[ 504 ] 

 LXXVl. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 325.] 

 Jan. 20, — npHE reading of a paper, entitled, " Researches in 

 184'2. JL Physical Geology:" Third Series. By William Hop- 

 kins, 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 Avas 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 siirface ; and the distance 

 between this surface and the outer one, the effective thickness of the 

 shell. 



The degree of solidity or fluidity at any point in the interior of 

 the earth must depend partly on the temperature at that point, and 

 may also depend partly on the pressure there. Both causes are 

 here assiimed to be effective : if the latter be not so, it will easily be 

 seen that the conclusion arrived at will, d fortiori, be true. 



If through any point in the interior of the earth, (as, for instance, 

 a point in the axis of rotation,) we take a surface of equal tempera- 

 ture, and through the same point, a surface of equal pressure, it is 

 evident that the surface of equal fluidity (or solidity) through that 

 point must be intermediate to these two surfaces. Its exact posi- 

 tion cannot be determined without an experimental knowledge, 

 which we do not possess, of the relative eftects of temperature in 

 opposing, and of pressure in promoting the process of solidification. 

 It is sufficient, however, for the purpose now in view, to know that 

 it nmst necessarily lie between the surfaces of equal temperature and 



