4. B. Quinby on the Overshot Water-Wheel. 3li 
through any — an earths water-wheel, will vary as 
the diameter of the w 
his result being Diane, it is proper, the next place, 
io notice, that in practice the water does not descend in the 
buckets entirely down to the lowest point 6, but is always 
discharged when at an angular distance of about 30° (on the 
wheel’s circumference,) from the point 6. Let this be grant- 
ed; and, then, 
Theorem 3. \f the circumference of the wheel move with 
the velocity due to the height of the fall above the wheel; 
the effect which, in practice, can be derived from any quantity : 
of water, acting through any fall upon an overshot water- 
wheel, will vary as 3} of the wheel’s diameter (very nearly.) | 
ns t, Fig. 5, be the point at which the water is discharged, 
and tn a perpendicular drawn from ¢ to the vertical diameter 
ba; then, by what was proved in Theorem 1, Fig. 2, the 
effect of any quantity of water in descending upon the wheel 
from a to ¢, will be to the effect e the same pas in de- 
apy quantity of water wie through any fall upon an over- 
shot water-wheel, will vary as 42 of the wheel’s diameter. 
t now remains to determine the velocity which the circum- 
ference of an overshot water-wheel must have, in order that 
the effect which in practice can be derived from a given quan- 
tity of water, shall be a maximum. 
Theorem 4. The greatest effect which in practice ean be de- 
rived from a given quantity of water, acting through a given 
fall upon an overshot water-wheel, is when the velocity of 
the circumference of the wheel is nes rex possib: 
Pat A=6F, Fig. 5, and e=aF; d put V=the v velocity 
due to the height aF, and v=the “velogity of the circum. 
ference of the wheel: then, by mechanics, a from what 
= been demonstrated, the effect which in practice can be 
derived from a given quantity of water, acting through the 
given fall Fb, upon the wheel ambE, will vary as the quan- 
*From this demonstration, and the others here given, it will be per- 
ceived kat the whole standing t theory, given in books, on the subject of 
the overshot water-wheel, is false, 
