ELECTRICITY. 



539 



Theoretical incompressible fluid used in these propositions, and a 

 Electricity, communication is also made between them by a canal 

 ^""""Y"~ *" of incompressible fluid, the fluid can have no tendency 

 to flow from one to the other. The truth of the latter 

 part of this corollary will appear by supposing an ima- 

 ginary canal of incompressible fluid to be continued 

 through the whole length of the real one. 



Por. 83. Prop. XXIII. Let now a communication be made be- 

 PLATE tween the two plates AB and DF, by the canal XUS 

 CCL1. of incompressible fluid of any length, and let the body 

 Fig. 17. H and the plate AB be overcliarged. It is plain that 

 the fluid will flow through that canal from AB to DF. 

 Now the whole force with which the fluid in the canai 

 is impelled along it, by the joint action of the two 

 plates, is the same with which the whole quantity 

 of fluid in the canal CG or eg is impelled by them, sup- 

 posing the canal N'RS to be every where of the same 

 breadth and thickness as CG or eg. For suppose that 

 the canal NRS, instead of communicating with the 

 plate DF, is bent back just before it touches it, and 

 continued infinitely along the line Ss ; the force with 

 which the two plates impel the fluid in 8.?, is the same 

 with which they impel that in EL, supposing S* to be 

 of the same breadth and thickness as EL, and is there- 

 fore nothing; therefore the force with which they im- 

 pel the fluid in N'RS, is the same with which they im- 

 pel that in NRS.9, which is the same with wluch they 

 impel that in CG. 



POP. 24. Prop. XXIV. Letnow xyz be a body of an infinite size, 

 containing just fluid enough to saturate it; and let a 

 communication be made between h and xyz, by the ca- 

 nal hy of incompressible fluid, of the same breadth and 

 thickness as ^ c or GC, the fluid will flow through it 

 from /i to xyz; and the force with which the fluid in 

 that canal is impelled along it, is equal to that with 

 which the fluid in N'RS is impelled by the two plates. 



If the canal hy is of so great a length, that the re- 

 pulsion of A on it is the same as if it was continued in- 

 finitely, then the thing is evident ; but if it is not, let 

 the canal hy, instead of communicating with xyz, so 

 that the fluid can flow out of the canal into xyz, be con- 

 tinued infinitely through ils substance, along the line 

 yv: now, it must beobserved, that a small part ofthebody 

 xyz, namely, that which is turned towards It, will, by the 

 action of h on it, be rendered undercharged, but all the 

 rest of the body will be saturated; for the fluid driven 

 out of the undercharged part will not make the remain- 

 der, which is supposed to be of an infinite size, sensibly 

 overcharged : now the force with which the fluid in the 

 infinite canal hyv, is impelled by the body h and tin- 

 undercharged part of xyz, is the same with which the 

 fluid in gc is impelled by them ; but as the fluid in nil 

 parts of xyz is in equilibria, a particle in any part of 

 yv cannot be impelled in any direction ; and therefore 

 the fluid in h y is impelled with as much force as that 

 in hyv, and therefore the fluid in hy is impelled with 

 as much force as that in gc, and is therefore impelled 

 with as much force as the fluid in NRS is impelled by 

 the two plates. 



It perhaps may be asked, whether this method of de- 

 monstration would not equally tend to prove that the 

 fluid in ii y was impelled with the same force as that in 

 NRS, though xyz did not contain just fluid enough to 

 saturate it ; but this is not the ca#e, for this demon-tra- 

 tion de]>endson the canal yv being continued, within the 

 body xyz, to an infinite distance beyond any over or 

 undercharged part, which could not be if xyz contained 

 either more or less fluid than that. 



PBOP. 2i. p r ,, /; XXV. Let two bodies B and b, Fig. 13. be join- 

 ed by a rylindric or prismatic canal Au, filled with real 



fluid, and not by an imaginary canal of incompressible Theoretic^ 

 fluid, as in the 16'th proposition, and let the fluid in K^tricity. 

 it be in equilibrio, the force with which the whole or pTIrE" 

 any given part of the fluid in the canal, is impelled in cCLI. 

 the direction of its axis, by the united repulsions and Fig. 13. 

 attractions of the redundant fluid or matter in the two 

 bodies and the canal, must be nothing ; or the force 

 with which it is impelled one way in the direction of 

 the axis of the canal, must be equal to that with which 

 it is impelled the other way. For as the canal is sup- 

 posed cylindric or prismatic, no particle of fluid in it 

 can be prevented from moving in the direction of its 

 axis, by the sides of the canal ; and therefore the force 

 with which each particle is impelled either way in the 

 direction of the axis, by the united attractions and re- 

 pulsions of the two bodies and the canal, must be no- 

 thing, otherwise it could not be at rest ; and therefore 

 the force with which the whole, or any given part of 

 the fluid in the canal, is impelled in the direction of the 

 axis, must be nothing. 



Carol. \ . If the fluid in the canal is disposed in such 

 manner, that the repulsion or attraction of the redun- 

 dant fluid or matter in it, on the whole or any given 

 part of the fluid in the canal, has no tendency to impel 

 it either way in the direction of the axis ; then the force 

 with which that whole or given part is impelled by the 

 two bodies, must be nothing ; or the force with which 

 it is impelled one way in the direction of the axis, by 

 the body B, must be equal to that with which it is im- 

 pelled in the contrary direction by the other body, but 

 not if the fluid in the canal is disposed in a different 

 manner. 



Carol. 2. If the bodies, and consequently the canal, 

 is overcharged ; then, in whatever manner the fluid in 

 the canal is disposed, the force with which the whole 

 quantity of redundant fluid in the canal is repelled by 

 the body B, in the direction Aa, must be equal to that 

 with which it is repelled by b, in the contrary direction. 

 For the force with which the redundant fluid is im- 

 pelled in the direction A a. by its own repulsion, is no- 

 thing ; for the repulsion of the particles of any body 

 on each other, have no tendency to make the whole 

 body move in any direction. 



SECT. II. Comparison of the preceding Ifi/pol/iesis with 

 Experiments. 



1. It appears from experiment, that some bodies Comparison 

 suffer the electric fluid to pass with great readiness of the pre- 

 between their pores, while others will not suffer it to do ceding hy- 



so without great difficulty, and some hardly suffer it to P oll "' sls 

 i ii i TI f i ! L i- 11 j with ex- 



do so at all. The first sort ot bodies are called con- r 



ductors, the, others tion-conduclur.t. It is evident that 

 the electric fluid in non-conductors may be considered 

 as moveable, or answering to the definition given of 

 that term immediately before Prop. I. As to the fluid 

 contained in non-conducting substances, though it dues 

 not absolutely answer to the definition of inmioveable, 

 as it is not absolutely confined from moving, but only 

 does so with great difficulty ; yet it may in most cases 

 be considered a? such without sensible error. Air does in 

 some measure permit theelectricfluid to pass through it ; 

 though, if it is dry, it lets it pass but very slowly, and 

 not without difficulty, it is therefore to be called a non- 

 conductor. 



It appears that conductors would readily suffer the 

 fluid to run in and out of them, were it not Cor the air 

 which surrounds them ; for if the end of a conductor is 

 inserted into a vacuum, the fluid runs in and out of it with 

 perfect readiness ; but when it is surrounded on aW 



