Electrification by induction 47 



quantity of fluid in that part of the canal which is nearest to B is so much 

 diminished, and its repulsion on the rest of the fluid in the canal is so 

 much diminished also as to compensate the repulsion of B: but as the 

 leg NPpn 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 that water is drawn out of a vessel through a siphon. 



49] 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 GPHpG, so that the fluid in the leg 

 MGpm does not join to that in NHpn; then it is plain that no fluid can 

 run out of A into D ; any more than water will run out of a vessel through 

 a siphon, if the height of the bend of the siphon above the water in the 

 vessel, is greater than that to which water will rise in vacuo. 



50] COR. 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 is 

 ever so great. 



51] PROP. XIV. Let ABC (Fig. 8) be a body overcharged with im- 

 moveable fluid, uniformly spread; let the 

 bodies near ABC on the outside be saturated 

 with immoveable fluid; and let D be a body 

 inclosed within ABC, and communicating by 

 the canal DG with other distant bodies satu- 

 rated with fluid; and let the fluid in D and 

 the canal and those bodies be moveable; then 

 will the body D be rendered undercharged. 



For let us first suppose that D and the canal are saturated, 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 

 repelled 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, 

 taking 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 therein is sufficient to balance the repulsion of the redundant 

 fluid in ABC. 



52] PROP. XV. If we now suppose that the fluid on the outside of 

 ABC is moveable; the matter adjacent to ABC on the outside will become 

 undercharged. I see no reason however to think that that will prevent 

 the body D from being undercharged; but I cannot 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 Prob. I 



