114 ON THE MOTION OF SOLIDS THROUGH A LIQUID. [CHAP. V. 



tinuous at the surface; viz. distinguishing by -r- and \ -j I its 

 values j Ust outside, and just inside, respectively, we have 



[dX~] (dX\ . _ 



-j- - \-j-Y = 4nrl ........................ (5). 



|_ dn J [ dn j 



But at ; a& internal point we have (Thomson and Tait, Art. 522), 



X=-Fx ................................. (6), 



where 



d\ 



+ xic . + x i ............ (7). 



a, b, c being the semiaxes of the ellipsoid. Hence 

 so that (5) gives 



Since JT of course satisfies (1), and has its derivatives zero at 

 infinity, it is plain that all the conditions of the question are 

 satisfied by 



The value of X at an external point (x, y, z) is (Thomson and 

 Tait, I c.), 



where the lower limit is the positive root of 



9 ^T&quot; &quot; 1&quot; iTo ~~i -v 



We have, in exactly the same way, 



where the values of G, ff, Y t Z may be written down from (7) 

 and (9) by symmetry. 



