Elastic Equilibrium of Semi-Infinite Solid. 



58 



and 



iP = 112x10-« = 0"-0023, 

 <p = 3-21 X 10-« = 0"-0066, 



,/, + <f = 4-33 X 10-« = 0"-()09 



nearly the same as the results in the former example. 



If we suppose the place of the observation to ])e very near to 

 the edge of the loaded area, tlien 



,/> = 5-0x10-« = 0' -01. 

 = 14-4x10-« = 0"-03, 



and 



greater than the maximum of the direct effect of the moon. 



Example V. • 



§39. Lastly, we shall take another example in whicli tlie 

 normal pressure of the form 



A.r) = 



II 



1 



27r« ^a?—r- 



(112) 



is applied to the boundary within a circle of radius a. which is 

 otherwise left free from ti'action. This problem has 1)een «iiscussed 

 also by Boussinesq and others, and the expression for the vertical 

 displacement at the l)oundarv has been found. In this case the 

 function Z{k) becomes 



^(«) = - ,. I' ^-ir — ; =-^ — ^mka. (113) 



Consequently we have 



àrra/i 



II 



4:7ta{)^ + fl) 



..CD 



dl 



(114) 



