DEVELOPMENT OF THE DISCOIDAL HYPOTHESIS 283 



weight, lies at a depth of 60 to 100 miles below sealevel, according to the 

 calculations of Hayford and Bowie. On the assumption that the depth 

 is everywhere the same, the figure of 76 miles l^est satisfies the observa- 

 tions of the deflection of the vertical and of the intensity of gravity and 

 is commonly referred to as the depth of the zone of compensation. This 

 is, however, an exact mathematical conclusion based on assumptions of 

 the distribution of gravity which are artificial, and it is therefore not a 

 geologic fact. 



The preceding considerations lead to the recognition of the isostatic 

 shell, an outer layer of rock whose upper surface is the uneven surface 

 of the earth and whose under surface is that continuous, but warped, 

 level at which the weights of unlike columns are equal and the horizontal 

 stresses are balanced. 



Any change in the levels of the upper surface changes the position of 

 the under surface, and thus modifies the stresses throughout the isostatic 

 shell. 



Beneath the isostatic shell differences of density, if they persist as 

 geologic reasoning shows they should, must occasion differential lateral 

 stresses which, since the columns lie below a surface at which the over- 

 lying loads are equal, must always be directed outward from the denser 

 toward and into the lighter column. 



In the solid mass below the isostatic shell, as in the isostatic shell 

 itself, stresses are oriented as to direction. They can become hydrostatic 

 only when some part of the mass is locally melted. 



It is desirable to consider the resultant stresses in case the relative 

 heights of adjacent columns are modified by geologic change. The domi- 

 nant and general case is that of erosion of uplands and burial of low- 

 lands or sea-bottoms. 



In that change of surface levels, whatever may have been the position 

 of the level of zero stress difference, it is gradually raised. As it passes 

 upward the lateral stresses change, those from the unloaded column de- 

 creasing and from the loaded column increasing. At any point which 

 passes below the level of zero stress difference, the direction of lateral 

 stress difference changes from toward the loaded to toward the unloaded 

 column. 



At the same time certain elastic stresses are set up by the unloading 

 and loading. They are vertical in direction and represent the effort of 

 the columnar mass, which may be regarded as an elastic spring, to ac- 

 commodate itself to the changing conditions of load. In the unloaded 

 column the vertical stress is upward, in the loaded it is downward. 



The resultants of these horizontal and vertical stresses are inclined at 



