In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.
Riemann's health had never been strong.
He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers "Preliminary Sketch of Bi-quaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.
Riemann's results are contained in the memoirs on " Abelian Integrals," &c. (Crelle, t.
The transformation may be applied to any curve u=o, which is thus rationally transformed into a curve u =o, by a rational transformation such as is considered in Riemann's theory: hence the two curves have the same deficiency.