On Lines of Magnetic Force (49) Let any surface be drawn, cutting the lines of magnetic force, and on this surface let any system of lines be drawn at small intervals, so as to lie side by side without cutting each other. Next, let any line be drawn on the surface cutting all these lines, and let <s>another<\s> a second line be drawn near it, its distance from the first being such that the value of M for each of the small spaces enclosed between these two lines and the lines of the first system is equal to unity. In this way let a second system of lines be drawn so that the value of M for every reticulation formed by the intersection of the two systems of lines is unity. Finally from every point of intersection of these reticulations let a line <s>of magnetic force<\s> be drawn through the field, always coinciding in direction with the direction of magnetic force. (50) In this way the whole field will be filled with lines of magnetic force at regular intervals, and the properties of the electromagnetic field will be completely expressed by them. For 1<sup>st<\sup> If any closed curve be drawn in the field, the value of M for that curve will be expressed by the <u>number<\u> of lines of force which <u>pass through<\u> that closed curve. 2<sup>nd<\sup> If this curve be a conducting circuit and be moved through the field an electromotive force will act in it, represented by the <s>number<\s> rate of decrease <s>in unit of time<\s> of the number of lines passing through the curve. 3<sup>rd<\sup> If a current be maintained in the circuit, <s>it<\s> the conductor will be acted on by forces tending to move it so as to increase the number of lines passing through it, and the amount of work done by these forces is equal to the current in the circuit multiplied by the number of additional lines.
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J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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