PRINCIPLE OF THE LEVER. 227 



Let the line LR be a lever ; F the fulcrum, s the small 

 weight, w the larger one: and let w be 41b. s lib. ; 

 w at 1 foot and s at 4 feet from the fulcrum. The two 

 weights will thus be in equipoise, 



because s=llb. X 4ft. =4 

 w 41b. X lft.=4 



% and although this fact has long been familiarly known ; 

 I have more than once sought, in vain, for an explana- 

 tion of it, in mechanical works. And when found, it 

 has generally been by the resolution offerees ; a method 

 not always much clearer than the fact to be explained. 

 If any of your readers have been equally unsuccess- 

 ful, and are desirous of a more self evident illustration; 

 the following may be a not unacceptable occupation 

 for a page or two of your Museum. 



Let a body, as w, be at rest ; to move it will require 

 some force. If it be required to have double the rate 

 of motion, the force wanted will be double; or if the 

 weight of the body be doubled, a double force will be 

 equally necessary to move it. 



And, the body thus put in motion, will require force 

 to stop it ; equal to that which was employed to move 

 it ; increasing, of course, in the same manner, accord- 

 ing to the weight of the moving body ; or to its rate of 

 motion, commonly called velocity. 



Thus, motion is a force communicated to a body; 

 the effect of which, called momentum, is in proportion 

 to the weight of the body, and to its velocity : that is, 

 to the velocity multiplied by the weight : a common 

 law of mechanics. 



Now, referring to our figures, let w be a weight to be 

 moved, and s a power employed to move it. w being 

 attached to a stiff bar, would move in the circumference 

 of a circle, of which FW is the radius, and s being at- 

 tached to another part of the same bar, would move in 

 a similar portion of another circle, of which FS is the ra- 

 dius see the dotted lines. And since the circumfer- 

 ences of circles are to each other, as their radii, the rate 

 of motion, or velocity, of s would be to that of w, as 

 their respective distances from the fulcrum. 



