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On Faraday's Lines of Force.


London, Taylor and Francis, 1864. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In "Transactions of the Cambridge Philosophical Society", Volume 10. Fine and clean. Pp. (27)-83, (1) + the pasted on title-page. ¶ First appearance of Maxwell's landmark - and his very first published on electromagnetism - paper in which he anticipates many of the fundamental ideas presented in his famous four-part paper "On Physical Lines of Force" (1861-2) in which he derived the equations of electromagnetism.
The present paper ushered in a new era of classical electrodynamics and catalyzed further progress in the mathematical field of vector calculus. Because of this, it is considered one of the most historically significant publications in the field of physics and of science in general.

Maxwell began his researches on electromagnetism following the completion of his studies at Cambridge in 1854. They were aimed at constructing, at a theoretical level, a unified mathematical theory of electric and magnetic phenomena that would express the methods and ideas of Faraday as an alternative to the theory of Weber." This programme was announced in his first article, 'On Faraday's lines of force', in 1856, and continued in two other major texts, 'On physical lines of force' in 1861-1862 and 'A dynamical theory of the electromagnetic field' in 1865. According to a famous passage in its preface, the Treatise (1873) represented the outcome of this programme" (Landmark Writings, p. 569).

"Maxwell's first paper, "On Faraday's Line of Force" (1855-1856), was divided into two parts, with supplementary) examples. Its origin may he traced in a long correspondence with Thomson, edited by Larmor in 1936. Part 1 was an exposition of the analogy between lines of force and streamlines in an incompressible fluid. It contained one notable extension to Thomson's treatment of the subject and also an illuminating opening discourse on the philosophical significance of analogies between different branches of physics. This was a theme to which Maxwell returned more than once. His biographers print in full an essay entitled "Analogies in Nature," which he read a few months later (February 1856) to the famous Apostles Club at Cambridge; this puts the subject in a wider setting and deserves careful reading despite its involved and cryptic style. Here, as elsewhere, Maxwell's metaphysical speculation discloses the influence of Sir William Hamilton, specifically of Hamilton's Kantian view that all human knowledge is of relations rather than of things. The use Maxwell saw in the method of analogy was twofold. It crossfertilized technique between different fields, and it served as a golden mean between analytic abstraction and the method of hypothesis. The essence of analogy (in contrast with identity) being partial resemblance, its limits must be recognized as clearly as its existence; yet analogies may help in guarding against too facile commitment to a hypothesis. The analogy of an electric current to two phenomena as different as conduction of heat and the motion of a fluid should, Maxwell later observed, prevent physicists from hastily assuming that "electricity is either a substance like water, or a state of agitation like heat. "The analogy is geometrical: "a similarity between relations, not a similarity between the things related."" (DSB)

The 1856 paper has been eclipsed by Maxwell's later work, but its originality and importance are greater than is usually thought. Besides interpreting Faraday's work and giving the electrotonic function, it contained the germ of a number of ideas which Maxwell was to revive or modify in 1868 and later an integral representation of the field equations (1868),the treatment of electrical action as analogous to the motion of an incompressible fluid (1869, 1873), the classification of vector functions into forces and fluxes (1870), and an interesting formal symmetry in the equations connecting A, B, E, and H, different from the symmetry commonly recognized in the completed field equations. The paper ended with solutions to a series of problems, including an application of the electrotonic function to calculate the action of a magnetic field on a spinning conducting sphere.

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