fabulous history, a son of Apollo by Stilbe. He was brother to Centaurus, and married Orione, daughter of Euronymus, by whom he had Phorbas and Periphas. The name of Lapithae was given to the numerous children of Phorbas and Periphas, or rather to the inhabitants of the country of which they had obtained the sovereignty. The chief of the Lapithae assembled to celebrate the nuptials of Perithous, one of their number. Amongst them were Theseus, Dryas, Hopleus, Mopsus, Phalerus, Exadius, Prolochus, Titaresius, and others. The Centaurs were also invited to partake of the common festivity; and the amusements would have been harmless and innocent, had not one of the intoxicated Centaurs offered violence to Hippodamia, the wife of Perithous. The Lapithae resented the injury, and the Centaurs supported their companions; upon which the quarrel became universal, and ended in blows and slaughter. Many of the Centaurs were slain, and they were at last obliged to retire. Theseus amongst the Lapithae showed himself brave and intrepid in supporting the cause of his friends; and Nestor also was not less active in the protection of chastity and innocence. Hesiod has described the battle of the Centaurs and Lapithae; as has also Ovid, in a more copious manner. The invention of bits and bridles for horses is attributed to the Lapithe.

Laplace, Pierre Simon, Marquis de, one of the greatest geometricians and physical astronomers that any age or country has produced, and scarcely less distinguished in the other natural sciences, was a native of Normandy, in which province he first saw the light on the 23rd of March 1749. It was observed, even at the commencement of his studies, that he was endowed with a prodigious memory; and that all the ordinary occupations of the mind were to him easy. He rapidly acquired an extensive knowledge of the ancient languages, and cultivated different branches of literature. Everything interested his rising genius, and everything served to unfold it. His first successes were achieved in theological studies; the most difficult points of controversy he treated with extraordinary talent and sagacity.

It is not known by what fortunate accident M. de Laplace passed from the study of scholastic learning to that of the higher geometry. This last science, which scarcely admits of a divided affection, now attracted and fixed his attention. From that time, he abandoned himself without reserve to the impulse of his genius, and became sensible that a residence in the capital had become necessary to him. D'Alembert then enjoyed all the splendour of his European reputation. It was he who had just informed the court of Turin, that its academy possessed a geometrician of the first order, Lagrange, who, but for this noble testimony to his merits, would have remained long unknown. D'Alembert had announced to the king of Prussia, that there was only one man in Europe fitted to replace at Berlin the illustrious Euler, who, having been recalled by the government of Russia, had consented to return to St. Petersburg. Amongst his inedited letters, Baron Fourier discovered the details of the negociation which fixed Lagrange as a resident at Berlin.

About the same time, M. de Laplace commenced that long career which was destined soon to become so illustrious. He presented himself at the house of D'Alembert, preceded by numerous recommendations, which might have been supposed to be all-powerful. But his attempts were vain; he was not even introduced. He then addressed to the man whose suffrage he had in vain solicited, a very remarkable letter on the general principles of mechanics, of which, at an after period of his life, he several times cited various fragments to his friend Baron Fourier. It was impossible that so great a geometrician as D'Alembert should not be struck with the singular profundity of this composition. The same day, he waited upon the author of the letter, and said to him, "Sir, you see that I pay little attention to recommendations; you have no need of them. You have made yourself better known; that is sufficient for me; you may command my support." A few days afterwards, he got M. de Laplace appointed professor of mathematics to the Military School of Paris. From this moment, having devoted himself exclusively to the science which he had selected, the latter gave to all his labours a fixed direction, from which he never afterwards deviated; for the imperceptible constancy of his views and steadiness of his application formed the principal characteristics of his genius. Already he had reached the known limits of the mathematical analysis; he was then master of all that was most ingenious or most powerful in that science; and no one seemed more capable than he of enlarging its domain. Having resolved a capital question of theoretical astronomy, he formed the design of consecrating his efforts to that sublime science, which he was destined to perfect, and which he alone could embrace in its full extent. He meditated deeply his glorious design; and he passed his whole life in accomplishing it, with a perseverance of which the history of the sciences scarcely presents any similar example.

