DEVELOPMENT OF THE DISCOIDAL HYPOTHESIS 281 



tion in accepting the postulate of hydrostatic pressures heneath the iso- 

 static shell, as was assumed hy Hayford and also hy Love, to simplify the 

 mathematical calculation of stresses. Barrell recognized the artificiality 

 of the postulate, but employed it, nevertheless, in his diagrams. In the 

 following discussion we adhere to the assumption of a solid earth, except 

 as fusion is temporary and local, and we must therefore recognize that 

 stresses beneath the isostatic shell can not in general be hydrostatic. 



For the general case, let it be assumed that there are two adjacent 

 columns, one of lighter, the other of denser material. In each column, 

 at any level below the upper surface, there is a vertical pressure pro- 

 portioned to the height of the column above that level, and there must 

 develop a corresponding shearing stress, by virtue of which the column 

 will tend to spread laterally. If the columns be juxtaposed, their lateral 

 stresses will be mutualh" opposed ; if equal, they will balance ; if unequal, 

 there will remain an unbalanced stress difference. It is with this unbal- 

 anced lateral stress difference that we have to deal. 



As an initial case, assume that the surfaces of the two columns are on 

 a level. Then, at any depth below the surface, the column of denser 

 material will weigh more than the same column of lighter material, and 

 the lateral stress difference will be from the heavier toward the lighter 

 column. This condition may have existed beneath a peneplain. 



If the surface of the lighter column should lie lower than that of the 

 heavier, the above condition would simply be exaggerated. The lateral 

 stres<? difference from the heavier toward the lighter would be increased. 



The case which commonly occurs and which is assumed in the discus- 

 sion of isostatic equilibrium is that in which the surface of the lighter 

 column stands above that of the heavier column. It is represented in 

 plate 13. 



At the level of the top of the heavier column its lateral stress is zero, 

 while that of the lighter column is a finite quantity. The stress difference 

 is, therefore, from the lighter toward the heavier. With every foot below 

 that leviel the weight of the heavier column, and consequently its lateral 

 stress, gains faster than the corresponding pressures in the lighter column. 

 The former will eventually equal the latter and the stress difference will 

 be zero. 



In plate 13 let the shaded triangle represent the lateral stresses and 

 the black triangles the stress differences. If the weights of the columns 

 be equal at the depth AC, the lateral stresses will be equal and the stress 

 difference will be zero at that level. Above the level of zero stress differ- 

 ence, the stress from the lighter toward the heavier column at anv level is 

 greater than the opposed stress by the width of the black triangle, whereas 



