324 Status of the Theory of Isostasy. 



portions of c — c have but little influence on the intensity 

 of gravity, since their attractive forces act nearly hori- 

 zontally. The added compensation, however, being more 

 nearly under the station, serves to offset the excess due 

 to c in the smaller zone. Next let the whole earth be 

 considered. The excess of mass, cc, and its compensa- 

 tion, c' — c', now become spherical shells. But the gravi- 

 tative force of a spherical shell acts on any outside 

 station the same as if its matter were concentrated at 

 the center. As the masses c — e and cf — & are concen- 

 tric and equal in magnitude, but positive and negative 

 in sign, they exactly neutralize each other. Therefore 

 when the whole earth is considered the influence of change 

 of datum cancels out. In Hayford and Bowie's work the 

 whole earth is considered ; consequently, change of datum 

 does not produce any effect on the computation of gravity 

 under the hypothesis of isostasy. 



Distribution of Isostatic Compensation. 



The solutions of the geodetic data do not give a sharply 

 defined depth to isostatic compensation. They show 

 unmistakably that such compensation does exist, but on 

 the assumption of uniform distribution, the most prob- 

 able depth ranges from 60 to 300 kilometers according 

 to the regional group of data taken. The largest depths 

 are the least reliable, and Bowie believes that the mean 

 given by much more extensive data will fall between 

 80 and 130 kilometers. For the present he takes 96 kilo- 

 meters as the most probable depth. Round figures have 

 an advantage in that they do not imply an accuracy which 

 does not exist. On the assumption of uniform distribu- 

 tion, 100 kilometers, 60 miles, may therefore be taken 

 as the most probable general depth. 



The next question is, as to how the compensation really 

 is distributed and how much it may vary in its mode of 

 distribution. Figure 5 shows several modes which satisfy 

 equally well the deflection data, giving an equally small 

 minimum to the sum of the squares of the residuals. The 

 computations on which the diagrams are based are given 

 by Hayford, 28 with the exception of the center of gravities 

 of distributions C and D, which were determined by the 

 writer. 



28 J. F. Hayford, op. cit., pp. 149-163. 



