ISOSTASY AS A WORKING HYPOTHESIS 267 



differences of density between heavier and lighter masses from the sur- 

 face to the bottom of the zone of compensation. In order that the density 

 differences should be uniform, each column must consist of the same rock 

 or of similar sequences of unlike "rocks many times repeated. The scheme 

 is too artificial to be generally real. 



Chamberhn suggested that density differences be assumed to decline 

 with depth.* This assumption limits the vertical heterogeneity of the 

 lithosphere, which must necessarily result from the geologic processes of 

 metamorphism and igneous intrusion, to a special case. It also is arti- 

 ficial, a concession to the limitations of mathematical analysis. f 



A comparison between the Hayford and Chamberlin assumptions is, 

 nevertheless, significant. Whereas by certain methods of calculation the 

 uniformly distributed density differences assumed by Hayford gave 76 

 miles as the depth of the zone of compensation, the same methods applied 

 to the Chamberlin assumption gave 178 miles as that depth. Since these 

 two artificial concepts yield results which differ by 250 per cent, it is 

 reasonable to conclude that actual differences in the distribution of 

 density in unlike columns may also greatly affect the depth of the zone 

 of compensation. 



Gilbert has definitely shown that this must be so. In hi'^ last contri- 

 bution to the subject he concludes : 



"The same moderate assumptions as to variation of density which Hayford 

 and Bowie apply to horizontal relations in discussing isostatic compensation 

 yield, if applied to vertical relations, departures in gravity intensity of the 

 same order of magnitude as the outstanding anomalies, after making allow- 

 ance for isostatic compensation." 



His final statement is : 



"At present the map (of gravity anomalies) seems to express chiefly an 

 effect of heterogeneity in the nucleus and an effect of irregularity in the ver- 

 tical distribution of densities within the crust." ^^ 



When thus interpreted the map of gravity anomalies refutes the as- 

 sumption of uniformly distributed densities, on which it is based. It 

 throws the field open to any rational assumption regarding distribution; 

 and the range of possible assumptions is broadened by recognition of the 

 probability that the depth of compensation is different for different dis- 

 tributions of density. The problem is taken out of the straight-jacket of 



* T. C. Chamberlin : Review. Chicago Jour, of Geol., vol. xv, 1907, p. 75. 



t T. C. Chamberlin : The mathematics of isostasy. Am. Jour. Sci., 4th series, vol. 

 xlix, 1920, pp. 312-313. 



" .G. K. Gilbert : Interpretation of anomalies of gravity. Part C, Professional Paper 

 85, U. S. Geol. Survey. Contributions to general geology, 1913, pp. 30-31 and 37. 



