318 A. Be Quinby on Crank Motions. 
» Ce gseGe igrlce qicypbt: » 
sisi Abie deca als Ce : Cc; there: 
but ig ha De Gergen Ce Ce 
Pat gar ZASa * cosZ Atd’*cos 2 ASa" cos Z ASa’ 
that is, (since the cos Z Atd is less than the cos Z 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. ~ 
The effects, therefore, at the several points of division of 
the quadrant are not to one another, as the perpendiculars 
respectively from those points to the line of force. 
Having now proved that the principle upon which Mr. 
Ward has founded his demonstration is false, I shall remark 
that an equality of ratio 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 ! 
. am able to perceive, any connexion whatever with a proper 
and screntific solution; and what consideration it was that 
led Mr. Ward to frame the inference, is not, I suspect, in 
the power of mathematics, whether “ pure,” or “mixed,” to 
discover. 
That the crank motion occasions ‘no loss of the acting 
power is true ; and may be demonstrated in the following 
Euc. El V. XIV. 
_ Describe, fig. 2, pl. 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- 
y, now, as the quadrantal arc AD; CD::CD: to 4 
fourth term. Make CG=this fourth term; and suppose 4 
wheel Giow, whose radius is equal to, CG, to be fitted pet- 
manently (in any way) upon the shaft or axle that carries 
nk : suppose, also, two racks G4 and vd to rest upon 
the teeth of the wheel Giow, and to stand parallel with the 
line of force SA. If, now, a power P be applied upon t 
end of the rack Gb, it is obvious that it will cause this 
rack to descend, and turn the wheel Gtow, and raise the 
rack td on the opposite side ; and, if a weight W,=to P; 
two 
other; and, if it be supposed to descend through any space 
