FOOTNOTES:

FOOTNOTES:[18]Conforming to general usage, and to Sir W. Herschel himself, we shall allude to this instrument as theforty-foottelescope, though M. Arago adheres to thirty-nine feet and drops the inches, probably because the Parisian foot is rather longer than the English.â€”Translator's Note.[19]It would be more correct to say four timesas muchlight.â€”Translator.[20]On comparing the Cassegrain telescopes with a small convex mirror, to the Gregorian telescopes with a small concave mirror, Captain Kater found that the former, in which the luminous rays do not cross each other before falling on the small mirror, possess, as to intensity, a marked advantage over the latter, in which this crossing takes place.[21]In the selection of Î¹ Bootis as a test, Arago has taken the precaution of giving its corresponding denomination in other catalogues, and Bailey appends the following note, No. 2062, to 44 Bootis. "In the British Catalogue this star is not denoted by any letter: but Bayer calls it Î¹, and on referring to the earliest MS. Catalogue in MSS. vol. xxv., I find it is there so designated; I have therefore restored the letter." (See Bailey's Edition of Flamsteed's British Catalogue of Stars, 1835.) The distance between the two members of this double star is 3".7 and position 23Â°.5. See "Bedford Cycle."â€”Translator.

[18]Conforming to general usage, and to Sir W. Herschel himself, we shall allude to this instrument as theforty-foottelescope, though M. Arago adheres to thirty-nine feet and drops the inches, probably because the Parisian foot is rather longer than the English.â€”Translator's Note.

[19]It would be more correct to say four timesas muchlight.â€”Translator.

[20]On comparing the Cassegrain telescopes with a small convex mirror, to the Gregorian telescopes with a small concave mirror, Captain Kater found that the former, in which the luminous rays do not cross each other before falling on the small mirror, possess, as to intensity, a marked advantage over the latter, in which this crossing takes place.

[21]In the selection of Î¹ Bootis as a test, Arago has taken the precaution of giving its corresponding denomination in other catalogues, and Bailey appends the following note, No. 2062, to 44 Bootis. "In the British Catalogue this star is not denoted by any letter: but Bayer calls it Î¹, and on referring to the earliest MS. Catalogue in MSS. vol. xxv., I find it is there so designated; I have therefore restored the letter." (See Bailey's Edition of Flamsteed's British Catalogue of Stars, 1835.) The distance between the two members of this double star is 3".7 and position 23Â°.5. See "Bedford Cycle."â€”Translator.

The curious phenomenon of a periodical change of intensity in certain stars, very early excited a keen attention in Herschel. The first memoir by that illustrious observer presented to the Royal Society of London and inserted in thePhilosophical Transactionstreats precisely of the changes of intensity of the staroin the neck of the Whale.

This memoir was still dated from Bath, May, 1780. Eleven years after, in the month of December, 1791, Herschel communicated a second time to that celebrated English Society the remarks that he had made by sometimes directing his telescopes to the mysterious star. At both those epochs the observer's attention was chiefly applied to the absolute values of themaximaandminimaof intensity.

The changeable star in the Whale was not the only periodical star with which Herschel occupied himself. His observations of 1795 and of 1796 proved that Î± Herculis also belongs to the category of variable stars, and that the time requisite for the accomplishment of all the changes of intensity, and for the star's return to any given state, was sixty days and a quarter. When Herschel obtained this result, about ten changeable stars were already known; but they were all either of very long or very short periods. The illustrious astronomer considered that, by introducing between two groups that exhibited very short and very long periods, a star of somewhat intermediate conditions,â€”for instance, one requiring sixty days to accomplish all its variations of intensity,â€”he had advanced the theory of these phenomena by an essential step; the theory at least that attributes every thing to a movement of rotation round their centres which the stars may undergo.

Sir William Herschel's catalogues of double stars offer a considerable number to which he ascribes a decided green or blue tint. In binary combinations, when the small star appears very blue or very green, the large one is usually yellow or red. It does not appear that the great astronomer took sufficient interest in this circumstance. I do not find, indeed, that the almost constant association of two complementary colours (of yellow and blue, or of red and green), ever led him to suspect that one of those colours might not have any thing real in it, that it often might be a mere illusion, a mere result of contrast. It was only in 1825, that I showed that there are stars whose contrast really explains their apparent colour; but I have proved besides, that blue is incontestably the colour of certain insulated stars, or stars that have only white ones, or other blue ones in their vicinity. Red is the only colour that the ancients ever distinguished from white in their catalogues.

Herschel also endeavoured to introduce numbers in the classification of stars as to magnitude; he has endeavoured, by means of numbers, to show the comparative intensity of a star of first magnitude, with one of second, or one of third magnitude, &c.

In one of the earliest of Herschel's memoirs, we find, that the apparent sidereal diameters are proved to be for the greater part factitious, even when the best made telescopes are used. Diameters estimated by seconds, that is to say, reduced according to the magnifying power, diminish as the magnifying power is increased. These results are of the greatest importance.

