129 



220. By applying the screw to other machines their effect 

 is greatly increased. If the power q, for example, applied to the 

 winch DE q, is made to turn the screw Z)C, the threads of which, Fig.121, 

 acting upon the teeth of the wheel W, cause it to turn, and with 

 it the cylinder /, around which passes the cord Kp carrying 

 the weight p ; the ratio of the power q to the weight p : may be 

 determined thus. Calling q / the force exerted by the thread 

 of the screw upon one of the teeth of the wheel W, we shall 

 have 



q : c( :: B : circum. DE, 21 & 



AB being the distance between two threads of the screw, and 

 circum. DE denoting the circumference of the circle described 

 by the power q. The force q' is a power, which applied to the 215. 

 circumference of the wheel, is exerted against the weight p] 

 accordingly we have 1S6 - 



q / : p : : IK : IL, 



and, by taking the product of the corresponding terms of the 

 two proportions, 



qq' : q' p ::AB X IK : circum. DE X /L, 

 or, 



q : p : : AE X IK : circum. DE X IL\ 



by which it will be seen that q has s"o much the more advantage 

 according as AE and IK are smaller, considered with reference 

 to circum. DE and IL. DC in this case is called a perpetual 

 screw* 



Of the Wedge. 



221. The wedge is a triangular prism intended to be intro- Fig.i2. 

 duced into a cleft for the purpose of enlarging it, or between two 

 surfaces, in order to separate them further from each other, or 

 to fix them at a determinate distance. 



The action of the wedge, considered as an instrument for 

 cleaving, is essentially modified by friction and other causes. 

 Mech. 1 7 



