494 Prof. Helmholtz on the Interaction of Natural Forces. 



"We find, in fact, that the work performed by the hammer is de- 

 termined 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 windmill, 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 re- 

 sisted perpetually by other forces, friction, resistance of the air, 

 &c., so that the motion is incessantly weakened and finally neu- 

 tralized. A body, however, which is opposed by no resisting 

 force, when once set in motion moves onward eternally with un- 

 diminished velocity. Thus we know that the planetary bodies 

 have moved without change through space for thousands of 

 years. Only by resisting 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 sum 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 ham- 

 mer 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 beings, 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 pressui'e against the surface which sup- 

 ports it, but does not produce any motion. 



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

 of a falHng mass of water, then in the form of a lifted hammer, 

 and thirdly in the form of the living force of the fallen ham- 

 mer. 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 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 production. It is 

 therefore equivalent to this quantity of work. 



Our clocks are driven by means of sinking weights, and 



