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bottom of tlie veffel will fuftain the reft. But on removing the 

 obftacle, the bottom of the veffel will be preffed in the fan:e 

 manner as before, and the weight which was fuftained by the 

 obftacle being now no longer fupported, will produce an efflux 

 of the water through the orifice. Whence it follows, that the 

 motion of the whole effluent v/ater is fuch as can be produced 

 by the weight of the column of water incumbent over the orifice. 

 For every particle of water defcends by its own weight, as far as 

 it is not impeded, with a uniformly accelerated motion, and as 

 far as it is impeded it will prefs the obftacle j that obftacle is 

 either the bottom of the veffel or the inferior defcending water, 

 and therefore that part of the weight which the bottom of the 

 veffel does not fuftain will prefs the effluent water, and generate 

 a motion proportional to it. 



Let F denote the area of the orifice, A the altitude of the 

 column of water over the orifice, V the velocity which a heavy 

 body would acquire in falling through the height A in the time 

 T, and x the velocity of the effluent water. Since in the time 

 T, a fpace equal to 2 A would be defcribed with the velocity V, 



a fpace equal to —,,— will be the fpace defcribed in the fame 



time with the velocity x. This, therefore, will be the length of 



the column difcharged in the time T, and the magnitude of this 



2A;^F . . . 2Ax'F 



cylinder will be — rj — , and its quantity of motion = — ^ — . 



But the quantity of motion, which, in the fame time, would be 

 generated in the column of water incumbent on the orifice, if 

 it were to fall freely as an heavy body through a fpace equal to 



M 2. its 



