If we put the interval 2 π, in which a Fourier series assumes every possible value, equal to the natural period2 of a geophysical element, we obtain the most natural and appropriate of all the common representations of the periodic process, since in this case the representing function and the function represented have the same periodicity. In addition to this, the individual waves attain a real significance in certain circumstances; for example, when the periodic process is to be attributed to stationary vibrations, as in the case of the diurnal variation of the atmospheric pressure. But even in the case in which the waves of higher order are to all appearances merely computation quantities, the physical analysis of the process represented, according to its causes, can still be effected by the series, though of course only with the assistance of modes of procedure lying quite outside the method (of Fourier); namely, by the comparison of the coefficients for different times and places in which the different causes act in opposite senses.It was with such aid that the author succeeded in showing that that field to which, according to Schuster‐Bezold,3 the diurnal variations of the Earth's magnetism are to be attributed, is composed of two parts, one corresponding to the “solar” part of the weather, the other to the “terrestrial” part. Both parts have the period 24 hours, so that in the Fourier representation the solar part is given by the first term, and the terrestrial part by the sum of all the rest. The solar part is thus represented by a stationary vibration, and the terrestrial part, in a purely mathematical way, by the terms of the second order; while the individual waves have, beyond this, no independent existence.