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omitting the detail of any important part. He explains the formation of the tables of the sun, moon, planets, satellites, and catalogues of the fixed stars, and gives everything which can serve to show the present state of astronomy, excepting a good collection of tables of the motions of the heavenly bodies. To supply this deficiency a person, who owns this work, would do well to procure Zach's or Delambre's solar tables, and the tables of the Planets and Satellites, whose titles are mentioned at the beginning of this review.

The Elementi di Astronomia, published in 1819, at Padua, by Santini, in two quarto volumes, contains the most noted theorems in spherics, and the formulas generally used in calculations of astronomy, particularly, a detailed account of the methods of Olbers and Gauss for computing the orbits of comets or planets, with Burckhardt's tables of motion for a parabola, and Gauss's tables for an ellipsis or hyperbola. It is a much smaller work than those just mentioned, does not contain the description of astronomical instruments, has but few plates, and no tables of the motions of the heavenly bodies, but is a good work of its kind.

About the year 1798, Schubert published a system of astronomy in 3 vols. 4to, in the German language, and in 1804, 1810, a smaller one, entitled Populáre Astronomie,' in 3 vols. 8vo. Each volume of this latter work treats of a different division of the science, spherical, theoretical, and physical. It is executed in the best manner, and is well adapted to popular use. Within a short time he has reprinted his large treatise, in the French language, making many improvements in it, to adapt it to the present state of science, so that it may be considered as a new work. The well known talents of the author are a sure pledge of its excellence. Many other useful works on astronomy, of a more limited extent, might be mentioned, as those published by Biot, Woodhouse, Brinkley, and others, but the limits of this Review will not permit a full enumeration of them.

In several of these treatises an abridged history of astronomy is given, and the same is likewise to be found in various Cyclopedias and histories of the mathematics, as Montucla's, and Bossut's. There are, likewise, separate works on this subject, as Bailly's Histoire de l’Astronomie Ancienne et Moderne, some parts of which are beautiful, though he endea

vors, throughout the whole work, to support his fanciful theory of the antediluvian origin of the science. It has, however, been objected to Bailly, that he took too much pains to render his writings, on scientific subjects, elegant, and that he sometimes sacrificed the truth to his fondness for polished sentences and antitheses. Baron de Zach, in speaking of him, makes this remark, Les astronomes n'ont que trop justement reproché a leur malhereux confrère Bailly, d'avoir été grand phrasier, ainsi que D'Alembert et Condorcet. Il a souvent sacrifié la vérité à une tirade, à une antithèse.'

Delambre published in 2 vols. 4to, in 1817, his Histoire de l’Astronomie Ancienne, giving extracts from each author, which enable the reader to form a correct idea of the works of the most noted astronomers of antiquity. He has continued the subject in his Histoire de l’Astronomie du Moyen Age, in 1 vol. 4to, in 1819, and his Histoire de l'Astronomie Moderne, in 2 vols. 4to, in 1821, in which the same plan is pursued. This history is continued to the end of the seventeenth century, and is an excellent work. Delambre's labors were extremely useful to astronomy. The history just mentioned, in 5 vols. 4to, his astronomy in 3 vols. 4to, and the work on the measure of the arch of the meridian,* in 3 vols. 4to, form by no means, the greater part of his labors. His tables of the Sun, Jupiter, Saturn, and the Satellites of Jupiter, required several years' incessant application to complete them. He invented and simplified numerous useful formulas, and in almost everything he wrote, there was a great degree of method and elegance. As perpetual Secretary of the Institute, he made several annual reports, and delivered a number of eulogies on the deceased members, which deserve high commendation for their completeness and impartiality.

The history of the appearances of comets is given by Pingré, in his Cométographie, in 2 vols. 4to, which contains, also, a collection of tables and formulas, for computing their motions.

The periodical journals exclusively devoted to astronomy are numerous; as the Nautical Almanac, Connoissance des Tems, Bode's Jahrbuch, etc. The two last works contain numerous memoirs and accounts of discoveries, useful for a history of the science. The Monatliche Correspondenz, published by Baron de Zach from 1500 to 1813, and his Correspondance Astronomique, from 1818 to the present time; to wbich we must add the Zeitschrift für Istronomie, by Lindeneau and Bohnenberger, froin 1816 to 1818, contain a very full and interesting account of all the discoveries and works on astronomy, during that period, so remarkable for the importance of those discoveries and the improvements in various branches of that science.

* Several astronomers assisted in this measure, as Méchain, Arago, Biot, &c. but the account of their labors was drawn up by Delambre.

