Assemblages of lines of force are widely used to represent electric and magnetic fields, the density of lines in the neighborhood of a point being proportional to the intensity of the vector at that point. It is not generally recognized, however, that the properties of continuity and individuality of such lines are irrelevant so far as observable electromagnetic phenomenon are concerned.

Contrary to widely held views, it is not possible generally to represent the magnetic field of a linear circuit carrying a steady current by such an assemblage of lines of force which are everywhere continuous. This is because the continuous magnetic lines of force do not generally form simple closed curves, which each link the circuit just once. The interlinkage which is significant is that between the circuit and arbitrarily chosen closed paths of integration of the magnetic vector.

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