## Calculation of the ancient radius of the Earth

A rather less involved method of testing the expanding Earth hypothesis entails determining the paleoradius of the Earth using paleomagnetic techniques (Egyed, 1960).

The method involves selecting sampling sites of the same age, on the same paleomeridian and differing as much as possible in paleolatitude. They must also be on a landmass that has been stable since the time the sites acquired their primary remanent magnetizations (Fig. 12.2). Determining the paleolatitudes of the sites then provides the angle originally subtended at the center of the Earth + ^2). The known separation of the sites (d) can then be used to calculate the paleoradius of the Earth (Ra) according to the relationship Ra = d/(^1 + ^2), where angles are expressed in radians. However, it is rare to find two paleomagnetic sampling sites on the same paleomeridian so, in practice, this method is of limited applicability. Ward (1963) devised a more general minimum dispersion method that facilitates an analysis of arbitrarily distributed sampling sites. The dispersion of paleomagnetic poles from sites of the same age and known relative paleogeographic position is calculated, using the Fisher (1953) method for disper-

sion on a sphere, for different values of the Earth's radius. The radius for which the dispersion of the poles is a minimum is taken to be the best estimate of the paleoradius. McElhinny et al. (1978) analyzed the paleo-magnetic data available at that time using this method. They found that for the past 400 Ma the average paleoradius has been 102 ± 2.8% of the present radius. A small contraction or very slight expansion of the Earth could be tolerated by this analysis, but the very large increase in radius required by the expanding Earth hypothesis can be ruled out. Additional analyses by McElhinny & McFadden (2000) produced very similar results.

The expanding Earth hypothesis clearly does not stand up to direct testing. Also, indirectly the hypothesis cannot account for presently observable phenomena. If continental drift results from this mechanism there would be no necessity for subduction zones for the consumption of oceanic lithosphere, and no explanation is provided for extensive zones affected by colli-sional tectonics. The majority of plates are presently spreading in an east-west sense. If such a pattern results from an expanding Earth it would imply a progressive increase in the size of the equatorial bulge, which is not occurring. An expansion of the Earth would imply the existence of extensive zones subjected to membrane stresses as plates attempt to adjust to the increasing radius of curvature of the Earth, and these do not exist. Finally, the theory does not provide a mechanism for the continental drift that is known to have occurred in pre-Mesozoic times (Section 11.5).

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