A. B. Quinby on Crank Motion. 321 
the tendency which the power P” has to produce rotation 
when at S or when the crank is at a, is expressed by the pro- 
duct of the tension of the shackle-bar, at that time, and the 
perpendicular Cc, the distance between the centre of rota- 
tion and the line in which the value of the power is estimated: 
wherefore the tendency of P’ to produce rotation when the 
crank is at a, is properly expressed by (poze x Cc 
UC 
=P” Cn: and in a similar manner it may be shewn that 
the tendency of P’ to produce rotation when the crank is 
at d, is properly expressed by P’'xCv. Hence the sum of 
the tendencies of the power P’' to produce rotation, when 
the crank is at the points a and d, is expressed by P XCn 
+P" x Co=P" x (Cn+Cv)=(because vt=in) P’ x 2Ct. 
It now remains to compare this sum wit sum of the 
tendencies which the equal power P’ has'to produce rota- 
tion, acting upon the crank (successively) at the two same 
points, a and d. oats 
From what has been already stated, the swm of the ten- 
dencies of P’ to produce rotation, at the points a and d, is 
ett by P’ xam+P' Xdm=P X2Ct. 
Whence it appears (because P’ and P” are equal) that 
. Pp 
Ing points whatever, in the + ga AD and 
Wherefore in the case in practice, as in the one before 
d ‘3 no loss of the acting power. Q. E. D. 
emonstrated, there is no loss of ting P OUINBY. 
Vot. VIL.—No. 2. 41 
