HYDRAULICS. 



most work in a given time, when the wheel 

 moves with one-third of the velocity of the wa- 

 ter. 



This theorem was first given by PARENT, Mem. de 

 TAcad. des Sciences, 1704. See also MACLAURIN^S 

 Fluxions, 907. EULER, Nov. Com. Pet. torn. vnr. 

 p. 230. BOSSUT, Hydrod. torn. i. 390. 



If c he the velocity of the stream, v that of the float- 

 hoard, a 2 the section of the stream, or the area of the 

 part struck, the impulse of the stream, by 293. 

 = ma?(c v) 2 , and the effect or quantity of work 

 done, in a given time, will be m c? (c - v) 2 v, which 



is a maximum when v = - . 

 3 



The quantity ma? (c z>) 2 , or the moving force he- 

 comes then m a 2 X - c 2 , which, making m = 1, as in 



y 



the first case of 297., and writing %gh for c~, 



Q O 



becomes - a?gh, or -- of the weight of the co- 



y y 



lumn of water that falls on the wheel. If m = 1 , 



JC 



as in the second case of 297., the moving force is 



4 



only - of the said column. According to the way 

 y 



in which the water strikes the wheel, the moving 

 force may therefore vary in the ratio of 2 to 1 . 



The 



