DIRGE, a song sung at funerals or in commemoration of the dead ; derived from the antiphon, Dirige, Domine, Deus rneus, in conspectu tuo viam meam (adapted from Ps. v. 9), of the open ing psalm in matins for the dead in the Roman Catholic Church. DIRICHLET, PETER GUSTAV LEJEUNE (1805 18S9), German mathematician, was born at Duren on Feb. 13, 1805. He was educated at Cologne, and later held professorships at Breslau and Berlin, and in 1855 he succeeded Gauss at Got tingen. He became a member of the Berlin Academy in 1832 and a foreign member of the Paris academy in 1854. Dirichlet's chief work was on the theory of numbers; he was the first to lecture on this subject at a German university. His researches on complex numbers were published in the Berichte der Berliner Akademie in 1841, 1842 and 1846; they were edited by Dedekind in 1863. Dirichlet also wrote on the theory of potential, on equations of the fifth degree and on definite integrals. In addition he wrote a num ber of memoirs on the work of Gauss, in order to make it more intelligible, but he did not live long enough to complete this work. Dirichlet died at Gottingen on May 5, 1859.