A, B. Quinby on Crank Motion. 317 



Describe about C, as a centre, fig. 1, pi. 2, the circle 

 ADBE ; representing that in which the crank moves : sup* 

 pose A and B, to be the upperand lower dead points. Join 

 B and A, and produce the line BA to S. Assume Ccr for one 

 position of the crank; and join Sa : then will Sa shew the 

 position of the shackle-bar when the crank is at a. From 

 C demit the perpendicular Ce, meeting Sa produced, in the 

 point e. Assume Cd for another position of the crank; 

 and from d with a radius equal to Sa, describe the arc gh, 

 cutting the line of force SA, in the point t. Draw the hne 

 id; and it will represent the 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 

 a and d demit upon the line of force, the perpendiculars am 

 and dn. Put P to denote the constant force that acts al- 

 ways in the line SA, upon the upper end of the shackle-bar, 

 as at S and t. 



Now by refering to what is demonstrated in vol. 1, chap. 

 VI. art. 1 95 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 Px '-—-; and the value of P, 



cosZASa 



estimated in the direction id, or the tension of the shackle- 

 bar when in the position td, is equal toPx ' — : and 



cos L ^td 



(by mechanics) the tendency which P has to produce rota- 

 tion when the crnnk 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 that time, multiplied by the distance C'e ; 



i. e. =(^Px l^p- ^xCe : and the effect produced at 



V co5^i ASa J 



the point d, is equal to (^Px — —— — ^ xCc: and, now, 



*^ V cos^AtdJ 



if the inference drawn by Mr. Ward were true, then 



would/^PX— ^"t^^)xC6:rPX-^:^-^XCc::am: 

 V cosZ.ASay \ cos /.Aid J 



dn ', or, (by dividing the first and second terms by Fxrad., 



and substituting in place of am and dn their proportionals 



Cc and Cc) ^V- : -- "CelCc; but, by 



cos/_ASa ' cos /.Atd' ' 



