244 PHILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



its repulsion on ao ; for, by the supposition, the repulsion of b on Ka may be 

 considered as the same as if it was continued infinitely ; and therefore the re- 

 pulsion of h on ag may be considered as the same as if it was continued in 

 finitely. 



N. B. If n was not greater than 1, it would be impossible for the length of 

 AG to be so great, that the repulsion of b on it might be considered as the same 

 as if it was continued infinitely; which was the reason for requiring n to be 

 greater than 1. 



Corol. By just the same method of reasoning it appears, that if the bodies 

 are undercharged, the quantity of deficient fluid in b will be to that in b, as 

 af"-' to AP"-'. 



Prop. "21. Let a thin flat plate be connected to any 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 re- 

 dundant 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 thick- 

 ness is very small in proportion to its breadth, or smallest diameter. For there 

 can be no doubt, but under that restriction, the fluid will be disposed very nearly 

 in the same manner in the plate, whatever its thickness may be ; and therefore 

 its repulsion on the fluid in the canal will be very nearly the same, whatever its 

 thickness may be. 



Prop. 11. Let AB and df, fig. 14, represent two equal and parallel circular 

 plates, whose centres are c and e ; let the plates be placed so, that a right line 

 joining their centres shall be perpendicular to the plates ; let the thickness of the 

 plates be very small in respect of their distance ce ; let the plate ab communicate 

 with the body h, and the plate df with the body l, by the canals cg and em of 

 incompressible fluid, such as are described in prop. 1 Q ; let these canals meet 

 their respective plates in their centres c and e, and be perpendicular to the 

 plane of the plates ; and let their length be so great, that the repulsion of the 

 plates on the fluid in them may be considered as the same as if they were con- 

 tinued infinitely; let the body h be overcharged, and let l be saturated. It is 

 plain, from prop. 12, that df will be undercharged, and ab will be more over- 

 charged than it would otherwise be. Suppose now, that the redundant fluid in 

 ab is disposed in the same manner as the deficient fluid is in df; let p be to 1, as 

 the force with which the plate ab would repel the fluid in ce, if the canal me was 

 continued to c, is to the force with which it would repel the fluid in cm ; and 

 let the force with which ab repels the fluid in cg, be to the force with which it 

 would repel it, if the redundant fluid in it was spread uniformly, as tt to 1 ; and 

 let the force with which the body h repels the fluid in cg, be the same with 

 which a quantity of redundant fluid, which we will call b, spread uniformly 



