740 JOSEPH BARRELL 



accordance of fact with theory is not a proof, but it raises a pre- 

 sumption that the theory is correct. 



Nature of stresses imposed by perfect isostasy. — This topic, 

 although not directly in line with the subject of this chapter, 

 must receive brief mention here since the stresses in the crust are 

 compounded of those due to the departures from isostasy with 

 those resulting from a state of perfect isostasy. The stress resulting 

 from the isostatic support of continents and mountains has been 

 ably worked out by Love.' But his treatment started with the 

 limiting though improbable assumption that at a depth of one- 

 fiftieth of the earth's radius all stress-differences disappeared, as 

 though the layer below were truly fluid. This required a com- 

 plicated and equally improbable curve of density, opposite in 

 sign above and below, in order that the topography should be com- 

 pensated, the ocean surface remain a level surface, and yet the 

 stress-differences become zero at the required depth. Neverthe- 

 less the solution is valuable as a limiting case in showing the general 

 character of the internal stresses which must exist. He showed 

 that isostatically compensated harmonic mountains and valleys 

 gave maximum stress-differences on the axial lines of mountains 

 and valleys and that it amounted to about one-fourth of the 

 theoretical hydrostatic pressure. The stresses decrease rapidly 

 with depth. 



In contrast to Love's hypothesis of the distribution of density, 

 that of Hayford may be considered. This is that the excess or 

 defect in density needed for compensation is uniformly distributed 

 to a depth of 122 km. Again, a rigorous mathematical treatment 

 must be left to those competent to undertake it, but it would appear 

 that such distributions of density would throw very considerable 

 stress-differences within the asthenosphere; or, if this was incompe- 

 tent to carry such, would bring large stress-differences upon the 

 bottom of the zone of compensation, opposite in sign to that in 

 the upper half, whereas at an intermediate level depending upon 

 the wave-length would be a region of no stress-difference. This 

 distribution of stress resulting from the hypothesis may be taken 

 as a strong argument against the existence of a uniform distribution 



' Some Problems of Geodynamics (191 1). 



