Chap. 7.] of Levers. 57 



lever of the third order (fig. 5.) is placed at I, it is 

 thep a lever whofe arm of power p f is to that of re- 

 fiftance R, as one is to-three; for the length of the 

 arm of the lever is always determined by its diftance 

 from the prop C. But if the power P, is placed at 2, 

 it is then a lever whofe arm of power P, is to that of 

 refinance R, as two is to three. 



It is the diftance of thefe forces from the prop 

 which determines the velocity of sheir motion, v/hich 

 is always in the fame proportion as the<diftances ; for 

 when the prop is at C (fig. 6.) one of the powers 

 at B, and the other at A, double the diftance fro-n 

 the prop, the latter power A will have a velocity 

 which is double that of the firft power at B. Be-' 

 caufe when the lever begins to move, while the point 

 B describes the arch B b, A will defcribe the arch A a, 

 which will be double the former, for arches are always 

 in proportion to their radii *. 



The force of a moving body is the remit of its mafs 

 multiplied by its velocity, it follows therefore in the firft 

 place, as has been obferved above, that a weight act- 

 ing by a lever produces a force fo much the greater, 

 as its diftance is greater from the prop, becaufe then it 

 pofihTes greater velocity ; fecondly, it follows that two 

 equal weights, acting in oppofite directions upon a 

 lever, are not in equilibrio when they are not at equal 

 diftances from the prop ; and thirdly, that two unequal 

 weights, acting upon a lever, will exert equal forces 

 when their diftances from the prop are in a reciprocal 

 proportion to their refpective mafles. / Hence it fol- 

 lows, that whatever is gained in power is loft in time, 

 and the contrary. 



In what has been hitherto obferved of the lever, it 



* The radius is the femidiameter of a circle, or that line which 

 jrcceeds direftly from the center to the circumference. 



has 



