338 A. B. Quinby on the Crank- 
Art. XIV.—Problem to determine the position of the 
Crank when the tendency of the power to praises rota- 
tion is a maximum. By Mr. A. B. QuinBy.* 
Pour P=power, a=Sa, r=Ca, | and aw=Ce, 
Then, yr2?—a?=ea, ¥ (a+ yr —x? jr? a2)? +4 +22=S8C. 
Now, by mechanics, the tendency of P to produce rota- 
tion= Pc" 50 Ce =Px a v (a+ = dicts 7? — a") a ae 
Se a+ Vr jy? — 42 
which is to be a maximum. 
his expression being vase into ieaions, and equated=0, 
can : and the proper value of 
x being had, the position of the crank is easily determined. 
Note. If it were required to determine the two o positions 
of the crank when the tendeney of P to produce rotation is 
equal to the mean tendency, (from A to B) we should have 
the following expression : 
Px V (a yr? —a*) #07 sepiotises!s t Or, sincé 
a Jr? —x? sess 
4 2 . o. 7 ad : 
Px is a constant quantity, the same points can be de- 
* This — was written (and also wrought out) in 1821, at Renpeeee 
ae apace nto Maj. Babcock and Lt. Brewerton, Corps of Engi 
. rmy 
+ See og demonstration of the cravik problem, Vol. VIL. of this Journal. 
+ The sign + before the quantity/r!—z2 giv 
the position in the up- 
ape and the tn 
aha sign — before the same pace Si gives the position 
