GALOIS, Evariste (1811-1832), an eminently original and profound French mathematician, born 26th October 1811, killed in a duel May 1832. A necrological notice by his friend Μ. Auguste Chevalier appeared in the Revue Encyclopédique, September 1832, p. 744; and his collected works are published, Lionville, t. xi. (1846), pp. 381-444, about fifty of these pages being occupied by researches on the resolubility of algebraic equations by radicals. But these researches, crowning as it were the previous labours of Lagrange, Gauss, and Abel, have in a signal manner advanced the theory, and it is not too much to say that they are the foundation of all that has since been done, or is doing, in the subject. The fundamental notion consists in the establishment of a group of permutations of the roots of an equation, such that every function of the roots invariable by the substitutions of the group is rationally known, and reciprocally that every rationally determinable function of the roots is invariable by the substitutions of the groups; some further explanation of the theorem, and in connexion with it an explanation of the notion of an adjoint radical, is given under Equation, No. 32. As part of the theory (but the investigation has a very high independent value as regards the Theory of Numbers, to which it properly belongs), Galois introduces the notion of the imaginary roots of an irreducible congruence of a degree superior to unity; i.e., such a congruence, F(a;) = 0 (mod. a prime number p y ), has no integer root; but what is done is to introduce a quantity i subjected to the condition of verifying the congruence in question, F(t)≡l (mod. ρ), which quantity i is an imaginary of an entirely new kind, occupying in the theory of numbers a position analogous to that of - ...√TT in algebra.
G ALU PPI, Baldassarre (1706-1785), a musical composer, was born in 1706, in the island of Burano, near Venice. His father, a barber by profession, was a musical amateur, and prepared his son for the music school of Venice called Conservatorio degi’ Incurabili, where the great Lotti became hi3 master. His first opera, written at the age cf sixteen, was a failure; but his comic opera named Dorvnda, produced seven years later, was a great success, and laid the foundation of the youthful composer’s fame. He was a prolific writer, and no less than seventy of his operas are enumerated, none of which, however, have kept the stage. Some of these were written for London, where Galuppi resided between 1741 and 1744, but his masterpiece in tragic opera was produced at St Petersburg in 1766. The composer had been induced by liberal offers to accept a position as imperial conductor of music, and to leave his native country for Russia, where he lived in high honour at the court of the czar, and is said to have in return done much for the progress of his art in Russia by introducing amongst other things Italian church-music. In 1768 he left Russia, and resumed his position as organist of the cathedral of St Mark at Venice, to which he had been appointed in 1762, and which had been kept open for him during his absence. He died in 1785, and left 50,000 lire to the poor of Venice. His best comic opera bears the title II mondo della luna. The libraries of Dresden and Vienna preserve several of his operas in MS. At Vienna also some of his works of sacred music may be found. Others are in Paris and Rome.
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