Prof. Hennessy — On the Internal Fluidity of the Earth. 217 



so remarkable a confirmation of conclusions, to wliicli I had been long 

 since led, and whicli I have developed in my publications, thus eman- 

 ating from such an eminent mathematician. At the time I thought it 

 imnecessary to put forward any claim as to priority, but since 1868 

 I have noticed that several geologists have quoted M, Delaunay's 

 results as if they were unexpected, and I may therefore be excused 

 for calling the attention of the Academy to what I had previously- 

 made public. In my " Eesearches in Terrestrial Physics," published 

 in the Philosophical Transactions for 1851, I endeavoured to in- 

 vestigate the structure of the earth by the aid of known physical 

 and mechanical laws. I was thus led to reject the hypothesis 

 always openly or tacitly made by mathematicians in treating of the 

 earth's figure, namely, that the particles of the fluid mass from which 

 it had partly solidified underwent no change of position during the 

 process of solidification. From a consideration of the mechanical 

 and physical properties of the materials of the earth's crust which 

 are known to us, I was led to conclude, that in the process of solidi- 

 fication of the crust, its interior surface would assume an ellipticity 

 at least as great as that of its exterior surface. 



A conclusion nearly equivalent was announced soon afterwards 

 by a distinguished geometer, Baron Plana, of Turin, in a paper 

 inserted in Schumacher's Astronomische Nachrichten, No. 860. This 

 result must follow, no matter what may be the law of density of the 

 strata of the interior fluid nucleus, because the removal of each suc- 

 cessive outer stratum by solidification and adhesion to the inner 

 surface of the crust modifies the pressure on the remaining fluid and 

 allows it to assume a shape possessing almost the same ellipticity as 

 the primitive spheroid. 



In the investigation made by Mr. Hopkins on the phenomena of 

 precession and nutation, he assumed the absence of friction between 

 the solid shell and its contained fluid, and in this way he was led to 

 establish the expression — 



P— P=(l— 5 



h 

 1+- 

 2 



-0 



where P^ denotes the observed precession, P^ that of a solid homo- 

 geneous spheriod having the ellipticity e^ equal to that of the 

 shell's outer surface, e is the ellipticity of the inner surface of the 

 shell, the other letters represent functions depending on the density 



of the shell and nucleus, but such that the quantity ^* 



is a small fraction, always much less than unity. The application 

 of the above formula to the question of the thickness of the earth's 



crust manifestly depends upon the value of the fraction - . In 



