140, 141] ELLIPSOID. 273 



and using this value of T, 



Accordingly a potential may be measured in this simple 

 manner by a measurement of P and r, P and r having been 

 observed. If the tube on which the bubble is blown is open to 

 the air, P = 0, and 



141. Distribution on an Ellipsoid. We have found the 

 potential clue to an equipotential layer of amount e distributed on 

 an ellipsoid of semi-axes a, b, c to be, 109 (12), 



v= e ~ r ds 



2Jx V(tt 2 + 8) (6 2 + *) (C 2 + S) ' 



where X is the greatest root of the cubic 



x 2 * z 



At the surface of the ellipsoid X = 



ds 



so that the capacity q is the elliptic integral 



2 



ds 



The surface density of the charge is given by 



1_ dV_ JL_ fdV 



~- 



which by 110 gives 

 e 



Ellipsoids of Rotation. 



If a = 6, the ellipsoid is one of rotation, arid the elliptic integral 

 simplifies into 



r ds 2 . Vo^c 2 , 



I , =- = .-- sin" 1 - , if a > c, 



W. E. 18 



