Status of the Theory of Isostasy. 297 



If the depth of compensation is taken as 100 kilometers, 

 the difference in densities between A and B for a dif- 

 ferential relief of 5 kilometers would be 5 per cent. This 

 is of the order of magnitude believed to exist. 



The compensation may be conceived either: first, as 

 existing in a certain part of the crust ; second, as great- 

 est near the surface and decreasing with depth ; or, third, 

 as uniformly distributed to the depth of compensation 

 and there sharply terminating. Various other modes may 

 be conceived as existing. A number of these modes of 

 distribution satisfy the geodetic data and the most prob- 

 able must be decided on geologic evidence. The depth 

 of compensation will, however, vary according to the 

 assumed mode of distribution. 



The depth of the level of complete compensation 

 under the hypothesis of uniform distribution Hayford 

 determined at first as 114 kilometers, later as 122 kilo- 

 meters, but the data do not form a sensitive index as 

 to depth. The latest and fullest analysis by Bowie leads 

 him to believe that future determinations will fall be- 

 tween 80 and 130 kilometers. Although the geodetic 

 data do not yield a precise figure for the depth, they do 

 show definitely that under any tenable mode of distribu- 

 tion practically all of the compensation lies within the 

 outer fiftieth of the earth's radius. 



In figure 1 regional compensation is indicated under 

 areas A and B and local compensation under C, D, E, 

 and F. The extreme of the hypothesis of local compen- 

 sation is found in the assumption that each unit area, 

 however small, is underlain by a corresponding density 

 in its vertical column. The limit of regional compensa- 

 tion is to conceive a whole continent as underlain by 

 crust of one density, an ocean basin by another density, 

 without regarding plateaus and basins as related. The 

 evidence indicates that neither of these extremes is near 

 the truth. The truth, as is so commonly the case, lies 

 between the two extremes. Regional compensation has 

 indeterminate limits. It presumably varies in different 

 regions, and certainly varies with the intensity and 

 breadth of the loads to be supported. The assumption 

 best adapted to mathematical calculation is, therefore, 

 that of local compensation. Each unit area is given its 

 appropriate density. Because gravity varies inversely 

 with the square of the distance, near the geodetic station 



