Original and Actual Fluidity of the Earth and Planets. 271 



of the constants to correspond with the supposed alteration of density of the shell in passing from 

 the fluid to the solid condition. As the hypotheses used to obtain this limit are arbitrary, the 

 limit itself must be considered only as of the same value as the limit in equation (28), deduced 

 from the improbable hypothesis of homogeneity in the shell and nucleus. The other limit is more 

 interesting, being assumed to be a minor limit to the thickness of the Earth's crust, and independent 

 of the law of density of the interior. 



On a careful examination of the hypotheses on which the determination of this limit depends, 

 I believe that it will be found, that one of them is inadmissible, and others arbitrary. If I under- 

 stand Mr. Hennessey aright, the following are the statements from which he deduces his minor limit 

 of the thickness of the Earth's crust: 



1 St. The shell is homogeneous and of the density of the rocks at the surface. 



2nd. The shell is bounded by similar surfaces, whose eUipticity is ^-r^ . 



3rd. The internal surface of the shell is perpendicular to gravity. 



4th. The external surface of the shell is not perpendicular to gravity, and its ellipticity, if it 

 were so, would be ^ . 



The fourth of these statements appears to me to be inadmissible for the following reasons : the 

 ellipticity of the surface perpendicular to gravity is assumed by Mr. Hennessey to be 5^, which 

 is a mean between the ellipticities -j^ and -^-z , deduced from the pendulum, and lunar inequalities,* 

 but the ellipticity deduced from the lunar observations, ^r, is identical with that deduced from the 

 measurement of meridian arcs, and although there may be some chance in this agreement, yet it is 

 sufficient to suggest the idea, that the surface of the Earth is rigorously perpendicular to gravity, 

 and that the pendulum experiments are influenced by variations of local attraction, arising from 

 variable density in the rocks, or from the position of land and water. Such are the usual explana- 

 tions of the difference between the ellipticity obtained from the pendulum and that deduced from 

 lunar observations; and unless some explanation be offered of the agreement between the ellip- 

 ticity of the actual surface obtained from meridian arcs, and the ellipticity of the surface perpen- 

 dicular to gravity deduced from the lunar inequalities, it is not allowable to assume, that the mean 

 of the results of the pendulum and lunar observations gives the surface perpendicular to gravity. 



In fact, the observations of the pendulum and of the Moon should give exactly the same ellip- 

 ticity, and would do so, were it not that the pendulum is liable to local variations, from which the 

 other method is exempt; the result of the latter is, therefore, more trustworthy, and this result 

 is almost identical with the ellipticity of the actual surface. It is certainly unphilosophic to take the 

 mean of observations which differ more from each other than they differ from the quantity with 



* The figures here given are those adopted by Mr. Hennessky, and are probably as near the tnith as any others Mhich 

 have been deduced. The ellipticity deducible from SAErxE's pendulum experimeuts is ^ _ ; aud from Boivakd, 



BuncKnAKDT, aud Burg's lunar observations, is ——— . (ilec. Cel., Tom. v. p. 45.) 



004 ■ I 



