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.
HOGARTH.
“I was born,” says Hogarth in his Memoirs of himself, “in the city of London, November 10, 1697. My father’s pen, like that of many authors, did not enable him to do more than put me in a way of shifting for myself. As I had naturally a good eye, and a fondness for drawing, shows of all sorts gave me uncommon pleasure when an infant; and mimicry, common to all children, was remarkable in me. An early access to a neighbouring painter drew my attention from play; and I was, at every possible opportunity, employed in making drawings. I picked up an acquaintance of the same turn, and soon learnt to draw the alphabet with great correctness. My exercises when at school were more remarkable for the ornaments which adorned them, than for the exercise itself. In the former I soon found that blockheads with better memories could much surpass me; but for the latter I was particularly distinguished.”
To this account of Hogarth’s childhood we have only to add, that his father, an enthusiastic and laborious scholar, who like many of his craft owed little to the favour of fortune, consulted these indications of talent as well as his means would allow, and bound his son apprentice to a silver-plate engraver. But Hogarth aspired after something higher than drawing cyphers and coats-of-arms; and before the expiration of his indentures he had made himself a good draughtsman, and obtained considerable knowledge of colouring. It was his ambition to become distinguished as an artist; and not content with being the mere copier of other men’s productions, he sought to combine the functions of the painter with those of the engraver, and to gain the power of delineating his own ideas, and the fruits of his acute observation. He has himself explained the nature of his views in a passage which is worth attention.
Engraved by J. Mollison.
HOGARTH.
From the original Picture by Himself
in the National Gallery.
Under the Superintendance of the Society for the Diffusion of Useful Knowledge.
London, Published by Charles Knight, Ludgate Street, & Pall Mall East.
“Many reasons led me to wish that I could find the shorter path,—fix forms and characters in my mind,—and instead of copying the lines try to read the language, and, if possible, find the grammar of the art by bringing into one focus the various observations I had made, and then trying by my power on the canvass how far my plan enabled me to combine and apply them to practice. For this purpose I considered what various ways, and to what different purposes, the memory might be applied; and fell upon one most suitable to my situation and idle disposition; laying it down first as an axiom, that he who could by any means acquire and retain in his memory perfect ideas of the subjects he meant to draw, would have as clear a knowledge of the figure as a man who can write freely hath of the twenty-five letters of the alphabet and their infinite combinations.” Acting on these principles, he improved by constant exercise his natural powers of observation and recollection. In his rambles among the motley scenes of London he was ever on the watch for striking features or incidents; and not trusting entirely to memory, he was accustomed, when any face struck him as peculiarly grotesque or expressive, to sketch it on his thumb-nail, to be treasured up on paper at his return home.