Canals of fluid compared with conducting wires 63 



is the same as if it was continued infinitely, then the thing is evident: 

 but if it is not, let the canal hy, instead of communicating with xyz, so 

 that the fluid can flow out of the canal into xyz, be continued infinitely 

 through its substance, along the line yv : now it must be observed that a 

 small part of the body xyz, namely, that which is turned towards h, will 

 by the action of h upon it, be rendered undercharged; but all the rest of 

 the body will be saturated; for the fluid driven out of the undercharged 

 part will not make the remainder, which is supposed to be of an infinite 

 size, sensibly overcharged: now the force with which the fluid in the 

 infinite canal hyv is impelled by the body h and the undercharged part 

 of xyz, is the same with which the fluid in gc is impelled by them ; but as 

 the fluid in all parts of xyz is in equilibrio, a particle in any part of yv 

 cannot be impelled in any direction; and therefore the fluid in hy is im- 

 pelled with as much force as that in hyv; and therefore the fluid in hy is 

 impelled with as much force as that in gc ; and is therefore impelled with 

 as much force as the fluid in NRS is impelled by the two plates. 



90] It perhaps may be asked, whether this method of demonstration 

 would not equally tend to prove that the fluid in hy was impelled with the 

 same force as that in NRS, though xyz did not contain just fluid enough 

 to saturate it. I answer not; for this demonstration depends on the canal 

 yv being continued, within the body xyz, to an infinite distance beyond 

 any over or undercharged part ; which could not be if xyz contained either 

 more or less fluid than that*. 



91] PROP. XXVII. Let two bodies B and b (Fig. 13) be joined by a 

 cylindric or prismatic canal Aa, filled with real fluid; and not by any 

 imaginary canal of incompressible fluid as in the 20th proposition; and 

 let the fluid therein be in equilibrio: the force with which the whole or 

 any given part of the fluid in the canal is impelled in the direction of its 

 axis by the united repulsions and attractions of the redundant fluid or 

 matter in the two bodies and the canal, must be nothing; or the force 

 with which it is impelled one way in the direction of the axis of the canal, 

 must be equal to that with which it is impelled the other way. 



For as the canal is supposed cylindric or prismatic, no particle of fluid 

 therein can be prevented from moving in the direction of the axis of it, 

 by the sides of the canal ; and therefore the force with which each particle 

 is impelled either way in the direction of the axis, by the united attractions 

 and repulsions of the two bodies and the canal, must be nothing, otherwise 

 it could not be at rest; and therefore the force with which the whole, or 

 any given part of the fluid in the canal, is impelled in the direction of the 

 axis, must be nothing. 



92] COR. I. If the fluid in the canal is disposed in such manner, that 

 the repulsion or attraction of the redundant fluid or matter in it, on the 



[* Note 5, p. 369.] 



