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James Clerk Maxwell: On Physical Lines of Force, first editionMAXWELL, JAMES CLERK.  On Physical Lines of Force, Parts 1 and 2

“With a century and a half of hindsight we can see the spinning cell model as a crucial bridge between old and new ideas—built from old materials but paving the way for a completely new type of theory, one which admits that we may never understand the detailed workings of nature… Scientific historians now look upon his spinning cells paper as one of the most remarkable ever written…” –Basil Mahon

FIRST EDITION of Maxwell’s celebrated mechanical model of the electromagnetic field, a significant step in the development of his equations describing electricity and magnetism.

“As early as 1857 Maxwell began to develop the idea of orienting molecular vortices along magnetic field lines, culminating in the publication of his paper ‘On physical lines of force’… He posited a honeycomb of vortices in which each vortex cell was separated from its neighbour by a layer of spherical particles, revolving in the opposite direction to the vortices. These ‘idle wheel’ particles communicated the rotatory velocity of the vortices from one part of the field to another. In this ether model, the most famous image in nineteenth-century physics, the analogy provides mechanical correlates for electromagnetic quantities. The angular velocity of the vortices corresponds to the magnetic field intensity, and the translational flow of the idle wheel particles to the flow of an electric current; the field equations are based on the rotation of molecular vortices in the ether. He emphasized that while the theory was mechanically conceivable, the model itself was provisional and temporary, even awkward, hardly ‘a mode of connexion existing in nature’ (Niven, 1.486), an argument that has generated much philosophical discussion about the role of models in physics” (DNB).

Maxwell “had not expected to extend his paper On Physical Lines of Force beyond Parts 1 and 2” but in the summer of 1861 he began extending his mechanical model to cover “electrostatics, displacement current and waves” [Part 3] and used “his model to explain why polarized light waves change their plane of vibration when they pass through a strong magnetic field [Part 4]” (Basil Mahon, The Man who Changed Everything: The Life of James Clerk Maxwell). NOTE: The present volume contains only Parts 1 and 2, not Parts 3 and 4 which were conceived later and published in the following year (1862).


In The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. Vol. XXI, Fourth Series, January—June, 1861, pp. 161-75; 281-91; 338-48. London: Taylor and Francis, 1861. The complete volume offered. Octavo, contemporary three-quarter navy polished calf, marbled boards, endpapers, and edges. Institutional stamp on two preliminaries of each volume. Bindings scuffed but text clean. $2800.

Famous plate of Maxwell's "vortices", click to enlarge:

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