In the course of his investigation of sidereal parallax, though without finding it, Herschel made an important discovery; that of the proper motion of our system. To show distinctly the direction of the motion of the solar system, not only was a displacement of the sidereal perspective required, but profound mathematical knowledge, and a peculiar tact. This peculiar tact Herschel possessed in an eminent degree. Moreover, the result deduced from the very small number of proper motions known at the beginning of 1783, has been found almost to agree with that found recently by clever astronomers, by the application of subtile analytical formulÃ¦, to a considerable number of exact observations.

The proper motions of the stars have been known and proved for more than a century, and already Fontenelle used to say in 1738, that the sun probably also moved in a similar way. The idea of partly attributing the displacement of the stars to a motion of the sun, had suggested itself to Bradley and to Mayer. And Lambert especially had been very explicit on the subject. Until then, however, there were only conjectures and mere probabilities. Herschel passed those limits. He himself proved that the sun positively moves; and that, in this respect also, that immense and dazzling body must be ranged among the stars; that the apparently inextricable irregularities of numerous sidereal proper motions arise in great measure from the displacement of the solar system; that, in short, the point of space towards which we are annually advancing, is situated in the constellation of Hercules.

These are magnificent results. The discovery of the proper motion of our system will always be accounted among Herschel's highest claims to glory, even after the mention that my duty as historian has obliged me to make of the anterior conjectures by Fontenelle, by Bradley, by Mayer, and by Lambert.

By the side of this great discovery we should place another, that seems likely to expand in future. The results which it allows us to hope for will be of extreme importance. The discovery here alluded to was announced to the learned world in 1803; it is that of the reciprocal dependence of several stars, connected the one with the other, as the several planets and their satellites of our system are with the sun.

Let us to these immortal labours add the ingenious ideas that we owe to Herschel on the nebulÃ¦, on the constitution of the Milky-way, on the universe as a whole; ideas which almost by themselves constitute the actual history of the formation of the worlds, and we cannot but have a deep reverence for that powerful genius that has scarcely ever erred, notwithstanding an ardent imagination.

Herschel occupied himself very much with the sun, but only relative to its physical constitution. The observations that the illustrious astronomer made on this subject, the consequences that he deduced from them, equal the most ingenious discoveries for which the sciences are indebted to him.

In his important memoir in 1795, the great astronomer declares himself convinced that the substance by the intermediation of which the sun shines, cannot be either a liquid, or an elastic fluid. It must be analogous to our clouds, and float in the transparent atmosphere of that body. The sun has, according to him, two atmospheres, endowed with motions quite independent of each other. An elastic fluid of an unknown nature is being constantly formed on the dark surface of the sun, and rising up on account of its specific lightness, it forms theporesin the stratum of reflecting clouds; then, combining with other gases, it produces the wrinkles in the region of luminous clouds. When the ascending currents are powerful, they give rise to thenuclei, to thepenumbrÃ¦, to thefaculÃ¦. If this explanation of the formation of solar spots is well founded, we must expect to find that the sun does not constantly emit similar quantities of light and heat. Recent observations have verified this conclusion. But large nuclei, large penumbrÃ¦, wrinkles, faculÃ¦, do they indicate an abundant luminous and calorific emission, as Herschel thought; that would be the result of his hypothesis on the existence of very active ascending currents, but direct experience seems to contradict it.

The following is the way in which a learned man, Sir David Brewster, appreciates this view of Herschel's: "It is not conceivable that luminous clouds, ceding to the lightest impulses and in a state of constant change, can be the source of the sun's devouring flame and of the dazzling light which it emits; nor can we admit besides, that the feeble barrier formed by planetary clouds would shelter the objects that it might cover, from the destructive effects of the superior elements."

Sir D. Brewster imagines that the non-luminous rays of caloric, which form a constituent part of the solar light, are emitted by the dark nucleus of the sun; whilst the visible coloured rays proceed from the luminous matter by which the nucleus is surrounded. "From thence," he says, "proceeds the reason of light and heat always appearing in a state of combination: the one emanation cannot be obtained without the other. With this hypothesis we should explain naturally why it is hottest when there are most spots, because the heat of the nucleus would then reach us without having been weakened by the atmosphere that it usually has to traverse." But it is far from being an ascertained fact, that we experience increased heat during the apparition of solar spots; the inverse phenomenon is more probably true.

Herschel occupied himself also with the physical constitution of the moon. In 1780, he sought to measure the height of our satellite's mountains. The conclusion that he drew from his observations was, that few of the lunar mountains exceed 800 metres (or 2600 feet). More recent selenographic studies differ from this conclusion. There is reason to observe on this occasion how much the result surmised by Herschel differs from any tendency to the extraordinary or the gigantic, that has been so unjustly assigned as the characteristic of the illustrious astronomer.

