Pliysics and Mathematics to Geology. 243 



The strains due to the action of the sun and moon being 

 comparatively insignificant, we need consider only the " cen- 

 trifugal " forces due to the earth's diurnal rotation, and the 

 gravitational forces due to the mutual attraction of its parts. 



The data supplied by Geology do not enable us to formu- 

 late any likely theory as to a probable distribution of density 

 and elasticity throughout the earth regarded as an elastic 

 solid. All we know with certainty is that the surface strata 

 are on an average considerably below the mean density, that 

 they differ widely in character, many being markedly aaolo- 

 tropic, and that frequently they are far from horizontal. 

 Thus, as our object is merely to consider what are the possi- 

 bilities on the hypothesis of solidity, it will be best to make 

 the hypothesis as simple as possible. Now, if the deviations 

 from the earth's mean density and from an isotropic elastic 

 structure were limited to the surface-strata, where alone we 

 are certain of their existence, the effect of the " centrifugal " 

 forces would be nearly the same as if these deviations did not 

 exist; but the effect of the gravitational forces on the eccen- 

 tricity of the surface may depend largely on the nature of 

 the deviations. I thus propose to treat the problem in 

 stages. 



The first stage neglects entirely the gravitational forces 

 and regards the earth as a slightly spheroidal body — which 

 has departed from the spherical form in consequence of its 

 rotation — of uniform density and of the same isotropic elastic 

 structure throughout, rotating with uniform angular velocity 

 c» about its polar axis. 



Let a denote the mean radius, d the difference between 

 the equatorial and polar semi-axes of the surface, E 

 Young's modulus, and 77 Poisson's ratio for the material. 

 Then the ratio d : a is given for various values of 77 in the 



loi 



ving Table * : — 



Table I. 











n= 



•2 25 



•3 



•4 



•5 



d 



a ' 



wp« 2 

 - E - >286 



330 -341 



•352 



•373 



•395 



In the case of an originally spherical solid assuming the 

 shape of the earth under rotation, it is of no practical im- 

 portance whether we regard a as the radius of the original 

 spherical surface, or as the mean radius under rotation, nor 

 does it matter practically whether the density be supposed 

 uniform previous to or during the rotation. There is, it is 



* See (a) formula (5) p. 267 ; or (e) Tables III., V., and VI. 



