r 9° ] 



heavy body would acquire in falling through the height of the 

 fluid. 



Professor Gravefende, who has confidered this fubjefl M-ith 

 particular attention, has alfo given us a demonftration, that the 

 velocity of the effluent water is equal to that which a body 

 v/ould acquire in falling through the entire height of the fluid. 

 But it appears liable to the following objedlions : Firft, it fuppofes, 

 that the velocities communicated to equal quantities of matter, in 

 moving through equal fpaces, a;c diredly as the generating forces, 

 without any regard to the tir^c in which thefe fpaces are run 

 over by the bodies moved. And fecondly, it fuppofes that the 

 forces acquired by the falling bodies arc equal when the heights 

 are inverfely as the mafles ; whereas they arc equal only when 

 the mafles are in the inverfe fubduplicate of the heights. 



I HAVE already fliewn how the demonftration given in the firft 

 edition of the Principia, when duly corredled, affords a legitimate 

 folution of this problem ; and the fame conclufion may, I think, 

 be thus otherwife made out in an unexceptionable manner. 



Let MNOP reprefent a vefl'el of water filled to the level 

 GH; MP the bottom, in which is the aperture C D ; CIKD 

 , the column of water flanding diredly above the orifice, and 

 CABD the loweft plate of water immediately contiguous to 

 the aperture. Alfo let v denote the velocity which a heavy body 

 would acquire in falling freely through the height B D of the 

 plate, and x the velocity acquired by the fame plate during its 

 defcent through the fame fpace until it is difcharged by the pref- 

 furc of the column CIKD. 



Suppose 



