236 PHILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



Corol. In like manner, if b is made untlercharged, some fluid will flow from 

 D to A, and also from that part of a near rs, to the part near mn. 



Prop. 13. Suppose now that the bodies A and d communicate by the bent 

 canal Mvanpm (fig. ^), instead of the straight one ef : let the bodies be either 

 saturated or over or undercharged, as before; and let the fluid be at rest; then 

 if the body b is made overcharged, some fluid will still run out of a into d ; pro- 

 vided the repulsion of b on the fluid in the canal is not too great. 



The repulsion of b on the fluid in the canal, will at first drive some fluid out 

 of the leg MVpm into a, and out of np/)w into d, till the 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 compen- 

 sate the repulsion of b : but as the leg NP/>n is longer than the other, the repul- 

 sion 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 

 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 gph/>g, so that the fluid in the leg mgj&ot does not 

 join to that in NH/>n; 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 syphon, if the height of the 

 bend of the syphon above the water in the vessel, is greater than that to which 

 water will rise in vacuo. 



Corol. 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. 



Prop. 14. Let ABC, fig. 8, be a body overcharged with immoveable fluid, 

 uniformly spread; let the bodies near abc on the outside be saturated with im- 

 moveable fluid ; and let d be a body inclosed within abc, and communicating 

 by the canal do with other distant bodies saturated with fluid; and let the fluid 

 in D and the canal and those bodies be moveable; then will the body d be ren- 

 dered 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 p, 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 dp, 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 there is sufficient to balance the repulsion of the redundant fluid in abc 



Prop. 15. If we now suppose that the fluid on the outside of abc is move- 

 able; the matter adjacent to abc on the outside will become undercharged. 