The part of astronomy, which treats of the mutual attractions of the heavenly bodies, may be studied most advantageously, in the works of Clairaut, Euler, D'Alembert, Lagrange, and Laplace. Clairaut's Théorie de la Figure de la Terre, is an important work. Several of his papers on the lunar theory were useful in their day, but have been superseded by the improved works of later authors. Euler's publications are extreinely voluminous. Besides his separate works on all points of the system of the world, there are numerous papers of his in the transactions of the Academies of Berlin and Petersburgh, many of which are highly finished compositions, fit to be studied as models of analytical elegance. D'Alembert published several literary works, eulogies of deceased academicians, and many important articles in the Cyclapedia, particularly the Introduction prefixed to the first volume, also numerous memoirs in the transactions of several academies, of which he was an associate, and at intervals, he gave separately his Opuscules, and other mathematical and philosophical papers, in about fifteen volumes, 4to. He introduced into the calculation of problems of dynamics, an important principle by which they were all reduced to the usual calculations of statics; he also showed how to express the motions of fluids in terms of partial differentials. Euler and D'Alembert were cotemporaries, and excelled all others of their time, in mathematical genius and invention. Their talents were different, but it was not easy to decide which, on the whole, deserved the preference. D'Alembert's inventive powers were great, but he generally did not take much pains in finishing and explaining his scientific discoveries. Euler devoted himself to the improvement of the methods of analysis, and with great patience would copy a whole volume, to make a few changes in its arrangement to render it more clear, or to ntroduce

some small corrections and modifications; and what D'Alembert invented, Euler would frequently simplify, adorn, and explain. The course of life of these two illustrious men was very different. D'Alembert's literary acquirements, bis great wit, mixed with some spice of malice, the boldness of his attacks on the most commonly received opinions in religion and government, as in some of the articles of the Cyclopedia, and his connexion and intercourse with Voltaire, raised up against him numerous enemies, who, by their incessant attacks, embittered his life, so that he was sometimes willing to retire a while from this vexatious scene, and take refuge, as he says in one of his letters, in his peaceful geometry. Euler's life, on the contrary, was peaceful and glorious. In his intercourse with the baughty Frederick of Prussia, at whose court he resided, as President of the Academy, he obtained at all times those attentions and civilities due to a man of his great worth, and for several years he experienced none of those ill natured sallies of wit and sarcasm, with which that monarch frequently indulged himself, at the expense of the literary and scientific men, whom he had collected around him. Upon some breach of decorum on the part of the King, Euler demanded his passports, which Frederick very reluctantly granted. Euler then accepted the invitation of the Empress Catherine, and went to Petersburgh, where he was placed at the head of the mathematical department of the Academy of Arts and Sciences of that city, and everything was done to render the situation agreeable to him and to his family. Among other honors, he had the offer of some military title, a circumstance which strongly marks the nature of the Russian government, where every one takes rank according to his military standing. It is unnecessary to say, that Euler declined the proposed honor. He continued at Petersburgh till his death, which happened in 1783, in the seventysixth year of his age. He had lost his sight several years before, but his astonishing powers of computation, by memory, remained unimpaired, and a few minutes before his dissolution, he had been employed on some calculations of the orbit of the then newly discovered planet Uranus.

Upon the decease of Euler, Lagrange remained undisputedly the greatest mathematician then living. He had

published many memoirs in the collections of several academies, with which he was associated ; among them may be particularly mentioned those, in which the discovery of the calcutus of variations is explained, a method, which extends the powers of the differential calculus, and simplifies, in a wonderful degree, the solution of a large class of interesting questions, in pure and mixed mathematics, useful in many cases of physical astronomy; also his papers on the libration of the moon, on the mutual attractions of the satellites, on the theory of functions; but, above all others, his Mécanique Analytique. In this work, he made a great improvement in the method of applying the principle of D'Alembert, for reducing the problems of dynamics to statics. The method used by D'Alembert was indirect, and sometimes troublesome, but Lagrange, by connecting with it the principle of virtual velocities, was enabled, in an extremely simple, elegant, and general manner, to reduce all the problems of mechanics to the common formulas of analysis, and the most complicated questions on the attractions of bodies were reduced to the solution of algebraical and differential equations. This work was written at Berlin, but Lagrange wished to have it printed at Paris, where it could be executed in a better style. A copy was made and forwarded to the care of the Abbé Marie, and it would now hardly be believed, that he could not, in 1788, get a printer to undertake the publication of that single quarto volume, without a guarantee to pay the expenses, in case the sale of the work should not be sufficient. The Abbé agreed to this condition, and did even more ; for, at his own expense, he procured the assistance of one of the first mathematicians of Paris, Legendre, to overlook the publication, and see that it was printed correctly. The second edition of this immortal work, was published in 1811, with many additions and improvements, showing the vigor of his mind, though in extreme

Unfortunately for science, he did not live to complete the whole of the second volume, and a few of , the last chapters are given exactly as in the first edition. This work ought to be studied frequently, by every one who wishes to learn the most approved methods of treating the science of physical astronomy. It is much easier to be read than Laplace's Mécanique Céleste, as it does not go into the

old age.

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