THE GEODETIC EVIDENCE OF ISOSTASY 3 1 



it be true that the observed deflections of the vertical are inde- 

 pendent of the known topography. This assumption, tacitly 

 made in the usual determinations of the figure of the earth, 

 such for example, as the Clark and Bessel determinations, 

 represents an impossible condition. It is a limiting case. 



If the depth of compensation is finite, the deflections of the 

 vertical due to topography will be partly counterbalanced by the 

 contrary deflections due to defects and excesses of density 

 below the surface. The counterbalancing will be more com- 

 plete the greater the distance from the station to the partic- 

 ular topographical features under consideration. Given an as- 

 sumed depth within which the compensation is complete, and 

 assuming that the compensation is uniformly distributed through 

 that depth, it is a simple matter to compute the corresponding 

 deflections. The computation takes account fully of the amount 

 by which the plumb line is drawn toward a given mountain 

 range by the direct attraction of the mass of the range, and 

 also of the smaller effect of the contrary sign produced upon 

 the plumb line by the relative defect of density below the range. 



Three complete solutions were made in turn upon the assump- 

 tions that the depth of compensation is 101, 75, and 71 miles. 

 These particular assumed depths were based upon preliminary 

 examinations. 



A comparison of the five solutions corresponding to assumed 

 depths of compensation, infinity, 101 miles, 75 miles, 71 miles, 

 and zero, showed that the sum of the squares of residuals was least 

 for the 71-mile solution. Therefore, 71 miles is the most probable 

 of these five assumed values for the depth of compensation. 



How strong and clear is the evidence that the actual condi- 

 tion of the earth is that called isostasy, with the isostatic com- 

 pensation uniformly distributed within the depth of 71 miles, 

 rather than that it is an earth in which there is no isostatic 

 compensation, on which the continents and oceans are main- 

 tained by rigidity? Compare the 71-mile solution with that for 

 assumed depth infinity, the last named being the solution cor- 

 responding to extreme rigidity. 



The sum of the squares of the residuals in the former solu- 

 tion is 8,000 and in the latter is 65,000, more than 8 times as 



