Elastic Equilibrium of Semi-Infinite Solid. 



51 



example may be applied to the discussion of contact of an elastic 

 body upon another with plane-surface. 



§38. Another application will be considered here. Suppose 

 we have a material loading of a semi-spheroidal form whose 

 equation is 



-^ + ^ = 1. (^<0) 



and of uniform density p. This load may be likened to the tidal 

 inequality in the North Atlantic ocean which afïects the gravity 



measurement. In this case 77 will be replaced b}^ T^a gp j^^ 



before, the deviation of the direction of gravity produced by tlie 

 attraction of this load is given b}^ 



tan (Jj 



^nd' g^ '/ k^a 



Ji{kr)dk, 



and the level-change due to tlie deformation of the ground arisen 

 from the load 1)y 



tan^ = — 



3^ À + 2/1 



-./- 



sin ka — ka cos ka 

 k'a 



J.ykr)dk. 



The evaluation of this integral can be undertaken in a manner 

 similar to those of (99) and will appear to be 



./ 



■" sin ka — ka cos ka 



kra 



J,{kr)dk 



r 

 2^ 



nr 

 4a 



\ ■ -^ a a /. or I ^ 



sm — /I — ÏÎL- } , a é r 



\ r r V r' / 



r é a 



(109) 



Tlius we have 



tan ^ = - J^ . ^^1 . Ji- (sm -^^-JL /i _ Zl , ,1 10) 

 ^ 27ra" g' a \ r r V /•' / ' 



