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‎Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen,‎

‎Berlin, Georg Reimer, 1858. 4to. Extracted from ""Journal für die reine und angewandte Mathematik Crelle/Borchardt"", 55. Band, 1. Heft.: 3. Pp. 25-55 and with titlepage to volume 55. A bit of browning to outer corners of titlepage.‎

‎Firsi printing of Helmholtz' seminal paper on the hydrodynamics of vortex motion, which is the first detailled analysis of fluid motion not constrained to being irrotational - being his most importent contribution to mathematical physics. The paper was the direct inspiration for J.J. Thomson's ""vortex atom"" (See Pais ""Inward Bound"", pp. 176 ff).""In 1857, in a work of genius that proved him to be a mathematician of first rank 'On the Integrals of the Hydrodynamic Equations which express Vortex-motion' (the paper offered), he gave the solution of some extremely difficult hydrodynamical problems. He rejected the earlier hypotheses, and followed up the analogies between the motion of fluids and the electromagnetic action of electrical currents, which were of such much importence for his subsequent work on the Theory of Electricity and Magnetism.""Leo Koenigsberger, p. 167 ff.)""In 1858 Helmholtz published his seminal memoir ""Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen,"" important for both its physical results and its mathematical methods. His motivations for taking up this new research interest remain unclear. One motive seems, however, to have been his interest in frictional phenomena, carried over from his interest in energetics"" another was his growing awareness of the power of Green’s theorem.""(DSB).Parkinson ""Breakthroughs"", 1858 P.‎