282 B. WILLIS DI^OIDAL STRUCTURE OF THE LITHOSPHERE 



below the level of zero stress difference the pressure from the heavier 

 toward the lighter column is the greater by the width of the lower black 

 triangle. 



The position of the level of zero stress difference depends on two 

 variables : the ratio of densities, of the two columns and the difference of 

 level of their upper surfaces. In any particular case the density ratio 

 is assumed to be fixed, but the relative levels of the upper surfaces vary 

 in course of geologic changes. 



When the two upper surfaces are on the same level the position of zero 

 stress difference coincides with that level, because the lateral stresses there 

 are both equal to zero. 



As the upper surface of the lighter column rises above that of the 

 heavier, the position of zero stress difference sinks lower. The greater 

 the altitude of the lighter column above the heavier, the deeper the level 

 of no stress difference. 



If we take the level of zero stress difference as the base of the two 

 columns, above which their heights are measured, and consider the ratio 

 of their heights, we may compare the latter with the ratio of their den- 

 sities. Since the lateral stresses can be equal only under equal weights, 

 other things being the same for both columns, the ratio of heights must 

 be inversely as the ratio of densities. In columns of indefinite extension 

 downward there will always be a depth at which the weights will be equal, 

 or at which the superincumbent columns will be in equilibrium with one 

 another. This is the condition of isostasy. 



Theoretically, isostatic equilibrium is always complete and perfect for 

 any difference of surface heights, at some lower level at which the weights 

 of the columns are equal. If the difference of surface heights changes, the 

 level of equilibrium rises or sinks and all stresses in the columns and 

 betw-een the columns are modified. In mobile material the readjustment 

 of stresses to the new conditions of equilibrium proceeds rapidly. In 

 rigid material the readjustment is delayed, and residual unbalanced 

 stresses persist during a period which is the more prolonged as the stresses 

 are relatively small as compared with high rigidity. 



In the case of the earth, changes in the weight of adjacent columns, 

 such as by erosion and deposition of sediment, proceed slowly, but the 

 stresses set up are very small and the rigidity of the earth is very high. 

 There is, therefore, a lag in the adjustment, which results in residual 

 stresses. The latter accumulate during periods of general planation and 

 are relieved during epochs of mountain growth. 



In the actual state of the lithosphere it appears that the level of no 

 horizontal stress difference, coinciding with the bases of columns of equal 



