. 
A. B. Quinby on the Overshot Water-Wheel. 305 
of its descent, will be sufficient to raise the particle W through 
an equal space. 
Let it next be considered, what effect the particle P would 
—— during its descent, through some particular or assumed 
Take Py=AB, and it will be manifest that the effect of the 
sent P, during its descent to the point y, will be properly 
expressed by the product P x Py, or P PxXAB=W xXBA, Let 
it also be considered, that during the descent of the ar 
ticle P, from P to y, the wheel will be made to turn through 
half a revolution; for, since by cons. AD : CD::CD : CG; 
and by the pro erty of circles AD: CD::tG: CG, it fol- 
lows thattG=CD; and, consequently, Gtu= 2CD= AB=Py: 
and, therefore, if we suppose a particle of water to be at A 
when the particle P shall begin to descend, it will have de- 
scribed the arc ADB, and have arrived at the point B, at the 
time that the particle P shall have arrived at Ye 
It is now proposed to estimate the effect which a particle 
of water P’,=to P, would have in descending from A, through 
the are ADB; in comparison with the effect that would be 
produced, during the same time, by the particle P, acting up- 
on the teeth of the wheel, at the point 
From P’ let fall the perpendicular P’n; and it is manifest 
that the tendency which the particle P’ has to produce rota- 
tion, is to that tla the perticle P_ has to Breen _Foetton, 
in the ratio of Cnto CG. If, therefore, CG be 
press the pee of the particle P to roduce raion then 
that of the particle P’ to produce rotation, will be properly 
expressed by the line Cn; the gh distance of the 
particle P’ from the line ACB. And, n general, the ten- 
dency of the particle P’ to produce ‘ota at any point 
whatever of the semicircle ADB, will be expressed by the 
perpendicular distance of that point from the line 
Hence, to determine the mean tendency of the particle E 
to produce ae (in terms of CG,) during its descent from 
A to B, in th , we must find the mean distance of 
the Be cede. are ADB from the line ACB; which, by 
Viiees Pinks 91, = —; but, CG be 
ince’s Flux. p. i ayy ; but, was made =AD >: 
and, therefore, the mean ee of the particle P’ to pro- 
dace rotation, during its descent, (from A to B, through the 
Voir 1X.—No. 2. 39 
