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its altitude, would be A F V. And thefe quantities of motion 



are equal, being botli generated in equal times, by the fame 



2 A .V * F 

 generating force; that is, AFV = x^ , whence V* = 2 ^ *, 



and Y:x:W 2 : i. Confeqnently fince V is the velocity which 

 a heavy body would acquire in falling through the entire altir- 

 tude A, one half of A will be the fpace through which a body 

 »defcending will acquire that velocity ^.v with which the water ibws 

 from the orifice. 



The latent fallacy of this argument confifts in this, that eack 

 ^late of water is fuppofed to be fuccelfively difcharged with a 

 -•uniform velocity, and the quantity of motion generated in ever^r 

 little portion of time in which each plate is difcharged is mea- 

 fured by the plate drawn into the uniform velocity of the efflux. 

 But this, on a little confideration, will be found not to be a true 

 ilatement of (he cafe-, for every plate of water is difcharged in 

 tione, and its velocity is uniformly encreafed from nothing, during 

 the dcfcent of the plate through its own altitude, at the end of 

 which little portion of time it attains that ultimate velocity wilh 

 which it afterwards continues to move uniformly. Hence, there- 

 fore, it follows that the quantity of motion really generated 

 •during the time of the difcharge of each plate of water is but 

 half that which is determined by funpofing the water to be dif- 

 charged at once with its full velocity. The corref^ir.n of this 

 error will lead us to a true folution of the queftion. Let the 

 time of a body's fall through the height A be divided into an 

 indefinite number of little portions, each equal to the time in 

 which a plats of water is difcharged by defccnding through its 



OWffi 



