Solids tinder Body Forces. 325 



\s=-^-[r*dx'di,'dz / 



-J^Wdx'dy' 



sin 



6'VJ 6 

 (with the same notation as before), 



where a 2 — R 2 sin 2 # — @, as before, 

 and R 2 — a 2 = p\ 



R being greater than a. 



5. For an ellipsoidal distribution (uniform) we have to 

 evaluate 



= -|7T 



3 



over an ellipsoid. 



^UVrftf'dTy'ek' 



This is -^ffidJdy'dz' 



"dx 



^jbCfLjtdx'dy'dz' 



where 



= #>v-v x '}, 



V= 1 =potential due to a uniform distribution 



and V x = l-dx'dy'dz' 



= potential due to a distribution of density varying as x 



=7ra Hoofe)( 1_ ra-)' 



and Q 2 =(a 2 + X)(b 2 + X)(e 2 + X). 



