

ELECTRICITY. 



PBOF. 17. 

 ** *' 



I'M*. 18. 



Fig. is. 



rcdbndant or .U-i'uii-nt fluid in It, * uuUl benr exactly 

 fog Mlue propoi \ hatever sort of mat- 



ter B consisted of, if it WM po*oil>U- for the redundant 

 or deficient fluid in .. -,<<Me<l acvur.it.-- 



1\ in the Mme ^"fify whatever sort of matter it con- 

 suU-d ot'. For Mippov* 15 to consist of any sort of mat- 

 tir : ami let thf tliiiil in the canal ami two bodies be 

 in rquilihrin: lit now 15 be iniulf to consist of some 

 nther sort of matter, which requires a different quanti- 

 ty of fluid to saturate it ; lint let tin- quantity ami dis- 

 jxjsition of tin- rrdimtliiiit or deficient fluid in it re- 

 main the tame as before : it is plain that the llui.l \\iil 



11 lir in equilibrio ; as the attraction or repulsion of 

 any Ixxly depends only on the quantity anil disposition 

 of the mhmdnnt ami deficient fluid in it. Therefore, 

 I'v the preceding proposition, the quantity of redundant 

 or deficient fluid in B, will actually bear very nearly 

 the sainc proportion to that in 6, whatever sort of mat- 

 ter Boon-UN of : provided tin. 1 quantity of redundant 

 or deficient fluid in it is very small in respect of the 

 whole. 



fro/>.XViI. Let two bodies B and i (Fig.l 1.) becon- 

 nected together by a very .-lender canal AD da, either 

 straight or crooked : let the canal be every where of 

 the same breadth and thickness ; so that all sections of 

 this canal made by planes perpendicular to the direc- 

 tion of the canal in that part, shall be equal and simi- 

 lar: let the canal lie composed of uniform matter ; and 

 let the electric fluid in it be supposed incompressible, 

 nnd of such density as exactly to saturate the matter 

 in it ; and let it nevertheless be able to move readily 

 along the canal ; and let each particle of fluid in the 

 canal be attracted and repelled by the matter and fluid 

 in tl'.e canal and in the bodies B and b, just in the same 

 manner that it would be if it was not incompressible ; 

 and let the bodies B and b be either over or under 

 charged. Then the force with which the whole quan- 

 iuid in the canal is impelled from A towards 

 I), in the direction of the axis of the canal, by the uni- 

 ted attractions and repulsions of the two bodies, must 

 be nothing; as otherwise the fluid in the canal could 

 not be at rest: observing that by the force with which 

 the whole quantity of fluid is impelled in the direction 

 >f the axis of the canal, is meiuit the sum of the for- 

 ces, with which the fliii.l in each part of the canal is 

 impelled in the direction c.f the axis of the canal in 

 that place, from A towards 1) ; anil observing also, 

 that an impulse in the contrary direction, from D to- 

 wards A, must be considered as negative. 



For as the canal i.s exactly saturated with fluid, the 

 fluid in it is attracted or repelled only by the redun- 

 dant matter or fluid in the two bodies. Suppose now 

 that the fluid in any section of the canal, as !>, is im- 

 pelled w ith any given force in the direction of the ca- 

 nal at that place, the section 1W would, in consequence 

 ofit.be impelled with exactly the same force in the 

 direction O f the canal nt D, if the Huid between Ee 

 and Dd was not at all attracted or repelled by the 

 two bodies ; and consequently the section Dd is im- 

 pelled in the direction of the canal, with the sum <.f 

 the fore* .-=, with which the finid in each part of the 

 canal is impelled, by the attraction or repulsion of the 

 two bodies in the direction of the axis in that port ; 

 . 'intently, unless this sum was nothing, the 

 fluid in Dtl could not be at i 



Corot. Therefore the force with which the fluid in 

 the c.-tii.d is im]>cllfd one way in the direction of the 

 axis, by the body B, must be equal to that with which 

 it i - iin|.flh-d by It in the contrary direction. 



prop. XVI U. Let two similar bodies B and I, Fig. 13. 



