5SB 



ELECTRICITY; 



PHOT. * 

 Kig. 15. 



Uw quantit) of redundant fluid in it would be B ; and 



if it wa nil collected iii the circumference, would be 

 jij 



"- _: .iM'l therefore the real quantity will be;, 

 tkiii H. iind lest than . 



. ' n 



vfoiv, if we suppose J to IK' equal to 1, 

 the quantity of redundant fluid in AB will exceed that in 



.the pbu- 1 1 . in a greater ratio tlian that MgBJ X 



3 n /AC\ 5 ~* 



- to !, and less than that of ( : I y. \ to one: 



\l r./ 



an I from the preceding remarks it appears, that the real 

 lUJ.tnlilv ol' redundant tluid in A 15 can hardly be much 



. i- than it would l>e if 3 was equal to 1. 

 ( oroi. \. Hence the re<lundant fluid in AB, suppo- 

 sing } to be equal to 1, will exceed that in the plate (I, 

 in a greater ratio tlian tluit of AC to 4-CE, and less than 

 that of AC to _ 



Carol, a. Let now the body H consist of a globe 

 whose diameter equals AB ; the globe l>eing situated in 

 such a manner that the canal CG, if continued, would 

 pass through its centre, the quantity of redundant fluid 

 iti the globe will be 2B; for the fluid will be spread 

 uniformly over the surface of the globe, and its repul- 

 sion on the canal will be the same as if it was all collect- 

 ed in the centre of the sphere, and will therefore be the 

 wiih 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 uniformly over the plate. 



it. (j. Therefore, if* 3 was equal to 1, the redun- 

 dant fluid in AB would exceed that in the globe, in the 

 of AC to 4CE ; and therefore it will in reality ex- 

 i ,-cd that in the globe, in a rather greater ratio than that 

 '. ' to 4CE ; but if the plates are very near together, 

 rt will approach very near to that ratio, and the nearer 

 the plate* arc, the nearer it will approach to it. 



( 'oral. 7. If the body H is as much undercharged as 

 it was before overcharged, AB will be as much under- 

 charged as it was before overcharged, and DF as 

 much overcharged as it was l>efore undercharged. 



Carol. 8. If the size and distance of the plates be al- 

 tered, the quantity of redundant or deficient fluid in the 

 body H remaining the same, it appears, by comparing 

 this proposition with the 18th and IQth propositions, 

 that the quantity of redundant and deficient fluid in 



\B, will be as AC"- 1 x \^r ) OT ^cm-^' SU PP- 

 \rA^/ r/L- i 



sing the value of 3 to remain the same. 



Prop. XXI. Let AE, Fig. 15. be a cylindric canal, in- 

 finitely continued beyond E ; and let AF be a bent ca- 

 nal 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 density : 

 then the force with which a particle of fluid P, placed 

 anywhere, at pleasure, repels the whole quantity of 

 fluid in F.F, 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 two circular arch- 

 < - HI) and bd, infinitely near to each other, cutting A K 

 in B and p, and AF in D and J; and draw the radii 

 Pi and Yd. As PB=PD, the force with which P re- 

 pels a particle at B, in the direction B0, is to that with 

 which it repels an equal particle at D, in the direction 

 -' Drf 11 



Theoretical 



' ** 



Bl 



' r M 



Bl DJ ' 



therefore ^ forcc 



with which it repels the whole fluid in IU, in the df- 



" hich it repels the whole 



fluid in 1)J. in tle direction DJ, that i* in the direction 

 (ii'tiie canal ; and therefore the fmve with which it re- 

 pel the whole fluid in AE, in the direction AK, is the 

 same with which it repels the whole fluid in AK, in the 

 direction of the canal. 



a/. If the bent canal ADF, instead of being infi- P(.ATE 

 nitely continued, meets the cylindric c.i'>; t i in I-',, as in I.I. 

 Fig.'lfi, the repulsion of P on the fluid in the U-iit F * 16 - 

 canal ADK, in the direction of the canal, will still be 

 equal to its repulsion on that in the cylindric canal AE, 

 in the direction AE. 



I'rop. XXII. If two bodies, for instance the plate AB PROP. it. 

 and the body H of 1'rop. 20, communicate with each 

 other by a canal filled with incompressible fluid, and are 

 either over or under charged; 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 into whatever part of the bodies 

 the canal is inserted, or in whatever manner the two bo- 

 dies We situated in respect of each other, provided that 

 their distance is infinite, or so great that the repulsion 

 of each body on the fluid in the canal shall not be sen- 

 sibly less than if ft was infinite. 



Let the parallelograms AB and DF, Fig. 17, repre- _. 

 sent the two plates, and H and L the bodies comrauni- * 1T ' 

 eating with them ; let now H be removed to /;, and let 

 it communicate with AB, by the bent canal gc, the 

 quantity of fluid in the plates and bodies remaining the 

 same as before, and let us, for the sake of ease in the 

 demonstration, suppose the canal gc to be every where 

 of the same thickness as the canal GC, though the pro- 

 position will evidently hold equally good whether it is 

 or not, then the fluid will still be in cquilibrio. For let 

 us first suppose the canal gc to be continued through the 

 substance of the plate AB to C, along the line crC ; the 

 part crC being of the same thickness as the rest of the ca- 

 nnl, and the fluid in it of the same density : by the pre- 

 ceding proposition, the repulsion or attraction of each 

 particle of fluid or matter in the plates AB and DF, on the 

 fluid in the whole canal Crcg, in the direction of that ca- 

 nal, is equal to its repulsion or attraction on the fluid in 

 the canal CO, in the direction CG ; and therefore the 

 whole repulsion or attraction of the two plates on the ca- 

 nal Crcg is equal to their repulsion or attraction on CG ; 

 but as the fluid in the plate AB is in equilibrio, each 

 particle of fluid in the part Crc of the canal, is implied 

 by the plates, with as much force in one direction as 

 the other, and consequently the plates impel the fluid 

 in the canal eg, with as much force as they do that in 

 the whole canal Crcg, that is, with the same force that 

 they impel the fluid in CG. In like manner the body 

 h impels the fluid in eg, with the same force that H does 

 the fluid in CG, and consequently h impels the fluid in 

 eg one way in the direction of the canal, with the same 

 force that the two plates impel it the contrary way, and 

 therefore the fluid in eg has no tendency to flow from 

 one body to the other. 



Corel. By the same method of reasoning, with the 

 help of the corollary to the 21st proposition, it appears 

 that if AB and H each communicate with a third body, 

 by canals of incompressible fluid, and a communication 

 it made between AB and H by another canal of incom- 

 pressible fluid, the fluid will have no tendency to flow 

 from one to the other through this canal, supposing that 

 the fluid was in equilibrio before this communication was 

 made. In like manner, if AB and H communicate with 

 each other, or each communicate with a third body, by 

 canals of real fluid, instead of the imaginary canals of 



