.3?8 Ai-clideacon Pratt on the Tliickness of 



P' = jO"1. Hence the above formula gives 



- = ^ — /3, or e less than ^e. 



Hence, because the ellipticity decreases in descending, the thick- 

 ness must be greater than would correspond with an ellipticity 

 of the inner surface of the shell —^ ellipticity of the outer 

 surface. 



li solidification took place solely from pressure, the surfaces 

 of equal density would be surfaces of equal solidity. From the 

 oi'dinary theory of the figui'e of the earth, considered as consist- 

 ing of strata (whether fluid or not) which follow the fluid law 



and the law of density ~, Mr. Hopkins shows that if the 



•'a 



ratio of the mean density to the superficial density = 2"4225, 

 the thickness of the crust must be one-fourth of the radius, if 

 the ellipticity of the inner surface = ^ e ; if the ratio of densi- 

 ties is a little larger than 3, the thickness is one-fifth of the 

 radius. But the ratio of densities is generally regarded as less 

 than the smaller of the above ratios. Hence we shall not be 

 over the mark in stating that the crust, under the hypothesis 

 that the solidification is produced by pressure alone, cannot be 

 less than one-fifth or one-fourth of the radius in thickness. 



But solidification depends upon temperature as well as pres- 

 sure, and Mr. Hopkins shows (Phil. Trans. 1842) that the iso- 

 thermal surfaces increase in ellipticity in passing downwards. 

 Now the ellipticities of the surfaces of equal degrees of solidity 

 must, under the double action of tem])erature and pressure, lie 

 between those of temperature and pressure considered alone. 

 Hence the surface of equal solidity passing through any point 

 will be more elliptic than the surface of equal pressure or density 

 passing through that point; and therefore the inner surface of 

 a solid shell, of which the ellipticity is |e, will be lower down in 

 the mass than a stratum of equal density of that same ellipticity ; 

 and the shell will be thicker than if pressure alone cause solidi- 

 fication. Also since /8 is not negative, the shell for that reason 

 will be thicker. The thickness, therefore, of 800 or 1000 miles 

 is by no means too large a limit. 



3. Mr. Hennessy's greatest thickness is 600 miles ; and his 

 conclusion is that the thickness may be so small as 18 miles. 

 But his whole calculation proceeds upon the assumption that 

 the shell is sufficiently rigid to resist, without change of form, the 

 pressure upon its inner surface which arises from its not con- 

 tinuing to be a surface of fluid-equilibrium. He supposes also 

 that the inner nucleus shrinks in cooling more than its solid 

 envelope, which is hardly allowable. Under these circumstances, 



