Researches in physical geology : third series

Abstract

In a paper formerly read to the Society, the author had investigated an analytical expression for the precession of the pole of the earth, on the hypothesis of the earth’s being composed of a heterogeneous solid shell inclosing a heterogeneous fluid ; and showed that its amount, deduced from that hypothesis, could not agree with its actual observed amount, unless the ellipticity of the interior surface of the shell were less by a certain quantity than that of the exterior surface. As the ellipticity of the inner surface (assuming always that the earth was originally fluid) depends on the thickness of the shell, the author, in the present paper, determines the least thickness which can be deemed compatible with the observed amount of precession. In his former communication, the author had contemplated only the case in which the transition from the solidity of the shell to the fluidity of the mass contained in it was immediate ; but in the case of the earth it must be gradual and continuous. It is remarked, however, that if in the actual case we were to consider all that portion of the mass as solid which is not perfectly fluid, we should take the thickness of the shell too great ; and, on the other hand, if we were to consider the whole of that as perfectly fluid which is not perfectly solid, we should take the thickness of the shell too small. There must, consequently, be some surface of equal fluidity, (or, if we please, of equal solidity,) such that if all above it were perfectly solid, and all beneath it perfectly fluid, the precession would be the same as in the case in which the transition from the solidity of the shell to the fluidity of the interior mass is continuous. This surface is termed by the author the effective inner surface ; and the distance between this surface and the outer one, the effective thickness of the shell.