PURPOSE OF PRESENT DISCUSSION 307 



must endeavor to reconcile, so far as possible, the interpretation of their 

 multitudinous and somewhat vague observations with that of the few but 

 precise data of geodesy. 



Purpose op present Discussion 



No new measurements are here brought forward, no detailed analyses. 

 None of the matters to be discussed are new. They have even received 

 emphasis heretofore. But numerous conversations and informal discus- 

 sions have led the writer to believe that they may merit coherent assembly 

 and fresh emphasis. 



Superior Strength of Surface Shell in horizontal Direction 



First, then, it appears reasonable that within a certain range of depth 

 there may be a more or less regular shell which will sustain, transmit, or 

 resist additional applied stress more effectively in the horizontal than in 

 the vertical direction. Barrell and others have touched upon this, but it 

 does not seem to have been fully developed anywhere. The actual earth, 

 of course, is lacking in homogeneity, but for the moment we must neglect 

 this. There seems to be general agreement that at some depth, under the 

 pressure of superincumbent matter # alone (but especially if this is com- 

 bined with an elevated temperature), rock matter will yield readily in 

 the direction of any open space or any region of accommodation. Willis 

 has given a convincing analysis of this. There are some who think that 

 this depth is very irregular, so that it is very different in different re- 

 gions. Others think that it is fairly definite and reasonably uniform, 

 when the actual slight inhomogeneity of the material is taken account of. 



At the surface most rock substances are rigid and elastic, capable of 

 sustaining, without any permanent deformation, considerable stresses en- 

 during for considerable intervals. Then let it be granted, or assumed, 

 that at some depth (in the actual earth different in different places, either 

 slightly or greatly, as the case may be) the rock matter will just begin 

 to yield under the pressure of the overlying material if any mode of ac- 

 commodation whatever is afforded. Then, somewhat above this depth, it 

 will not, under ordinary circumstances, yield. Let us now consider a 

 slender column of rock substance extending upward to the surface from 

 this depth, at which it will almost, but not quite, yield. This column is 

 confined by the surrounding rock substance and can not expand laterally; 

 yet each unit of it bears the load of all superincumbent units and would, 

 if not so confined, expand laterally to a certain extent; but, above the 

 depth of incipient potential yielding, its lateral expansion would not equal 



