Status of the Theory of Isostasy. 299 



Although the average disagreement between the ob- 

 served and calculated values was reduced by the intro- 

 duction of the hypothesis of isostasy, the disagreements 

 for many stations remained larger. These outstanding 

 quantities need careful study and must be frequently 

 referred to. For the deflections of the vertical, the out- 

 standing discrepancies are known as the deflection resid- 

 uals. For the intensity of gravity, the variations which 

 remain unaccounted for by the theory of isostasy are 

 known as the gravity anomalies. 



Let several competing hypotheses, in regard to depth 

 of compensation, named for convenience solutions E, H, 

 G, etc., be tried, and the deflection residuals and gravity 

 anomalies be determined under each hypothesis for each 

 station. They will be different for each hypothesis. Take 

 the squares of these individual quantities and find the 

 sum of the squares for each hypothesis. That hypothesis 

 which is nearest the truth will give on the average small 

 residuals and anomalies. The relative probabilities of 

 the hypotheses are measured by the smallness of the 

 sum of the squares. This is a test familiar in the exact 

 sciences, but less familiar to other branches of knowledge. 

 Thus it is quite conclusive that under the hypothesis of 

 uniform vertical distribution of compensation to the 

 depth of compensation, that depth is much nearer 100 

 kilometers than 500 kilometers and certainly cannot be 

 as great as 1,000 kilometers. This is true unless some 

 unconscious assumption has been introduced into the cal- 

 culation which modifies the residuals and anomalies in 

 the same direction as the hypothesis to be tested. Sev- 

 eral suggestions of such false assumptions have been put 

 forward by critics of the geodetic evidence, but they have 

 failed to apply or prove their own criticisms. It should 

 be carefully noted, however, that such a test does not 

 prove the uniform distribution of compensation to be 

 true, but only, if assumed, what would be its depth. 

 That much gained, the next step is to determine the rela- 

 tive probability of the mode of distribution, whether 

 uniform or variable. 



Interpretations Favoring Local and Nearly Perfect 



Isostasy. 



The theory of isostasy, after half a century of discus- 

 sion, was placed securely upon a quantitative basis by 

 the publication in 1909 by J. F. Hayford, inspector of 



Am. Jour. Sci— Fourth Series, Vol. XLVIII, No. 286.— October, 1919. 

 21 



