Note on the magnetic potential at the geographic pole

Abstract

In the following the general formulae are developed to calculate the magnetic potential of the permanent field at the geographic pole from the horizontal components of the magnetic force on the surface—a subject in which our lamented colleague Bauer was greatly interested.If V is the potential of the permanent field of terrestrial magnetism and X, Y, and Z are the components of magnetic force towards geographic north, east, and vertically upwards, we have urn:x-wiley:00968013:media:tma31649:tma31649-math-0001 where u is the co‐latitude, λ the longitude, R the Earth's radius. From equations (1) the well known theorems follow: (a) If X is known at all points of the surface, Y can be determined; and (b) if Y is known at all points of the surface and X at all points of one meridian line, or more generally at all points of a line on the surface from the north to the south geographic pole, then X can also be determined at every point.