ON THE CONSERVATION OF FORCE 11 



without being compelled to use a corresponding exertion in 

 raising the weight? 



The answer to this is, that all these machines, in that 

 degree in which for the moment they facilitate 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 hun- 

 dredweight by means of a rope pass- 

 ing 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 

 comparison, let us suppose the same 

 load hung to a block of four pulleys, 

 as represented in FIG. 91. A single 

 labourer would now be able to raise 

 the load by the same exertion 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 uni- 

 formly 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 expendi- 

 ture of work is the same, whether 

 four labourers work for a quarter of 

 an hour or one works for an hour. 



If, instead of human labour, we 

 introduce the work of a weight, and 

 hang to the block a load of 400, and 

 at a, where otherwise the labourer 

 works, a weight of 100 pounds, the 



block is then in equilibrium, and. without any appreciable 

 exertion of the arm, may be set in motion. The weight of 



