VOL. LXI.] PHILOSOPHICAL TRANSACTIONS. 243 



in the direction of the canal at that place, the section nd would, in consequence 

 of it, be impelled with exactly the same force in the direction of the canal at d, 

 if the fluid between ep and X)d was not at all attracted or repelled by the two 

 bodies; and consequently the section od is impelled in the direction of the 

 caufil, with the sum of the forces, with which the fluid in each part of the canal 

 is impelled, by the attraction or repulsion of the two bodies in the direction of 

 the axis in that parti and consequently, unless this sum was nothing, the fluid 

 in vd could not be at rest. 



CoroL Therefore the force with which the fluid in the canal is impelled one 

 way in the direction of the axis, by the body b, must be equal to that with which 

 it is impelled by b in the contrary direction. 



Prof). 20. Let two similar bodies b and b, fig. 13, be connected by the very 

 slender cylindric or prismatic canal Ao, filled with incompressible fluid, in the same 

 manner as described in the preceding proposition: let the bodies be overcharged ; 

 but let the quantity of redundant fluid in each bear so small a proportion to the 

 whole, that the fluid may be considered as disposed in a similar manner in both; 

 let the bodies also be similarly situated in respect of the canal Aa ; and let 

 them be placed at an infinite distance from each other, or at so great a one, 

 that the repulsion of either body on the fluid in the canal, shall not be sensibly 

 less than if they were at an infinite distance: then, if the electric attraction and 

 repulsion is inversely as the n power of the distance, n being greater than 1, and 

 less than 3, the quantity of redundant fluid in the two bodies will be to each 

 other, as the n — 1 power of their corresponding diameters af and of. 



For if the quantity of redundant fluid in the two bodies is in this proportion, 

 the repulsion of one body on the fluid in the canal, will be equal to that of the 

 other body on it, in the contrary direction; and consequently the fluid will have 

 no tendency to flow from one body to the other, as may thus be proved. Take 

 the points d and e very near to each other; and take da to da, and ea to ea, as 

 fl/ to AF ; the repulsion of the body b on a particle at d, will be to the repulsion 

 of i on a particle at d, as — to -r. ; for, as the fluid is disposed similarly in both 

 bodies, the quantity of fluid in any small part of b, is to the quantity in the cor- 

 responding part of b, as af""' to af^_^; and consequently the repulsion of that 

 small part of b, on D, is to the repulsion of the corresponding part of b on d, as 



■ — ;- , or — to -J. But the quantity of fluid in the small part de of the canal, 



is to that in de, as de to de, or as af to af; therefore the repulsion of b on the 

 fluid in DE, is equal to that of h on the fluid in de : therefore, taking ag to 

 AQ, as af to AF, the repulsion of b on the fluid in ag, is equal to that of b on 

 the fluid in xa; but the repulsion of b on ag may be considered as the same as 



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