Elastic Equilibrium of Semi-Infinite Solid. 



The constants Bm, Cm and Dm are not independent of one 

 another, but are connected bv the relation 



2/^ 



(13) 



which follows from the definition of J. 



§8. Next, the solutions corresponding to ^ which has sin md 

 in its factor can l)e found in a similar way. They are distinguished 

 from the above by placing a bar on every quantity. 



J= C,J,XJ^r)e-''ämmO, 



y L '2//. J Av J 



uh= I r ^''^'" C,„z-B,l JILj^x^r) + A,J-,Xkr)\e-''co?imd, 



(1^) 



with 



k{B„-Dj 



_J_+_3/^(7 



(15) 



§U. The stress can be calculated Ity using the formulae 



ZZ = U + 2n--"-'-, 



'bz 





zd 



p;^ III, \ 

 I Iz Ir )' 



;•/• = /J + 2« 



(16) 



' I Ir r r W J 



Thus corresponding to the first solution (12), we obtain 



