148 JOSEPH BARRELL 



to very great distances from each station, the first to make a con- 

 siderable number of trial solutions upon various assumptions as to 

 the depth of the zone of isostatic compensation, with the result that 

 the reduction of the observations gave the dimensions of the earth 

 with a considerably smaller probable error than any previous 

 computations/ 



But the conclusions in regard to the strength of the crust, drawn 

 in the first part of this article from the study of deltas, stand in 

 strong contrast to certain statements by Hayford and later by 

 Hayford and Bowie. This second part must therefore outline the 

 results reached by them and show what reconsiderations are neces- 

 sary in order to bring into harmony their conclusions and the 

 evidence derived from the previous geologic study. A preliminary 

 review without criticism is given of their work in order to bring 

 out their methods and results, and the geologic conclusions which 

 they draw from those results. It is followed by a re-examination of 

 the subject of regional versus local compensation. This is the 

 problem of the size of the area over which, by virtue of the rigidity 

 of the crust, irregularities of density and topography do not have 

 individual relationships but do largely compensate each other over 

 the region as a whole. It is a measure, therefore, of the areal limits 

 of crustal strength. The tests employed by Hayford and Bowie 

 are, as they note, indeterminate up to radii above 58.8 but less 

 than 166.7 km. in length. Consequently Hayford did not change 

 his opinion, based upon previous investigations, that regional com- 

 pensation was limited to areas of less than one square degree. In 



' The final publications have been issued by the United States Coast and Geodetic 

 Survey and are as follows: Hayford, "The Figure of the Earth and Isostasy from 

 Measurements in the United States (up to 1906),'' 1909; referred to in this paper as 

 Hayford, 1906; Hayford, "Supplementary Investigation in 1909 of the Figure of the 

 Earth and Isostasy," 1910; referred to in this paper as Hayford, 1909; Hayford and 

 Bowie, "The Eiiect of Topography and Isostatic Compensation upon the Intensity of 

 Gravity," 1912; referred to in this paper as Hayford and Bowie, 1912; Bowie, "EiJect 

 of Topography and Isostatic Compensation upon the Intensity of Gravity" (second 

 paper), 1912; referred to in this paper as Bowie, 1912. 



In addition Bowie has published in the American Journal of Science, "Some 

 Relations between Gravity Anomalies and the Geologic Formations in the United 

 States," (4) XXXIII (19 12), 237-40. 



The following discussion of their geodetic measurements and results will be con- 

 fined to the work in these five papers. 



