310 4. B. Quindy on the Overshot Water-Wheel. 
The foregoing general result now being established, it is 
roposed next to examine, not the effect which a given quan- 
tity of water twill produce, or is capable of producing ; but 
the effect which in practice can be derived from a given quan- 
tity of water, pete through a given fall upon a overshot 
water-wheel, under given circumstances. 
o 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 ar 
e eerorsboe water-wheel, will vary as the diameter of the 
Let ambE E, Fig. me represent an overshot wheel; and sup- 
pose a conduit amber, as represented in the figure 5 ; and 
suppose, also, a vertical column of water zy, equal in size to 
the conduit ambg, and equal in height to the vertical line nc, 
or to the diameter ba, 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 62, (at the point b,) to 
which it is fastened sk 
These conditions being granted, it is plain. 
tl that if the part 
Famb, of the conduit, be filled with water, and the proper 
supply be delivered at F, the plug i will be driven from b, 
towards the extremity g, and wiih a velocity equal to that 
which is due to the height aF. And it is also plain, that 
while the plug 42 shall be driven through any space whatever, 
towards the part g, the column zy will be raised through an 
equal space. Hence, taking 6g=5F, and supposing the 
water to descend from F until the plug 67 be driven to g, the 
column zy will, be raised through a vertical space=dF. 
Whence it is obvious that zy expresses the effect which, om 
practice, can be derived from a given quantity of water (vizs 
that contained in the part bg of the conduit) acting through 
the given fall FS upon the wheel ambE; the whole effect 
being expressed by bg, or 6F. But zy is=ha, the diameter 
of the wheel; and 6F is = the whole height of the fall— 
hes 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, m 
Practice, can be derived from any quantity of water, acting 
eo 