At the close of 1787, Herschel presented a memoir to the Royal Society, the title of which must have made a strong impression on people's imaginations. The author therein relates that on the 19th of April, 1787, he had observed in the non-illuminated part of the moon, that is, in the then dark portion, three volcanoes in a state of ignition. Two of these volcanoes appeared to be on the decline, the other appeared to be active. Such was then Herschel's conviction of the reality of the phenomenon, that the next morning he wrote thus of his first observation: "The volcano burns with more violence than last night." The real diameter of the volcanic light was 5000 metres (16,400 English feet). Its intensity appeared very superior to that of the nucleus of a comet then in apparition. The observer added: "The objects situated near the crater are feebly illuminated by the light that emanates from it." Herschel concludes thus: "In short, this eruption very much resembles the one I witnessed on the 4th of May, 1783."

How happens it, after such exact observations, that few astronomers now admit the existence of active volcanoes in the moon? I will explain this singularity in a few words.

The various parts of our satellite are not all equally reflecting. Here, it may depend on the form, elsewhere, on the nature of the materials. Those persons who have examined the moon with telescopes, know how very considerable the difference arising from these two causes may be, how much brighter one point of the moon sometimes is than those around it. Now, it is quite evident that the relations of intensity between the faint parts and the brilliant parts must continue to exist, whatever be the origin of the illuminating light. In the portion of the lunar globe that is illuminated by the sun, there are, everybody knows, some points, the brightness of which is extraordinary compared to those around them; those same points, when they are seen in that portion of the moon that is only lighted by the earth, or in the ash-coloured part, will still predominate over the neighbouring regions by their comparative intensity. Thus we may explain the observations of the Slough astronomer, without recurring to volcanoes. Whilst the great observer was studying in the non-illuminated portion of the moon, the supposed volcano of the 20th of April, 1787, his nine-foot telescope showed him in truth, by the aid of the secondary rays proceeding from the earth, even the darkest spots.

Herschel did not recur to the discussion of the supposed actually burning lunar volcanoes, until 1791. In the volume of thePhilosophical Transactionsfor 1792, he relates that, in directing a twenty-foot telescope, magnifying 360 times, to the entirely eclipsed moon on the 22d of October, 1790, there were visible, over the whole face of the satellite, about a hundred and fifty very luminous red points. The author declares that he will observe the greatest reserve relative to the similarity of all these points, their great brightness, and their remarkable colour.

Yet is not red the usual colour of the moon when eclipsed, and when it has not entirely disappeared? Could the solar rays reaching our satellite by the effect of refraction, and after an absorption experienced in the lowest strata of the terrestrial atmosphere, receive another tint? Are there not in the moon, when freely illuminated, and opposite to the sun, from one to two hundred little points, remarkable by the brightness of their light? Would it be possible for those little points not to be also distinguishable in the moon, when it receives only the portion of solar light which is refracted and coloured by our atmosphere?

Herschel was more successful in his remarks on the absence of a lunar atmosphere. During the solar eclipse of the 5th September, 1793, the illustrious astronomer particularly directed his attention to the shape of the acute horn resulting from the intersection of the limbs of the moon and of the sun. He deduced from his observation that if towards the point of the horn there had been a deviation of only one second, occasioned by the refraction of the solar light in the lunar atmosphere, it would not have escaped him.

Herschel made the planets the object of numerous researches. Mercury was the one with which he least occupied himself; he found its disk perfectly round on observing it during its projection, that is to say, in astronomical language, during its transit over the sun on the 9th of November, 1802. He sought to determine the time of the rotation of Venus since the year 1777. He published two memoirs relative to Mars, the one in 1781, the other in 1784, and the discovery of its being flattened at the poles we owe to him. After the discovery of the small planets, Ceres, Pallas, Juno, and Vesta, by Piazzi, Olbers, and Harding, Herschel applied himself to measuring their angular diameter. He concluded from his researches that those four new bodies did not deserve the name of planets, and he proposed to call them asteroÃ¯ds. This epithet was subsequently adopted; though bitterly criticized by a historian of the Royal Society of London, Dr. Thomson, who went so far as to suppose that the learned astronomer "had wished to deprive the first observers of those bodies, of all idea of rating themselves as high as him (Herschel) in the scale of astronomical discoverers." I should require nothing farther to annihilate such an imputation, than to put it by the side of the following passage, extracted from a memoir by this celebrated astronomer, published in thePhilosophical Transactions, for the year 1805: "The specific difference existing between planets and asteroÃ¯ds appears now, by the addition of a third individual of the latter species, to be more completely established, and that circumstance, in my opinion, has added more to theornamentof our system than the discovery of a new planet could have done."

Although much has not resulted from Herschel's having occupied himself with the physical constitution of Jupiter, astronomy is indebted to him for several important results relative to the duration of that planet's rotation. He also made numerous observations on the intensities and comparative magnitudes of its satellites.

The compression of Saturn, the duration of its rotation, the physical constitution of this planet and that of its ring, were, on the part of Herschel, the object of numerous researches which have much contributed to the progress of planetary astronomy. But on this subject two important discoveries especially added new glory to the great astronomer.

