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 it presents the form of the rhombic dodecahedron. Its specific gravity is 2.38 to 2.45, and its hardness about 5.5, so that being comparatively soft it tends, when polished, to lose its lustre rather readily. The colour is generally a fine azure or rich Berlin blue, but some varieties exhibit green, violet and even red tints, or may be altogether colourless. The colour is sometimes improved by heating the stone. Under artificial illumination the dark-blue stones may appear almost black. The mineral is opaque, with only slight translucency at thin edges.

Analyses of lapis lazuli show considerable variation in composition, and this led long ago to doubt as to its homogeneity. This doubt was confirmed by the microscopic studies of L. H. Fischer, F. Zirkel and H. P. J. Vogelsang, who found that sections showed bluish particles in a white matrix; but it was reserved for Professor W. C. Brögger and H. Bäckström, of Christiania, to separate the several constituents and subject them to analysis, thus demonstrating the true constitution of lapis lazuli, and proving that it is a rock rather than a definite mineral species. The essential part of most lapis lazuli is a blue mineral allied to sodalite and crystallized in the cubic system, which Brögger distinguishes as lazurite, but this is intimately associated with a closely related mineral which has long been known as haüyne, or haüynite. The lazurite, sometimes regarded as true lapis lazuli, is a sulphur-bearing sodium and aluminium silicate, having the formula: Na4(NaS3Al) Al2 (SiO4)3. As the lazurite and the haüynite seem to occur in molecular intermixture, various kinds of lapis lazuli are formed; and it has been proposed to distinguish some of them as lazurite-lapis and haüyne-lapis, according as one or the other mineral prevails. The lazurite of lapis lazuli is to be carefully distinguished from lazulite, an aluminium-magnesium phosphate, related to turquoise. In addition to the blue cubic minerals in lapis lazuli, the following minerals have also been found: a non-ferriferous diopside, an amphibole called, from the Russian mineralogist, koksharovite, orthoclase, plagioclase, a muscovite-like mica, apatite, titanite, zircon, calcite and pyrite. The calcite seems to form in some cases a great part of the lapis; and the pyrite, which may occur in patches, is often altered to limonite.

Lapis lazuli usually occurs in crystalline limestone, and seems to be a product of contact metamorphism. It is recorded from Persia, Tartary, Tibet and China, but many of the localities are vague and some doubtful. The best known and probably the most important locality is in Badakshan. There it occurs in limestone, in the valley of the river Kokcha, a tributary to the Oxus, south of Firgamu. The mines were visited by Marco Polo in 1271, by J. B. Fraser in 1825, and by Captain John Wood in 1837–1838. The rock is split by aid of fire. Three varieties of the lapis lazuli are recognized by the miners: nili of indigo-blue colour, asmani sky-blue, and sabzi of green tint. Another locality for lapis lazuli is in Siberia near the western extremity of Lake Baikal, where it occurs in limestone at its contact with granite. Fine masses of lapis lazuli occur in the Andes, in the vicinity of Ovalle, Chile. In Europe lapis lazuli is found as a rarity in the peperino of Latium, near Rome, and in the ejected blocks of Monte Somma, Vesuvius.

LAPITHAE, a mythical race, whose home was in Thessaly in the valley of the Peneus. The genealogies make them a kindred race with the Centaurs, their king Peirithoüs being the son, and the Centaurs the grandchildren (or sons) of Ixion. The best-known legends with which they are connected are those of (q.v.) and the battle with the  (q.v.). A well-known Lapith was Caeneus, said to have been originally a girl named Caenis, the favourite of Poseidon, who changed her into a man and made her invulnerable (Ovid, Metam. xii. 146 ff). In the Centaur battle, having been crushed by rocks and trunks of trees, he was changed into a bird; or he disappeared into the depths of the earth unharmed. According to some, the Lapithae are representatives of the giants of fable, or spirits of the storm; according to others, they are a semi-legendary; semi-historical race, like the Myrmidons and other Thessalian tribes. The Greek sculptors of the school of Pheidias conceived of the battle of the Lapithae and Centaurs as a struggle between mankind and mischievous monsters, and symbolical of the great conflict between the Greeks and Persians. Sidney Colvin (Journ. Hellen. Stud. i. 64) explains it as a contest of the physical powers of nature, and the mythical expression of the terrible effects of swollen waters.

LA PLACE (Lat. Placaeus), JOSUÉ DE (1606?–1665), French Protestant divine, was born in Brittany. He studied and afterwards taught philosophy at Saumur. In 1625 he became pastor of the Reformed Church at Nantes, and in 1632 was appointed professor of theology at Saumur, where he had as his colleagues, appointed at the same time, Moses Amyraut and Louis Cappell. In 1640 he published a work, Theses theologicae de statu hominis lapsi ante gratiam, which was looked upon with some suspicion as containing liberal ideas about the doctrine of original sin. The view that the original sin of Adam was not imputed to his descendants was condemned at the synod of Charenton (1645), without special reference being made to La Place, whose position perhaps was not quite clear. As a matter of fact La Place distinguished between a direct and indirect imputation, and after his death his views, as well as those of Amyraut, were rejected in the Formula consensus of 1675. He died on the 17th of August 1665.

La Place’s defence was published with the title Disputationes academicae (3 vols., 1649–1651; and again in 1665); his work De imputatione primi peccati Adami in 1655. A collected edition of his works appeared at Franeker in 1699, and at Aubencit in 1702.

LAPLACE, PIERRE SIMON, (1749–1827), French mathematician and astronomer, was born at Beaumont-en-Auge in Normandy, on the 28th of March 1749. His father was a small farmer, and he owed his education to the interest excited by his lively parts in some persons of position. His first distinctions are said to have been gained in theological controversy, but at an early age he became mathematical teacher in the military school of Beaumont, the classes of which he had attended as an extern. He was not more than eighteen when, armed with letters of recommendation, he approached J. B. d’Alembert, then at the height of his fame, in the hope of finding a career in Paris. The letters remained unnoticed, but Laplace was not crushed by the rebuff. He wrote to the great geometer a letter on the principles of mechanics, which evoked an immediate and enthusiastic response. “You,” said d’Alembert to him, “needed no introduction; you have recommended yourself; my support is your due.” He accordingly obtained for him an appointment as professor of mathematics in the École Militaire of Paris, and continued zealously to forward his interests.

Laplace had not yet completed his twenty-fourth year when he entered upon the course of discovery which earned him the title of “the Newton of France.” Having in his first published paper shown his mastery of analysis, he proceeded to apply its resources to the great outstanding problems in celestial mechanics. Of these the most conspicuous was offered by the opposite inequalities of Jupiter and Saturn, which the emulous efforts of L. Euler and J. L. Lagrange had failed to bring within the bounds of theory. The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton. In a paper read before the Academy of Sciences, on the 10th of February 1773 (Mém. présentés par divers savans, tom. vii., 1776), Laplace announced his celebrated conclusion of the invariability of planetary mean motions, carrying the proof as far as the cubes of the eccentricities and inclinations. This was the first and most important step in the establishment of the stability of the solar system. It was followed by a series of profound investigations, in which Lagrange and Laplace alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits. The analytical tournament closed with the communication to the Academy by Laplace,