declared that he would stop writing for Crelle's Journal if Plücker continued to contribute to it.66 The result was that many of Plücker's researches were published in foreign journals, and that his work came to be better known in France and England than in his native country. The charge was also brought against Plücker that, though occupying the chair of physics, he was no physicist. This induced him to relinquish
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 Betrachtung 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,
and were partly synthetic. He solved the problem to construct any tenth point of such a surface when nine points are given. The analogous problem for a conic had been solved by Pascal
by means of the hexagram. A difficult problem confronting mathematicians of this time was that of elimination. Plücker
had seen that the main advantage of his special method in analytic geometry lay in the avoidance of algebraic elimination. Hesse, however, showed how by determinants to make algebraic elimination easy. In his earlier results he was anticipated by Sylvester, who published his dialytic method
of elimination in 1840. These advances in algebra Hesse applied to the analytic study of curves of the third order. By linear substitutions, he reduced a form of the third degree in three variables to one of only four