A. B Quinby on Crank Motion. 319 
This, I understand to be a case in which there is no loss 
of power. ; : ; 
_ Let it next be considered what effect P would have du- 
ring its descent through some particular, or assumed Space. 
ake Py=AB, and it will be manifest that the effect of 
", during its descent from P to y, will be properly express- 
ed by PxPy, or PXAB=WxBA.. Let it also be con- 
sidered, that during the descent of P to the point y, the 
wheel and crank will be made to turn through half a revo- 
lution ; for, since, by cons. AD: CD::CD: CG; and by 
the property of circles AD ; CD::#G : CG, it follows that 
(G@ is=CG; and consequently Gin =2CD=AB=Py: 
and, therefore, if the crank be at A when P shall begin to 
descend, it will have described the arc ADB, and have ar 
rived at the lower dead point B, at the time that P shall 
have arrived at y. é 
ssume, now, Ca for one position of the crank; and 
suppose a shackle bar, az, having upon its upper end the 
Power P’,=P, to stand perpendicular, and rest upon the 
wrist of the crank at a :—it is proposed to consider the ten- 
dency that P’ would have acting upon the wrist of the ank 
at a, to produce rotation, (or to give angular motion to the 
wheel and crank); in comparison with the tendency which 
P has to produce rotation, acting upon the teeth of the 
Wheel, at the point G. Produce za to m3 and draw the 
sine am; and it will be plain that the tendency of P’, to 
produce rotation, will be to that of P, as Cn, or am, to CG, 
If, therefore, CG be taken to express the tendency of P 
‘o produce rotation; then that of P’ to produce rotation, 
will be properly expressed by am; the perpendicular dis- 
tance of the point a from the line ACB. And, in general, 
the tendency of P’ to produce rotation, at any point what- 
ever of the semicircle ADB will be expressed by the per- 
\pendicular distance of that point from the line ACB. 
Hence to determine the mean tendency of P’ to produce 
rotation, (in terms of CG,) during its descent from A to B, 
i must find the mean distance of the 
Cc 
Flux. p. 97, iso but, CG was made= AD”? and, 
therefore, the mean tendency of P’ to produce rotation, du- 