The immensity of the subject flattered the just pride of his genius. He undertook to compose the Almagest of his age, we mean the work which he has left us under the title of Traité de Mécanique Céleste; a work which is as superior to that of Ptolemy, as the analytical science of the moderns surpasses the elements of Euclid. Time, which alone dispenses literary glory with justice, and which consigns to oblivion contemporary mediocrity, perpetuates the remembrance of great works. It is they only which carry to posterity the character of each age. Thus the name of M. de Laplace will live throughout all ages. But enlightened and faithful history will not separate his renown from that of the other successors of Newton. It will unite in one and the same series the illustrious names of D'Alembert, Clairaut, Euler, Lagrange, and Laplace. After Euler, Lagrange contributed most largely to found the mathematical analysis, which, in the writings of these two great geometers, became a distinct science, the only one of the mathematical theories of which it could be said that it had been completely and rigorously demonstrated. Lagrange was born to invent and to enlarge all the sciences of calculation. If he had been the contemporary of Archimedes and of Conon, he would have shared the glory of the most memorable discoveries; and at Alexandria he would have been the rival of Diophantus.

M. de Laplace had received from nature all that force of genius which was required for an immense enterprise; and in his Almagest of the nineteenth century, he has not only comprised all that had previously been discovered in the mathematical and physical sciences, and which serves as the foundation of astronomy; but he added to this science capital discoveries peculiar to himself; and which had escaped all his predecessors. Either by his own methods, or by those of which Euler and Lagrange had previously indicated the principles, he resolved questions the most important, and certainly the most difficult of all those which had been considered before his time. Thus, in the motions of the moon he discovered an acceleration of which no one had previously been able to explain the cause. It had been supposed that this effect might proceed from the resistance of the ethereal medium in which the heavenly bodies revolved. But if this were so, the same cause, affecting the courses of the planets, would tend more and more to change the primitive order. These stars would be incessantly disturbed in or deflected from their orbits, and would end by precipitating themselves upon the mass of the sun; and it would be necessary for the creative power to interpose anew in order to prevent or to repair the immense confusion which the lapse of time had produced. This cosmological question was assuredly one of the greatest which the human mind could propose to itself; and it is now completely resolved. The early researches of M. de Laplace respecting the invariability of the dimensions of the solar system, and his explanation of the secular equation of the moon, conducted him to this solution.

He had at first inquired if the acceleration of the lunar movement could be explained by supposing that the action of gravity was not instantaneous, but subjected to a successive transmission, like that of light. In this way, however, he could not discover the true cause. But a new investigation, based upon a sounder principle, led him to the desired object; and, on the 19th of March 1787, he gave to the Academy of Sciences a clear and unexpected solution of this capital difficulty, proving distinctly that the acceleration observed is a necessary effect of universal gravitation. This great discovery threw new light upon the most important points in the system of the world. From it he deduced, that if the action of gravitation on the stars was not instantaneous, this principle must be propagated at least fifty million times more rapidly than light, the velocity of which is seventy thousand leagues a second. He also concluded that the medium in which the heavenly bodies revolve opposes no sensible resistance to the courses of the planets; since this cause would especially affect the motion of the moon; in which, however, it produces no observable effect. The same principle is also fertile in remarkable consequences. It follows from it, that the motion of rotation of the earth on its own axis is invariable. The duration of the day has not changed the hundredth part of a second during two thousand years. The distance of the sun from the earth may also be deduced with certainty from the assiduous observation of the lunar motions. But the most striking consequence, perhaps, is that which relates to the figure of the earth, the form of which is imprinted in certain inequalities in the course of the moon, which could not have taken place if the earth had been perfectly spherical. The quantity of the terrestrial oblateness may be determined from the lunar movements alone; and the results which have been deduced from these agree with the actual measures which have been obtained from geodesical operations at the equator, in the northern regions of Europe, in India, and in various other countries.

