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194 H. HelmhoUz on the Interactio7i of Natural Forces. 



change through space for thousands of years. Only "by resist- 

 ing forces can motion be diminished or destroyed. A moving 

 body, such as the hammer or the musket-ball, Avhen it strikes 

 against another, presses the latter together, or penetrates it, until 

 the sura of the resisting forces which the body struck presents 

 to its pressure, or to the separation of its particles, is sufficiently 

 great to destroy the motion of the hammer or of the bullet. 

 The motion of a mass regarded as taking the place of working 

 force is called the living force {vis viva) of the mass. The word 

 "living'^ has of course here no reference whatever to living be- 

 ings, but is intended to represent solely the force of the motion 

 as distinguished from the state of unchanged rest — from the 

 gravity of a motionless body, for example, which produces an 

 incessant pressure against the surface which supports it, but 

 does not produce any motion. 



In the case before us, therefore, we had first power in the form 

 of a falling mass of water, then in' the form of a lifted hammer, 

 and thirdly in the form of the living force of the falling hammer. 

 We should transform the third form into the 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 favorable case would reach a 

 height equal to that from w^hich it fell, but would never riser 

 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 production. 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 Avho winds 

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



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

 municated is gradually given out again during the lbllovvin| 

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

 to overcome the friction of the wheels and the resistance which 

 the pendulum encounters from the air. The wheelwork of the 

 clock therefore exhibits 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 w^e after- 

 wardB open the cock of a gun and admit the compressed air into 



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