310 A. B. Quinby on the Overshot Water- f'Vhed, 



The foregoing general result now being established, it is 

 proposed next to examine, not the effect which a given quan- 

 tity of wQiev will produce, or is capable of producing ; but 

 the effect which in practice can be derived from a given quan- 

 tity of water, acting through a given fall upon an overshot 

 water-wheel, under given circumstances. 



To do this, let it be given that the velocity of the circum- 

 ference of the wheel shall be equal to that which is due to 

 the height of the fall above the wheel : then, 



Theorem 2. The effect which, in practice, can be derived 

 from any quantity of water, acting through any fall upon an 

 an overshot water-wheel, will vary as the diameter of the 

 wheel. 



Let amblEi, Fig. 4, represent an overshot wheel ; and sup- 

 pose a conduit Yamhg, as represented in the figure ; and 

 suppose, also, a vertical column of water zy, equal in size to 

 the condnxi amhg, and equal in height to the vertical line nc^ 

 or to the diameter ha, to be suspended to the cord se, which 

 passes over the pulley M, and under the pulley N, and thence 

 (through a hole at m,) to the plug hi, (at the point 5,) to 

 which it is fastened 



These conditions being granted, it is plain, that if the part 

 Ydmh, of the conduit, be filled with water, and the proper 

 supply be delivered at F, the plug hi will be driven from &, 

 towards the extremity g, and with a velocity equal to that 

 which is due to the height oF. And it is also plain, that 

 while the plug hi shall be driven through any space whatever, 

 towards the part o^, the column zy will be raised through an 

 equal space. Hence, taking hg=-bY, and supposing the 

 water to descend from F until the plug hi be driven to g, the 

 column zy will be raised through a vertical space=6F. 

 Whence it is obvious that zy expresses the effect which, in 

 practice, can be derived from a given quantity of water (viz. 

 that contained in the part hg of the conduit) acting through 

 the given fall Yh upon the wheel am6E; the whole effect 

 being expressed by hg^ or hY. But zy is = ba, the diameter 

 of the wheel ; and hY is = the whole height of the fall — 

 hence it is determined, that if the circumference of an over- 

 shot wheel move with a velocity equal to that which is due 

 to the height of the fall above the wheel, the effect which, in 

 practice, can be derived from any quantity of water, acting 



