Forces in opposing Distortion of an Elastic Sphere. 441 



If there are no surface tractions one of the boundary con- 

 ditions is 



\.i'A + 



Xbx dr r ) 



(11) 



where 



Z, = xu +yv + zw 



_ Kpi* ^ n + 4 n 

 ~ X+V^ 6(^+3) V** 1 ' 



The terms contributed to the left-hand side of (11) by the 

 particular integrals we have just found are 



~xrfc le " {^'-Q»+i + * Gi^Taj ^ 



n + 4 3/jn .j 



+ /i 



a 



c^Q» +I ) y 



x+2 At Ze »i (?l+ ^2n+3L a* aAr^tvj 



Xow we want to make every term in the preceding ex- 

 pression into a spherical solid harmonic, and since it is the 

 surface value of the expression that occurs in the boundary 

 condition we may put a (the value of r at the surface) for r 

 wherever we choose. 



In solid harmonics the preceding expression becomes 



X + 2^ • *** \\2n + 3 + 3 ) -da 2n + s' ^v \ i^V J 



In the case of tidal forces or c; centrifugal force " the only 

 significant part of K is — - . With this value of K the above 

 expression becomes 



