What topics were taught in late-19th century electricity and/or magnetism courses in Europe?
contemplated four volumes; the printing of the first volume began in 1862 and was completed in 1867. The other three volumes never appeared.
It was intended to be an all-comprehensive treatise on physical science, the foundations being laid in kinematics and dynamics, and the structure completed with the properties of matter, heat, light, electricity and magnetism. But the literary partnership ceased in about eighteen years, when only the first portion of the plan had been completed, because each of the members felt he could work to better advantage separately than jointly.
Tait, who held the chair of Natural Pilosophy at Edinburgh from 1860 until shortly before his death in 1901, on his own produced books on:
Sketch of Thermodynamics (1877);
Properties of Matter (1885).
In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. The four re-formulated Maxwell's equations describe the nature of electric charges (both static and moving), magnetic fields, and the relationship between the two, namely electromagnetic fields.
Joseph John Thomson, that in 1884 was chosen to become Cavendish Professor of Physics at the University of Cambridge, published in 1895 his Elements of the Mathematical Theory of Electricity and Magnetism:
[it] was a readable introduction to a wide variety of subjects, and achieved considerable popularity as a textbook.
These 2 volumes discuss research and academic courses in physics in the 19th century at German universities:
Christa Jungnickel and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 1: The Torch of Mathematics, 1800 to 1870. University of Chicago Press, paper cover, 1990a. ISBN 0-226-41582-1. Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925. University of Chicago Press, Paper cover, 1990b. ISBN 0-226-41585-6.
For example, in the years 1890-1893 Ludwig Boltzmann held the Chair of Theoretical Physics at the University of Munich and taught the theory of electrodynamics there. His lecture notes were written up by his students and published in two parts in 1891 and 1892. Quoting from the Volume 2 mentioned above, here is how he treated Maxwell's theory (which he supported):
In the second volume of his lectures on Maxwell's theory, Boltzmann proceeded from the hypothesis that the ether communicates electric and magnetic actions from volume element to the neighboring volume element. Each element supposedly contains an unknown motion causing a displacement, which Boltzmann called theelectrotonic state', following Faraday's terminology. As a starting point for the imagination, Boltzmann conceived of the displacement as the turning angle of a nucleus within each element, any change of which gives rise to a kinetic energy. To represent th e potential energy of an element, Boltzmann fell back on Maxwell's idea that between two rotating nuclei are particles, which serve as friction rollers; the potential energy is then proportional to the work done by the displacement of these particles. By substituting the terms for the kinetic and potential energies into the equation that express Hamilton's principle, Boltzmann derived one set of Maxwell's equations; the other set simply states the assumptions of the derivation.
It was part of Boltzmann intention in his lectures to show how ideas from the distance-action theories relate to Maxwell's theory and to treat special problems by Maxwell's theory as thoroughly as they were treated by the other theories, making it unnecessary for students to go to the older textbooks any longer. In the language of potentials, Boltzmann compared Maxwell's equations with those of the older theories. As the potentials are expressed as integrals
over all space rather than in terms of states of neighboring volume elements, Boltzmann referred to the integral equations as ``Maxwell's distance-action equations' in contrast to his `contact-action' partial differential equations. Boltzmann went on to derive Neumann's induction law, Helmholtz's general theory, and other parts of the older electrodynamics."