MOVEMENTS AND DEFORMATIONS OF THE EARTH'S BODY. 579 



If it be assumed that the rigidity increases as the squares of the density 

 ratios, the following values are obtained: 



Distances from 



center in terms of 



radius. 



Densities under 

 Laplace's law. 



Density ratios. 



Density ratios 

 squared. 



Deduced rigidities. 



1.00 



.75 

 .50 

 .25 

 .00 



2.8 



5.7 



8.39 



10.27 



10.95 



1 



2 

 3 



3.7 

 3.9 



1 



4 



9 



13.7 



15.2 



0.16 Steel 



0.6 



1.5 



2.3 



2.5 



These values seem fairly consistent with the apparent requirements 

 of the case. 



If the distribution of rigidity were of this nature, the average rigidity 

 would be much less than that of steel, for more than half the volume 

 lies in the outer division, between 1.00 and .75 radius, and yet the 

 effective resistance to tidal deformation would be high, for, according 

 to G, H. Darwin,^ the tidal stress-differences are eight times as great in 

 the center as at the surface. The rigidity would, therefore, be dis- 

 tributed so as to be much more effective in resistance than if it were 

 uniform. The suggestion arises here that the tidal stresses and other 

 analogous stresses arising from astronomical sources may be in them- 

 selves the causes of some such distribution of rigidity as this. The 

 tidal stresses are rhythmical and give rise to a kind of kneading of the 

 body of the earth, small in measure to be sure, but persistent and 

 rapidly recurrent. Since these stress-differences at the center are 

 eight tirnes those at the surface, and since also the gravitative stress at 

 the center is 3,000,000 times that at the surface, there is a series of 

 persistently recurring stress-differences, greatest at the center and 

 declining outwards, superposed on enormous static stresses, also intens- 

 est at the center and declining outwards. Now, if the earth material 

 were once made up of a mixture of minerals of different fusibility, some 

 of which became more mobile (whether fluid or viscous) than others 

 under the rising temperature of the interior, it seems that the more 

 mobile portion must have tended to move from the regions of greater 

 stress-differences to those of lesser stress-differences. The persistence 

 and the rhythmical nature of the tidal stress-differences seem well 

 suited to aid the mobile parts in gradually working their way outwards. 

 At the same time the more solid and resistant portions should remain 



^ Nat. Phil. Thompson & Tait, Vol. II, p. 424, 1890. 



