Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/341

repeating an experiment which had been previously suggested by H. A. Rowland, obtained a new action of a magnetic field on electric currents. A strip of gold leaf mounted on glass, forming part of an electric circuit through which a current was passing, was placed between the poles of an electromagnet, the plane of the strip being perpendicular to the lines of magnetic force. The two poles of a sensitive galvanometer were then placed in connexion with different parts of the strip, until two points at the same potential were found. When the magnetic field was created or destroyed, a deflection of the galvanometer needle was observed, indicating a change in the relative potential of the two poles. It was thus shown that the magnetic field produces in the strip of gold leaf a new electromotive force, at right angles to the primary electromotive force and to the magnetic force, and proportional to the product of these forces.

From the physical point of view we may therefore regard Hall's effect as an additional electromotive force generated by the action of the magnetic field on the current; or alternatively we may regard it as a modification of the ohmic resistance of the metal, such as would be produced if the molecules of the metal assumed a helicoidal structure about the lines of magnetic force. From the latter point of view, all that is needed is to modify Ohm's law

$\mathbf {S} =k\mathbf {E}$

(where S denotes electric current, k specific conductivity, and E electric force) so that it takes the form

$\mathbf {S} =k\mathbf {E} +h[\mathbf {E.H} ]$

where H denotes the imposed magnetic force, and h denotes a constant on which the magnitude of Hall's phenomenon depends. It is a curious circumstance that the occurrence, in the case of magnetized bodies, of an additional term in Ohm's law, formed from a vector-product of E, had been expressly suggested in Maxwell's Treatise^[1]: although Maxwell had not indicated the possibility of realizing it by Hall's experiment.

1. Elect, and Mag., § 303. Cf. Hopkinson, Phil. Mag. x (1880), p. 430.

Y