ELECTRICITY. 



533 



r-rnc-.i '. of thran, as D, be overcharged; the other body A will 

 :it >'- be so also. For as the fluid in the canal is repelled by 

 the redundant fluid in D, it is plain, that unless A was 

 overcharged, so as to balance that repulsion, the fluid 

 would run out of D into A. In like manner, if one is 

 undercharged, the other must be so too. 



Prop. IX. Let the body A (Fig. 6.) be either sat-i- 

 rated, or over or under charged, and let the fluid within 

 it be in equilibrio. Let now the body B, placed near 

 it, be rendered overcharged, the fluid within it being 

 supposed immoveable, and disposed in such a manner 

 that no part of it shall be undercharged ; the fluid in 

 A will no longer be in equilibrio, but will be repelled 

 from B ; therefore the fluid will flow from those parts 

 of A -which are nearest to B, to those which are more dis- 

 tant from it ; and consequently the part adjacent to MX" 

 (that part of the surface of A which is turned toward-; 

 B) will be made to contain less electric fluid than it did 

 l>efore, and that adjacent to the opposite surface RS will 

 contain more than before. 



It must be observed, that when a sufficient quantity 

 of fluid has flowed from MX toward* RS,the repulsion, 

 which the fluid in the part adjacent to MX exerts on 

 the rest of the fluid in A, will be so much weakened, 

 and the repulsion of that in the part near RS will be so 

 much increased, .is to compensate the repulsion of B, 

 which will prevent anymore fluid flowing from MX to 

 .RS. The reason why the fluid in B is supposed to be 

 jnmioveablc, i, that otherwise a question might arise, 

 whether the attraction or repulsion of the body A might 

 not cause such an alteration in the disposition of the 

 fluid in B, as to cause some parts of it to be underchar- 

 ged ; which might make it doubtful, whether B did on 

 the whole repel the fluid in A. It is evident, however, 

 that thi.i proposition would hold good, though some 

 parts of B wore undercharged, provided it did on the 

 v. hole repel the fluid in A. 



Carol. If B had been made undercharged instead of 

 overcharged, it is plain that some fluid would have flow- 

 ed from the farther part RS to the nearer part MX, in- 

 stead of from MX to U.S. 



Prop. X. Let us now suppose that the body A com- 

 municates by the canal EF, with another body D pla- 

 ced on the contrary side of it from B, as in Fig. 5, and 

 let these two bodies be either saturated, or over or un- 

 der charged, and let the fluid within them be in equili- 

 brio. Let now the body B be overcharged : it is plain 

 th.it some fluid will be driven from the nearer part M X 

 to the farther part RS, as in the former proposition ; 

 un<l also some fluid will be driven from RS, through 

 the canal, to the body D ; so that the quantity of fluid 

 in D will thus be increased, and the quantity in A, ta- 

 l.ing the whole body together, will be diminished, the 

 quantity in the part near MX will also be diminished : 

 but whether the quantity in the part near IIS will he 

 diminished or not, does not appear for certain ; but Mr 

 Cavendish imagines it would be not much altered. 



Coral. In like manner, if B is made undercharged, 

 some fluid will flow from D to A, and also from that 

 part of A near RS to the part near MX. 



Prop. XI. Suppose now, that the bodies A and D 

 communicate by the bent canal MPX nr,m (Fig. 7), 

 instead of the straight one EF : let the bodies be cither 

 saturated, or over or under charged, as before, and let 

 the fluid be ;:t rrst ; then if the body B is made over- 

 charged, ^mi" fluid will still run out of A into 1), pro- 

 vided die repulsion of B on the fluid in the canal is not 

 .eat 



The rcputa'oD of B on tiie fluid in the caoajj, wilj at 



5 



Por. 10. 



r*or. 11. 



first drive some fluid out of the leg MP/im into A, and 

 out of NP/>n into D, till the qti.-urtity of fluid in tli;:i 

 part of the canal which is nearest to B is so much di- 

 mini&hed, and its repulsion on the rest of the fluid in . 



the canal is so much diminished also, as to compen- Fi . 7. 

 sate the repulsion of B; but as the log NPp'n is 

 longer than the other, the repulsion of B on the 

 fluid in it will be greater ; consequently some fluid 

 will run out of A into D, on the same principle thai 

 water is drawn out of a vessel through a syphon : but 

 if the repulsion of B on the fluid in the canal is so great, 

 as to drive all the fluid out of the space (il'll^'V. so 

 that the fluid in the leg MGpm does not join to that in 

 NHp, then it is plain that no fluid can run out of A 

 into D, any more than water will run out of a \essel 

 through a syphon, if the height of the bend of" the sy- 

 phon above the water in the vessel is greater than that 

 to which water will rise in vacuo. 



Corel. If B is made undercharged, some fluid will 

 run out of D into A, and that though the attraction of 

 B on the fluid in the canal ig ever so great. 



Pro^.XII. Let ABC (Fig.8.) be a body overcharged I>KOI>. 1?. 

 with immoveable fluid uniformly spread ; let the bodies Fig- M. 

 near ABC on the outside bo .-nturatevl with immoveable 

 fluid ; and let D be a body inclosed within ABC, and 

 communicating by the canal 1)G with other distant bo- 

 dies saturated with fluid ; and let the fluid in D, and 

 the canal and thooe bodies be moveable ; then will the 

 body I) be rendered underchar 



For let us first suppose that 1) and the canal are sa- 

 turated, and that D is nearer to B than to the opposite 

 part of the body C ; then will all the fluid in the canal 

 be repelled from C by the redundant fluid in ABC ; 

 but if D is nearer to C than to B, take the point F, such 

 that a particle placed there would be repelled from C 

 with as much force, as one at D is repelled towards C ;. 

 the fluid in DF, taking the whole together, will be re- 

 pelled with as much force one way as the other, and 

 the fluid in FG is all of it repelled from C : therefore, 

 in both cases, the fluid in the canal, Inking the whole 

 together, is repelled from C ; consequently some fluid 

 will run out of D and the canal, till the attraction of 

 the unsaturated matter there is sufficient to balance the 

 repulsion of the redundant fluid in ABC. 



Prop. XIII. If we now suppose that the fluid on the PBOP. IS. 

 outside of ABC is moveable, the matter adjacent to 

 ABC on the outside will become undercharged. There 

 is no reason, however, to think, that that will pre- 

 vent the body D from being undercharged ; but it is not 

 easy to say exactly what effect it will have, except 

 when ABC is spherical, and the repulsion is inversely 

 as the square of the distance. In this case, it appears 

 by I'rob. I . that the fluid in the part DB of the canal 

 will be repelled from C, with just as much force as in 

 the last proposition ; but the fluid in the part BG will 

 not be repelled at nil : consequently 1) will be under- 

 charged, but not so much as in the last proposition. 



Corol. If ABC is now supposed to be undercharged, 

 it is certain that D will be overcharged, provided the 

 matter near ABC on the outside is saturated with im- 

 moveable fluid ; and there fe great reason to think that 

 it w'H bo so, though the fluid in that matter is move- 

 abl.-. 



Prop. XIV. Let AEFB, Fig. 9. be a long cylindric P? or - I*- 

 body, and I) an undercharged body ; ;<i:d let the qu.in- Klg ' 9- 

 tity of fluid in AEFB l>e such, that the part near EF 

 shall be saturated. It appears from what has been said 

 before, that the part near AB will be overcharged ; anil 

 moreover there will be a certain space, as An5B, aJ- 



