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 COMBERMERE a new attempt in 1825, by forming a similar establishment on a large scale at Orbiston, near Glasgow, which however proved unsuc- cessful. He wrote " Sketches of the Old and New Systems," and "The Religious Creed of the New System." III. Andrew, a Scottish physician and author, brother of the preceding, born in Edinburgh, Oct. 27, 1797, died there, Aug. 9, 1847. He studied medicine in Edin- burgh and Paris, and began practice in Edin- burgh in 1823. In 1836 he was appointed physician to King Leopold of Belgium, and afterward physician in Scotland to Queen Vic- toria. He contributed largely to phrenological and medical journals. His principal works, all of which have passed through many editions, are : " Observations on Mental Derangement " (1831) ; " Principles of Physiology " (1834) ; "The Physiology of Digestion" (1836); and "The Management of Infancy" (1840). His death was hastened by exposure to the vitiated atmosphere of an emigrant ship in which he made a voyage to America; the knowledge which he gained on this voyage was embodied in a letter to the " Times," published a month after his death, which led to the passage of a law regulating the sanitary arrangements in emigrant vessels. His "Life and Correspon- dence " was published by his brother, George Combe (2 vols., Edinburgh, 1850). COMBERMERE, Stapleton Cotton, viscount, a British soldier, born in Denbighshire, Nov. 17, 1773, died at Clifton, Feb. 21, 1865. He entered the army at an early age, and served in India in the war against Tippoo Saib. In 1808 he was sent to the peninsula in command of a brigade of cavalry, and participated in nearly all the great actions, from Talavera to the close of the war. In 1810 he was appointed to the command of the whole allied cavalry under the duke of Wellington. He was repeatedly thanked by parliament for his services, and upon the con- clusion of peace was elevated to the peerage. He was afterward governor of Barbadoes, and commanded the British forces in India from 1822 to 1826. He also distinguished himself at the capture of Bhurtpoor (1826), for which he was made a viscount. In 1834 he .was made a privy councillor, and in 1852 succeeded the duke of "Wellington as constable of the tower of London and lord lieutenant of the Tower Hamlets. In 1855 he became field marshal. COMBES, Edmond, a French traveller, born June 8, 1812, died in 1872. He was vice con- sul at Scala Nova, Asia Minor, and at Rabat, Morocco ; explored the coasts of the Red sea, a portion of Arabia, Abyssinia, and E. Africa, where he was the first to ascertain the altitude of the mountains of the Moon ; and in 1841 he travelled in Nubia and Egypt. With his com- panion, M. Tamisier, he published Voyage en Abyssinie, dans les pays des Gallas, de Choa et d'Ifat, precede d'une excursion dans VArabie Heureuse (4 vols., Paris, 1837-'8). COMBINATIONS, Theory of, in mathematics, a statement of the laws which determine the COMBUSTION 135 possible variations in the grouping of any num- ber of given signs. The signs and groups are known as elements and forms. There are three processes of combination. The first, which is termed permutation, consists in changing the order of the given elements so that the same arrangement is never repeated. The second, which is specially termed combination, consists in arranging the elements into partial groups, so that, without regarding the arrangement, precisely the same elements are not repeated in any form. In permutation, all the elements are contained in each form. In combination, each form may consist of two, three, or any other number of elements less than the whole num- ber given. The third process, termed variation, is a union of the other two. It consists in first making all the forms possible by combination, and then multiplying each of these forms by permutation. In permutation there is a change in the order ; in combination, in the contents or matter; and in variation, in both. The complication and possible number of forms is greatly increased when the elements are re- peated. The theory of combinations has ap- plication to ideas, sounds, colors, and even to fo.od and other material compounds; but its principal use is hi mathematical analysis and in the calculation of chances. The first important contribution to its development was by Buteo (1559), who represented all the throws possible with four dice. Pascal applied it to games, Mersenne to musical tones, and Guldin reckon- ed the number of words which could be formed from 23 letters. Leibnitz recognized its sig- nificance, and sought in vain to make use of it in discovering philosophical truths. Bernoulli and Euler labored upon it, but the first who gave it a scientific character was Hindenburg in 1778 ; and it was subsequently developed by Lagrange, Laplace, Poisson, Pfaff, Eschenbach, and Rothe. Among the treatises on the sub- ject are the Lehrbuch der comlinatorischen Analysis, by Weingartner (Leipsic, 1800-1801), and Vollstandiger Lehrbegriff der reinen Com- linationslehre, by Spehr (Brunswick, 1824). COMBUSTION, a chemical process, in which bodies combine to form a new compound, with the evolution of heat, and usually light. In ordinary cases of combustion, oxygen is one of the combining bodies, and the substance with which it unites disappears with it in a gaseous form. It was formerly regarded as an essential element in combustion, but the phenomena of light and heat, characteristic of rapid combus- tion, are observed when chlorine combines with phosphorus and with some metals when these are in a powdered state ; also in the action of cyan- ogen and potassium, and of sulphur upon iron filings and copper leaf. Some bodies also burn in the vapors of iodine, bromine, and fluorine. ^ As commonly witnessed, combustion is a pro- cess taking place in the presence of atmospheric air, which furnishes the oxygen to support^ it; and it is conducted, not, as most other chemical operations are, for the sake of its products, but