246 PHILOSOPHICAL TBANSACTIONS. ANNO 1771. 



Remarks. If dp was not undercharged, it is certain that ab would be consi- 

 derably more overcharged near the circumference of the circle than near the 

 centre ; for if the fluid was spread uniformly, a particle placed any where at a 

 distance from the centre, as at n, would be repelled with considerably more 

 force towards the circumference, than it would towards the centre. If the plates 

 are very near together, and consequently dp nearly as much undercharged as ab 

 is overchai-ged, ab will still be more overcharged near the circumference than 

 near the centre, but the difference will not be near so great as in the former 

 ease: for, let nr be many times greater than ce, and ns less than ce; and take 

 Er and e^ equal to or and cs; there can be no doubt, he thinks, but that the 

 deficient fluid in dp will be lodged nearly in the same manner as the redundant 

 fluid in AB ; and therefore the repulsion of the redundant fluid at r, on a par- 

 ticle at n, will be very nearly balanced by the attraction of the redundant matter 

 at r, for r is not much nearer to n than r is; but the repulsion of s will not be 

 near balanced by that of s ; for the distance of s from n is much less than that 

 of s. Let now a small circle, whose diameter is st, be drawn round the centre 

 N, on the plane of the plate; as the density of the fluid is greater at x than at s, 

 the repulsion of the redundant fluid within the small circle tends to impel the 

 point N towards c ; but as there is a much greater quantity of fluid between N 

 and B, than between n and a, the repulsion of the fluid without the small circle 

 tends to balance that ; but the effect of the fluid within the small circle is not 

 much less than it would be, if dp was not undercharged; whereas much the 

 greater part of the effect of that part of the plate on the outside of the circle, is 

 taken off by the effect of the corresponding part of dp: consequently the dif- 

 ference of density between t and s will not be near so great, as if dp was not 

 undercharged. Hence he imagines, that if the two plates are very nearly together, 

 the density of the redundant fluid near the centre will not be much less than the 

 mean density, or S will not be much less than 1 ; moreover, the less the distance 

 of the plates, the nearer will S approach to 1 . 



Corol. 2. Let now the body h consist of a circular plate, of the same size as 

 AB, placed so, that the canal cg shall pass through its centre, and be perpendi- 

 cular to its plane; by the supposition, the force with which h repels the fluid in 

 the canal cg, is the same with which a quantity of fluid, equal to b, spread uni- 

 formly over AB, would repel it in the contrary direction: therefore, if the fluid 

 in the plate h was spread uniformly, the quantity of redundant fluid in it would 

 be B ; and if it was all collected in the circumference, would be ; and there- 



2b 

 fore the real quantity will be greater than B, and less than 3^3^. 



Corol. 3. Therefore, if we suppose S to be equal to I, the quantity of redun- 

 dant fluid in AB will exceed that in the plate h, in a greater ratio than that of 



