4. B. Quinby on Crank Motion. $17 
Describe about C, asa centre, fix. 1, pl. 2, the circle 
ADBE ; representing that in which the ant moves : sup- 
ose Aland B, to be the upperand lower dead points. Join 
and A, and produce the line BA to S.. Assume Ca for one 
position of the crank ; and join Sa: then will Sa shew. the 
position of the shackle-bar when the crank is ata. From 
C demit the perpendicular Gr meeting Sx produced, in the 
point e. Assume Cd for another position of the crank; 
and from d mites a radius na to Sa, describe the are gh, 
cutting the line of force SA, in.the point t.. Draw the line 
tds and _ it will represent he position of the shackle-bar 
when the crank is at d.. From C let fall the perpendicular 
Cc, meeting td produced, in the point c. From the points 
aand d demit upon the line of force, the perpendiculars am 
and dx. Put P to denote the constant force that acts al- 
ways.in bag yee SA, upon the upper end of the shackle-bar, 
as at 
Now = Re he to what is demonstrated in vol. 1, chap, 
V1. art. 195 of Gregory’s mechanics, it is obvious that the 
value of P, estimated in the direction Sa, or, which is the 
same thing, the tension of the shackle-bar when in the po- 
sition Sa, is equal to pee : S.° and the value of P, 
estimated in the direction td, or the tension of the shackle- 
wrens 
(by mechanies) the tendency which P has to > prolidoaiaege 
tion when the crank is at a; or, the effect produced by P 
when the crank is at a, is equal to the tension of the 
shackle-bar, at as time, multiplied by the distance ©e; 
hint =(Px—= )xCe: : and the effect produced at 
bar when in the position fd, is equal to Px 
ya 
the point d,.is equal to (Px— yeve 
if the inference drawn by Mr. “Ward ip ‘true, then 
ee ms id) xCe:( Px) Ce: ca 
dn; or, oy dividing the first and esoedtd So. by P xrad., 
and substituting in pate of am and dn their proportionals 
a ig e Cc; 2 but, by 
xe and, omy 
Ce and 3 
os £ Abe * cosZ Atd** 
