his fortunes. Fortunately he united simple tastes with an independent, fearless, and benevolent mind; and it is said that he gave away one-half of his income, when it did not amount to 350l. His own account of his own character, written in the third person, runs in the following terms, and is confirmed by the testimony of his friends :-" Devoted to study and privacy till the age of twenty-five, he entered late into the world, and was never much pleased with it. He could never bend himself to learn its usages and language, and perhaps even indulged a sort of petty vanity in despising them. He is never rude, because he is neither brutal nor severe; but he is sometimes blunt, through inattention or ignorance. Compliments embarrass him, because he never can find a suitable answer immediately; when he says flattering things, it is always because he thinks them. The basis of his character is frankness and truth, often rather blunt, but never disgusting. He is impatient and angry, even to violence, when anything goes wrong, but it all evaporates in words. He is soon satisfied and easily governed, provided he does not see what you aim at; for his love of independence amounts to fanaticism, so that he often denies himself things which would be agreeable to him, because he is afraid that they would put him under some restraint; which makes some of his friends call him, justly enough, the slave of his liberty." In his religious opinions D'Alembert was, in the true meaning of the word, a sceptic, and his name has obtained an unenviable notoriety as coeditor, with Diderot, of the celebrated Encyclopédie. His superintendence, however, extended only to the end of the second volume, after which the work was stopped by the French Government; and on its resumption D'Alembert confined himself strictly to the mathematical department. In one respect his

conduct may be advantageously contrasted with that of some of his colleagues; he intruded his own opinions on no man, and he took no pleasure in shocking others, by insulting what they hold sacred. "I knew D'Alembert," says La Harpe, 66 well enough to say that he was sceptical in everything but mathematics. He would no more have said positively that there was no religion than that there was a God; he only thought that the probabilities were in favour of theism, and against revelation. On this subject he tolerated all opinions: and this disposition made him think the intolerant arrogance of the Atheists odious and unbearable. I do not think that he ever printed a sentence which marks either hatred or contempt of religion.”

We proceed to mention the most remarkable of D'Alembert's mathematical works. He published in 1743 a treatise on Dynamics, in which he enunciated the law now known under the name of D'Alembert's principle, one of the most valuable of modern contributions to mechanical science. In the following year appeared a treatise on the Equilibrium and Motion of Fluids; and in 1746, Reflections on the general Causes of Winds, which obtained the prize of the Academy of Berlin. This work is remarkable as the first which contained the general equations of the motion of fluids, as well as the first announcement and use of the calculus of partial differences. We may add to the list of his discoveries the analytical solutions of the problem of vibrating chords, and the motion of a column of air; of the precession of the equinoxes, and the nutation of the earth's axis, the phenomenon itself having been recently observed by Bradley. In 1752 he completed his researches into fluids, by an Essay on the Resistance of Fluids. We have to add to the list his Essay on the Problem of Three Bodies,

as it is called by astronomers, an investigation of the law by which three bodies mutually gravitating affect each other; and Researches on various points connected with the system of the Universe: the former published in 1747, and the latter in 1754-6. His Opuscules, or minor pieces, were collected in eight volumes, towards the end of his life.

Of his connexion with the Encyclopédie we have already spoken. He is said to be singularly clear and happy in his expositions of the metaphysical difficulties of abstract science. He is also honourably known in less abstruse departments of literature by his Mélanges de Philosophie, Memoirs of Christina of Sweden, Essay on the Servility of Men of Letters to the Great, Elements of Philosophy, and a work on the Destruction of the Jesuits. On his election to the office of perpetual Secretary to the Academy, he wrote the Eloges of the members deceased from 1700 up to that date. His works and correspondence were collected and published in eighteen volumes 8vo., Paris, 1805, by M. Bastien, to whose first volume we refer the reader for complete information on this subject.

LEONARD EULER* was born at Basle, April 15, 1707. His father was the clergyman of Reichen, near Basle, and had himself been a pupil of James Bernouilli. He intended his son for his own profession, and, after having been himself his first instructor in mathematics, sent him to the university of Basle. John Bernouilli was at this time Professor, and his sons, Nicolas and Daniel, two more of the eight Bernouillis known to the history of science, were under him. With the sons Euler contracted an intimate friendship; and obtained such a degree of favour even with their father, that the latter gave him a private lesson weekly, upon points more ad

We

We have followed the éloge of Condorcet as to facts and dates. should have preferred that of M. Fuss, but have not had the opportunity of seeing it. The mere biographical details of Euler's life are, however, of the simplest character.