"The explanation of the moon's acceleration," says Professor Playfair, in his masterly and eloquent review of the Système du Monde, "and the proof that it is not constantly increasing, but merely a periodical inequality, is a great step in the philosophy of the heavens. The continual increase of the moon's angular velocity, which this phenomenon seemed to indicate, argued a constant diminution of her distance from the earth, and gave some countenance to the notion that the planetary orbits were continually diminishing, and that there was, amongst the bodies of our system, a tendency to descend to the centre of gravity of the whole, where their union must finally terminate the present order of nature. To this catastrophe an elegant and philosophic poet has beautifully alluded.

Roll on, ye stars, exult in youthful prime, Mark with bright curves the printless steps of time; Near and more near your beamy cars approach, And lessening orbs on lessening orbs encroach. Flowers of the sky! ye too to age must yield, Frail as your silken sisters of the field! Star after star from heaven's high arch shall rush, Suns sink on suns, and systems systems crush; Headlong, extinct, to one dark centre fall, And death, and night, and chaos mingle all; Till o'er the wreck, emerging from the storm, Immortal Nature lifts her changeful form; Mounts from her funeral pyre on wings of flame, And soars and shines another and the same!

The destiny of nature is, however, more noble than that which this magnificent description holds up to the fancy; and the algebraist has extracted from his calculus a more sublime conclusion than the invention of a poet has been able to attain. The constancy of nature, amidst all the changes she undergoes, is upheld by the constitution of those changes, which prescribes to each its limits, and forces it to recur in a series, which in time reduces to nothing the sum of all the deviations from the mean. Thus, the amount of the whole is permanent, though the terms themselves are perpetually changing; and hence nature is rendered immortal, not by emerging from the storm, but by being ever superior to its power; its order is not renovated, but preserved; and the wisdom of its Author has provided an antidote to evil, that renders all remedies unnecessary."

We cannot undertake to indicate here the continuation of his labours, and the discoveries which resulted from them. The bare enumeration, however rapid, would exceed the limits prescribed to us. Besides his researches on the secular equation of the moon, and the discovery, not less important and difficult, of the cause of the great inequalities of Jupiter and of Saturn, we would require to cite his admirable theorems on the libration of the satellites of

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1 Darwin's Botanic Garden, cant. iv. p. 1. 2 Edinburgh Review, vol. xv. pp. 411, 412. Jupiter, to recall his analytical labours on the flux and reflux of the sea, and to show the immense extent which he has given to that question. In fact, there was no point of importance in physical astronomy which he did not make the object of profound study and discussion; and he subjected to calculation the greater part of the physical conditions which his predecessors had omitted. In the question, already so complex, of the form and the motion of rotation of the earth, he considered the effect of the presence of the waters distributed between the continents of land, the compression of the interior strata, and the secular diminution of the dimensions of the globe. Amongst these researches may also be remarked those which relate to the stability of the grand phenomena of nature. No subject can possibly be more worthy the attention of philosophers. Thus, it has been ascertained that the causes, whether fortuitous or constant, which disturb the equilibrium of the seas, are subjected to limits which cannot be passed. The specific gravity of the waters being much less than that of the solid earth, it follows that the oscillations of the ocean are always included within very narrow limits, which would not happen if the liquid diffused over the globe was much more heavy. In general, nature keeps in reserve conservative forces, which, being always present, act as soon as the disturbance commences, and with a vigour proportioned to the alteration, until the accustomed order has been re-established. In the primitive and liquid state of the terrestrial globe, the heaviest substances must, by their own weight, have approached nearest the centre; and this condition has determined the stability of the seas.

