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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, his 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 awhile 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 haughty 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 calculus 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 old age. 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
detail and numerical calculations, which are necessary in the application of the formulas. Lagrange succeeded Euler in the direction of the academy at Berlin, and he resided there till the death of Frederick; soon after which, in the year 1787, he was invited by the French minister to accept an appointment at Paris, where he remained till his decease, in 1813. For several years after his return to Paris, he was affected with a melancholy depression of spirits, or apathy, which made him wholly inattentive to mathematical pursuits; he said his enthusiasm was extinct; and, for two years after his Mécanique Analytique had been printed, his curiosity had not been sufficiently excited to cut open the leaves and look at his printed copy. A mind like Lagrange's could not, however, be unoccupied. The discoveries that had been made in chemistry, and the new nomenclature, attracted his attention; he studied that science, which had formerly appeared obscure, and was surprised to find it, to use his own expression, as easy as algebra; he attended also to other branches of science, to literature, and to metaphysics. The revolution, which soon after took place, again excited him, and renewed his zeal for his former pursuits; and, in the few last years of his life, he appeared with all the energy of his best days. He was a great admirer of the talents and writings of Newton, but remarked, that Newton must be considered as very fortunate, in being born at a time, when an opportunity was given him to explain the system of the world; a good fortune, added he, with an air of chagrin, that one does not meet with every day. He recommended the writings of Euler to students as models, without seeming to be aware, that nothing better could be offered for their imitation than some of his own works.
The discoveries of Laplace, who now takes the lead in mathematical acquirements, have been very numerous and important; several of them have already been mentioned. It would extend too far the limits of this review to attempt to analyse, or give a particular account of his great work, the Mécanique Céleste, in which all his improvements are embodied with those of the eminent men, who preceded him; the whole forming a complete and beautiful system of all that is now known in physical astronomy. Those, who take pleasure in the abstruse investigation of modern analysis, may there VOL. XX.-No. 47.
find it applied, with great elegance, to the demonstration of all the principles of dynamics, to the figures and motions of the planetary bodies, satellites, and comets, and to the effects of their mutual attractions. The theorems and principles contained in this work have been explained by Laplace, in as popular a manner as the nature of the subject would admit, in his Exposition du Système du Monde, which has gone through five editions, with numerous improvements. Whoever will make himself master of these works, will have no need to seek in other sources for anything relative to the principles of physical astronomy, or the application of those principles to the system of the world.
ART. V.-Letters on the Gospels. By MISS HANNAH ADAMS. 18mo. pp. 216. Cambridge. Hilliard & Metcalf. 1824.
THE author of these letters has long been known to the public, as a successful writer on theological subjects, and as having rendered essential service to religion, by the productions of her pen. Her Views of Religions, or, as she denominates it in the last edition, her Dictionary of all Religions and Religious Denominations, has been a popular work from the time of its first publication. It has passed through four editions, the last of which is enlarged and greatly improved. It was published in England, with a preface and additions, by Mr Andrew Fuller; and also in another form by Mr Thomas Williams, who likewise made alterations. To both these editors, Miss Adams acknowledges herself indebted, for some of the improvements of her fourth edition. This work is the best manual with which we are acquainted, for giving information respecting the religious views now entertained by Christians, and such as have prevailed in different ages, since the origin of Christianity. It has the peculiar merit of the strictest candor and impartiality; and so completely has the author divested herself of all individual prepossessions, that it may be doubted whether, from a single passage in the whole work, her own religious sentiments can be inferred. This freedom from personal bias, in exhibiting the views of others, especially on topics rarely touched without calling out private opinion, in
spires confidence in her statements, as well as respect for her judgment and christian charity.
The public is also indebted to Miss Adams for a History of the Jews, from the Destruction of Jerusalem to the Nineteenth Century. This is a judicious and well arranged compilation from the best authors, and brings to the knowledge of the reader, all the important incidents in the history of that remarkable people, from the destruction of their city, down to recent times. It speaks of the persecution suffered by the Jews, their religious ceremonies and tenets, their various conditions as a people, and their steadfastness in adhering, under every vicissitude of fortune, to their national peculiarities.
Miss Adams's Summary History of New England has been commended for its accuracy, and the perspicuity of its style.
The reputation, which she has acquired by the above works, will not suffer by her Letters on the Gospels. She professes to have written them for the improvement of the young, and to this end they are exceedingly well adapted. Every one knows, that throughout the writings of the Evangelists, perpetual allusions are made to the customs of the times, local circumstances, the religion of the Jews, and habits of thinking peculiar to the age; and that, without a knowledge of these particulars, the meaning of Scripture is, in many parts, obscure and uncertain. Had facts of this sort always been sought out and carefully studied, by those who have undertaken to interpret the Scriptures, the world might have been spared a thousand absurdities, which have gone abroad in the garb of commentaries and annotations, and the substance of religion might have been profited by the labor and ingenuity, that have been wasted on its unreal forms. In her first letter, Miss Adams has the following just remarks; 'While attentively perusing the New Testament, always bear in mind that the Gospel was first preached to the Jews, in Judea, and that the Evangelists and Apostles, with the exception, perhaps, of St Luke, were all of the Hebrew nation. Much of the peculiar beauty of the inspired writings cannot be perceived, unless the history, condition, and character of the Jews have become objects of your attention, not only during the period of the Mosaic dispensation, as recorded in the Old Testa