THE THEORY OF ISOSTASY 611 



complete, and furthermore the fact that he later attempted to find 

 the degree of completeness implies that there is no reason to believe 

 at the outset in complete compensation. In view of this fact the 

 method of determining the degree of completeness of compensation 

 is questionable. 



Criticism of method of finding degree of completeness of compen- 

 sation. — Hayford's method is best explained by an example. Sup- 

 pose the topographic deflection at some station is 35.79'' This 

 is assuming no isostatic compensation. Suppose that the residual 

 assuming complete compensation at a depth of 76 miles is 3.33", 

 or in other words, suppose that the difference of the true deflection 

 and the deflection which would exist if the compensation were 

 complete at a depth of 76 miles is 3.33'' This value (3.33") is 

 apparently the part of the topographic deflection which has not 

 been made up for by isostatic compensation. The ratio of 3.33 

 to 35 . 79 is, therefore, taken by Hayford as a measure of the incom- 

 pleteness of compensation. In explanation of this method Hayford 

 writes as follows: 



The residuals of solution G 1 furnish a test of the departures of the facts from 

 the assumed condition of complete isostatic compensation uniformly distri- 

 buted to a limiting depth of 113. 7 kilometers. In order to obtain definite 

 ideas let the whole of the residuals of this solution be credited to the incomplete- 

 ness of the compensation. The conclusion as to the completeness of compen- 

 sation will then be in error in that the actual approach to completeness will 

 be considerably closer than that represented by the conclusion — that is, the 

 conclusion will be an extreme limit of incompleteness rather than a direct 

 measure. For by this process of reasoning every portion of a residual of solu- 

 tion G, due to the departure of the actual distribution of compensation with 

 respect to depth from the assumed distribution, or due to the error in the 

 assumed mean depth of compensation, or to regional variation from a fixed 

 depth of compensation, or due to errors of observation in the astronomic 

 determinations and the triangulation which affect the observed deflection of 

 the vertical, or due to errors of computation, is credited to incompleteness of 

 compensation. 2 



The objection to the paragraph quoted is that it apparently is 

 taken for granted that the error in the assumed mean depth of 



1 Solution G, the most probable solution according to the first report, was made 

 assuming a depth of compensation of 70 miles. 



2 Quoted from p. 164 of iqoq report. 



