64 



FERGUSON'S LECTURES. 



LECT. 

 III. 



O 



But if a weight W hangs at the 

 ^ lower end of the moveable block p of 

 the pulley D, and the cord G F goes 

 under that pulley, it is plain that 

 the half G of the cord bears one half 

 of the weight W, and the half F the 

 other ; for they bear the whole be- 

 tween them. Therefore, whatever 

 holds the upper end of either rope, 

 sustains one half of the weight: and 

 if the cord at F be drawn up so as 

 to raise the pulley D to C, the cord 

 will then be extended to its own 

 length, all but that part which goes 

 under the pulley ; and consequent- 

 ly, the power that draws the cord 

 will have moved twice as far as the 

 pulley D with its weight W rises ; 

 on which account, a power whose 

 intensity is equal to one half of the 

 weight will be able to support it, because if the power 

 moves (by means of a small addition) its velocity will be 

 double the velocity of the weight ; as may be seen by put- 

 ting the cord over the fixed pulley C (which only changes 

 the direction of the power, without giving any advantage 

 to it) and hanging on the weight P, which is equal only 

 to one half of the weight W / in which case there will be 

 an equilibrium, and a little addition to P will cause it to 

 descend, and raise W through a space equal to one half 

 of that through which P descends. Hence, the advan- 

 tage gained will be always equal to twice the number of 

 pulleys in the moveable or undermost block. So that, 

 when the upper or fixed block u contains two pulleys, 

 which only turn on their axes, and the lower or move- 

 able block U contains two pulleys, which not only turn 

 upon their axes, but also rise with the block and 