Of the five known satellites of Saturn at the close of the 17th century, Huygens had discovered the fourth; Cassini the others.

The subject seemed to be exhausted, when news from Slough showed what a mistake this was.

On the 28th of August, 1789, the great forty-foot telescope revealed to Herschel a satellite still nearer to the ring than the other five already observed. According to the principles of the nomenclature previously adopted, the small body of the 28th August ought to have been called the first satellite of Saturn, the numbers indicating the places of the other five would then have been each increased by a unity. But the fear of introducing confusion into science by these continual changes of denomination, induced a preference for calling the new satellite the sixth.

Thanks to the prodigious powers of the forty-foot telescope, a last satellite, the seventh, showed itself on the 17th of September, 1789, between the sixth and the ring.

This seventh satellite is extremely faint. Herschel, however, succeeding in seeing it whenever circumstances were very favourable, even by the aid of the twenty-foot telescope.

The discovery of the planet Uranus, the detection of its satellites, will always occupy one of the highest places among those by which modern astronomy is honoured.

On the 13th of March, 1781, between ten and eleven o'clock at night, Herschel was examining the small stars near H Geminorum with a seven-foot telescope, bearing a magnifying power of 227 times. One of these stars seemed to him to have an unusual diameter. The celebrated astronomer, therefore, thought it was a comet. It was under this denomination that it was then discussed at the Royal Society of London. But the researches of Herschel and of Laplace showed later that the orbit of the new body was nearly circular, and Uranus was elevated to the rank of a planet.

The immense distance of Uranus, its small angular diameter, the feebleness of its light, did not allow the hope, that if that body had satellites, the magnitudes of which were, relatively to its own size, what the satellites of Jupiter, of Saturn are, compared to those two large planets, any observer could perceive them, from the earth. Herschel was not a man to be deterred by such discouraging conjectures. Therefore, since powerful telescopes of the ordinary construction, that is to say, with two mirrors conjugated, had not enabled him to discover any thing, he substituted, in the beginning of January, 1787,front viewtelescopes, that is, telescopes throwing much more light on the objects, the small mirror being then suppressed, and with it one of the causes of loss of light is got rid of.

By patient labour, by observations requiring a rare perseverance, Herschel attained (from the 11th of January, 1787, to the 28th of February, 1794,) to the discovery of the six satellites of his planet, and thus to complete theworldof a system that belongs entirely to himself.

There are several of Herschel's memoirs on comets. In analyzing them, we shall see that this great observer could not touch any thing without making further discoveries in the subject.

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:â€”

"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.

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.

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 theAnnuaire 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: theTraitÃ© de MÃ©canique CÃ©leste, theExposition du SystÃ¨me du Monde, and theThÃ©orie Analytique des ProbabilitÃ©s. 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 theMÃ©canique CÃ©lesteitself 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 thechef d'Å“uvreof our countryman by the excellent geometer Bowditch. These fears, let us hasten to state, were not well founded. To republish theMÃ©canique CÃ©lestewas, 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'EvÃªque 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 theMÃ©canique CÃ©lestethrough 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 theMÃ©canique CÃ©lesteand theExposition du SystÃ¨me 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 theBureau 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 theMÃ©canique CÃ©lestewere 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. TheThÃ©orie des ProbabilitÃ©swas 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 preÃ«minence 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 WÃ¼rtemberg 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, byharmoniclaws. 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,â€”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 coÃ¶peration 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 thePrincipia Mathematica PhilosophiÃ¦ 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.

Let us now consider the action of a second force. Let us take into account the attraction which the sun exercises upon the moon, in other words, instead of two bodies, let us suppose three to operate on each other, the Keplerian ellipse will now furnish merely a rough indication of the motion of our satellite. In some parts the attraction of the sun will tend to enlarge the orbit, and will in reality do so; in other parts the effect will be the reverse of this. In a word, by the introduction of a third attractive body, the greatest complication will succeed to a simple regular movement upon which the mind reposed with complacency.

If Newton gave a complete solution of the question of the celestial movements in the case wherein two bodies attract each other, he did not even attempt an analytical investigation of the infinitely more difficult problem of three bodies. The problem of three bodies (this is the name by which it has become celebrated), the problem for determining the movement of a body subjected to the attractive influence of two other bodies, was solved for the first time, by our countryman Clairaut.[26]From this solution we may date the important improvements of the lunar tables effected in the last century.

The most beautiful astronomical discovery of antiquity, is that of the precession of the equinoxes. Hipparchus, to whom the honour of it is due, gave a complete and precise statement of all the consequences which flow from this movement. Two of these have more especially attracted attention.

By reason of the precession of the equinoxes, it is not always the same groups of stars, the same constellations, which are perceived in the heavens at the same season of the year. In the lapse of ages the constellations of winter will become those of summer and reciprocally.

