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Rh (held by him together with his appointments at Mézières), and was received as a member of the Académie; his intimate friendship with C. L. Berthollet began at this time. In 1783, quitting Mézières, he was, on the death of É. Bézout, appointed examiner of naval candidates. Although pressed by the minister to prepare for them a complete course of mathematics, he declined to do so, on the ground that it would deprive Mme Bézout of her only income, from the sale of the works of her late husband; he wrote, however (1786), his Traité élémentaire de la statique.

Monge contributed (1770–1790) to the Memoirs of the Academy of Turin, the Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir “Sur la théorie des déblais et des remblais” (Mém. de l’acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in connexion with it his capital discovery of the curves of curvature of a surface. Léonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him. Monge’s memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795. A memoir in the volume for 1783 relates to the production of water by the combustion of hydrogen; but Monge’s results had been anticipated by Henry Cavendish.

In 1792, on the creation by the Legislative Assembly of an executive council, Monge accepted the office of minister of the marine, but retained it only until April 1793. When the Committee of Public Safety made an appeal to the savants to assist in producing the matériel required for the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his indefatigable activity therein; he wrote at this time his Description de l’art de fabriquer les canons, and his Avis aux ouvriers en fer sur la fabrication de l’acier. He took a very active part in the measures for the establishment of the normal school (which existed only during the first four months of the year 1795), and of the school for public works, afterwards the polytechnic school, and was at each of them professor for descriptive geometry; his methods in that science were first published in the form in which the shorthand writers took down his lessons given at the normal school in 1795, and again in 1798–1799. In 1796 Monge was sent into Italy with C. L. Berthollet and some artists to receive the pictures and statues levied from several Italian towns, and made there the acquaintance of General Bonaparte. Two years afterwards he was sent to Rome on a political mission, which terminated in the establishment, under A. Masséna, of the short-lived Roman republic; and he thence joined the expedition to Egypt, taking part with his friend Berthollet as well in various operations of the war as in the scientific labours of the Egyptian Institute of Sciences and Arts; they accompanied Bonaparte to Syria, and returned with him in 1798 to, France. Monge was appointed president of the Egyptian commission, and he resumed his connexion with the polytechnic school. His later mathematical papers are published (1794–1816) in the Journal and the Correspondance of the polytechnic school. On the formation of the Senate he was appointed a member of that body, with an ample provision and the title of count of Pelusium; but on the fall of Napoleon he was deprived of all his honours, and even excluded from the list of members of the reconstituted Institute. He died at Paris on the 28th of July 1818.

For further information see B. Brisson, Notice historique sur Gaspard Monge; Dupin, Essai historique sur les services et les travaux scientifiques de Gaspard Monge (Paris, 1819), which contains (pp. 162–166) a list of Monge’s memoirs and works; and the biography by F. Arago (Œuvres, t. ii., 1854).

Monge’s various mathematical papers are to a considerable extent reproduced in the Application de l’analyse à la géométrie (4th ed., last revised by the author, Paris, 1819); the pure text of this is reproduced in the 5th ed. (revue, corrigée et annotée par M. Liouville) (Paris, 1850), which contains also Gauss’s Memoir, “Disquisitiones generales circa superficies curvas,” and some valuable notes by the editor. The other principal separate works are Traité élémentaire de la statique, 8ᵉ édition, conformée à la precédente, par M. Hachette, et suivie d’une note &c., par M. Canchy (Paris, 1846); and the Géométrie descriptive (originating, as mentioned above, in the lessons given at the normal school). The 4th edition, published shortly after the author’s death, seems to have been substantially the same as the 7th (Géométrie déscriptive par G. Monge, suivie d’une théorie des ombres et de la perspective, extraite des papiers de l’auteur, par M. Brisson (Paris, 1847).

MONGHYR, a town and district of British India, in the Bhagalpur division of Bengal. The town is on the right bank of the Ganges, and has a railway station, with steam ferry to the railway on the opposite bank of the river. Pop. (1901), 35,880. In 1195 Monghyr, a fortress of great natural strength, appears to have been taken by Mahommed Bakhiyar Khilji, the first Moslem conqueror of Bengal. Henceforth it is often mentioned by the Mahommedan chroniclers as a place of military importance, and was frequently chosen as the seat of the local government. After 1590, when Akbar established his supremacy over the Afghan chiefs of Bengal, Monghyr was long the headquarters of his general, Todar Mal; and it also figures prominently during the rebellion of Sultan Shuja against his brother, Aurangzeb. In more recent times Nawab Mir Kasim, in his war with the English, selected it as his residence and the centre of his military preparations. Monghyr is famous for its manufactures of iron: firearms, swords, and iron articles of every kind are produced in abundance but are noted for cheapness rather than quality. The art of inlaying sword-hilts and other articles with gold and silver affords employment to a few families.

The has an area of 3922 sq. m. The Ganges divides it into two portions. The northern, intersected by the Burhi Gandak and Tiljuga, two important tributaries of the Ganges, is always liable to inundation during the rainy season, and is a rich, flat, wheat and rice country, supporting a large population. A considerable area, immediately bordering the banks of the great rivers, is devoted to permanent pasture. Immense herds of buffaloes are sent every hot season to graze on these marshy prairies; and the ghi, or clarified butter, made from their milk forms an important article of export to Calcutta. To the south of the Ganges the country is dry, much less fertile, and broken up by fragmentary ridges. Irrigation is necessary throughout the section lying on the south of the Ganges. The population in 1901 was 2,068,804, showing an increase of 1.6% in the decade. The principal exports sent to Calcutta, both by rail and by river, are oil-seeds, wheat, rice, indigo, grain and pulse, hides and tobacco; and the chief imports consist of European piece-goods, salt and sugar. The southern portion of the district is well provided with railways. At Lakhisarai junction the arc and chord lines of the East Indian railway divide, and here also starts the branch to Gaya. At Jamalpur, which is the junction for Monghyr, are the engineering workshops of the company. In the early years of British rule Monghyr formed a part of Bhagalpur, and was not created a separate district till 1832.

MŌNG NAI (called by the Burmese and on most old maps Monē), one of the largest and most important of the states in the eastern subdivision of the southern Shan States of Burma. The state of Kéng Tawng (Burmese Kyaing Taung) is a dependency of Mōng Nai. It lies approximately between 20° 10′ and 21° N. and between 97° 30′ and 98° 45′ E., and occupies an area of 2717 sq. m.; pop. (1901), 44,252, of whom more than five-sixths are Shans. The Salween river bounds it on the east. The main state and the sub-state of Kēng Tawng consist of two plains with a ridge between them. There is much flat rice bottom, but a considerable portion consists of gently undulating plain-land. In the central plain rice is the only crop. Outside this considerable quantities of sugar are produced. Tobacco of a quality highly esteemed by the Shans is grown in the Nawng Wawp circle at an altitude of 3100 ft. above sea-level; gram,