B 



C 



D 



35-3 



36-3 



370 



70-7 



109-0 



178-6 



45-2 



501 



57-2 



500 



55-5 



63-1 



Status of the Theory of Isostasy. 327 



Comparative distribution of compensation. 



A 



Depth of center of gravity, miles. . . 32- 



Depth of bottom, miles 37- 



Percentage above 32 miles 50-0 



Percentage above center of gravity 50-0 



It is observed that the center of gravity would be high- 

 est for compensation reduced to an indefinitely thin plate. 

 The center of gravity for that assumption would lie at 

 a depth of between 31 and 32 miles. Under the hy- 

 pothesis of uniform distribution through the thickest 

 possible shell compatible with the least squares, the center 

 of gravity would descend, as shown in B, about 4 miles 

 to 35-3 miles. Of course, a much thicker shell might be 

 arbitrarily assumed, but the sum of the squares of the 

 residuals between the computed and observed deflections 

 would be much larger with increasing depth, a clear in- 

 dication that such an assumption has no application and 

 must be rejected. 



Under the hypothesis of uniformly decreasing com- 

 pensation, the center of gravity is at a depth of 36-3 

 miles, an increase of only one mile over the center of 

 gravity of the uniform compensation, but the compensa- 

 tion does not vanish until a depth of 109 miles is attained. 

 This extension of nearly 40 miles in depth is offset, how- 

 ever, by an increase in the proportion of the compensa- 

 tion above the center of gravity, and especially near the 

 surface. 



In the compensation extending to great depth, curve 

 D, when this depth is taken as 178-6 miles, it is seen 

 that because of the greater depth a still larger propor- 

 tion of the compensation lies between the surface and 

 32 miles than in the other three type solutions. Fur- 

 thermore, although the vanishing point has descended 

 70 miles below that for uniformly decreasing compensa- 

 tion, the center of gravity has descended less than one 

 mile, and 63 per cent, of the compensation now lies above 

 the center of gravity. 



From this series of four cases we may deduce what 

 would be the effective distribution of compensation if it 

 were assumed to extend to still greater depth. The center 

 of gravity would only descend slightly. Probably it 

 would not be over 38 miles deep if the compensation 



