In this and all the following propositions and lemmata the electric attraction and repulsion is supposed to be inversely as the square of the distance.

140] PROP. XXIX. Let a thin circular plate be connected to a globe [of the same diameter] placed at an infinite distance from it by a straight canal of incompressible fluid such as is described in Pr. xix., perpendicular to the plane of the plate and meeting it in its center, and let them be overcharged.

If we suppose that part of the redundant fluid in the plate is spread uniformly, and that the remainder is disposed in its circumference, and that the part which is spread uniformly is to that which is disposed in the circumference as p to one, the quantity of redundant fluid in the plate will be to that in the globe as p + 1 to 2p + 1.

For by Prop. XXII., Cor. v., the force with which that part of the redundant fluid in the plate which is disposed in the circumference repels the fluid in the canal is the same with which an equal quantity placed in the globe repels it in the contrary direction, and the repulsion of that part which is spread uniformly is the same as that of twice that quantity placed in the globe, and therefore the repulsion of a quantity of fluid equal to p + 1 disposed in the plate as expressed in the proposition is equal to that of the quantity 2p + 1 placed in the globe