the total quantity of magnetization in the circuit is the number of lines which pass through any section, , where is the element of the section, and the summation is performed over the whole section.
The intensity of magnetization at any point, or the force required to keep up the magnetization, is measured by , and the total intensity of magnetization in the circuit is measured by the sum of the local intensities all round the circuit,
,
where is the element of length in the circuit, and the summation is extended round the entire circuit.
In the same circuit we have always , where is the total resistance of the circuit, and depends on its form and the matter of which it is composed.
On the Action of closed Currents at a Distance.
The mathematical laws of the attractions and repulsions of conductors have been most ably investigated by Ampère, and his results have stood the test of subsequent experiments.
From the single assumption, that the action of an element of one current upon an element of another current is an attractive or repulsive force acting in the direction of the line joining the two elements, he has determined by the simplest experiments the mathematical form of the law of attraction, and has put this law into several most elegant and useful forms. We must recollect however that no experiments have been made on these elements of currents except under the form of closed currents either in rigid conductors or in fluids, and that the laws of closed currents can only be deduced from such experiments. Hence if Ampère’s formulæ applied to closed currents give true results, their truth is not proved for elements of currents unless we assume that the action between two such elements must be along the line which joins them. Although this assumption is most warrantable and philosophical in the present state of science, it will be more conducive to freedom of investigation if we endeavour to do without it, and to assume the laws of closed currents as the ultimate datum of experiment.
