The Geomagnetic Ring‐Current: I— Its Radial Stability

§ 1. Introduction —In our theory 1 of geomagnetic storms, we attribute the main phase to a hypothetical electric ring‐current, with a radius which is only a small multiple ( Z ) of the radius ( a ) of the Earth; the influence of such a ring on the variations of cosmic‐ray intensity has also been suspected. 2 In the original account of our theory we discussed, 3 inter alia , the mode of formation of the ring, its size, density, current‐intensity, and rate of decay. We hope to supplement that discussion in a series of Notes; in this, the first, we assume the existence of the ring, and consider its radial stability. For mathematical convenience we idealize the problem by making it “cylindrical”; in this respect the present Note resembles our recent “Theory of the first phase of a geomagnetic storm,” 4 which will here be referred to by the initials FP .