682 JOSEPH BARRELL 



flow is 600 km. deep, the actual lateral movement, if all depths 

 move equally, will be but 0.83 km., since 0.83X600 = 500. If the 

 flowage is supposed to increase regularly from top and bottom to 

 the middle the movement of the middle layer would be i . 66 km. 

 A previously vertical line 600 miles long through this asthenosphere 

 would then be bent at the middle by this amount and its two 

 halves make angles of o°i9' with the vertical. Each layer a kilo- 

 meter thick would move horizontally 5.6m. with respect to each 

 adjacent layer of kilometer thickness. These figures bring out the 

 insignificant degree of the plastic deformation in such a deep zone 

 which is needed to restore isostatic equilibrium, even for a large 

 interior continental area after erosion amounting to two-thirds 

 of the present average elevation of the North American continent. 



As a matter of fact the cross-section of the plastic deformation 

 would not be a triangle, but a sinusoidal curve, so that the maximum 

 linear flow for thickness of 600 km. would be between 0.83 and 

 1 .66 km. 



This illustration makes it clear that the isostatic rejuvenation 

 of continental interiors as well as of the margins, which meets such 

 grave difficulties under the hypothesis of a thin and shallow zone 

 of isostatic undertow, is eliminated by adopting the hypothesis 

 of a thick and plastic sublithospheric shell, such as has been found 

 to be suggested by independent evidence. 



The idea of folding as a result of isostatic undertow definitely 

 may be abandoned, but the absence of a notable isostatic gradient 

 has some further significance. It is seen from Fig. 14 that if the 

 fields of great erosion and deposition are within a few hundred 

 kilometers of each other the rejuvenative undertow, under the 

 laws of stress distribution in plastic bodies, would involve mostly 

 a limited tract in the outer part of the asthenosphere; whereas, if 

 the undertow must extend over distances of 1,000 km. or more, 

 then the whole depth of the asthenosphere will become involved. 

 The amount of stress-difference and of plastic shear per unit of 

 volume may therefore be no greater in the one case than in the other. 

 Especially, if the middle of the asthenosphere is its weakest part, 

 a movement generated by areas large enough to involve the whole 

 of this zone would go forward under less stress-dift"erence per unit 