Whatever may be the physical cause of the formation of the planets, it has impressed upon all these bodies a motion of projection in the same direction around an immense globe; and by this motion the solar system has become stable. The same effect is produced in the system of the satellites and the rings. In these, order is also maintained by the power of the central mass. It is not, then, as Newton and Euler had both suspected, an adventitious force, which might one day repair or prevent the disturbance caused by time. It is the law of gravitation itself; a law which regulates all, is sufficient for all, and maintains variety and order amongst all. Having once emanated from the supreme wisdom, it has presided since the origin of time, and rendered all disorder impossible. Newton and Euler did not know all the perfections of the universe. In general, as often as any doubt has arisen in regard to the universality of the Newtonian law, and the accession of some new cause has been proposed to explain apparent irregularities, it has always happened that, after a profound investigation, the primordial law has been verified. It now explains all the known phenomena. The more precise observations have become, the more conformable they are found to be to the theory of gravitation. Of all geometricians, M. de Laplace is the one who has most profoundly investigated these great questions, which, if we may so express it, he has also terminated. It cannot indeed be affirmed that it was given to him to create an entirely new science, like Archimedes and Galileo; or to give to mathematical doctrines original principles and an immense extent, like Descartes, Newton, and Leibnitz; or, like Newton, to be the first to transport to the heavens, and extend throughout the whole universe, the terrestrial dynamics of Galileo. But, to use the words of Baron Fourier, M. de Laplace was born "pour tout perfectionner, pour tout approfondir, pour reculer toutes les limites, pour résoudre ce que l'on aurait pu croire insoluble." He would have completed the science of the heavens, if that science could have been completed.

Professor Playfair thus sums up his analysis of the great work of Laplace, the Traité de Mécanique Céleste, wherein the discoveries which had first been communicated by the author, in the Memoirs of the Academy of Sciences, are brought together into one view, and the general results deduced from them by one uniform method of investigation.

"Such is the work of Laplace," says he, "affording an example, which is yet solitary in the history of human knowledge, of a theory entirely complete; one that has not only accounted for all the phenomena that were known, but that has discovered many before unknown, which observation has since recognised. In this theory, not only the elliptic motion of the planets, relatively to the sun, but the irregularities produced by their mutual action, whether of the primary on the primary, of the primary on the secondary, or of the secondary on one another, are all deduced from the principle of gravitation, that mysterious power, which unites the most distant regions of space, and the most remote periods of duration. To this we must add the great truths brought into view and fully demonstrated, by tracing the action of the same power through all its mazes—That all the inequalities in our system are periodical; that, by a fixed appointment in nature, they are each destined to revolve in the same order, and between the same limits; that the mean distances of the planets from the sun, and the time of their revolutions round that body, are susceptible of no change whatsoever; that our system is thus secured against natural decay,—order and regularity preserved in the midst of so many disturbing causes,—and anarchy and misrule eternally proscribed.

"The work where this sublime picture is delineated, does honour, not to the author only, but to the human race; and marks, undoubtedly, the highest point to which man has yet ascended in the scale of intellectual attainment. The glory, therefore, of having produced this work, belongs, not to the author alone, but must be shared, in various proportions, among the philosophers and mathematicians of all ages. Their efforts, from the age of Euclid and Archimedes, to the time of Newton and Laplace, have all been required to the accomplishment of this great object; they have been all necessary to form one man for the author, and a few for the readers, of the work before us. Every mathematician who has extended the bounds of his science; every astronomer who has added to the number of facts, and the accuracy of observation; every artist who has improved the construction of the instruments of astronomy,—all have co-operated in preparing a state of knowledge in which such a book could exist, and in which its merit could be appreciated. They have collected the materials, sharpened the tools, or constructed the engines employed in the great edifice, founded by Newton, and completed by Laplace.

"In this estimate we detract nothing from the merit of the author himself; his originality, his invention, and comprehensive views, are above all praise; nor can any man boast of a higher honour, than that the Genius of the human race is the only rival of his fame."

The same general character is exemplified in his researches on the analysis of probabilities; a science altogether modern, but of immense extent, and one the applications of which will one day embrace the whole range of human knowledge, forming a happy supplement to the imperfection of our nature. The doctrine of probabilities owes its origin to a single glance of the intuitive and fertile genius of Pascal; and it was from the first cultivated by Fermat and Huygens. A geometrician and philosopher, James Bernoulli, was its principal founder. A sin-

1 Edinburgh Review, vol. xi. pp. 277, 278. gularly happy discovery of Stirling, the researches of Eu- ler, and, above all, an ingenious and important application made by Lagrange, improved this doctrine; whilst new light was shed upon it by the objections of D'Alembert, and by the philosophical views of Condorcet. But it was re- served for M. de Laplace to collect and to fix its prin- ciples. In his hands it became a new science, subjected to a single analytical method, and of prodigious extent. Fertile in useful applications, this science will one day serve to illustrate all the branches of natural philosophy.

