the incomparable sagacity of its author the Principia contained merely a rough outline of the planetary perturbations. If this sublime sketch did not become a complete portrait we must not attribute the circumstance to any want of ardour or perseverance; the efforts of the great philosopher were always superhuman, the questions which he did not solve were incapable of solution in his time. When the mathematicians of the continent entered upon the same career, when they wished to establish the Newtonian system upon an incontrovertible basis, and to improve the tables of astronomy, they actually found in their way difficulties which the genius of Newton had failed to surmount.

Five geometers, Clairaut, Euler, D'Alembert, Lagrange, and Laplace, shared between them the world of which Newton had disclosed the existence. They explored it in all directions, penetrated into regions which had been supposed inaccessible, pointed out there a multitude of phenomena which observation had not yet detected; finally, and it is this which constitutes their imperishable glory, they reduced under the domain of a single principle, a single law, every thing that was most refined and mysterious in the celestial movements. Geometry had thus the boldness to dispose of the future; the evolutions of ages are scrupulously ratifying the decisions of science.

We shall not occupy our attention with the magnificent labours of Euler, we shall, on the contrary, present the reader with a rapid analysis of the discoveries of his four rivals, our countrymen.[25]

If a celestial body, the moon, for example, gravitated solely towards the centre of the earth, it would describe a mathematical ellipse; it would strictly obey the laws of Kepler, or, which is the same thing, the principles of mechanics expounded by Newton in the first sections of his immortal work.