physics at Bonn. Until 1846 his original researches were on geometry. In 1828 and in 1831 he published his Analytisch-Geometrische Untersuchungen in two volumes. Therein he adopted the abbreviated notation (used before him in a more restricted way by Bobillier), and avoided the tedious process of algebraic elimination by a geometric consideration. In the second volume the principle of duality is formulated analytically. With him duality and homogeneity found expression already in his system of co-ordinates. The homogenous or tri-linear system used by him is much the same as the co-ordinates of Möbius. In the identity of analytical operation and geometric construction Plücker looked for the source of his proofs. The System der Analytischen Geometrie, 1835, contains a complete classification of plane curves of the third order, based on the nature of the points at infinity. The Theorie der Algebraischen Curven, 1839, contains, besides an enumeration of curves of the fourth order, the analytic relations between the ordinary singularities of plane curves known as "Plücker's equations," by which he was able to explain "Poncelet's paradox." The discovery of these relations is, says Cayley, "the most important one beyond all comparison in the entire subject of modern geometry." But in Germany Plücker's researches met with no favour. His method was declared to be unproductive as compared with the synthetic method of Steiner and Poncelet! His relations with Jacobi were not altogether friendly. Steiner once 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 relin-
