36 ME. J. H. JEANS ON THE POTENTIAL OF ELLIPSOIDAL BODIES, AND 



The equation reduces to 



' ) >- ' ' (28) 



of which the solution is readily found to be 



These values are found to satisfy the conditions of 7, so that the potentials are 

 given by 



1 / a? if z* 



-*** xJ^jrv, W+x + /TTx + ??x ' 



T ^ 

 ~5 --- r T^ --- r , -------- 1 Ui\. 



J 3 



III. yl Distorted Ellipsoid. 



11. For an ellipsoid distorted in any way, and without any limitation (at present) 

 as to the distortion being small, assume 



4>(x, y, z, \) = + (\)(f+t) 



where \// (x) and f have the same meanings as before, being given by equations (27) and 

 (29), and <jt is any general function of x, y, z, and X. The boundary of the distorted 

 ellipsoid is of course 



Equation (19) becomes 



in which x', y', z', \' have been replaced by x, y, z, X now that there is no danger of 

 confusion, and A, B, C are written for a 2 + X, 1r + X, c 2 + X. If we further put 



- _ 



2 C a ~ 3x ' 



