320 A. B. Quinhy on Crank Motion. 



ring its descent, (from A to B, through the arc ADB,) is 

 equal to that of P, estimated for the same time. 



And as the effects produced by the two equal powers,?', 

 and P, during any given time, will obviously be to one an- 

 other, as the mean tendencies of those powers, (during that 

 time,) to produce rotation ; it follows that the effect produ- 

 ced by P', in descending from A to B, in the arc ADB, 

 will be equal to that produced by P, in the same time ; or, 

 =WxPy. 



Hence, if the power applied to the crank be supposed to 

 act, at all times, in a direction parallel to the line SA ; or, 

 which is the same, if we suppose the shackle-bar to main- 

 tain its parallelism there will be no loss of the acting power. 



It now remains to be proved, that in the case in practice^ 

 in which the upper end of the shackle-bar is confined to the 

 same vertical line, and the lower end is made to vary from 

 that line, there is also no loss of the acting power. 



Repeat, fig. 3, pi. 2, the first part of the last construction. 

 Assume the two points a and d, in the semicircle ADB, equi- 

 distant from the dead points. Join Qa and Cc?; and draw 

 ti)e lines am and dm. Let Sa represent the shackle-bar, 

 when the crank is at a. Through d draw f/N, parallel to 

 Sa ; and it will shew the position of the shackle-bar when 

 the crank is at d. 



Produce Sa to /?, and from the centre C demit upon San 

 the perpendicular Cc. Join ad: and suppose the three 

 powers P, P', P , to be all equal to one another. 



It is proposed now to consider the tendency that the pow- 

 er P" has to produce rotation when at the point S, or when 

 the shackle-bar is in the position Sa; and, likewise to consid- 

 er the tendency of the same power to produce rotation when 

 the shackle bar is in the position N(i : and, secondly, to 

 compare the sum of these tendencies with the sum of the 

 tendencies of the equal power P', to produce rotation, 

 acting successively at the two same points a and J. 



By refering again to Gregory's Mechanics, vol. 1, art. 

 195, the value of P'', estimated in the oblique or inflected 

 direction Sa ; or the tension of the shackle-bar when in the 



position Sa, will be found to be equal to P" X 



Sa /I • .-XT*,.. .Cn 



cos /_ ASa 



P"X = (by sim. tri.) P'X-^-; and (by mechanics) 



Sw Cc 



