Elastic Equilibrium of Semi-Infinite Solid. 



15 



s- 



Fis. 1 



As seen from the diagram the state of affairs in the neighl)Our- 

 hood of the origin and even at a finite distance from it is an 

 impossible one, and the mathematical theory of elasticity does not 

 apply to such a case. The above argument must, if possible, be 

 amended l)y a suitable process of analysis. The general solution 

 found above is restricted to a special class of functions f^r) which 

 satisfy the integral theorem (26). The hypothesis of point con- 

 centration of given pressure does not, in a strictly mathematical 

 sense, satisfy this important condition, and the solution deduced 

 from it may not be looked upon as a legitimate one, at least in the 

 vicinity of the origin.'^ What follows from the assumption of 

 point-concentration of given pressure may, however, be considered, 

 except locally, as the limiting case of the effect of a pressure which 



1) A quite similar failure of the solution will occur in the problem of the deep-sea 

 water-wave and allied problems which can be solved by the aid of Fourier's Integral 

 Theorem. 



