On Detecting Changes in the Earth's Radius

Abstract

Summary Estimates of the Earth’s radius in the geological past can be made from paleomagnetic evidence. A method appropriate to the spherical environment of the data for dealing with this problem is given, which is applied to Devonian, Permian and Triassic data from Europe and Siberia, yielding estimated radii for these periods of 1.12, 0.94 and 0.99 times the present radius respectively. These estimates are not considered to be significantly different from the present radius. Egyed (1960) has suggested that paleomagnetic data could be used to find probable ancient radii for the Earth; the idea is that the mean direction of magnetization of rocks of the same geological age from widely separated collecting sites should be consistent with a geocentric dipole field. The problem is of interest since it has been suggested on geological and cosmological grounds that the Earth’s radius has changed greatly in the geological past. For example, Egyed (1956, 1957) requires a change of z per cent since the Paleozoic, and Carey (1958) a change of 45 per cent in the same time. Cox and Doell (1961) have applied Egyed’s method of calculation to Permian data from Europe and Siberia and gave an estimated Permian radius of 0.991 times the present radius. In this article a generalization of Egyed’s method of calculation is given, which is applied to Devonian and Triassic data as well as Permian data from this region into which some recent values not available to Cox and Doell have been incorporated, yielding estimates of the ancient radii for these three geological periods not significantly different from the present radius. Triassic and Carboniferous data from the North American continent have also been studied, but as yet there are not enough data from this continent to yield a meaningful result. The method given here, like that of Egyed, is based on the assumptions that during any change in the Earth’s radius, the size of each continent remains constant, and that during the particular geological age being studied, the position of the pole has not changed markedly, together with the usual assumptions involved in paleomagnetic studies; that the Earth’s field at the time in question may be represented by a geocentric dipole, and that it is possible by a study of rocks from a given rock unit to determine the approximate direction of the Earth’s field at that place at a known time. The set of relevant observations from a rock unit consists of four quantities, which are average values for the rock unit as a whole: the mean longitude +$ and latitude A$ of the rock unit, and the declination Di and inclination It of the estimated