VOL. LXI.] PHILOSOPHICAL TKANSACTIONS. 2^9 



CG. In like manner the body h impels the fluid in eg, with the same force that 

 H does the fluid in CG ; and consequently h impels the fluid in eg, one way in 

 the direction of the canal, with the same force that the two plates impel it the 

 contrary way; and therefore the fluid in eg has no tendency to flow from one 

 body to the other. 



Carol. By the same method of reasoning, with the help of the corollary to 

 the 23d proposition, it appears that if ab and h each communicate with a third 

 body, by canals of incompressible fluid, and a communication is made between 

 ab and h by another canal of incompressible fluid, the fluid will have no ten- 

 dency to flow from one to the other through this canal ; supposing that the fluid 

 was in equilibrio before this communication was made. In like manner, if ab 

 and h communicate with each other, or each communicate with a third body, by 

 canals of real fluid, instead of the imaginary canals of incompressible fluid used 

 in these propositions, and a communication is also made between them by a canal 

 of incompressible fluid, the fluid can have no tendency to flow from one to the 

 other. The truth of the latter part of this corollary will appear by supposing an 

 imaginary canal of incompressible fluid to be continued through the whole length 

 of the real one. 



Prop. 25. Let now a communication be made between the two plates ab and 

 DP, by the canal nrs of incompressible fluid, of any length ; and let the body 

 h and the plate ab be overcharged. It is plain that the fluid will flow through 

 that canal from ab to dp. Now the whole force with which the fluid in the 

 canal is impelled along it, by the joint action of the two plates, is the same with 

 which the whole quantity of fluid in the canal cg or eg is impelled by them; 

 supposing the canal nrs to be every where of the same breadth and thickness as 

 CG or eg. For suppose that the canal nrs, instead of communicating with the 

 plate DP, is bent back just before it touches it, and continued infinitely along 

 the line ss; the force with which the two plates impel the fluid in as, is the 

 same with which they impel that in el, supposing ss to be of the same breadth 

 and thickness as el; and is therefore nothing; therefore the force with which 

 they impel the fluid in nrs, is the same with which they impel that in nrsj; 

 which is the same with which they impel that in cg. 



Prop. 26. Let now xyz be a body of an infinite size, containing just fluid 

 enough to saturate it; and let a communication be made between A and xyz, by 

 the canal % of incompressible fluid, of the same breadth and thickness as ge or 

 GC ; the fluid will flow through it from h to xyz; and the force with which the 

 fluid in that canal is impelled along it, is equal to that with which the fluid in 

 NRS is impelled by the two plates. 



If the canal hy is of so great a length, that the repulsion of h on it is the 

 same as if it was continued infinitely, then the thing is evident; but if it is not, 



VOL. ^III. K K 



