image of . Bisect the arc in , so that , and draw to meet the sphere in . is the point required. Also through , the centre of the sphere, and draw meeting the sphere in and . Then if be any point in the bowl, the surface-density at on the side which is separated from by the completed spherical surface, induced by a quantity of electricity at , will be
where denotes the chord drawn from , the pole of the bowl, to the rim of the bowl.