the Weight <>/ ( 'nnt'nn nf.s and Mountains. 261 



If the elastic solid be highly compressible the stress-differ- 

 ences are not nearly so great as on the hypothesis of incom- 

 iv. In all the other cases considered in this paper 

 compressibility makes practically no difference in the results. 

 On evaluating the stress-difference, on the hypothesis of 

 incompressibility, arising from given ellipticity in a spheroid of 

 the size and density of the earth, it appears that if the excess 

 or defect of ellipticity above or below the equilibrium value 

 (namely, ^-g- for the homogeneous earth), were ^dlm then the 

 stress-difference at the center would be eight tohs per square 

 inch; and, accordingly, if the sphere were made of material as 

 strong as brass it would be just on the point of rupture. 

 Again, if the homogeneous earth, with ellipticity -^, were to 

 stop rotating, the central stress-difference would be 33 tons per 

 square inch, and it would rupture if made of any material 

 excepting the finest steel. 



A rough calculation* will show that if the planet Mars has 

 ellipticity ^ (about twice the ellipticity on the hypothesis of 

 homogeneity), the central stress-difference must be six tons 

 per square inch. It was formerly si ippo>ed thai lie ellipticity 

 of the planet was even greater than ^ and even if the latest 

 telescopic evidence had not been adverse to such a conclusion, 

 we should feel bound to regard such supposed ellipticity with 

 the greatest suspicion, in the face of the result just stated. 



The state of internal stress of an elastic sphere under tide- 

 generating forces is identical with that eaused by ellipticity of 

 figure.f Hence the investigation of $ f> gives the distribution 

 of stress-difference caused in the earth l»y the moon's attraction. 

 Computation shows that the stress-djfference at the surface, 

 due to the lunar tide-generating forces, is 16 grams per 

 square centimeter, and at the center eight times as much. 

 These stresses are considerable, although very small compared 

 with those due to terrestrial inequalities, as will appear below. 

 In § 6 the stresses produced by harmonic inequalities 

 of high orders are considered. This is, in effect, the case in a 

 series of parallel mountains and valleys, corrugating a mean 

 level surface with an infinite series of parallel ridges and fur- 

 rows. In this ease compressibility makes absolutely no differ- 

 ence in the result, as shown in Jj 10. 



It is found that the stress-dillerence depends only on the 

 depth below the mean surface, and is independent of the posi- 

 tion of the point considered with regard to ridge and furrow; 



u<\ ':■:. r.-s,,.,! 



i qualifications noticed ii 