By reason of the precession of the equinoxes, the pole does not always occupy the same place in the starry vault. The moderately bright star which is very justly named in the present day, the pole star, was far removed from the pole in the time of Hipparchus; in the course of a few centuries it will again appear removed from it. The designation of pole star has been, and will be, applied to stars very distant from each other.

When the inquirer in attempting to explain natural phenomena has the misfortune to enter upon a wrong path, each precise observation throws him into new complications. Seven spheres of crystal did not suffice for representing the phenomena as soon as the illustrious astronomer of Rhodes discovered precession. An eighth sphere was then wanted to account for a movement in which all the stars participated at the same time.

Copernicus having deprived the earth of its alleged immobility, gave a very simple explanation of the most minute circumstances of precession. He supposed that the axis of rotation does not remain exactly parallel to itself; that in the course of each complete revolution of the earth around the sun, the axis deviates from its position by a small quantity; in a word, instead of supposing the circumpolar stars to advance in a certain way towards the pole, he makes the pole advance towards the stars. This hypothesis divested the mechanism of the universe of the greatest complication which the love of theorizing had introduced into it. A new Alphonse would have then wanted a pretext to address to his astronomical synod the profound remark, so erroneously interpreted, which history ascribes to the king of Castile.

If the conception of Copernicus improved by Kepler had, as we have just seen, introduced a striking improvement into the mechanism of the heavens, it still remained to discover the motive force which, by altering the position of the terrestrial axis during each successive year, would cause it to describe an entire circle of nearly 50Â° in diameter, in a period of about 26,000 years.

Newton conjectured that this force arose from the action of the sun and moon upon the redundant matter accumulated in the equatorial regions of the earth: thus he made the precession of the equinoxes depend upon the spheroidal figure of the earth; he declared that upon a round planet no precession would exist.

All this was quite true, but Newton did not succeed in establishing it by a mathematical process. Now this great man had introduced into philosophy the severe and just rule: Consider as certain only what has been demonstrated. The demonstration of the Newtonian conception of the precession of the equinoxes was, then, a great discovery, and it is to D'Alembert that the glory of it is due.[27]The illustrious geometer gave a complete explanation of the general movement, in virtue of which the terrestrial axis returns to the same stars in a period of about 26,000 years. He also connected with the theory of gravitation the perturbation of precession discovered by Bradley, that remarkable oscillation which the earth's axis experiences continually during its movement of progression, and the period of which, amounting to about eighteen years, is exactly equal to the time which the intersection of the moon's orbit with the ecliptic employs in describing the 360Â° of the entire circumference.

Geometers and astronomers are justly occupied as much with the figure and physical constitution which the earth might have had in remote ages as with its present figure and constitution.

As soon as our countryman Richer discovered that a body, whatever be its nature, weighs less when it is transported nearer the equatorial regions, everybody perceived that the earth, if it was originally fluid, ought to bulge out at the equator. Huyghens and Newton did more; they calculated the difference between the greatest and least axes, the excess of the equatorial diameter over the line of the poles.[28]

The calculation of Huyghens was founded upon hypothetic properties of the attractive force which were wholly inadmissible; that of Newton upon a theorem which he ought to have demonstrated; the theory of the latter was characterized by a defect of a still more serious nature: it supposed the density of the earth during the original state of fluidity, to be homogeneous.[29]When in attempting the solution of great problems we have recourse to such simplifications; when, in order to elude difficulties of calculation, we depart so widely from natural and physical conditions, the results relate to an ideal world, they are in reality nothing more than flights of the imagination.

In order to apply mathematical analysis usefully to the determination of the figure of the earth it was necessary to abandon all idea of homogeneity, all constrained resemblance between the forms of the superposed and unequally dense strata; it was necessary also to examine the case of a central solid nucleus. This generality increased tenfold the difficulties of the problem; neither Clairaut nor D'Alembert was, however, arrested by them. Thanks to the efforts of these two eminent geometers, thanks to some essential developments due to their immediate successors, and especially to the illustrious Legendre, the theoretical determination of the figure of the earth has attained all desirable perfection. There now reigns the most satisfactory accordance between the results of calculation and those of direct measurement. The earth, then, was originally fluid: analysis has enabled us to ascend to the earliest ages of our planet.[30]

In the time of Alexander comets were supposed by the majority of the Greek philosophers to be merely meteors generated in our atmosphere. During the middle ages, persons, without giving themselves much concern about the nature of those bodies, supposed them to prognosticate sinister events. Regiomontanus and Tycho BrahÃ© proved by their observations that they are situate beyond the moon; Hevelius, DÃ¶rfel, &c., made them revolve around the sun; Newton established that they move under the immediate influence of the attractive force of that body, that they do not describe right lines, that, in fact, they obey the laws of Kepler. It was necessary, then, to prove that the orbits of comets are curves which return into themselves, or that the same comet has been seen on several distinct occasions. This discovery was reserved for Halley. By a minute investigation of the circumstances connected with the apparitions of all the comets to be met with in the records of history, in ancient chronicles, and in astronomical annals, this eminent philosopher was enabled to prove that the comets of 1682, of 1607, and of 1531, were in reality so many successive apparitions of one and the same body.

