Elastic EquiliVn-ium of Semi-Infinite Solid. 



57 



where *S" stands for 



S' = ^[/' + i--a?f + 4.d'z'. (122) 



For z = ^). til is formula is still applicable, if we take 



8' = r — d' for r >- a, | 

 T= d' — y- for y <; a. J 



Siiuilarly. putting 



r = ^S'-~{r + y'-d'), I 



(123) 



we have 



/"-*' ■ 7 TH \in aU^ - r- + d')Q + z{z' + r^ + a.^)P ..o.x 



P 



"'shila . jn-yMl- 



aQ-zP 





(125) 

 (120) 



Til us. for the case of incorapressibility, we have 



rr = 



// jP z(aQ-zP) z [dz'-r' + d)Q + z(z--\-r' + a')P] \ ] 



r-^S'- 



S"* 



7' 



dß 



^_ // (_P_ziciQ-zI>)\ 



- ^ _ // { P ^^a{r-i' + d)Q+j(f+r^^-)P'] \ 



> (127) 



zz = — ., .^ ■»-- + 



Fr = — 



/y^ f r(-r + r--a-)P + 2a.^g | 

 2V2WI Ä" i' 



for the stress coinponent^ 



V. Boussinesq's Problem, 



§43. The problem of Lamé and Clapeykon is a special case 

 of those known as Boussinesq's, which can be stated as follows: 