After what has been said of these brilliant discoveries, it is scarcely necessary to add, that M. de Laplace was a mem- ber of all the learned academies of Europe. He was also invested with high political dignities. After the 18th Bru- maire, the First Consul appointed him minister of the in- terior; but in this office, it appears, he gave little satis- faction. "A geometrician of the first class," says Napo- leon, "he did not reach mediocrity as a statesman. From the first, the consuls became sensible they had made a mistake in the appointment. He never viewed any sub- ject in a true light; he was always occupied with subtle- ties; his notions were all problematic; and he carried the spirit of the infiniment petit into the administration." Ac- cordingly, at the end of six weeks, he surrendered to Lucien Bonaparte the portefeuille of his office. But he was created a senator, then made vice-chancellor, and at length chan- cellor of the conservative senate, and at the same time a member of the legion of honour. In 1805, he presented a report to the senate, in which he proved the necessity of re- storing the Gregorian calendar, and abolishing that of the republic. In 1814, he voted for the abdication of Napo- leon, an act which reflects no great honour on his memory. During the Hundred Days he did not make his appearance at the Tuileries, apprehensive, no doubt, of being re- proached with tergiversation and ingratitude. Soon after the restoration, he was created a peer of France with the title of Marquis; an honour for which he was more indebt- ed, perhaps, to the vote he had given in 1814, than to all his eminence in science. But the immortal author of the Mécanique Céleste required none of those arbitrary and adventitious distinctions, which are so often the reward of political subserviency. His genius and his fame were incapable of receiving any secondary or reflected illustra- tion. The only points of real importance in his life are the eternal truths which he discovered, not the dignities with which he was invested; the immutable laws of the stability of the world which he unfolded, not the rank which he for several years held in the senate called con- servative; and the example which he has left to all those who cultivate the sciences of patient thinking and incom- parable perseverance.

M. de Laplace enjoyed an advantage which fortune does not always afford to great men. From his early youth, his merits were fully appreciated by his illustrious friends. D'Alembert, as we have seen, lost no time in introducing him to the Military School of France, and in providing for him, had it been necessary, a better establishment at Ber- lin. The President Bochard de Saron caused to be print- ed, at his own expense, the early works of Laplace. All the testimonies of friendship which were given him recall great labours and great discoveries; but nothing could contribute more to the progress of physical knowledge than his relations with the illustrious Lavoisier, whose name, hallowed in the history of the sciences, has become an object of eternal respect and sorrow. These two cele- brated men combined their efforts for the advancement of science. They undertook and completed extensive re- searches, in order to measure one of the most important elements of the physical theory of heat. They made also, about the same time, a long series of experiments on the dilatations of solid substances. The works of Newton show the importance which that great geometrician attached to the special study of the physical sciences. Of all his suc- cessors, M. de Laplace is the one who has made most of his experimental method; he was almost as great a natural philosopher as a geometrician. His researches on refrac- tion, capillary attraction, barometrical measurements, the statical properties of electricity, the propagation of sound, molecular action, and the properties of gas, prove that every thing connected with the investigation of nature was fami- liar to him. He desired above all things the perfection of instruments, and caused to be constructed, at his own ex- pense, by a celebrated artist, a valuable astronomical instru- ment, which he presented to the Observatory of France.

All sorts of phenomena were perfectly known to him. He was connected by ancient friendship with two natural philosophers, whose discoveries have thrown light upon all the arts and all the chemical theories. History will asso- ciate the names of Berthollet and of Chaptal with that of M. de Laplace. He took pleasure in meeting them toge- ther, and the conversations which then ensued had all for their object the advancement of science. The gardens of Berthollet at his house at Arcueil were contiguous to those of M. de Laplace. Interesting recollections and great re- grets have illustrated this locality. It was there that La- place received celebrated foreigners, and men in power, from whom science had received, or hoped to receive, benefits, but, above all, those whom a sincere zeal had attached to the sanctuary of the sciences. He receiv- ed all with extreme politeness—those who were just com- mencing their career, as well as the veterans who were soon to finish it; and he carried this so far, that persons who did not know the full extent of his genius would per- haps have supposed that he derived some advantage from their conversation.