This identity involved a conclusion before which more than one astronomer shrunk. It was necessary to admit that the time of a complete revolution of the comet was subject to a great variation, amounting to as much as two years in seventy-six.

Were such great discordances due to the disturbing action of the planets?

The answer to this question would introduce comets into the category of ordinary planets or would exclude them for ever. The calculation was difficult: Clairaut discovered the means of effecting it. While success was still uncertain, the illustrious geometer gave proof of the greatest boldness, for in the course of the year 1758 he undertook to determine the time of the following year when the comet of 1682 would reappear. He designated the constellations, nay the stars, which it would encounter in its progress.

This was not one of those remote predictions which astrologers and others formerly combined very skilfully with the tables of mortality, so that they might not be falsified during their lifetime: the event was close at hand. The question at issue was nothing less than the creation of a new era in cometary astronomy, or the casting of a reproach upon science, the consequences of which it would long continue to feel.

Clairaut found by a long process of calculation, conducted with great skill, that the action of Jupiter and Saturn ought to have retarded the movement of the comet; that the time of revolution compared with that immediately preceding, would be increased 518 days by the disturbing action of Jupiter, and 100 days by the action of Saturn, forming a total of 618 days, or more than a year and eight months.

Never did a question of astronomy excite a more intense, a more legitimate curiosity. All classes of society awaited with equal interest the announced apparition. A Saxon peasant, Palitzch, first perceived the comet. Henceforward, from one extremity of Europe to the other, a thousand telescopes traced each night the path of the body through the constellations. The route was always, within the limits of precision of the calculations, that which Clairaut had indicated beforehand. The prediction of the illustrious geometer was verified in regard both to time and space: astronomy had just achieved a great and important triumph, and, as usual, had destroyed at one blow a disgraceful and inveterate prejudice. As soon as it was established that the returns of comets might be calculated beforehand, those bodies lost for ever their ancient prestige. The most timid minds troubled themselves quite as little about them as about eclipses of the sun and moon, which are equally subject to calculation. In fine, the labours of Clairaut had produced a deeper impression on the public mind than the learned, ingenious, and acute reasoning of Bayle.

The heavens offer to reflecting minds nothing more curious or more strange than the equality which subsists between the movements of rotation and revolution of our satellite. By reason of this perfect equality the moon always presents the same side to the earth. The hemisphere which we see in the present day is precisely that which our ancestors saw in the most remote ages; it is exactly the hemisphere which future generations will perceive.

The doctrine of final causes which certain philosophers have so abundantly made use of in endeavouring to account for a great number of natural phenomena was in this particular case totally inapplicable. In fact, how could it be pretended that mankind could have any interest in perceiving incessantly the same hemisphere of the moon, in never obtaining a glimpse of the opposite hemisphere? On the other hand, the existence of a perfect, mathematical equality between elements having no necessary connectionâ€”such as the movements of translation and rotation of a given celestial bodyâ€”was not less repugnant to all ideas of probability. There were besides two other numerical coincidences quite as extraordinary; an identity of direction, relative to the stars, of the equator and orbit of the moon; exactly the same precessional movements of these two planes. This group of singular phenomena, discovered by J.D. Cassini, constituted the mathematical code of what is called theLibration of the Moon.

The libration of the moon formed a very imperfect part of physical astronomy when Lagrange made it depend on a circumstance connected with the figure of our satellite which was not observable from the earth, and thereby connected it completely with the principles of universal gravitation.

At the time when the moon was converted into a solid body, the action of the earth compelled it to assume a less regular figure than if no attracting body had been situate in its vicinity. The action of our globe rendered elliptical an equator which otherwise would have been circular. This disturbing action did not prevent the lunar equator from bulging out in every direction, but the prominence of the equatorial diameter directed towards the earth became four times greater than that of the diameter which we see perpendicularly.

The moon would appear then, to an observer situate in space and examining it transversely, to be elongated towards the earth, to be a sort of pendulum without a point of suspension. When a pendulum deviates from the vertical, the action of gravity brings it back; when the principal axis of the moon recedes from its usual direction, the earth in like manner compels it to return.

We have here, then, a complete explanation of a singular phenomenon, without the necessity of having recourse to the existence of an almost miraculous equality between two movements of translation and rotation, entirely independent of each other. Mankind will never see but one face of the moon. Observation had informed us of this fact; now we know further that this is due to a physical cause which may be calculated, and which is visible only to the mind's eye,â€”that it is attributable to the elongation which the diameter of the moon experienced when it passed from the liquid to the solid state under the attractive influence of the earth.

If there had existed originally a slight difference between the movements of rotation and revolution of the moon, the attraction of the earth would have reduced these movements to a rigorous equality. This attraction would have even sufficed to cause the disappearance of a slight want of coincidence in the intersections of the equator and orbit of the moon with the plane of the ecliptic.

