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LAP In 1782 he was intrusted with the task of destroying the English settlements on Hudson's Bay. Three vessels were placed under his command for this purpose, in which he was completely successful. Fort Prince of Wales and Fort York were razed to the ground, the English garrison having left them. La Pérouse, who had already given abundant proofs of his valour and ability, now displayed a humanity that was no less creditable to him. Hearing that several English were then in the woods, exposed to death either from starvation or by the tomahawks of the savages, he left some provisions and arms for their use. At Fort York he took possession of the traveller Hearne's manuscript, but returned it to him on the understanding that it should be published as soon as he returned to England. Peace having been signed in 1783, the French government, anxious to emulate the discoveries recently made by Cook and other illustrious English navigators, fitted up two frigates, the Boussole and the Astrolabe, expressly for this purpose, and gave the command of the expedition to La Pérouse. He sailed from Brest in the former vessel, August 1, 1785, doubled Cape Horn, and by June of the following year had reached 60° north latitude. After completing the researches of Cook and Vancouver on the shores of California, he sailed across to China, anchoring at Macao in January, 1787. His explorations hitherto had been anticipated by former voyagers, but the researches which he now commenced on the coast of Tartary and Kamtschatka were of real interest and importance. He arrived at Avatsha in the latter country in September, 1787, and thence sent one of his officers, De Lesseps, with the journals of his voyage, to Paris overland. From Avatsha he proceeded to the Navigators' Islands, where a terrible calamity befel him—De Langle, the captain of the Astrolabe, and eleven of his companions being surprised and slain by the natives. In December, 1787, La Pérouse called at the Friendly Islands; subsequently touched at Norfolk Island; and in January, 1788, landed in Botany Bay, where Governor Phillip had recently arrived for the purpose of forming a British colony. From Botany Bay La Pérouse addressed his last letter to the French minister of marine, and then resumed his voyage. Years passed by, and nothing more was heard of him. Even amidst the storm and trouble of the Revolution he was not forgotten by his countrymen, and several vessels were despatched in order to ascertain his fate. All their efforts to do so were fruitless; and it was not until 1826 that an English captain, Peter Dillon, navigating amongst the Queen Charlotte Islands, discovered at Wanicoro the remains of the shipwrecked vessels. He was assured by some of the older natives that many of the crew long survived their disaster. Be this as it may, a French vessel visited the spot in 1828, and a rough mausoleum and obelisk were erected by the captain on the lonely island to the memory of the gallant and unfortunate La Pérouse.—W. J. P.  LAPIDE,, or , a learned and pious jesuit, who was born at Bucold in the diocese of Liege, and died at Rome in 1637. He lectured at Rome on the sacred writings, and left esteemed commentaries on all the books of the Bible, which were reprinted in a collected form at Venice in 1711 in 16 vols. folio.—G. BL.  LAPLACE,, Marquis de, one of the greatest mathematicians of the age, was born at Beaumont-en-Auge, in the department of Calvados, on the 23rd March, 1749. He was the son of a farmer, who was unable to give him a good education; but having shown a great aptitude for mathematics, some of his wealthy neighbours were at the expense of educating him, and so rapid was his progress that at a very early age he taught mathematics at his native place. Ambitious of distinction, he went to Paris in 1767 with a letter of introduction to D'Alembert; but having received no attention from the great mathematician, he addressed to him a letter on a subject in mechanics which evinced such a knowledge of mathematics that D'Alembert became his friend and patron. From this time Laplace took a high position among the great men who then adorned the French capital. On the resignation of Bezout he was appointed examiner of the pupils in the royal corps of artillery, and he is said to have at this time made the discovery of the invariability of the mean distances of the planets from the sun. In 1772 he communicated to the Academy of Sciences at Turin a memoir "On the Integration of Equations of Finite Differences;" and in two successive papers published in the Memoirs of the Academy of Sciences in Paris for 1777 and 1779, he gave an account of improvements upon this method of integration. Lagrange had shown in 1782 that, on the hypothesis that the derangements of each planet of our system were produced by a continual variation of the elliptic elements, the secular variation of the elements was always such that the stability of the planetary system was permanently insured. In studying this subject Laplace arrived at the same result, without any hypothetical considerations. In his memoir of 1784 he has given the two following theorems, founded only on the supposition, or rather the fact, that all the planets revolve round the sun in the same direction:—1. That if the mass of each planet is multiplied by the square of the eccentricity, and this product by the square root of the mean distance, the sum of these products will be invariable; and 2. That if the mass of each body be multiplied by the square of the tangent of the orbits' inclination to a fixed plane, and that product by the square root of the mean distance, the sum of these products will also be invariable. The same memoir which contains this great discovery, contains also the earliest notice of other two of the most important discoveries in physical astronomy made by Laplace. The first of these is the explanation of the large inequality of Jupiter and Saturn, which long appeared inexplicable by the theory of gravitation, and which he found to arise from the mean motions of the two planets being nearly commensurable—five times the mean motion of Saturn being nearly equal to twice the mean motion of Jupiter. The second of these discoveries was his explanation of the remarkable relations between the epochs and the mean motions of the three inner satellites of Jupiter. The mean motion of the first satellite was nearly double that of the second, and that of the second nearly double that of the third. It was also proved that the mean longitude of the first satellite plus the mean longitude of the third, minus thrice the mean longitude of the second, was nearly equal to 180°. Another of Laplace's great discoveries was made in 1787. The cause of the acceleration in the mean motion of the moon had baffled the analysis of Euler and Lagrange. Laplace, however, has demonstrated that it arises from a variation in the mean action of the sun, occasioned by a variation in the eccentricity of the earth's orbit. Laplace discovered also that an inequality in the moon's longitude, amounting to about 8´´, was produced by the spheroidal figure of the earth. We owe to Laplace also the singular discovery that there is an invariable plane in every system of bodies, and that in the planetary system this plane is inclined in 1750, 1° 35´ 31´´ to the ecliptic, with its ascending node in longitude 102° 57´ 30´´. Two hundred years later, namely, in 1950, there will be no change in the inclination, and a change of only 15´ in the place of the node.

After having made these and other discoveries in physical astronomy, which our limits will not allow us to describe, Laplace resolved to publish them all in his "Mecanique Celeste"—a work in five octavo volumes, which, like that of the Principia of Newton, may be regarded as one of the noblest monuments of human genius. The two first volumes of the "Mecanique Celeste" were published in 1799; the third volume appeared in 1802; the fourth in 1805; and the fifth in 1825. The work is divided into sixteen books, of which ten occupy the first four volumes. The first book treats of the general laws of equilibrium and motion; the second of the laws of gravitation and of the centre of gravity of the planets; the third of the figure of the planets; the fourth of the oscillations of the sea and the atmosphere; the fifth of the motions of the planets about their centres of gravity; the sixth of particular theories of the planets; the seventh of the theory of the moon; the eighth of the theory of the other satellites: the ninth of the theory of comets; the tenth on various points in the system of the universe, and a supplement to book tenth on capillary attraction; the eleventh on the figure and rotation of the earth; the twelfth on the attraction and repulsion of spheres, and on 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 motion of the planets about their centres of gravity; the fifteenth on the motion of the planets and comets; the sixteenth on the motion of satellites, with a second supplement on an extended theory of capillary attraction. A short and posthumous supplement was published in 1827, on the development of the distance of two planets and of its elliptic co-ordinates, and on the tides of the atmosphere.

This great work was translated by Dr. Nathaniel Bowditch of Salem, Massachusetts, and published with a copious running commentary, at Boston, in four large quarto volumes, in the years 