In referring to the mathematical works of M. de Laplace, we have particularly noticed the depth of his researches and the importance of his discoveries. But these works are distinguished by another quality, which all readers have appreciated, we mean the literary merit of the composi- tion. The Système du Monde, in particular, is remarkable for the elegant simplicity of the style and the purity of the language. There had hitherto been no example of a work of this kind; but it would be a mistake to suppose that a real knowledge of the phenomena of the heavens can be acquired from such writings. The suppression of the signs peculiar to the language of the calculus cannot conduce to clearness, or render the perusal more easy. The work is a perfectly regular exposition of the results of profound study; it is an ingenious and admirable sum- mary of the principal discoveries. The precision of the style, the choice of the methods, the grandeur of the sub- ject, give a singular interest to this vast picture; but its real utility consists in recalling to geometers the theo- rems, the demonstrations of which were previously known to them. "C'est, il proprement parler," says M. Fourier, "une table de matières d'un traité mathématique." The purely historical works of Laplace have another object. He therein presents to geometers, with admirable talent, the progress of the human mind in the invention of the sciences. The most abstract theories have, in fact, a beauty of expression which is peculiar to them. This is what may

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1 See an admirable account of the Essai Philosophique sur les Probabilités (which is only an abstract of the large work by the same author, entitled Théorie Analytique des Probabilités, Paris, 1812), in the Edinburgh Review, vol. xxiii. p. 320, &c., and which is known to have proceeded from the pen of Professor Playfair. be observed in several treatises of Descartes, and in some pages of Galileo, of Newton, and of Lagrange. The novelty of the views, the elevation of the thoughts, and their relation to the great objects of nature, attach and occupy the mind. It is sufficient that the style be pure, and of a noble simplicity. It is this species of literature which M. de Laplace selected; and it is certain that he placed himself in its first rank. If he writes the history of great astronomical discoveries, he becomes a model of elegance and precision. No leading feature of the subject ever escapes him, and the expression is never either ambitious or obscure. Every thing that he calls great is in fact great; whatever he omits does not deserve to be mentioned.

M. de Laplace retained at a very advanced age that extraordinary memory for which he had been so remarkable from his earliest years; a precious endowment, which, though not genius itself, enables genius to acquire and to preserve. He had not cultivated the fine arts, but he appreciated them. He loved the music of Italy and the verses of Racine; and he often amused himself in reciting from memory various passages of that great poet. The compositions of Raffaelle adorned his apartments. Beside them were the portraits of Descartes, Vietta, Newton, Galileo, and Euler. M. de Laplace had always accustomed himself to a light diet, which he diminished more and more even to excess. His very delicate sight required continual precautions, and he succeeded in preserving it without any alteration. His care of himself had never any other object than that of reserving all his time and all his powers for the labours of the mind. He lived for the sciences, and the sciences in return have rendered his memory immortal.

At the commencement of the malady which ultimately carried him off, his friends observed with dismay an instant of delirium. But even in that state the sciences still occupied him. He spoke with unusual ardour of the motion of the stars, and then of an experiment in physics, which he declared to be a capital one; announcing to the persons he believed to be present, that he would soon communicate these questions to the Academy. Meanwhile his strength rapidly declined. His physician, Majendie, who merited all his confidence by superior talents, and by those attentions which friendship alone could inspire, watched beside his bed. M. Bouvard, his fellow-labourer and friend, never quitted him for an instant. The persons who attended him at his last moments recited the titles of his glory, and spoke of his most splendid discoveries. "What we do know," replied the dying man, "is a small matter; what we do not know is immense." This is all that could be collected; these were the last articulate expressions that dropped from his lips. He soon afterwards expired without pain; the powerful genius which had so long animated him separated itself from its mortal habitation, and returned to the God who gave it. He died on the 5th of March 1827, in the seventy-eighth year of his age.