The memoir in which Lagrange has so successfully connected the laws of libration with the principles of gravitation, is no less remarkable for intrinsic excellence than style of execution. After having perused this production, the reader will have no difficulty in admitting that the wordelegancemay be appropriately applied to mathematical researches.

In this analysis we have merely glanced at the astronomical discoveries of Clairaut, D'Alembert, and Lagrange. We shall be somewhat less concise in noticing the labours of Laplace.

After having enumerated the various forces which must result from the mutual action of the planets and satellites of our system, even the great Newton did not venture to investigate the general nature of the effects produced by them. In the midst of the labyrinth formed by increases and diminutions of velocity, variations in the forms of the orbits, changes of distances and inclinations, which these forces must evidently produce, the most learned geometer would fail to discover a trustworthy guide. This extreme complication gave birth to a discouraging reflection. Forces so numerous, so variable in position, so different in intensity, seemed to be incapable of maintaining a condition of equilibrium except by a sort of miracle. Newton even went so far as to suppose that the planetary system did not contain within itself the elements of indefinite stability; he was of opinion that a powerful hand must intervene from time to time, to repair the derangements occasioned by the mutual action of the various bodies. Euler, although farther advanced than Newton in a knowledge of the planetary pertubations, refused also to admit that the solar system was constituted so as to endure for ever.

Never did a greater philosophical question offer itself to the inquiries of mankind. Laplace attacked it with boldness, perseverance, and success. The profound and long-continued researches of the illustrious geometer established with complete evidence that the planetary ellipses are perpetually variable; that the extremities of their major axes make the tour of the heavens; that, independently of an oscillatory motion, the planes of their orbits experienced a displacement in virtue of which their intersections with the plane of the terrestrial orbit are each year directed towards different stars. In the midst of this apparent chaos there is one element which remains constant or is merely subject to small periodic changes; namely, the major axis of each orbit, and consequently the time of revolution of each planet. This is the element which ought to have chiefly varied, according to the learned speculations of Newton and Euler.

The principle of universal gravitation suffices for preserving the stability of the solar system. It maintains the forms and inclinations of the orbits in a mean condition which is subject to slight oscillations; variety does not entail disorder; the universe offers the example of harmonious relations, of a state of perfection which Newton himself doubted. This depends on circumstances which calculation disclosed to Laplace, and which, upon a superficial view of the subject, would not seem to be capable of exercising so great an influence. Instead of planets revolving all in the same direction in slightly eccentric orbits, and in planes inclined at small angles towards each other, substitute different conditions and the stability of the universe will again be put in jeopardy, and according to all probability there will result a frightful chaos.[31]

Although the invariability of the mean distances of the planetary orbits has been more completely demonstrated since the appearance of the memoir above referred to, that is to say by pushing the analytical approximations to a greater extent, it will, notwithstanding, always constitute one of the admirable discoveries of the author of theMÃ©canique CÃ©leste. Dates, in the case of such subjects, are no luxury of erudition. The memoir in which Laplace communicated his results on the invariability of the mean motions or mean distances, is dated 1773.[32]It was in 1784 only, that he established the stability of the other elements of the system from the smallness of the planetary masses, the inconsiderable eccentricity of the orbits, and the revolution of the planets in one common direction around the sun.

The discovery of which I have just given an account to the reader excluded at least from the solar system the idea of the Newtonian attraction being a cause of disorder. But might not other forces, by combining with attraction, produce gradually increasing perturbations as Newton and Euler dreaded? Facts of a positive nature seemed to justify these fears.

A comparison of ancient with modern observations revealed the existence of a continual acceleration of the mean motions of the moon and the planet Jupiter, and an equally striking diminution of the mean motion of Saturn. These variations led to conclusions of the most singular nature.

In accordance with the presumed cause of these perturbations, to say that the velocity of a body increased from century to century was equivalent to asserting that the body continually approached the centre of motion; on the other hand, when the velocity diminished, the body must be receding from the centre.

Thus, by a strange arrangement of nature, our planetary system seemed destined to lose Saturn, its most mysterious ornament,â€”to see the planet accompanied by its ring and seven satellites, plunge gradually into unknown regions, whither the eye armed with the most powerful telescopes has never penetrated. Jupiter, on the other hand, the planet compared with which the earth is so insignificant, appeared to be moving in the opposite direction, so as to be ultimately absorbed in the incandescent matter of the sun. Finally, the moon seemed as if it would one day precipitate itself upon the earth.

There was nothing doubtful or speculative in these sinister forebodings. The precise dates of the approaching catastrophes were alone uncertain. It was known, however, that they were very distant. Accordingly, neither the learned dissertations of men of science nor the animated descriptions of certain poets produced any impression upon the public mind.

