192 HELMHOLTZ 



100 pounds sinks, that of 400 rises. Without any meas- 

 urable expenditure of force, the heavy weight has been 

 raised by the sinking of the smaller one. But observe that 

 the smaller weight will have sunk through four times the 

 distance that the greater one has risen. But a fall of 100 



FIG. 94 



pounds through four feet is just as much 400 foot-pounds as 

 a fall of 400 pounds through one foot. 



The action of levers in all their various modifications is 

 precisely similar. Let a b, FIG. 92, be a simple lever, sup- 

 ported at c, the arm c b being four times as long as the other 

 arm a c. Let a weight of one pound be hung at b, and a 

 weight of four pounds at a, the lever is then in equilibrium, 

 and the least pressure of the finger is sufficient, without any 

 appreciable exertion of force, to place it in the position 

 o 1 V", in which the heavy weight of four pounds has been 

 raised, while the one-pound weight has sunk. But here, 

 also, you will observe no work has been gained, for while the 

 heavy weight has been raised through one inch, the lighter 

 one has fallen through four inches ; and four pounds through 

 one inch is, as work, equivalent to the product of one pound 

 through four inches. 



Most other fixed parts of machines may be regarded as 

 modified and compound levers ; a toothed-wheel, for instance 

 as a series of levers, the ends of which are represented by 