;i.-cted by the M ry .-lender rylindric or pri-m.i- Tho 

 tic canal A<;, filled with incompressible fluid, in the J_ 

 same manner as described in the preceding proposition : j^J ~" 

 let the bodie- be overcharged ; but let the quantity of ( , i.|. 

 redundant fluid in each bear so small a proportion to t'ig. 13. 

 the whole, that the fluid may bo considered as di-]x>- 

 M-d in a similar manner in both ; let the Ixidie.i also 

 be similarly situated in respect of the canal A<i ; and 

 let them be placed at an infinite distance from each 

 other, or at so great a one, that the repulsion of ci- 

 ther body on the fluid in the canal, shall not br sen- 

 sibly less than if they were at an infinite di-tamc- 

 then, if the electric attraction and repulsion is in\ . 

 ly as the 11 power of the distance, being greater than 

 1, nnd less than :!, the quantity of redundant fluid in 

 the two bodies will be to each other, as the 1 po\\ er 

 of their corresponding diameters AF :md <if. 



For if the quantity of redundant fluid in the twn 

 bodies is in this proportion, the repulsion ofo:i<*body 

 on the fluid in the canal, will be equal to that of the 

 other body on it. in the contrary direction : and con- 

 sequently the fluid will have no tendency to flow from 

 one body to the other, as may thus be proved. Take 

 the points 1) and E very near to each other; and 

 take dn to DA, and fa to KA, as af to AF ; the re- 

 pulsion of the body B on a particle at D, will be to 



the repulsion of b on a particle at il, as j-=, to , ; for, 



as the fluid is disposed similarly in both bodies, the 

 quantity of fluid in any small part of B, is to the quan- 

 tity in the corresponding part of 6, as AF" ' to /./ 

 and consequently the repulsion of that small part of 

 B, on D, is to the repulsion of the corresponding part 



of b on tl, as . , or - p to 



/\ \- '* A I* 



uf 



But the quantity 



of fluid in the small part DE of the canal, is to that 

 in de, as DE to tie, or as AF to af; therefore the repul- 

 sion of B on the fluid in DE, is equal to that ofo on 

 the fluid in tie: therefore hiking a to \u. as /'to AF, 

 the repulsion of b on the fluid in ap, is equal to that of B 

 on the fluid in Aa ; but the repulsion of b on u may 

 be considered as the same as its repulsion on An ; for, 

 by the supposition, the repulsion of 15 on \<i may be 

 considered as the same as if it was continued infinitely ; 

 and therefore the repulsion of b on n<j may be consi- 

 dered as the same as if it was continued infinitely. 



Carol. 15y just the same method of reasoning it ap- 

 pears, that if the bodies are undercharged, the quan- 

 tity of deficient fluid in b will be to that in 13, as nf>~ ' to 

 AF"~'. 



Pro]>. XIX. Let a thin flat plate be connected to any Psor. 19. 

 other body, as in the preceding proposition, by a canal 

 of incompressible fluid, perpendicular to the plane of 

 the plate ; and let that body be overcharged ; then 

 the quantity of redundant fluid in the plate will bear 

 very nearly the same proportion to that in the other 

 body, whatever the thickness of the plate may be, 

 provided its thickness is very small in proportion to its 

 breadth, or smallest diameter. For there can Ix,- no 

 doubt, but under that restriction, the fluid will be dis- 

 posed very nearly in the same manner in the plate. 

 whatever its thickness may be; and therefore its im- 

 pulsion on the fluid in the canal will be very nearly 

 the same, whatever its thickness may l>e. 



Prop. XX. Let AB and DF, Fig. U, reprc-ent two Paor. ?0. 

 equal and parallel circular plates, whose centres are C l-i 8- '* 

 anil F, ; let the plates be placed so, that a right line 

 joining their centres shall be perpendicular to the 



