Elastic Eqiiilibi-ium of Semi-Infinite Solid. 



47 



we have 



/ 







J 



J^{h-)cU- = -— , 



k a or 



siuka — kacoska r/i \n ^ tt-/ 1 1 



^-^; jAknak = F[ , — 



Jrci? ^ ^ 3>- \ 2 2 



5 (T 



{ (101) 



2a I ^. 2 a- / r ^2a ^ r / 



for a ^ r. Consequently 



{ii,% 



II 



1 



47Ï.X+IJL) r 





>(102) 



for a ^ r. 



§30. To ßncl the expressions for the displacement within the 

 loaded circle, we proceed as follows: 



Making use of the power series of the Bessel function, we 

 have 







a ,^„ ;,!(,,+ !)! \2aJ " ^"^ 

 y ;_,.| ,inka-kacoska y^,j^.,.^^jj^. 



_ 1 ^-. (-1/ / r V-^j 

 a „4i («!)' \ 2a/ ""\ a 



(103) 



where i2 stands for 







By the aid of the formuke 



