Esq., M.A., and Charles James Buchanan Riddell, Esq., Lieut, in the Royal Artillery, were balloted for, and severally elected Fellows of the Society.
A paper was in part read, entitled, " Researches in Physical Geo- logy :" Third Series. By William Hopkins, Esq., M.A., F.R.S.
January 20, 1842.
SIR JOHN WILLIAM LUBBOCK, Bart., V.P. and Treas., in the Chair.
His Majesty the King of Prussia was balloted for, and duly elected a Fellow of the Society.
John Tricker Conquest, M.D., and Francis Henry Ramsbotham, M.D., were severally balloted for, but not elected into the Society.
1. The reading of a paper, entitled, " Researches in Physical Geology:" Third Series. By William Hopkins, Esq., M.A., F.R.S., was resumed and concluded.
In a paper formerly read to the Society, the author had investi- gated an analytical expression for the precession of the pole of the earth, on the hypothesis of the earth's being composed of a hetero- geneous 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 pre- cession.
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 por- tion 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
