113, 114] ATTRACTION OF ELLIPSOIDS. 215 



dV 



r 



, 



JT a 2 + wVa 2 



d*V r du 



(a 2 + u) V(a 2 + u) (6 2 + u) (c 2 + u) 



fol 1 



(a 2 + cr) (a 2 -f o-) (6 2 4- a) (c 2 + <r) 

 Now by 19, (5), 



"dx a? 



. 8 2 F , , , ,. 



Forming - 2 an( ^ r an d adding, 



a? + u b 2 + u c 2 + u 



+ 



The integration may be at once effected. 

 Since 



U V W 



we have 



(V(a 2 + w)(6 2 + w 



(a 2 + w) (6 2 + tt) (c 2 + u) 



..If 1 J_ ! I 

 2 }a* + u b* + u c z + u) V(a 2 + 



The integral becomes then 



which cancels the second term, and AF= 0. 

 For an internal point 



3 2 F *' P dw 



o 



