STRENGTH OF SURFACE SHELL IN HORIZONTAL DIRECTION 309 



for a steady configuration. This postulates nothing as to the mechanism 

 of yielding. In the intervening shell there is thought to be a compara- 

 tively rapid growth of the lateral stress with depth. Nothing is here said 

 as to quantities. But the form of the curve of lateral stress as it increases 

 with depth, compared with the curve of vertical stress, which increases 

 uniformly with depth as the load increases, may be illustrated by the 

 diagram, figure 1. No meaning is here attached to the scale of this dia- 

 gram. Moreover, this is not a complete picture of the conditions, for it 

 does not take into account the intimate tethering of particles in an elastic 

 medium more completely than this is cared for by Poisson's ratio; but 

 this picture will serve to bring out the writer's point, that a given stress 

 which, applied vertically at a given depth, would just produce potential 

 yielding, would, if applied horizontally at the same point, simply add to 

 the stress from load, leaving the whole bearable. Thus the outermost 

 shell down to a certain depth may sustain, resist, or transmit toward 

 regions of weakness horizonal — that is, tangential — stresses which, ap- 

 plied vertically, would produce isostatic adjustment. It may be that this 

 point will help to clarify the uncertain status of opinion regarding the 

 strength of the earth's crust. 



Spherical continuity of surface Shell confining yielding Layer 



A second point — a very obvious one — that the present writer would lay 

 stress upon is that every earth prism, down to the level of incipient yield- 

 ing, is contained and constrained by those which surround it, except at 

 its surface, probably more effectively than any like control in laboratory 

 experimentation. Though we know it well, we must not forget, even 

 momentarily, that the earth is a globe, and this outermost fairly rigid 

 layer of it a continuous spherical shell. Therefore it is hardly legitimate, 

 especially in thinking of the isostatic problem, where the whole earth is 

 necessarily involved, to consider elements of the shell as plane slabs with 

 free boundaries, or with hypothetical abutments of absolutely rigid matter 

 which may be supposed to apply stresses from without upon the edges of 

 the slab. Nor should these elements be thought of as flat domes unsup- 

 ported beneath, with free boundaries, or hypothetical abutments like 

 those specified for the slab. For example, there is no doubt that such 

 domes, if unsupported below or at the sides, would slump down under 

 their own weight, even when of small area; and either domes or slabs 

 might, if standing alone, break or shear, and thus fail to sustain or trans- 

 mit horizontal stress imposed from without. But it seems not to be a 

 necessary consequence that elements of a continuous spherical shell of the 



