r 



[ 89 ] 



in which the accelerating force ads on the plate, is inverfely as 

 the velocity with which the plate iffues ; therefore the fquare of 

 the velocity is diredly as the force, and the velocity as the fquare 

 root of the force, that is, as the fquare root of the height of the 

 water above the orifice. But the adual velocity of the effluent 

 water would not even thus be afcertained. 



The Abbe Winkler's demonftration is built on the fame foun- 

 dation with Hehham's. 



Musscheneroeck's demonftration of this principle is liable to 

 a three-fold objecfition : Firft, it is founded on a falfe meafure 

 of the force of bodies in motion, to wit, the quantity of matter 

 and the fquare of the velocity. Secondly, it involves a con- 

 fufion of what is an equal ratio with a ratio of equality. 

 Thirdly, it implies that equal forces generate equal velocities, 

 without any regard to the times in which they ad, or the quan- 

 tities of matter which they move. 



Varignon proves only, that the velocities of fpouting fluids 

 are in the fubduplicate ratios of the heights of the fluids above 

 the apertures, but does not afcertain the adual velocity, which 

 is the principal objed of enquiry. See Acad. Science. An. 1703. 



Belidor's demonftration is fubjed to the fecond imperfedion 

 of Muftxhenbroeck's. For from proving, after Varignon, that the 

 velocity of the cflluent water is proportional to the fquare root of 

 the height of the water, and therefore follows the fame law of 

 acceleration with that of falling bodies, lie concludes, that the 

 velocity of the fpouting water is adually the fame which a 



N heavy 



