180 G. p. BECKER ISOSTASY AND RADIOACTIVITY 



that is, mountains attract less than would be anticipated from their vol- 

 ume, as if they overlay regions of relatively small density ; while lakes or 

 other depressions diminish the attraction less than would be expected if 

 the underlying material were of average density. 



Mr. Hayford has considered eight trial hypotheses as to the distribu- 

 tio]i of compensation, of which five suppose uniform distribution each to 

 some particular depth. Of these, two represent extremes; one, solution 

 B,-" supposes the depth infinite, which is equivalent to assuming that 

 there is no compensation at all, while the other solution, A, assumes that 

 it is complete at the surface, which amoimts to the assumption that topo- 

 graphic forms exert no effect on the direction of the vertical. Three solu- 

 tions, called E, H, and G, assume uniform complete compensation at 

 depths of 162.2 kilometers, 120.9 kilometers, and 113.7 kilometers re- 

 spectively. Three other hypotheses which deal with selected representa- 

 tive data are (1) that compensation is confined to a layer 10 miles in 

 thickness at a mean depth to be determined, and which turns out to be 40 

 miles; (2) that it diminishes uniformly from the surface; (3) that it 

 diminishes by a law suggested by Mr. T. C. Chamberlin. 



Discussion of the residuals by least squares at once throws out the hy- 

 potheses of no compensation or of compensation complete at the surface. 

 Hence there really is compensation nearly or quite complete at a finite 

 depth. Thus Hayford has proved Laplace's dictum that the irregulari- 

 ties of the earth and the causes which disturb its surface extend to but a 

 small depth compared with the earth's radius. Of the three hypothetical 

 depths for imiform compensation, solution H, or 120.9 kilometers, gives 

 the smallest sum of the squares of the residuals, and this sum is less than 

 a tenth of that found on the assumption that there is no compensation. 

 Compared with the opposite extreme of complete surface compensation, 

 the sum of the squares of the residuals for solution H is 53 per cent. 

 Thus for miiform distribution the depth of complete compensation is 

 near 120 kilometers. 



As might have been anticipated from Stokes's investigation, however, 

 the defiections of the vertical do not decide between various configurations 

 of compensation. Within the limits of errors of observation a compen- 

 sating layer 10 miles thick, at a mean depth of 40 miles, or a wedge, 

 widest at the surface and extending to a depth of 117 miles (or having 



^ Solution B corresponds to the Bouguer reduction. Althougli Boiigner recognized that 

 some mountains did not exert the attraction he expected of them, he would have been 

 rash to assume that a mountainous conformation was in general attended by correspond- 

 ing subterranean defleiencies of mass. Helmert 30 years ago found it best, as suggested 

 by Faye, to rely on the free-air reduction, or solution A, which leads to errors in a sense 

 opposite to those of Bonguer"s reduction, but affords a closer approximation to the ob- 

 served deflections. Sitzangsber. k. Preuss. Akad. der Wiss., 1912, Jan. to June, p. 308. 



