5S0 



GEOLOGY. 



behind, and thus come to constitute the dominant material of the 

 central regions where stress-differences were greatest, and so, as it 

 were, concentrate rigidity there. The process may still be in action. 



If it be assumed that the rhythmical stresses have thus developed' 

 a resistance to deformation proportional to their intensity, we may 

 combine this with density to form the basis of another hypothetical 

 distribution of rigidity, as follows: 



Distances from 



center in terms of 



radius. 



Densities under 

 Laplace's law. 



Density ratios. 



Ratios adjusted to 



stress-differences. 



(1 :8) 



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 



3.5 



5.4 



7 

 8 



. 16 Steel 

 0.58 '' 

 0.90 " 

 1.16 " 

 1.33 " 



The average rigidity is here also much less than that of steel, but its 

 distribution is such as to render it ideally fitted to resist tidal distortion. 



These hypothetical distributions of rigidity have no claims to special 

 value in themselves, for the grounds on which they are based are quite 

 inadequate, but they are not without importance in giving tangible 

 form to considerations that bear vitally not only on tidal problems, 

 but on many others connected with the internal constitution and 

 dynamics of the earth. 



Sphericity as a factor in deformation. 



It is obvious that if the earth shrinks, its crust must become too 

 large for the reduced spheroid, and must be compressed or distorted 

 to fit the new form. The amount of distortion required for any given 

 shrinkage is easily computed from the ratio of the radius to the circum- 

 ference of a sphere, which is approximately 1 : 6 . 28. If, for example, 

 the radius shortens 5 miles, each great circle must on the average be 

 compressed, wrinkled, or otherwise distorted to the extent of about 

 31 miles, or, in reversed application, if the mountain foldings on any 

 great circle together show a shortening of 100 miles, the appropriate 

 radial shortening is 16 miles. The ratio of 1:6+ furnishes a convenient 

 check on hypotheses that assign specific thrusts to specific sinkings of 

 adjacent segments. A segment 3000 miles across, for example, such 

 as the bottom of the North Atlantic basin, sinking three miles, about 

 the full depth of the basin, would give a lateral thrust of about 2.2 



