306 W. T. LEE BUILDIXG OF SOUTHERN ROCKY MOUXTAIXS 



Tor an average value we mav take in round numbers 



,x = 3.6X 10^^ C. G. S. units, 



K = 6 X 10^^ C. G. S. units, 



E = 9 X lO^^C. G.S. units. 



The ratio between tlie adopted values of fx, k, and E implies that Poisson's 

 ratio, (T, is equa.1 to %. The average value of o- was in fact very nearly 

 y^ for the sjDecimens tested. 



Let us consider a section of the earth's crust extending down to the 

 zone of flow, say 100 kilometers (62.1 miles), and supj^ose that on this is 

 placed a load of sediment 10,000 feet (3,01:8 meters) thick and of density 

 2.3, about that of sandstone. There are three limiting cases which may 

 be readily computed and which may throw light on the elastic yielding 

 of the crust. 



(1) SupjDose the rock to be compressed as a fluid, with no rigidity or 

 resistance to shear — that is, fx = — l3ut having a resistance to change of 

 volume measured by k = (y Y^ 10^^ C. G. S. units; and suppose further 

 that this fluid rock is confined by unyielding walls at the bottom and 

 sides, so that the only yielding is in the vertical direction and the pressure 

 is, of course, uniform in all directions. The relative decrease in length, e, 

 is given by the formula 



^=^. (I) 



K 



where p is the j^ressure per unit area. This case, while probably the most 

 artificial of the three as regards what would haj^pen within a short time 

 after the sudden application of the pressure, may yet give a fair aj)proxi- 

 mation to what would happen if time were allowed for the rock to flow — 

 that is, we know that under the long-continued application of force the 

 rock may lose its rigidity and fx become equal to zero. 



(2) Suppose the section of crust to be supported at the bottom, but to 

 be unconfined at the sides, the pressure being applied at the surface as 

 before. The pro1)lem is then one of comj^ression under the usual experi- 

 mental conditions, and we have 



-i- (^) 



(3) Suppose the section of crust to be supported at the bottom, and 

 that just enough j^ressure is applied at the sides to keep them from bulg- 

 ing out. This condition is one not usually contemplated in the theory 

 of elasticity, but the formula for it may be deduced from the fundamental 

 equations, 



