THE STRENGTH OF THE EARTH'S CRUST 159 



well as by vertical movement of the whole area to a level best 

 satisfying the stress. The western United States is known to be 

 such a region, which in the late Tertiary and up to the present has 

 been markedly affected by block faulting and differential vertical 

 movements. 



Suppose, then, that the mean radius of regional compensation in 

 a mountainous region is 300 km. but that unit areas exist ranging in 

 radius from 100 to 500 km. Of mountain stations located at 

 random, a fraction of the total number would be situated within or 

 near areas where regional compensation did not extend to 166 . 7 km. 

 Let the stations be divided into one group consisting of those below 

 the mean regional elevation and another group above the mean 

 regional elevation. Let the anomahes be computed successively 

 according to hypotheses of regional compensation to successive 

 limits and the mean of the group for each limit be taken. This is 

 the test applied by Hayford and Bowie. It has been seen that for 

 radii of 18.8 and 58.8 km. the results are indeterminate. For a 

 larger radius the group anomaly might be expected to show an 

 increase as soon as the assumed radius exceeded the actual radii of 

 a part of the areas. Consequently, if the hypothesis be true that 

 the areas of regional compensation are variable in size, the mean 

 anomahes of the two groups of 22 and 18 stations, found with regard 

 to sign to be +0.005 ^-nd — o.oio respectively for radius of 166.7 

 km., do not show that regional compensation on the whole does not 

 exist to those Hmits. It may indicate only that some areas are less 

 than that radius. The mean radius of regional compensation may 

 be 166.7 km. or possibly even larger. Other tests must therefore 

 be sought which will give a more conclusive answer. 



Further, it is to be noted that the mean anomalies with regard 

 to sign for the hj^pothesis of regional compensation to radius of 

 166.7 km., although somewhat greater than for the other hypoth- 

 eses, are yet of the same order of magnitude; and in all cases are 

 but a fraction of the mean anomaly without regard to sign. Appar- 

 ently, then, the assumption of regional compensation to 166.7 km. 

 introduces a smaller error than the assumption of uniform and com- 

 plete compensation with an average specific gravity of 2.67 to a 

 constant depth of 114 km. 



