WORK AND MACHINES 165 



fulcrum as a centre. The lever is supposed to remain fixed 

 so far as motion from one place to another is concerned. 

 No rotary motion occurs when the value of the effort balances 

 that of the resistance, and the lever then is in a state of 

 equilibrium. It is wholly free to move, and is acted upon by 

 forces capable of moving it, but the effects of P and W 

 are so counter-balanced that no motion occurs. 



The effect of P is calculated by multiplying together the 

 value of P and the length of Pa. This product is called the 

 moment of P, and the use of this term may properly be con- 

 fined to forces acting on bodies to produce rotary motion. 

 The moment of W is calculated in a similar manner, and P 

 and W are in equilibrium when their moments are equal 

 regardless of the kind of lever employed. The term applies 

 equally well in the use of pulleys. 



It becomes evident from any such discussion of moments 

 that to maintain equilibrium, or to have the moment of P 

 sufficiently large to cause W to be moved, it is possible to 

 employ a small value for P if Pa be correspondingly long. 

 If Pa be made shorter and shorter then P must become larger 

 and larger, and will exceed the value of W when the power 

 arm is shorter than the weight arm as in third class levers. 



The farther out from F either P or W is placed the longer 

 will be the arc of the circle described by them in any move- 

 ment of the lever. The lengths of these arcs covered by P 

 and W in any one turn of the lever bear the same relation 

 to each other as do the lengths of the arms. It is thus 

 possible to state that P times the distance through which P 

 moves (Pd) = W times the distance through which W moves 

 (Wd). 



As the time taken for P and W to move through these 

 different distances is the same for both, it follows that which- 

 ever is the farther from F and passes over the longer arc 

 will move at a correspondingly greater velocity. Thus it is 



