670 JOSEPH BARRELL 



unit shearing stress would be multiplied only by two or three and 

 would still imply a weakness in this part of the crust to resist 

 long-enduring shear or bending stresses, its capacity being only 

 3 or 5 per cent at most as great as is found to exist in surface rocks 

 for stresses of human duration. 



Relief oj stress accompanying restoration of isostasy. — It is seen 

 from the preceding analysis that the movement of the unbalanced 

 columns toward a new state of equilibrium will be partly by vertical 

 shear in the neutral ground between them, but, where the areas 

 are large in comparison with the thickness of the zone of compensa- 

 tion, the easiest mode of yielding may be by flexure, showing at the 

 surface as crustal warping. Both modes of yielding serve to trans- 

 mit the excess vertical stresses of the heavy and sinking column 

 into the asthenosphere. If the latter be indeed a shell of weakness 

 it will transmit these pressures more or less hydrostatically. The 

 vertical pressure- differences will act within it as lateral pressures 

 making for flow toward the lighter column. It is shown in Fig. 13B 

 that the maximum horizontal stress in so far as it approaches 

 a hydrostatic distribution acts throughout the whole depth of this 

 zone, so that it not only is weaker than the crust above, but is 

 subjected to maximum stress over a greater area. It will yield 

 by flowage therefore either if of small depth and very plastic, or of 

 great depth but more rigid. If the columns are adjacent and nar- 

 row as compared to the thickness of the shell of weakness, then the 

 principles of plastic flow would require that the flow be chiefly in 

 the upper part of this shell. If, however, the columns are of con- 

 siderable breadth compared to the thickness of the asthenosphere, 

 and especially if at a distance from each other, then the principle of 

 least work would determine that the middle strata of this shell 

 should flow the farthest and the whole would to some degree 

 participate. If an imaginary partition were extended downward 

 through this shell as shown in A and B of Fig. 13 this partition 

 would be found warped after the movement as shown in C of the 

 same figure. 



It was seen in an earlier part of this discussion that, even sup- 

 posing deformation became effective by means of the lateral 

 stresses within the lithosphere and without the existence of a zone 



