318 A. B, Quinby on Crank Motion, 



Euc. El V. XIV. -~?4_- : — ?^ y.Ce'.Cc; there- 

 cos A. Aba cos /_ Aha 



e _ Ce Cc Ce Cc 

 tore ex aequo ♦ • • •, 



cos l_ ASa C05 Z. Aid ' ' cos ^ ASa cos /_ ASa ' 

 that is, (since the cos ^ Aid is less than the cos /_ ASa,) the 

 same magnitude has the same ratio to a greater magnitude 

 that it has to a less, which (Euc. El. V. XIV.) is absurd. 



1 he effects, therefore, at the several points of division of 

 the quadrant are not to one another, as the perpendiculars 

 respectively irom those points to the line of force. 



Having now proved that the principle upoa which Mr. 

 Ward has founded his demonstration is false, J shall remark 

 that an equality of 7-atio between the effects produced at 

 any two points of the quadrant, and the perpendiculars 

 drawn from those points to the line of force, has not, as I 

 am able to perceive, any connexion whatever with a proper 

 and scientific solution ; and what consideration it was that 

 led Mr. Ward to frame the inference, is not, 1 suspect, in 

 the power of mathematics, whether "^wrr," or " mixed,'''' to 

 discover. 



That the crank motion occasions no loss of the acting 

 power is true ; and may be demonstrated in the following 

 manner : 



Describe, fig 2, pi. 2. the circle ADBE, to represent that 

 in which the crank moves : suppose A and B to be the up- 

 per and lower dead points : join them ; and draw the di- 

 ameter ED at right angles to AB. Produce BA to S. 

 Say, now, as the quadrantal arc AU : CD;; CD : to a 

 fourth term. Make CG=this fourth term ; and suppose a 

 wheel GtvxD, whose radius is equal to CG, to be fifed per-: 

 manently (in any way) upon the shaft or axle that carries 

 the crank : suppose, also, two racks G6 and vd to rest upoa 

 the teeth of the wheel Gtvw, and to stand parallel with the 

 line of force SA. If, now, a power P be applied upon the 

 end of the rack G6, it is obvious that it will cause this 

 rack to descend, and turn the wheel Glvw, and raise the 

 rack xdon the opposite side ; and, if a weight W,=to P, 

 be attached to the lower end of the rack vd it is plain thai 

 the two masses P and W will reciprocally balance each 

 other; and, if it be supposed to descend through any space 

 whatever, its effect during the time of descent, will be sufB- 

 cient to raise the weight W through an eqtml space. 



