122 ANNUAL OF SCIENTIFIC DISCOVERY. 



the necessary height, it again liberates it, and the hammer falls upon the 

 metal mass which is pushed beneath it. But why does the falling hammer 

 here exercise a greater force than when it is permitted simply to press with 

 its own weight on the mass of metal ? Why is its power greater as the 

 height from which it falls is increased ? We rind, in fact, that the work per- 

 formed by the hammer is determined by its velocity. In other cases, also, 

 the velocity of moving masses is a means of producing great effects. I only 

 remind you of the destructive effects of musket-bullets, which, in a state of 

 rest, are the most harmless things in the world. I remind you of the wind- 

 mill, which derives its force from the moving air. It may appear surprising 

 that motion, which we are accustomed to regard as a non-essential and 

 transitory endowment of bodies, can produce such great effects. But the 

 fact is, that motion appears to us, under ordinary circumstances, transitory, 

 because the movement of all terrestrial bodies is resisted perpetually by other 

 forces, friction, resistance of the air, etc., so that motion is incessantly 

 weakened and finally neutralized. A body, however, which is opposed by 

 no resisting force, when once set in motion, moves onwards eternally with 

 undiminished velocity. Thus we know that the planetary bodies have 

 moved without change, through space, for thousands of years. Only by re- 

 sisting forces can motion be diminished or destroyed. A moving body, 

 such as the hammer or the musket-ball, when it strikes against another, 

 presses the latter together, or penetrates it, until the sun* 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 vira) of the mass. The word "living" 

 has of course here no reference whatever to living beings, but is intended to 

 represent solely the force of the motion as distinguished from the state of un- 

 changed 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 fall- 

 ing mass of water, then in the form of a lifted hammer, and, thirdly, in the 

 form of the living force of the fallen 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 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 gene- 

 rate 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 



