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time he resumed his geometrical investigations, but only lived to see the 

 publication of the first part of the treatise upon which he was engaged. 



He took an active part in the management of the University, having 

 been twice Rector, frequently Dean of the Faculty of Philosophy, for 

 many years Member of the Academic Senate and the Examination Com- 

 mission. He was a Member of the Academies of Munich, Haarlem, Rot- 

 terdam, Lund, and Upsala, of the Societe royale de Liege, of the Societe 

 des Sciences Naturelles de Cherbourg, of the Societe Philomathique of Paris, 

 Honorary Member of the Cambridge Philosophical Society, Corresponding 

 Member of the Institute, of the Academies of Vienna, Gottingen, and 

 the Physikalische Verein of Frankfort ; his election as Foreign Member 

 of the Royal Society was in 1855. The Copley Medal for the year 1866 

 was awarded to him for his researches in Analytical Geometry, Magnetism, 

 and Spectral Analysis. 



His separate works are : — 



Analyseos applicatio ad georuetriam altiorem et mechanicam (Bonnee, 

 1824). 



Analytisch-geometrische Entwickelungen (Essen, 1831). 

 System, der analytischen Geometrie (Berlin, 1835). 

 Theorie der algebraischen Curven (Bonn, 1839). 



System der Geometrie des Raumes in neuer analytischer Behandlungs- 

 weise (Diisseldorf, 1846, second edition, 1852). 



Enumeratio novorum phenomenorum in doctrina de magnetismo inven- 

 torum (Bonnae, 1849). 



De crystallorum et gazorum conditione magnetica (Bonnse, 1850). 



Neue Geometrie des Raumes, gegriindet auf die Betrachtung der gera- 

 den Linie als Raumelement (Leipzig, 186S, Erste Abtheilung). 



He also edited a work by his former pupil, Professor August Beer, 

 entitled " Einleitung in die Electrostatic, die Lehre vom Magnetismus und 

 die Electrodynamik," left in manuscript by the latter at his death. 



His papers in the * Transactions' of the Royal Society are : — 



On the Magnetic Induction of Crystals, March 26, 185/. 



On the Spectra of Ignited Gases and Vapours, with especial regard to 

 the different Spectra of the same elementary gaseous substance, conjointly 

 with Dr. S. W. Hittorf, February 23, 1864. 



On a New Geometry of Space, December 22, 1864. 



Fundamental Views regarding Mechanics, May 29, 1866. 



He is also the author of numerous papers on analysis, geometry, elec- 

 tricity, magnetism, physical optics, and spectral analysis, in Crelle's 

 ' Journal,' Gergonne's 'Annalen, 5 Liouville's 'Journal,' Poggendorff's 

 ' Annalen,' the Abbe Moigno's ' Les Mondes,' the ' Philosophical Maga- 

 zine,' the ' Annali di Matematica.' 



He died at Bonn on the 22nd of May, 1868. 



