298 Status of the Theory of Isostasy. 



these unit areas are small. Far away they are large. 

 They are chosen so that each unit area will have a unit 

 gravitative effect. But no one conceives this extreme 

 form of local compensation to be true, but calculations 

 of the deflection of the vertical and intensity of gravity 

 based on such local compensation agree essentially with 

 those based on regional compensation over areas at least 

 as large as a square degree. For mountain regions and 

 those near continental borders the assumption of regional 

 compensation restricted to radial distances of 60 kilo- 

 meters or less appears to give slightly better results than 

 the assumption of regional compensation over radial dis- 

 tances of 167 kilometers or greater, but the discrepancies 

 involved in taking isostasy as regional with a radius of 

 167 kilometers are small in comparison with other dis- 

 turbing factors. At the present time the best tests as 

 to the horizontal relationships between relief and density 

 appear to the writer to be geologic, based on the limits 

 of the loads which can be imposed on the crust without 

 yielding. 



Since enormous strains exist in the crust above, which 

 when too great produce folding or faulting, it seems 

 clear that, in so far as isostasy is true, the absence of 

 notable strains in the zone below, notwithstanding the 

 existence of geological agencies which tend to bring 

 stresses upon it, implies a lack of strength in that zone. 

 Rock flowage, like glacial flowage, must occur nearly as 

 fast as the strains accumulate. The writer has, there- 

 fore, proposed for that zone of ready yielding the name 

 of the astheno sphere, the sphere of weakness, as con- 

 trasted to the lithosphere above, which by comparison is 

 a sphere of strength, and the centrosphere below, which 

 is probably also more resistant. 



The geodetic evidence of isostasy is founded upon a 

 comparison of the true and calculated directions of the 

 plumb-line at numerous stations over the United States, 

 and in later work also upon a comparison of the true 

 and calculated values of gravity. By introducing the 

 hypothesis of isostatic compensation of density corre- 

 sponding to the relief, the discrepancies between calcu- 

 lated and observed values of the direction of the vertical 

 and the intensity of gravity were reduced on the average, 

 as previously noted, to a fraction of what they were if 

 no such hypothesis of density variations was introduced. 



