PRELIMINARY PROPOSITIONS 



[From the MS. in the possession of the Duke of Devonshire, N. 4 ; hitherto 



unpublished.] 



{See Table of Contents at the beginning of this volume.} 



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 uni- 

 formly, 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 + i to 2p + i. 



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 + i disposed in the plate as expressed 

 in the proposition is equal to that of the quantity 2p + i placed in the globe. 



141] PROP. XXX. Fig. i. Let two equal thin circular plates AB and ab 

 communicate with each other, and also with a third circular plate EF of the 

 same size and shape and placed at an infinite distance from them, by the straight 

 canal CD of incompressible fluid. Let the three plates be all parallel to each 



T) 



Fig. i. 



other and be placed so that CD shall pass through their centers and be per- 

 pendicular to their planes, and let the plates be overcharged. The quantity of 

 redundant fluid in each of the plates AB and ab will be to that in EF as the 

 repulsion of the plate ab on the canal cD to the sum of the repulsions on cD 



