ON THE HYPOTHESIS OF ISOSTASY in 



tative judgment from the sum of the squares of the residuals which 

 depends, not only upon the imperfections of the theory, but upon 

 the imperfections of the observations as well ? Obviously, it 

 cannot be done. The estimate of 250 feet is little more than a 

 guess, however shrewd the guess may be. If we use the 9,000-foot 

 level as the basis of our guess, then the average elevation of the 

 United States is 11,500 feet, and the average departure from com- 

 plete isostasy is 1,150 feet of rocks instead of 250 feet. It would 

 not be altogether fair, however, to make this direct substitution, 

 for the reduction of the sum of the squares of the residuals from 

 65,434 to 8,013 was accomplished on the sea-level hypothesis, and 

 the reduction might be quite different under another hypothesis. 



From a purely mathematical point of view, any set of a finite 

 number of observations of the intensity and direction of gravity 

 can be satisfied, not approximately, but exactly, in infinitely many 

 ways by a proper distribution of density in the earth. The virtue 

 of the theory of isostasy, therefore, lies, not in the mere fact 

 that the observations are more nearly satisfied by the theory 

 than without it, but in the fact that a definite principle is laid 

 down for the variations of density, and that this principle brings 

 theory and observations into a satisfactory accord. As Hayford's 

 four distinct hypotheses show, any smoothly uniform hypothesis 

 of isostasy can be regarded only as a first approximation to the 

 actual situation, and Hayford has been successful in showing that 

 any one of these four hypotheses is a good first approximation. It 

 is equally clear that such delicate points as "depth of compen- 

 sation" and size of "areas of compensation" depend for their suc- 

 cessful determination upon the vastly more difficult matter of 

 second and higher approximations, and these approximations can 

 be obtained, if at all, only by a very much more dense net of obser- 

 vations, and quite likely the observations themselves would have 

 to be still further refined. 



While the theory of isostasy has made a very successful approach 

 to the solution of the problem of bringing the anomalies of obser- 

 vation into accord with the theory of gravity, it must be admitted 

 that there is no evidence to show that the solution of the problem 

 is necessarily isostatic. 



