CAPACITY OF AN ELLIPSOID. 6 1 



The ellipsoid being represented by the equation 



the total mass of electricity is 



M = ^nz&r[(i+a)3-i],3 

 From this we get 



M _ M 



7*a / z* 



The potential in the interior being constant, it is sufficient to 

 calculate its value at the centre. We have then, if r be the 

 radius ON, 



fov/S M CpdS 



V= = - \- , 



r ^irabc r 



/ / 



and the capacity of the ellipsoid is given by the equation 

 C ^.irabc J r 



75. For an ellipsoid with three unequal axes the capacity is an 

 elliptical function, but it may be easily obtained in the case of an 

 ellipsoid of revolution. 



Let us take as element of surface ^S, the zone described by an 

 element ds of the meridian curve, and let us suppose that the axis a 

 is the axis of rotation. We have then 



2irydx 



from which 



= 2irb <i dx. 



