'230 l-HILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



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 A on it, be rendered under- 

 charged; 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 inflnite 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 

 ocyz, 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 o{ yv cannot be impelled 

 in any direction ; and therefore the fluid in hy is impelled 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 nks is impelled 

 by the two plates. 



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 nhs, though xyz did not contain just fluid enough to saturate it. He 

 answers 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. 



Prop. IT . Let two bodies B and b, fig. 13, be joined by a cylindric or pris- 

 matic canal Kd, filled with real fluid; and not by an imaginary canal of incom- 

 pressible fluid as in the 20th proposition ; and let the fluid in it 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 in it can be pre- 

 vented from moving in the direction of its axis, by the sides of the canal ; and 

 therefore the force with which each particle is impelled either way in the direc- 

 tion 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 im- 

 pelled in the direction of the axis, must be nothing. 



Corol. 1 . If the fluid in the canal is disposed in such manner, that the repul- 

 sion or attraction of the redundant fluid or matter in it, on the whole or any 

 given part of the fluid in the canal, has no tendency to impel it either way in 

 the direction of the axis ; then the force with which that whole or given part is 

 impelled by the two bodies, must be nothing; or the force with which it is im- 



