184 HINT* RELATIVE TO 



fcrew" ferves exaftly the fame purpofe as this imaginary 

 lever, and makes the weight act upon the threads like a 

 body fuftained on an inclined plane by a force parallel 

 to its bafe; and as the force to overcome both the 

 -weight and the fri6tion is reciprocally as the diftance 

 from the center of the axis, therefore the diftance of the 

 power from the center of the axis, is to the diftance from 

 the fame center to the middle of the threads of the fcrew, 

 as the force neceffary to fuftain the body on the in- 

 clined plane, to the fame force in the fcrew at the dif- 

 tance of the power. The fame proportion holds good 

 whether the threads be cut perpendicular to the axis 

 or in an angle; for in the firft, the common plane is to 

 be taken ; and in the fecond, the inclined orangularone, 

 confidered in the fourth Propofition: Wherefore if d be 

 the diltance from the center of the axis to the middle 

 of the threads of the fcrew, D the diftance of fame center 

 to the point where the force is applied, the force to 

 overcome the weight and fric~lion is Wd (tnjL.f) : 

 (n=t) D, where the letters exprefs the fame things as 

 before, and the upper fign is for the moving, and the 

 lower for the fufpending force. N. B. t is the natural 

 tangent of the angle made by a line touching one of the 

 threads, and a plane at right angles to the axis of the 

 fcrew ; or it is equal to the diftance of the refpe&ive 

 edges of two threads, divided by the circumference of 

 the cylinder, out of which the fcrew is cut. 



Corollary 1. When lines drawn from the center of 

 the axis of the fcrew to coincide with the threads, are 

 at right angles to the axis, the above expreffion becomes 

 Wd (tn*=*i) : (rfTt) D, for/ becomes radius or unity. 



Corollary 2. When n is equal to t, the moving force 



will be infinites alfo the fufpending force will be no- 



1 thing 



