156 JOSEPH BARRELL 



given a discussion which it is thought brings out certain errors in the 

 conclusions drawn from the geodetic work and thereby reconciles 

 the two lines of evidence. 



REGIONAL VERSUS LOCAL DISTRIBUTION OF COMPENSATION 



Conclusions on this topic by Hayford and Bowie. — -Under this 

 heading Hayford and Bowie state : 



The question whether each topographic feature is completely compensated 

 for by a defect or excess of mass exactly equal in amount directly under it, or 

 whether the topographic feature is compensated for by a defect or excess of 

 mass distributed through a more extensive portion of the earth's crust than 

 that which lies directly beneath it, is a very important one. The theory of local 

 compensation postulates that the defect or excess of mass under any topographic 

 feature is uniformly distributed in a column extending from the topographic 

 feature to a depth of 113 . 7 kilometers below sea level. The theory of regional 

 compensation postulates, on the other hand, that the individual topographic 

 features are not compensated for locally, but that compensation does exist for 

 regions of considerable area considered as a whole. 



In order to have local compensation there must be a lower effective rigidity 

 in the earth's crust than under the theory of regional compensation only. In 

 the latter case there must be sufficient rigidity in the earth's crust to support 

 individual features, such as Pikes Peak, for instance, but not rigidity enough to 

 support the topography covering large areas. 



Certain computations have been made to ascertain which is more nearly 

 correct, the assumption of local compensation or the assumption of regional 

 compensation only. In making such computations it is necessary to adopt 

 limits for the areas within which compensation is to be considered complete. 

 A reconnoissance showed that the distant topography and compensation need 

 not be considered, for their effect would be practically the same for both kinds 

 of distribution. As a result of this reconnoissance it was decided to make the 

 test for three areas, the first extending from the station to the outer limit of 

 zone K (18. 8 kilometers), the second from the station to the outer limit of zone 

 M (58.8 kilometers), and the third, to the outer limit of zone O (166.7 

 kilometers) .' 



The average anomaly with regard to sign by the new method with local 

 compensation, and the average anomaly by each of the three new-method 

 reductions with regional distribution of the compensation are respectively 

 — 0.002, — o.ooi, — o.ooi, and —0.002 dyne. The means without regard to 

 sign for the different distributions of the compensation are respectively, 

 0.020, 0.019, 0.019, and 0.020 dyne. These mean anomalies give only 

 negative evidence.^ 



^ Hayford and Bowie, 1912, p. 98. ^ Bowie. 1912, p. 22. 



