CONTENTS

Art. Page

639. The force acting on a particle of a substance due to its magnetization .. .. .. .. .. .. .. .. .. .. 251
640. Electromagnetic force due to an electric current passing through it .. .. .. .. .. .. .. .. .. .. .. .. 252
641. Explanation of these forces by the hypothesis of stress in a medium Maxwell's theory that magnetic forces are transmitted through a physical medium (the ether) rather than acting at a distance. .. .. .. .. .. .. .. .. .. .. .. 253
642. General character of the stress required to produce the phenomena .. .. .. .. .. .. .. .. .. .. .. 255
643. When there is no magnetization, the stress is a tension in the direction of the lines of magnetic force, combined with a pressure in all directions at right angles to these lines; the magnitude of the tension and pressure being $\frac{1}{8π} \mathfrak{H}^2$, where $\mathfrak{H}$ is the magnetic force .. .. .. .. .. .. .. .. 256
644. Force acting on a conductor carrying a current .. .. .. .. 257
645. Theory of stress in a medium as stated by Faraday .. .. .. 257
646. Numerical value of magnetic tension .. .. .. .. .. .. 258

CHAPTER XII.

CURRENT-SHEETS.

A "current-sheet" refers to an idealized thin surface or membrane through which electricity flows.

647. Definition of a current-sheet .. .. .. .. .. .. .. 259
648. Current-function A mathematical scalar function used to describe the flow of current in a two-dimensional surface. .. .. .. .. .. .. .. .. .. 259
649. Electric potential .. .. .. .. .. .. .. .. .. 260
650. Theory of steady currents .. .. .. .. .. .. .. 260
651. Case of uniform conductivity .. .. .. .. .. .. 260
652. Magnetic action of a current-sheet with closed currents .. 261
653. Magnetic potential due to a current-sheet .. .. .. .. 262
654. Induction of currents in a sheet of infinite conductivity .. 262
655. Such a sheet is impervious to magnetic action .. .. .. 263
656. Theory of a plane current-sheet .. .. .. .. .. .. 263
657. The magnetic functions expressed as derivatives of a single function .. .. .. .. .. .. .. .. .. .. 264
658. Action of a variable magnetic system on the sheet .. .. 266
659. When there is no external action the currents decay, and their magnetic action diminishes as if the sheet had moved off with constant velocity R .. .. .. .. .. .. .. .. 267
660. The currents, excited by the instantaneous introduction of a magnetic system, produce an effect equivalent to an image of that system Similar to an optical image in a mirror, this refers to a mathematical representation of the magnetic field on the opposite side of the sheet. .. .. .. .. .. .. .. .. .. 267
661. This image moves away from its original position with velocity R .. .. .. .. .. .. .. .. .. .. 268
662. Trail of images formed by a magnetic system in continuous motion .. .. .. .. .. .. .. .. .. .. 268