492 Mr. W. B. Morton on the 



ponent of (J'g h) 



_ /F t + g i\ + hF 3 _ 

 VF^+F^ + Fa 2 ' 



(7 = 



or putting in the values we have found for (f g h) in terms 



of <£, 



fc^ + foFa + fffaF, 



VF^ + F^ + Fs 2 



V F 1 2 4-F 2 2 + F 3 2 ' 



Now the perpendicular from the origin on the tangent plane 

 to F(# y 2) = C at the point (so y z) is 



_ gFi + ,yF 2 + zF 3 

 P 7F 1 8 + F 2 2 + F 8 2r 



and the perpendicular from the origin on the tangent plane 

 to F(#, y, kty = G at (# y £) is 



/(d¥\* , /tfF\* /rfFV 



VF^ + F^ + PFs 2 



= a?F!+yF 8 -fgF 8 



VF^ + F^ + FFs 2 ' 



CT __ A/9 



If now"F(#y *) = C is an ellipsoid, then we know that 

 o-' oc p 7 , therefore also a (x p, that is the arrangement of 

 charge on the moving ellipsoid is the same as if it were 

 at rest. 



7. Applying the above to the ellipsoid (a b c), we find that 

 <fias a function of (so y £) is the potential of a free distri- 

 bution on the ellipsoid 



