54 First published Paper on Electricity 



deficient fluid in it. Therefore, by the preceding proposition, the quantity 

 of redundant or deficient fluid in B, will actually bear very nearly the 

 same proportion to that in b, whatever sort of matter B consists of; pro- 

 vided the quantity of redundant or deficient fluid in it is very small in 

 respect of the whole. [See Exp. IV, Art. 269.] 



69] PROP. XIX. Let two bodies B and b (Fig. 12) be connected to- 

 gether by a very slender canal ADda, either 

 straight or crooked: let the canal be every- 

 where of the same breadth and thickness; 

 so that all sections of this canal made by 

 planes perpendicular to the direction of the 

 canal in that part, shall be equal and 

 similar : let the canal be composed of uniform 

 matter ; and let the electric fluid therein be 

 supposed incompressible, and of such density 

 as exactly to saturate the matter therein; 

 and let it, nevertheless, be able to move readily along the canal; and let 

 each particle of fluid in the canal be attracted and repelled by the matter 

 and fluid in the canal and in the bodies B and b, just in the same manner 

 that it would be if it was not incompressible * ; and let the bodies B and b 

 be either over or undercharged. I say that the force with which the whole 

 quantity of fluid in the canal is impelled from A towards D, in the direction 

 of the axis of the canal, by the united attractions and repulsions of the 

 two bodies, must be nothing ; as otherwise the fluid in the canal could not 

 be at rest: observing that by the force with which the whole quantity of 

 fluid is impelled in the direction of the axis of the canal, I mean the sum 

 of the forces, with which the fluid in each part of the canal is impelled in 

 the direction of the axis of the canal in that place, from A towards D; 

 and observing also, that an impulse in the contrary direction from D 

 towards A must be looked upon as negative. 



For as the canal is exactly saturated with fluid, the fluid therein is 

 attracted or repelled only by the redundant matter or fluid in the two 

 bodies. Suppose now that the fluid in any section of the canal, as Ee, is 

 impelled with any given force in the direction of the canal at that place, 

 the section Dd would, in consequence thereof, be impelled with exactly 

 the same force in the direction of the canal at D, if the fluid between Ee 

 and Dd was not at all attracted or repelled by the two bodies ; and, conse- 

 quently, the section Dd is impelled in the direction of the canal, 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 



* This supposition of the fluid in the canal being incompressible, is not men- 

 tioned as a thing which can ever take place in nature, but is merely imaginary; 

 the reason for making of which will be given hereafter. 



