The magnetic condition of the Earth expressed as a function of the time by V. Carlheim‐Gyllensköld

Abstract

It is doubtless generally recognized that all attempts hitherto made to express the secular variation of the magnetic elements by means of formulas were in the nature of preparatory or preliminary investigations. The derived formulae, invariably referring to particular stations, were purely interpolation formulae, the apparently simple law revealed in general by the formulae being the only fact of material significance. L. A. Bauer's well‐known thesis, however, in which for the first time a law governing the secular variation over the greater portion of the earth was shown to hold true, marked an important step forward.The natural method to be pursued in a theoretical investigation of the secular variation was clearly indicated in Gauss's analytical representation of the earth's magnetic potential. In this representation, the magnetic condition of the earth was expressed as a function of the geographical coordinates without making any assumptions whatsoever with regard to the distribution of the earth's magnetism (with the exception of the one, fully justified by the results obtained, that the earth's entire magnetic force could be referred to a potential of internal forces alone). This analytical representation then formed the simplest and surest basis for all further theoretical investigations. One step, however, remained—to express likewise the magnetic condition of the earth as a function of the time. The magnetic condition at any time being expressed in the only form suitable, that of solid spherical harmonic functions, the introduction of the time variable could only be accomplished with the aid of a similar series of terms, in which, however, the coefficients would be functions of the time.