On vertical electric currents and the relation between terrestrial magnetism and atmospheric electricity

1. To what extent the magnetic forces as observed on the surface of the Earth can be referred to a potential, is a subject of paramount interest. The solution of the problem is of great importance, both as regards the constitution of the so‐called permanent magnetic field of the Earth and the systems giving rise to the manifold variations to which the terrestrial magnetic field is continually subject.2. Any electric currents circulating above or below the Earth's surface in concentric layers, i. e., parallel to the surface, will give rise to magnetic forces which may be represented by a potential. Electric currents, on the other hand, cutting the Earth's surface, produce, in general, a mixed magnetic system: the horizontal components of such currents give rise to a magnetic potential, whereas, the vertical components cause magnetic forces which cannot be referred to a potential. As is well known, the test of the existence of a potential is the vanishing of the line‐integral of the magnetic force taken around a closed curve, or circuit, on the Earth's surface. If the line‐integral does not vanish and its departure from zero cannot be explained by error of observation, or local magnetic disturbances in the region of the circuit, then the existence of a non‐potential is revealed; from the magnitude and sign of the integral we may then determine the strength and direction of the electric currents passing perpendicularly through the surface of the region enclosed by the circuit.