It was not so with our scientific societies, the members of which regarded with regret the approaching destruction of our planetary system. The Academy of Sciences called the attention of geometers of all countries to these menacing perturbations. Euler and Lagrange descended into the arena. Never did their mathematical genius shine with a brighter lustre. Still, the question remained undecided. The inutility of such efforts seemed to suggest only a feeling of resignation on the subject, when from two disdained corners of the theories of analysis, the author of theMÃ©canique CÃ©lestecaused the laws of these great phenomena clearly to emerge. The variations of velocity of Jupiter, Saturn, and the Moon flowed then from evident physical causes, and entered into the category of ordinary periodic perturbations depending upon the principle of attraction. The variations in the dimensions of the orbits which were so much dreaded resolved themselves into simple oscillations included within narrow limits. Finally, by the powerful instrumentality of mathematical analysis, the physical universe was again established on a firm foundation.

I cannot quit this subject without at least alluding to the circumstances in the solar system upon which depend the so long unexplained variations of velocity of the Moon, Jupiter, and Saturn.

The motion of the earth around the sun is mainly effected in an ellipse, the form of which is liable to vary from the effects of planetary perturbation. These alterations of form are periodic; sometimes the curve, without ceasing to be elliptic, approaches the form of a circle, while at other times it deviates more and more from that form. From the epoch of the earliest recorded observations, the eccentricity of the terrestrial orbit has been diminishing from year to year; at some future epoch the orbit, on the contrary, will begin to deviate from the form of a circle, and the eccentricity will increase to the same extent as it previously diminished, and according to the same laws.

Now, Laplace has shown that the mean motion of the moon around the earth is connected with the form of the ellipse which the earth describes around the sun; that a diminution of the eccentricity of the ellipse inevitably induces an increase in the velocity of our satellite, andvice versÃ¢; finally, that this cause suffices to explain the numerical value of the acceleration which the mean motion of the moon has experienced from the earliest ages down to the present time.[33]

The origin of the inequalities in the mean motions of Jupiter and Saturn will be, I hope, as easy to conceive.

Mathematical analysis has not served to represent in finite terms the values of the derangements which each planet experiences in its movement from the action of all the other planets. In the present state of science, this value is exhibited in the form of an indefinite series of terms diminishing rapidly in magnitude. In calculation, it is usual to neglect such of those terms as correspond in the order of magnitude to quantities beneath the errors of observation. But there are cases in which the order of the term in the series does not decide whether it be small or great. Certain numerical relations between the primitive elements of the disturbing and disturbed planets may impart sensible values to terms which usually admit of being neglected. This case occurs in the perturbations of Saturn produced by Jupiter, and in those of Jupiter produced by Saturn. There exists between the mean motions of these two great planets a simple relation of commensurability, five times the mean motion of Saturn, being, in fact, very nearly equal to twice the mean motion of Jupiter. It happens, in consequence, that certain terms, which would otherwise be very small, acquire from this circumstance considerable values. Hence arise in the movements of these two planets, inequalities of long duration which require more than 900 years for their complete development, and which represent with marvellous accuracy all the irregularities disclosed by observation.

Is it not astonishing to find in the commensurability of the mean motions of two planets, a cause of perturbation of so influential a nature; to discover that the definitive solution of an immense difficultyâ€”which baffled the genius of Euler, and which even led persons to doubt whether the theory of gravitation was capable of accounting for all the phenomena of the heavensâ€”should depend upon the fortuitous circumstance of five times the mean motion of Saturn being equal to twice the mean motion of Jupiter? The beauty of the conception and the ultimate result are here equally worthy of admiration.[34]

We have just explained how Laplace demonstrated that the solar system can experience only small periodic oscillations around a certain mean state. Let us now see in what way he succeeded in determining the absolute dimensions of the orbits.

What is the distance of the sun from the earth? No scientific question has occupied in a greater degree the attention of mankind; mathematically speaking, nothing is more simple. It suffices, as in common operations of surveying, to draw visual lines from the two extremities of a known base to an inaccessible object. The remainder is a process of elementary calculation. Unfortunately, in the case of the sun, the distance is great and the bases which can be measured upon the earth are comparatively very small. In such a case the slightest errors in the direction of the visual lines exercise an enormous influence upon the results.

In the beginning of the last century Halley remarked that certain interpositions of Venus between the earth and the sun, or, to use an expression applied to such conjunctions, that thetransitsof the planet across the sun's disk, would furnish at each observatory an indirect means of fixing the position of the visual ray very superior in accuracy to the most perfect direct methods.[35]

Such was the object of the scientific expeditions undertaken in 1761 and 1769, on which occasions France, not to speak of stations in Europe, was represented at the Isle of Rodrigo by PingrÃ©, at the Isle of St. Domingo by Fleurin, at California by the AbbÃ© Chappe, at Pondicherry by Legentil. At the same epochs England sent Maskelyne to St. Helena, Wales to Hudson's Bay, Mason to the Cape of Good Hope, Captain Cooke to Otaheite, &c. The observations of the southern hemisphere compared with those of Europe, and especially with the observations made by an Austrian astronomer Father Hell at Wardhus in Lapland, gave for the distance of the sun the result which has since figured in all treatises on astronomy and navigation.

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