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* LEGENDRE. 91 LEGEEDEMAIN. made with respect to the angles. The method of least squares was introduced in his Xouvellcs melhodts mentioned below, although Gauss had already (1795) used it. The celebrated law of quadratic reciprocity (see Xumber), which Gauss called "the gem of arithmetic,' appeared in a memoir of 1785, but the first proof was given in his Theorie dcs nomhres. The most im- [tortant of Legendre's works is the Trait c des fonciions elliptiques, upon which he worked for forty jears. It is a tribute to his generosity that just as his work was appearing the labors of Abel and Jacobi became known, and were at once recognized by him as superior to his own. He even went so far as to embody them, with due credit, in his last volume. (See Fl'>'Ctions. ) The work which had the greatest popularity, and which was a classic for a century, was his Elements de geometric (1794. 15th ed. 1881; Ger. trans, by Crelle, 6th ed. 1873; Eng. trans. 1800). The later editions of this work contain his proof of the irrationality of tt and ir". His other works are: Essai siir la theorie des nom- hres (1798: 4th ed. 1900; Ger. trans, by Maser, 1886); youvelle theorie des paralleles ' {1S03) ; Kouvelles ntcthodes pour la determination des orbites des cometes (1805) ; Exercices de calciil integral (1807; new ed., 3 vols., 1819); Traite des fonetions elliptiques et integrales Euleriennes (3 vols., 1826-32). LEGEB, le-zha'. Loos PAri. JIahie (1843 — ) . A French writer and linguist, born at Toulouse. He was educated at the Lycee Louis- le-Grand, and early turned his attention to the study of Slavic languages. In 1864 he went to Bohemia, and this visit was followed by many others to that country. Hungary, Poland, and especially to Russia. After teaching at the Sor- bonne. he was at the Eeole Speciale des Langues Orientales, where he became full professor in 1877. In 1885 he was appointed professor of the Slavic languages and literatures at the Col- lege of France. Besides his contributions to the important journals of the day, he wrote such works as Etudes slares (1875) ; youvelles etudes ■slaves (1880; second series 1886) ; Contes slaves (1882); Chronique dite de Xestor (1884); La Save, Ir Dannie et le Balkan (1884); La Bulijarie (1885) ; Bistoire de I'Autriclie-Hongric (1878 and 1889) ; Russes et Slaves (1890) ; and La littcrature riisse (1892). LEGERDEMAIN, ]ej'er-d*-nian' (Fr., sleight of hand). The art of performing tricks of de- ception — in the narrower sense, with the hands alone: broadly, with any aid of physical ap- pliances. The arts of magic, seemingly as ancient as human intelligence, are of two general types: ( 1 ) Forms such as necromancy, divination, sor- cery or enchantment, perhaps astrology-, in which the magician works by means of spells, incanta- tions, or of some occult science supposed to give liim knowledge of superhuman agencies and power to direct them: (2) legerdemain and jugglery in which the magician displays his own skill at wonder-working. Ordinarily, among primitive peoples, the magician — witch-doctor, medicine man. or what not — is himself deceived by the usages of magic of the first type, receiving them as mysteries of his cult and implicitly relying upon their efficacy. Magic of the second type, however, is used and understood by him merely as a means of impressing his more ignorant Voi^ XII.— 7. fellow-men with a sense of his power; it is con- scious deception. This distinction is significant in the history of magic and is maintained even in modern civilization; for, although many forms of the first type of magic are imitated by tricks of legerdemain, notoriously in the spiritualistic seance, there still persists credulity in oco'.ltism in connection with the frankest recognition of the natural causes of the deceptions of jugglery. Legerdemain and jugglery are sometimes grouped under the title natural magic,' probably on the analog)- of 'natural philosophy,' since so many of their deceptions are applications of sim- ple principles of physics and chemistry; but the two terms are not precisely synonymous. Jug- glery is the broader term, denoting not only tricks of deception, but performances with para- phernalia demanding great skill and dexterity, in which no deception is intended. Legerdemain, however, is confined simply to tricks of deception. The diverse development is perhaps illustrated in the jugglers of India and those of Japan. The performances of the former so often cited, such as the mango trick, the basket trick, and the snake- charming trick, are properly legerdemain, de- pending for their deception upon some type of substitution ; whereas the feats of the Japanese are very largely feats of equilibration, as the balancing of objects upon various parts of the body, demanding great skill, but not as a rule designed to deceive. In legerdemain proper the essential feature is generally an act of substitution, as when, for ex- ample, the performer seems to discover eggs, money, and the like objects in places previously perceived to be empty. Often the substitution requires for its efficiency elaborate mechanical devices, though the most skillful thaumaturgists prefer to rely upon their own manual dexterity. The power of deceiving is almost invariably due to power of diverting the percipient's attention at a crucial moment — the moment of the substi- tution. In this even more than in celerity of movement lies the essence of the art. The psychological principles underlying the deception rest wholly upon the laws of attention. In pro- portion as attention is intensified, its scope be- comes narrowed; as, for example, concentrated inspection of any object renders stimuli affecting the marginal i-egions of the field of vision prac- tically invisible. It is, accordingly, the first duty of the performer to centre the percipient's at- tention as strongly as possible upon the object- matter of the trick to be performed. Succeed- ing in this, he gains a practical control over the percipient's range of vision and has little diffi- culty in diverting it at the crucial moment. It may thus be said that the keenest scrutiny is the likeliest to fall victim to the trick. The part of the legerdemainist himself, how- ever, is one of great difficulty: for he must be able to discoordinate his actions and diversify his attention to a degree only attainable by long practice. His hands and eyes mvist be trained to work apart — the hands performing the substitu- tion, eyes and bodily pose misleading the per- cipient. Similarly, his attention must compre- hend and direct many diverse details at once. The origin of thaumaturgy is of remote an- tiquity. Savages the world over have developed cults and mysteries which transmit, with other lore, tricks of leserdeniain from generation to generation. The Navaho Indians perform a trick