quish mathematics, and for nearly twenty years to devote his energies to physics. Important discoveries on Fresnel's wave-surface, magnetism, spectrum-analysis were made by him. But towards the close of his life he returned to his first love,—mathematics,—and enriched it with new discoveries. By considering space as made up of lines he created a "new geometry of space." Regarding a right line as a curve involving four arbitrary parameters, one has the whole system of lines in space. By connecting them by a single relation, he got a "complex" of lines; by connecting them with a twofold relation, he got a "congruency" of lines. His first researches on this subject were laid before the Royal Society in 1865. His further investigations thereon appeared in 1868 in a posthumous work entitled Neue Geometrie des Raumes gegründet auf die Betractung der geraden Linie als Raumelement, edited by Felix Klein. Plücker's analysis lacks the elegance found in Lagrange, Jacobi, Hesse, and Clebsch. For many years he had not kept up with the progress of geometry, so that many investigations in his last work had already received more general treatment on the part of others. The work contained, nevertheless, much that was fresh and original. The theory of complexes of the second degree, left unfinished by Plücker, was continued by Felix Klein, who greatly extended and supplemented the ideas of his master.
Ludwig Otto Hesse (1811–1874) was born at Königsberg, and studied at the university of his native place under Bessel, Jacobi, Richelot, and F. Neumann. Having taken the doctor's degree in 1840, he became docent at Königsberg, and in 1845 extraordinary professor there. Among his pupils at that time were Durège, Carl Neumann, Clebsch, Kirchhoff. The Königsberg period was one of great activity for Hesse. Every new discovery increased his zeal for still greater achievement. His earliest researches were on surfaces of the second order,