The successors of this great man will see accomplished the phenomena, the laws of which he discovered. They will observe in the lunar motions the changes which he has predicted, and of which he alone could assign the cause. The continual observation of the satellites of Jupiter will perpetuate the memory of the inventor of the theorems which express the laws according to which their courses are regulated. The great inequalities of Jupiter and of Saturn, pursuing their long periods, and giving to these planetary stars new situations, will incessantly recall one of his most astonishing discoveries. These are the titles of a true glory, which nothing can ever destroy. The spectacle of the heavens will be changed; but, at the remote epoch when this shall occur, the glory of the discoverer will remain unchanged. The traces of his genius bear the stamp of immortality.

The following list of the works of M. de Laplace, for which we are chiefly indebted to La France Littéraire by M. Quérard, includes not only the titles of his different publications which appeared in a separate form; but also those of the numerous memoirs with which, during a period extending to rather more than half a century, he enriched the collections of the Academy and the Institute, and the Journal of the Polytechnic School:

1. Essai Philosophique sur les Probabilités, Paris, 1814, in 4to. Another edition of this work was published the same year in 8vo, and the work was reprinted in 1816, 1819, and 1825. The Essai Philosophique is merely an abstract of the large work on the same subject.

2. Exposition du Système du Monde, in five books, the fifth edition, revised and augmented by the author, Paris, 1824, in 4to, and in two vols. 8vo. The first edition of this work appeared in 1796, in two vols. 8vo. In five books the author treats, 1st, of the apparent motions of the heavenly bodies; 2d, of the real motions of those bodies; 3d, of the laws of their motions; and, 4th, of the theory of universal gravitation. The fifth book contains an abridgment of the history of astronomy.

3. Précis de l'Histoire de l'Astronomie, Paris, 1821, in 8vo. This is merely the fifth book of the fifth edition of the Exposition du Système du Monde, published separately.

4. Théorie Analytique des Probabilités, third edition, revised and augmented by the author. The first edition of this work appeared in 1812, in 4to. From 1816 to 1825 M. de Laplace published four supplements, which the publisher, after having sold them for some years separately, added to the volume to which they now serve as a complement. These supplements treat, 1st, of the application of the calculus of probabilities to natural philosophy; 2d, of the application of the calculus of probabilities to geodesical operations; and, 3d, of the application of geodesical formulae of probability to the meridian of France. The fourth contains an abridgment of the theory of probabilities.

5. Théorie des Attractions Sphériques, et de la Figure des Planètes, Paris, 1785, in 4to. This is a memoir extracted from the collection of the Academy of Sciences.

6. Théorie du Mouvement et de la Figure elliptique des Planètes, Paris, 1784, in 4to. This work was printed at the expense of President Boichard de Suron, who only caused two hundred copies to be struck off, for the purpose of being distributed gratuitously.

7. Traité de Mécanique Céleste, in sixteen books, Paris, 1799-1825, in five vols. 4to, with four supplements published at different times. The first book treats of the general laws of the equilibrium of motion; the second, of the law of universal gravitation, and the motion of the centres of gravity of the heavenly bodies; the third, of the figure of the heavenly bodies; the fourth, of the oscillations of the sea and the atmosphere; the fifth, of the motions of the heavenly bodies around their proper centres of gravity; the sixth, of the theory of the planetary motions; the seventh, of the theory of the moon; the eighth, of the theory of the satellites of Jupiter, Saturn, and Uranus; the ninth, of the theory of comets; the tenth, on different points relative to the system of the world; the eleventh, on the figure and rotation of the earth; the twelfth, on the attraction and repulsion of spheres; and the laws of the equilibrium and motion of elastic fluids; the thirteenth, on the oscillation of the fluids which cover the planets; the fourteenth, on the motions of the heavenly bodies around their centres of gravity; the fifteenth, on the motions of the planets and the comets; and the sixteenth, on the motions of the satellites. A second edition of the first two volumes of this work was published at Paris in 1829, 1830. In this country no attempt has yet been made, so far as we know, to translate the Traité de Mécanique Céleste into English; but, in 1830, an English translation of the first volume, with a commentary, was published at Boston in the United States of America. Both the translation and Laplace, the commentary are by Dr Bowditch of Boston; but the amount of the latter is out of all proportion to the text, being intended to enable persons but moderately skilled in the mathematics to comprehend the profound analytical investigations of the great astronomer, and to follow him to his beautiful and striking results.

