MECHANICS. 



45 



screw in the direction of its length, 

 through a space equal to the interval 

 between two contiguous threads, every 

 revolution. 



Fig. 82. 



* The convex screw is generally called 

 the screw, and the concave screw is de- 

 nominated the nut. 



(100.) We have here considered the 

 power to be applied at the circumference 

 of the screw; and if we consider the screw 

 as a simple machine, we must suppose 

 it thus applied. But, in practice, the 

 screw never is used as a simple ma- 

 chine, and the power is always applied 

 to a lever at the head of the screw, in 

 the same manner as it is applied in the 

 wheel and axle, and as represented in 

 Jig. 83. In this case the machine is 

 really complex, being composed of a 

 lever" and a screw. The proportion of 

 the power to the weight is easily inves- 

 tigated. Let P be the power, and let x 



Fig. 83. 



be the effect of this power at the cir- 

 cumference of the screw. Let R be the 

 arm of the lever by which the power 

 acts, and let r be the radius of the sec- 



tion of the screw, at right angles to its 

 length. By the principles established 

 in Chap. III., we have 



P x R = x x r, 

 or P ; : x : : r : R. 

 But the radii of circles are as their cir- 

 cumferences. Let C be the circumfe- 

 rence described by the power, and whose 

 radius is R, and c the circumference of 

 the screw, whose radius is r. 

 r : R : : c : C 

 Hence, we have 



P : x : : c : C, 

 or P x C = x x c. 

 But, by (99), 



x : W : : D : c, 



where D signifies the distance between 

 the threads. Hence, we have 

 o?Xc = WXD.'.PxC = WXD 



"or P : W : : D : C. 

 That is, " the power, multiplied by the 

 circumference which it describes, is 

 equal to the weight or resistance, mul- 

 tiplied by the distance between two con- 

 tiguous 'threads ;" or, " The power is 

 to the weight, as the distance between 

 two contiguous threads is to the cir- 

 cumference described by the power." 



It frequently happens, that the lever 

 by which the power acts is attached to 

 the nut, and the screw is capable only 

 of a longitudinal motion. Thus, in the 

 press represented in jig. 84, the board 



C, moveable between the sides of the 

 frame, is urged by the screw C B, capa- 



