Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/369

In the special case of the field which surrounds a straight wire carrying a continuous current, the lines of magnetic force are circles round the axis of the wire, while the lines of electric force are directed along the wire; hence energy must be flowing in the medium in a direction at right angles to the axis of the wire. A current in any conductor may therefore be regarded as consisting essentially of a convergence of electric and magnetic energy from the medium upon the conductor, and its transformation there into other forms.

This association of a current with motions at right angles to the wire in which it flows doubtless suggested to Poynting the conceptions of a memoir which he published^[1] in the following year. When an electric current flowing in a straight wire is gradually increased in strength from zero, the surrounding space becomes filled with lines of magnetic force, which have the form of circles round the axis of the wire. Poynting, adopting Faraday's idea of the physical reality of lines of force, assumed that these lines of force arrive at their places by moving outwards from the wire; so that the magnetic field grows by a continual emission from the wire of lines of force, which enlarge and spread out like the circular ripples from the place where a stone is dropped into a pond. The electromotive force which is associated with a changing magnetic field was now attributed directly to the motion of the lines of force, so that wherever electromotive force is produced by change in the magnetic field, or by motion of matter through the field, the electric intensity is equal to the number of tubes of magnetic force intersected by unit length in unit time.

A similar conception was introduced in regard to lines of electric force. It was assumed that any change in the total

where W denotes the vector

$-(k+4n/3){\text{div }}\mathbf {e.e} +n[{\text{curl }}\mathbf {e.{\dot {e}}} ]$;

and since the expression which is differentiated with respect to t represents the sum of the kinetic and potential energies per unit volume of the solid (save for terms which give only surface-integrals), it is seen that W is the analogue of the Poynting vector. Cf. L. Donati, Bologna Mem. (5) vii (1899), p. 633.

1. Phil. Trans, clxxvi (1885), p. 277.