312 A. B. Quinby on the Overshot Water-Wheel. 
tity (V —»)2 $i(h—x) 5 which will a a miaxi- 
mum when v is the least posstble.* ae 
Theorem 5. if the ciroumferenee of an overshot wheel 
i ocity due to the height ihe fall above the 
: be ciocy and circumference of the 
| eect the diameter of the wheel is 
ut and z?=AF: then the circumference 
lt s gniats9 ee. are -x?); and the product of the velo- 
city and cin ul er rerx will be 4/2gx? X 3.14159, 8.(h — x*); 
ichi S cimum ; or, by rejecting constant factors 
=max. Wherefore, hx —3u2x=0; ; Of, 
eek rene. of an overshot wheel 
move with the velocity ‘de to the height of the fall above the 
wheel, the wheel will have its Sreatest angular motion, or will 
perform the most revolutions in a given time, when its diam- 
eter is the least possible, 
Reta e same notation, we have for, for the angular motion 
of tbe icea (i= aay = 3.1arb ote. *h—ae 
which viously be greatest when n the | jnamity h—w?, 
(the diameter of the wheel.) is the least possi le. 
Note. The author deems it proper to state, ihat all the 
sha aaa demonstrations were made out in January last; 
but for certain causes were not arranged and offered for pub- 
lication until the present time. 
Dec. 28, 1824. 
Remark by the Editor.—Mr. Quinby, in a letter to the 
Editor, es Veb. 12, Li an promises to communicate a pa- 
per, fora ent number of this Journal, applying the 
above theory the * Pitch-back” and “Breast Wheels.” 
es sche St in his eraizinnen 4 states that, “In an sea wheel, 
t as 
onstration exhibits Whats in Dr. Gregory’s Mechanics, is 
gi en to express the greatest perfection of the machine; or, as it is in . 
the-deak. edition of his work, the greatest pgs 3 velocity Sreagesn. it 
is presumed, angular Menges of the wheel. But it is on that the 
quantity exhibited in nstration does not express the greatest 
perfection of the mutniae on the greatest rotary > aouity of the 
whee 
