[ 9' ] 



Suppose the lowcft plate of water ACBD to fall as a heavy 

 body through the height B D, its moving force will be its own 

 weight. Again, fuppofe it to be accelerated by its own weight 

 and that of the incumbent water, that is, by the weight of the 

 column CIKD through the fame fpace, that is, while it is acce- 

 lerated from quiefcence until it is adually difcharged. The velo- 

 city in the former cafe will be to that in the latter as the . 

 moving forces and the times in which they a(£l diredly, and 

 the quantities of matter moved inverfely. But the moving 

 forces are to each other as the heights BD and KD; the times 

 in which they a£t are inverfely as the-velocities, the fpace through 

 which the body is accelerated being given ; and the quantities of 



, , . BD KD - 



matter moved are equal; therefore v:x:: : ; conle- 



V X 



quently t;*:^''::BD:KD. But v is the velocity which a 

 heavy body would acquire in falling through the fpace BDj 

 therefore x, the velocity of the fpouting fluid, is that which a 

 heavy body would acquire in falling through K D, the height of 

 the fluid above the orifice. 



In the fame manner it may be fhewn, that if a pipe be inferted 

 horizontally in the veflel NO MP, the plate of water ACBD 

 will be difcharged with the fame velocity as before, whatever be 

 the thicknefs of the plate; this velocity not depending on a 

 continual acceleration through the length of the tube, otherwife 

 the cfiluent water could not attain its full velocity, until a co- 

 lumn had been difcharged whofe bafe is equal to the orifice and 

 height equal to the length of the tube : whereas we find by expe- 

 rience, that this full velocity can be attained by the thinneft 

 plate which v/e can let efcape from the aperture. 



N 2 What 



