242 PHILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



any kind, and be either over or undercliarged : it is plain that the quantity of 

 redundant or deficient fluid in b, would bear exactly the same proportion to that 

 in b, whatever sort of matter b consisted of, if it was possible for the redundant 

 or deficient fluid in any body, to be disposed accurately in the same manner, 

 whatever sort of matter it consisted of. For suppose b to consist of any sort of 

 matter ; and let the fluid in the canal and two bodies be in equilibrio : let now b 

 be made to consist of some other sort of matter, which requires a different 

 quantity of fluid to saturate it ; but let the quantity and disposition ofe^iie 

 redundant or deficient fluid in it remain the same as before : it is plain that the 

 fluid will still be in equilibrio ; as the attraction or repulsion of any body depends 

 only on the quantity and disposition of the redundant and 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 h, whatever 

 sort of matter b consists of; provided the quantity of redundant or deficient fluid 

 in it is very small in respect of the whole. 



Prop. 19. Let two bodies b and b, fig. 11,, be connected together by a very 

 slender canal xoda, 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 in it be sup- 

 posed incompressible, and of such density as exactly to saturate the matter 

 in it ; 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. Then 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, he means 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 considered as negative. 



For as the canal is exactly saturated with fluid, the fluid in it 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 



* This supposition of the fluid in the canal being incompressible, is not mentioned as a thing 

 which can ever take place in nature, but is merely imaginary ; the reason for making of which will 

 be givai hereafter. 



