ON THE CONSERVATION OF FORCE. 



287 



a ship to the quay. Now, it may be asked, If a large, heavy 

 weight had been used for driving a machine, would it not be 

 very easy, by means of a crane or a system of pulleys, to raise it 

 anew, so that it could again be used FIG. 39. 



as a motor, and thus acquire motive 

 power, without being compelled to 

 use a corresponding exertion in rais- 

 ing the weight ? 



The answer to this is, that all 

 these machines, in that degree in 

 which for the moment they facili- 

 tate the exertion, also prolong it, so 

 that by their help no motive power 

 is ultimately gained. Let us assume 

 that four labourers have to raise 

 a load of four hundredweight by 

 means of a rope passing over a 

 single pulley. Every time the rope 

 is pulled down through four feet, 

 the load is also raised through four 

 feet. But now, for the sake of com- 

 parison, let us suppose the same 

 load hung to a block of four pul- 

 leys, as represented in Fig. 39. A 

 single labourer would now be able 

 to raise the load by the same exer- 

 tion of force as each one of the 

 four put forth. But when he pulls 

 the rope through four feet, the load 

 only rises one foot, for the length 

 through which he pulls the rope, 

 at a, is uniformly distributed 

 in the block over four ropes, so 

 that each of these is only shortened 

 by a foot. To raise the load, therefore, to the same height, 

 the one man must necessarily work four times as long as the 

 four together did. But the total expenditure of work is the 



