144 ON THE INTERACTION OF NATURAL FORCES. 



second, if we, for example, permitted the hammer to fall upon 

 a highly elastic steel beam strong enough to resist the shock. 

 The hammer would rebound, and in the most favourable case- 

 would reach a height equal to that from which it fell, but would 

 never rise higher. In this way its mass would ascend; and at 

 the moment when its highest point has been attained it would 

 represent the same number of raised foot-pounds as before it 

 fell, never a greater number ; that is to say, living force can 

 generate the same amount of work as that expended in its pro- 

 duction. It is therefore equivalent to this quantity of work. 



Our clocks are driven by means of sinking weights, and our 

 watches by means of the tension of springs. A weight which 

 lies on the ground, an elastic spring which is without tension, 

 can produce no effects : to obtain such we must first raise the 

 weight or impart tension to the spring, which is accomplished 

 when we wind up our clocks and watches. The man who winds 

 the clock or watch communicates to the weight or to the spring 

 a certain amount of power, and exactly so much as is thus com- 

 municated is gradually given out again during the following 

 twenty-four hours, the original force being thus slowly consumed 

 to overcome the friction of the wheels and the resistance which 

 the pendulum encounters from the air. The wheel work of the 

 clock therefore develops no working force which was not pre- 

 viously communicated to it, but simply distributes the force 

 given to it uniformly over a longer time. 



Into the chamber of an air-gun we squeeze, by means of a 

 condensing air-pump, a great quantity of air. When we after- 

 wards open the cock of the gun and admit the compressed air 

 into the barrel, the ball is driven out of the latter with a force 

 similar to that exerted by ignited powder. Now we may de- 

 termine the work consumed in the pumping-in of the air, and 

 the living force which, upon firing, is communicated to the ball, 

 but we shall never find the latter greater than the former. 

 The compressed air has generated no working force, but simply 

 gives to the bullet that which has been previously communicated 

 to it. And while we have pumped for perhaps a quarter of an 

 hour to charge the gun, the force is expended in a few seconds 



