668 JOSEPH BARRELL 



diagrams at the base of the lithosphere in case B. Supposing that 

 vertical readjustment of the columns is prevented for a time by the 

 strength of the crust, the vertical stresses will be taken up by a 

 vertical shearing strain along the partition between the two 

 columns. This shear is equal in amount to the difference in total 

 weights of the columns. Let the shear per unit area be called s. 

 It acts over a surface taken as 122 km. high. Let this height be 

 called h. The weight of the columns will vary with their breadth 

 in the plane of the drawing. If the breadth of each be taken as h 

 and the weights per unit area as M and N {N including rock, sedi- 

 ment, and sea-water), then for a cross-section of unit thickness 

 the total difference in weight is {N—M)h and the total shear 

 is this same amount, provided that the columns are not sus- 

 tained in part by other boundaries. But the total shear is also sh. 

 Therefore 



sh={N-M)b 



s=^{N-M)\ 



For narrow columns h is small, giving to 5 a small value and con- 

 sequently one within the elastic limit. Let h become broad and s 

 will then become large and exceed the elastic limit. The lateral 

 pressures, on the contrary, are less dependent upon the breadth, 

 and, if the problem were regarded as one of hydrostatic pressures, 

 would be wholly independent of breadth. The formula shows that 

 the broader the columns, the more readily they will readjust by 

 vertical shear between the columns. Now unless failure by vertical 

 shear took place between the upper part of the columns the heavy 

 column would be held up, the light column would be held down, 

 except for the partial effect of sagging in case the columns were 

 very broad. The lateral landward pressure at the base could 

 therefore not become effective. The loaded portion of the crust 

 must fail first by shear or flexure of its upper portion. Whatever 

 be the distribution of strength it would appear then that the primary 

 yielding is the vertical one and the landward force of undertow 

 can become only secondarily effective. 



The hypothesis of local and nearly complete isostasy requires 

 that the elastic limit for vertical shear should be very low in order 



