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‎Über die Integrale linearer Differentialgleichungen mit periodischen Coëfficienten.‎

‎Wien, Karl Gerold's Sohn, 1868. 8vo. Uncut and unopened in orig. printed wrappers. In: ""Sitzungsberichte der kaiserlichen Akademie der Wissenschaften"", 58. Band, 1. Heft - Juni. Pp. (1-) 155 a. 7 plates.(Entire issue offered). Boltzmann's paper: pp. 54-59. Clean and fine.‎

‎First apperance of an importent paper in which Boltzmann from a mathematical point of view defends atomism. ""Throughout his career, even in his works on subjects other than kinetic theory Boltzmann was concerned with the mathematical problems arising from the atomic nature of matter. Thus, an early paper with the title ""Über die Integrale linearer Differentialgleichungen mit periodischcn Koeffizienten"" (1868) turned out to be an investigation of the validity of Cauchy’s theorem on this subject, which is needed to justify the application of the equations for an elastic continuum to a crystalline solid in which the local properties vary periodically from one atom to the next."" (DSB). The issue contains an importent paper by JOHANN JOSEPH LOSCHMIDT ""Ableitung des Potentiales bewegter elektrischer Massen aus dem Potentiale für die Ruhestand"", pp. 7-14, in which he attempted to derive the Weber-Ampère law from that of Coulomb, and, in accordance with Kirchhoff, to derive Ohm’s law from hydrodynamic flow laws, analogous to Poiseuille’s law.‎