278 



THE PULLEY. 



the power, which is therefore the amount of the weight. In the second sys- 

 tem, the rope P A D is stretched by the power. The rope A E B C acts 

 against the united tensions A P and A D ; and therefore the tension of A E or 

 E B is twice the power. Thus the weight acts against three tensions : two 

 of which are equal to twice the power, and the remaining one is equal to the 

 power. The weight is therefore equal to five times the power. 



A single rope may be so arranged with one moveable pulley as to support a 

 weight equal to three times the power. In fig. 13, this arrangement is repre- 

 sented, where the numbers sufficiently indicate the tension of the rope, and 

 the proportion of the weight and power. In fig. 14, another method of produ- 

 > cing the same effect with two ropes is represented. 



Fig. 13. 



Fig. 14. 



Fig. 15. 



If several single moveable pulleys be made successively to act upon each 

 other, the effect is doubled by every additional pulley : such a system as this 

 is represented in fig. 15. The tension of the first rope is equal to the power ; 

 the second rope acts against twice the tension of the first, and therefore it is 

 stretched with a force equal to twice the power ; the third rope acts against 

 twice this tension, and therefore it is stretched with a force equal to four times 

 the power, and so on. 



In this system, it is obvious that the ropes will require to have different de- 

 grees of strength, since the tension to which they are subject increases in a 

 double proportion from the power to the weight. 



If each of the ropes, instead of being attached to fixed points at the top, are 

 carried over fixed pulleys, and attached to the several moveable pulleys re- 

 spectively, as in fig. 16, the power of the machine will be greatly increased ; 

 for in that case the forces which stretch the successive ropes increase in a 



Fig. 16. 



Fig. 18. 



