VOL. LXl.] VHILOSOPHICAL TRANSACTIONS. %Af 



(^f"x ^^^ to 1, ahd less than that of (— )' "x i to 1: and from the 

 preceding remarks it appears, that the real quantity of redundant fluid in ab can 

 hardly be much greater than it would be if i was equal to 1 . 



Carol. 4. Hence, if the electric attraction and repulsion is inversely as the 

 square of the distance, the redundant fluid in ab, supposing i to be equal to 1, 

 will exceed that in the plate h, in a greater ratio than that of ac to 4ce, and 

 less than that of ac to 2ce. 



Corol. 5. Let now the body H consist of a globe, whose diameter equals ab; 

 the globe being situated in such a manner, that the canal cg, if continued, 

 would pass through its centre; and let the electric attraction and repulsion be 

 inversely as the square of the distance, the quantity of redundant fluid in the 

 globe will be 2b ; for the fluid will be spread uniformly over the surface of thd 

 globe, and its repulsion on the canal will be the same as if it was all collected in 

 \the centre of the sphere, and will therefore be the same with which an equal 

 quantity, disposed in the circumference of ab, would repel it in the contrary 

 direction, or with which half that quantity, or b, would repel it, if spread uni- 

 formly over the plate. 



Corol. 6. Therefore, if ^ was equal to 1, the redundant fluid in ab would 

 exceed that in the globe, in the ratio of ac to 4ce ; and therefore it will in reality 

 exceed that in the globe, in a rather greater ratio than that of ac to 4ce; but 

 if the plates are very near together, it will approach very near to that ratio, and 

 the nearer the plates are, the nearer it will approach to it. 



Corol. 7. Whether the electric repulsion is inversely as the square of the dis- 

 tance or not, if the body h is as much undercharged, as it was before over- 

 charged, AB will be as much undercharged as it was before overcharged, and df 

 as much overcharged as it was before undercharged. 



Corol. 8. If the size and distance of the plates be altered, the quantity of 

 redundant or deficient fluid in the body h remaining the same, it appears, by 

 comparing this proposition with the 20th and 21st propositions, that the quan- 

 tity of redundant and deficient fluid in ab, will be as ac - ' 



AC 3 - * AC* • 1 1 r 



X (— ) , or as — ^— , supposmg the value of S to remam the same. 



Prop. 23. Let ae, fig. 15, be a cylindric canal, infinitely continued beyond 

 b; and let af be a bent canal, meeting the other at a, and infinitely continued 

 beyond f: let the section of this canal, in all parts of it, be equal to that of the 

 cylindric canal, and let both canals be filled with uniform fluid of the same den- 

 sity: then the force with which a particle of fluid p, placed any where at plea- 

 sure, repels the whole quantity of fluid in af, in the direction of the canal, is 

 the same with which it repels the fluid in the canal ae, in the direction ae. — 

 On the centre p, draw 1 circular arches bd and bd, infinitely near to each other, 



