Elastic Equilibrium of Semi-Infinite Solid. 



19 



Fis. 2. 



By integrating (t(z)o over the surface, it may be easily seen 

 that the total depression of the surface appears to be infinitely 

 great, though it is caused l;)y a finite normal pressure of total 

 amount /7. This seems again to be paradoxical, but that is not the 

 case; if we calculate the work done by the given pressure, instead 



of total depression, it will appear to be finite, equal to -0 — • \)2^ ' 

 inversely as a. 



§18. Let us now proceed to appl}' the results of this example 

 to the theory of rupture of a foundation over which a heavy load is 

 spread. There have been proposed several hypotheses concerning 

 the conditions under which an elastic body is ruptured or nearly 

 so. Among tliose hypotheses usually adopted there are two in 

 which a limitation on stress is taken as the measure of tendency to 

 rupture: the one which was introduced by Lam/, is that the 

 greatest tension should be less than a certain limit which is 



