Spherical-harmonic analyses of American and Soviet isomagnetic charts for 1955.0. An integration method is developed from Poisson's integral, and for it, a new surface grid based on a spherical icosahedron's subdivisions. Also discussed are the changes since 1835 in the earth's magnetic moment and dipole axis and an extrapolation of the geomagnetic field into the earth's mantle and below.
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