8. Besides the works which we have just enumerated, M. de Laplace is also the author of a series of very important Memoirs, in which, from 1772 to 1823, he published the collections of the old and the new Academy of Sciences, that of the Institute, and the Journal of the Polytechnic School. The subjects of these Memoirs are exceedingly various. We give the following list in the chronological order of their impression, viz.: 1. On the Particular Solutions of Differential Equations, and on the Secular Inequalities of the Planets, 1772; 2. On the Integral Calculus, and on the System of the World, 1772; 3. On the Integral Calculus of Partial Differences, 1773; 4. On recurring Series, and their Uses in the Theory of Chances, 1774; 5. On the Probability of Causes afforded by Events, 1774; 6. On some Points in the System of the World, 1775 and 1776; 7. On the Integration of Differential Equations with Finite Differences, 1776; 8. On the Mean Inclination of the Orbits of Comets, id.; 9. On the Use of the Calculus of Partial Differences in the Theory of recurring Series, 1777; 10. On the Precession of the Equinoxes, id.; 11. On the Integration of Differential Equations by Approximation, id.; 12. On Probabilities, 1778; 13. On Series, 1779; 14. On the Determination of the Orbits of Comets, id.; 15. On Heat, id.; 16. On the Electricity which Bodies absorb when reduced to Vapour, 1781; 17. On the Approximations of Formulae which are functions of very great numbers, 1782, 1783; 18. On the Figure of the Earth, 1783; 19. On the Births, Marriages, and Deaths at Paris from 1772 to 1784; 20. On the Population of France, and the Number of Inhabitants in the Country, 1783-1788; 21. On the Secular Inequalities of the Planets and of the Satellites, 1784; 22. Theory of Jupiter and of Saturn, 1787; 23. On the Secular Equation of the Moon, 1786; 24. On the Theory of Saturn's Ring, 1787; 25. On the Secular Variations in the Orbits of the Planets, id.; 26. Theory of the Satellites of Jupiter, 1788, 1789; 27. On the Theory of the Satellites of Jupiter, 1789; 28. On the Flux and Reflux of the Sea, 1790; 29. On the Determination of a Plane which remains always parallel to itself, in the movement of a system of bodies acting upon each other in any manner whatsoever, and free from all foreign action, 1798; 30. On Mechanics, id.; 31. On the Motions of the Heavenly Bodies round their Centres of Gravity, id.; 32. On the Secular Equations of the Motions of the Moon, of her Apogee, and of her Nodes, 1799; 33. On the Motion of the orbits of the Satellites of Saturn and Uranus, 1801; 34. On the Theory of the Moon, id.; 35. On Different Points of Analysis, 1809; 36. On the Motion of Light in Diaphanous Media, id.; 37. On the Approximations of the Formulae which are functions of very great numbers, and on their application to Probabilities, id.; 38. On the Figure of the Earth, 1817; 39. On the Flux and Reflux of the Sea, 1818; 40. Addition to the Memoir on the Figure of the Earth, id.; 41. On the Developments of the true Anomaly, and of the Elliptical Radius Vector, in series arranged according to the powers of the eccentricity, 1823. Lastly, the Marquis de Laplace contributed, in the mathematical department, to the *Leçons de l'École Normale*.

(See *Éloge Historique de M. le Marquis de Laplace*, by Baron Fourier, in the *Mémoires de l'Académie Royal des Sciences de l'Institut de la France*, tom. x. p. lxxxi.; Quérard, *La France Littéraire*, art. Laplace; *Revue Encyclopédique*, tom. xxxiii. p. 880; *Edinburgh Review*, vol. xi. p. 249, et seqq., vol. xv. p. 396, et seqq., and vol. xxiii. p. Lapland, 320, containing masterly criticisms on the *Mécanique Céleste*, the *Exposition du Système du Monde*, and the *Essai Philosophique sur les Probabilités*; and Dissertations Third and Fourth, prefixed to the present work.)