Theory of bent connecting canal 



61 



into whatever part of the bodies the canal is inserted, or in whatever 

 manner the two bodies are situated in respect of each other; provided 

 that their distance is infinite, or so great that the repulsion of each body 

 on the fluid in the canal shall not be sensibly less than if it was infinite. 

 Let the parallelograms AB and DF (Fig. 17) represent the two plates, 

 and H and L the bodies communicating with them: let now H be re- 

 moved to h; and let it communicate with AB by the bent canal gc; the 

 quantity of fluid in the plates and bodies remaining the same as before ; 

 and let us, for the sake of ease in the demonstration, suppose the canal gc 

 to be everywhere of the same thickness as the canal GC; though the 

 proposition will evidently hold good equally, whether it is or not : the 

 fluid will still be in equilibrio. For let us first suppose the canal gc to be 



Fig. 17 



continued through the substance of the plate AB, to C. along the line 

 crC; the part crC being of the same thickness as the rest of the canal, and 

 the fluid in it of the same density: by the preceding proposition, the 

 repulsion' or attraction of each particle of fluid or matter in the plates AB 

 and DF, on the fluid in the whole canal Crcg, in the direction of that canal, 

 is equal to its repulsion or attraction on the fluid in the canal CG, in the 

 direction CG; and therefore the whole repulsion or attraction of the two 

 plates on the canal Crcg, is equal to their repulsion or attraction on CG: 

 but as the fluid in the plate A B is in equilibrio, each particle of fluid in 

 the part Crc of the canal is impelled by the plates with as much force in 

 one direction as the other; and consequently the plates impel the fluid 

 in the canal eg with as much force as they do that in the whole canal 

 Crcg, that is, with the same force that they impel the fluid in CG. In like 



