PFAFF, Christian Heinrich (1773-1852), chemist and physicist, younger brother of J. F. Pfaff noticed below, took his degree as doctor of medicine at Stuttgart in 1793. He travelled with a noble family as physician, and practised for a time at Heidenheim; but he afterwards became professor (extraordinary in 1797, ordinary in 1801) of medicine, physics, and chemistry at the university of Kiel. He was a most prolific author of memoirs on sanitary and medical, and especially on chemical and physical, subjects. His work in chemistry was chiefly analytical and mineralogical. In physics he was distinguished as one of the earlier experimenters with the voltaic current, and had a considerable share in the experimental investigation of its properties. He also made important researches on the carrying power of magnets, more particularly on the effect of the extent of the attracting surface. Comparatively few of his memoirs are now quoted, owing to the fact that none of his results contained any capital discovery; nevertheless he deserves to be remembered as one of the energetic workmen who aided in raising the stately pile of modern experimental science....
PFAFF, Johann Friedrich (1765-1825), German mathematician, was born on 22d December 1765 at Stuttgart. He received his early education at the Carlsschule, where Schiller, afterwards his life-long friend, was a schoolcompanion. His mathematical capacity was early noticed; and after leaving school he pursued his studies in that department at Göttingen under Kästner, author of a History of Mathematics·, and in 1787 he went to Berlin and studied practical astronomy under Bode. In 1788 Pfaff became professor of mathematics in Helmstädt, and so continued until that university was abolished in 1810. From that time till his death (20th April 1825) he held the chair of mathematics at Halle. Pfaff’s researches bore chiefly on the theory of series, to which he applied the methods of the so-called Combinatorial School of German mathematicians, and on the solution of differential equations. His two principal works are Disquisitiones analyticae maxime ad calculum integralem et doctrinam serierum pertinentes (4to, vol. i., Helmstädt, 1797) and “Methodus generalis, aequationes differentiarum particularum, nec non aequationes differentiales vulgares, utrasque primi ordinis inter quotcumque variabiles, complete integrandi” in Abh. d. Berl. Acad. (1814-15). The former work contains Pfaff’s discussion of the equation (a + bx η f x 1 d 2 y ∣ dx i + (c + ex r f xdy/dx + (∕+gx r f y = X, which generally bears his name, but which had originally been treated in a less complete manner by Euler. The latter work contains an important addition to the theory of partial differential equations as it had been left by Lagrange.
An interesting review of Pfaffs memoir was published by Gauss in the Göttingen Gelehrte Anzeigen for 1815 (republished in vol. iv. of his complete works). For fuller details regarding Pfaff and his work, consult Gerhardt, Geschichte der Mathematik in Deutschland (Munich, 1877, p. 198), and Pfaff s correspondence, edited by C. H. Pfaff.
Another brother of this family, Johann Wilhelm Andreas Pfaff (1774-1835), was professor of pure and applied mathematics successively at Dorpat, Nuremberg, Würzburg, and Erlangen.
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