THE THEORY OF ISOSTASY 613 



alone, neither the depth nor the degree of completeness of isostatic 

 compensation can as yet be considered settled. 1 



Criticism of C -solution. — The criticism might be made of the 

 C-solution that the assumption of complete compensation at depth 

 zero under oceans obviously does not correspond to the facts and 

 that, by trying several depths, a combination might be found which 

 would appear to be, so far as the information available could test 

 it, as close to the actual conditions as any other hypothesis. From 

 the wide departure of the C-solution it seems, however, rather 

 improbable that such a depth could be found. 



FURTHER CONSIDERATIONS 



Possibilities of an incomplete compensation. — Since Hay ford 

 only considered the case of complete compensation, it is desirable 

 to see whether or not an incomplete compensation would meet the 

 geodetic requirements as well as a complete compensation. Any 

 test of incomplete compensation based on Hayford's residuals is 

 apt to be misleading since these residuals may involve two errors 

 that tend to counterbalance each other. By a study of the reduc- 

 tion factor, however, we may be able to tell whether or not an 

 incomplete compensation would be as probable from the geodetic 

 point of view as complete compensation. 



According to the definition given in this paper the degree of 

 completeness of compensation is 



M = Wh • (I) 



If there is isostatic compensation, there will be a compensating 

 density difference between the material in column A and the 

 material in column B . 2 If at any given depth the density of column 

 A be &a and of column B, 8 B , then the compensating density differ- 

 ence at that depth will be K=$a—$b which is of course negative 

 when A is a land segment. It follows that 8 B —S A — 8 I . Now 



1 It should be noted that so far as the nature of compensation is questionable, 

 Hayford's values for the size and figure of the earth are also open to question. 



2 See definition of M, p. 607-8. 



