ON THE HYPOTHESIS OF ISOSTASY 107 



rather likely to gain the impression from Hayford's writings that 

 the "depth of compensation 1 ' is in the neighborhood of 122 kilo- 

 meters and that this "depth" is as well established as are the 

 broader outlines of the theory. This is not true, for we do not 

 know that the compensation is uniform. From the hypothesis of 

 uniformly decreasing compensation Hayford finds the depth of 

 compensation to be 175 kilometers, and from the "Chamberlin 

 compensation" 286 kilometers. Clearly, the "depth of compen- 

 sation" is very sensitive to change of hypothesis, and it is further 

 clear that with a slight modification of the hypothesis the "depth 

 of compensation" could be made to retreat to the center of the 

 earth, or even to vanish altogether. 1 From this it is obvious that 

 the existence of a precise depth of compensation is not an essential 

 part of the theory of isostasy. These considerations deprive the 

 depth of 122 kilometers of the importance or weight which con- 

 stant repetition is likely to attach to it. It is still doubtful whether 

 the term "depth of compensation" corresponds to any physical 

 reality, however useful the idea may be in our hypotheses. 



If the solid portion of the earth were altogether lacking in 

 rigidity, and if the concentric layers were homogeneous in density, 

 then the upper surface of the solid earth would be an oblate spheroid, 

 and this surface would lie about 9,000 feet below the present sea- 

 level. It would be covered uniformly by the waters of the ocean, 

 and the pressure at any interior point would be a function of lati- 

 tude and depth only, and not a function of the longitude. Let us 

 suppose now that this solid spheroid is endowed with a certain 

 amount of rigidity and is differentiated somewhat with respect to 

 density, particularly in the neighborhood of the surface. If the 

 rigidity were not too great, it seems clear that the heavy regions 

 would be depressed by the excessive weight, and that the lighter 

 regions would rise on account of their deficiency of weight. If the 

 differentiation of density were sufficiently great, it is clear that the 



1 The idea implied in this definition of the phrase "depth of compensation" that 

 the isostatic compensation is complete within some depth much less than the radius 

 of the earth is not ordinarily expressed in the literature of the subject, but it is an idea 

 which is difficult to avoid if the subject is studied carefully from any point of view. — 

 Hayford and Bowie, The Effect of Topography and Isostatic Compensation upon the 

 Intensity of Gravity, p. 10. 



