6o 



First published Paper on Electricity 



Fig. 15- 



before overcharged, AB will be as much undercharged as it was before 

 overcharged, and DF as much overcharged as it was before undercharged. 



83] COR. VIII. 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 2Oth and 2ist 

 propositions, that the quantity of redundant and deficient fluid in AB 



AC\ 3 ~ n AC 2 



will be as AC"- 1 x "=J , or as EC s-n - supposing the value of 8 to 



remain the same*. 



84] PROP. XXIII. Let AE (Fig. 15) be a cylindric canal, infinitely 

 continued beyond E ; and let A F 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 I 

 that of the cylindric canal, and let both canals be filled 

 with uniform fluid of the same density: the force with 

 which a particle of fluid P, placed anywhere at pleasure, 

 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 center P, draw two circular arches BD and bd, 

 infinitely near to each other, cutting AE in B and , and AF in D and 8, 

 and draw the radii Pb and Pd. As PB = PD, the force with which P 

 repels a particle at B, in the direction Bp, is to that with which it repels an 



equal particle at D, in the direction Z)8, as ^ to ^ , or as ^ to ^~ ; 



and therefore, the force with which it repels the whole fluid in Bf$, in the 

 direction Eft, is the same with which it repels the whole fluid in DS, in 

 the direction D8, that is in the direction of the canal; and therefore, the 

 force with which it repels the whole fluid in AE, in the direction AE, is 

 the same with which it repels the whole fluid in AF, in the direction of 

 the canal. 



85] COR. If the bent canal A DF, instead of being infinitely continued, 

 meets the cylindric canal in E, as in Fig. 16, the repulsion of 

 P on the fluid in the bent canal ADE, in the direction of the 

 canal, will still be equal to its repulsion on that in the 

 cylindric canal AE, in the direction AE. 



86] PROP. XXIV. If two bodies, for instance the plate 

 AB, and the body H, of Prop. XXII, communicate with each 

 other, by a canal filled with incompressible fluid, and are 

 either over or undercharged, the quantity of redundant 

 fluid in them will bear the same proportion to each other, 

 whether the canal by which they communicate is straight or crooked, or 



[ Note 4, p. 368.] 



