DEVELOPMENT OF THE DISCOIDAL HYPOTHESIS 275 



"although the relations of continents and ocean basins show with respect to 

 each other a high degree of isostasy, there is but little such adjustment within 

 areas 200 to 300 kilometers in diameter. Individual mountains and mountain 

 ranges may stand by virtue of the rigidity of the crust. Even under level 

 plains equally great loads are permanently borne, loads produced by wide- 

 spread irregularities of density not in accord with the topography above. 

 Isostasj'. then, is nearly perfect or is very imperfect, or even non-existent, 

 according to the size and relief of the area considered." '" 



Barren's statement is a confirmation, after the consideration of the data 

 accumulated during twenty-four years, of that which was formulated by 

 Gilbert as a result of the studies inspired by Lake Bonneville. Gilbert 

 stated as a working hypothesis that — 



"Mountains, mountain ranges, and valleys of magnitude equivalent to moun- 

 tains exist generally in virtue of the rigidity of the earth's crust; continents, 

 continental plateaus, and oceanic basins exist in virtue of isostatic equilibrium 

 in a crust heterogeneous as to density." " 



Gilbert's studies of Lake Bonneville led him to estimate the residual 

 strain which the earth's crust could bear without yielding as equivalent 

 to that which would be imposed by an excess of weight of 400 to 600 

 cubic miles of rock. In the discussion which followed his paper, Cham- 

 berlin asked to what area he would limit that cubic mass. Gilbert re- 

 plied :32 



"That raises a question I have not answered to my own satisfaction. It 

 seems clear to me that the imposition of a long, narrow ridge will be no more 

 effective in producing deformation than a small portion of the same ridge ; but 

 it is not clear whether a broad lens of added matter will be as effective as a 

 compact lens of the same weight." 



The problem raised by Chamberlin's question may be regarded as that 

 of the length, breadth, and thickness of a slab of the earth's crust which 

 would support the weight of 400 to 600 cubic miles of rock. With any 

 ordinary slab the resistance to bending is a simple function of the thick- 

 ness of the slab; but, as we have seen in the preceding section, the 

 strength which the isostatic shell opposes to vertical weight is great only 

 in the outer 10 or 20 miles of the crust. Below that its relative strength 

 rapidly lessens. This gives to the horizontal dimensions a peculiar im- 

 portance. A greater load on a narrow base would be supported more 

 rigidly than a less load on a wide base, provided the proportions were 



» J. Barrel! : The strength of the earth's crust. Chicago .Tour, of Geol., vol. xxii, 

 parts I, 11. and 111, 1914 ; part ill, 1915, pp. 650-7. 



» G. K. Gilhert : Strength of the earth's crust. Bull. Geol. Soc. Am., vol. 1, 1890, 

 p. 25. 



« Ibid., p. 26. 



