348 Professor Helmholtz on the Law of the [April 12, 



changed in form. Some special examples will enable you better to 

 understand this law than any general theories. We will begin with 

 gravity ; that most general force, which not only exerts its influence 

 over the whole universe, but which at the same time gives the means of 

 moving to a great number of our machines. Clocks and smaller 

 machines, you know, are often set in motion by a weight. The same 

 is really the case with water-mills. Water-mills are driven by falling 

 water ; and it is the gravity, the weight of the falling water, which 

 moves the mill. Now you know that by water-mills, or by a falling 

 weightf every machine can be put in motion ; and that by these motive 

 powers every sort of work can be done which can be done at all by 

 any machine. You see, therefore, that the weight of a heavy body, 

 either solid or fluid, which descends from a higher place to a lower 

 place is a motive power, and can do every sort of mechanical work. 

 Now if the weight has fallen down to the earth, then it has the same 

 amount of gravity, the same intensity of gravity ; but its power to 

 move, its power to work, is exhausted ; it must become again raised 

 before it can work anew. In this sense, therefore, I say that the 

 faculty of producing new work is exhausted — is lost ; and this is true 

 of every power of nature when this power has produced alteration. 

 Hence, therefore, the faculty of producing work, of doing work, does 

 not depend upon the intensity of gravity. The intensity of gravity 

 may be the same, the weight may be in a higher position or in a lower 

 position, but the power to work may be quite different. The power of 

 a weight to work, or the amount of work which can be produced by a 

 weight, is measured by the product of the height to which it is raised 

 and the weight itself. Therefore our common measure is foot-pound ; 

 that is, the product of the number of feet and the number of pounds. 

 Now we can by the force of a falling weight raise another weight ; 

 as, for example, the falling water in a water-mill may raise the weight 

 of a hammer. Therefore it can be shown that the work of the raised 

 hammer, expressed in foot-pounds, that is, the weight of the hammer 

 multiplied by the height expressed in feet to which it is raised, that 

 this amount of work cannot be greater than the product of the weight 

 of water which is falling down, and the height from which it fell down. 

 Now we have another form of motive power, of mechanical motive 

 power ; that is, velocity. The velocity of any body in this sense, if it 

 is producing work, is called vis viva, or living force, of that body. 

 You will find many examples of it. Take the ball of a gun. If it is 

 shot off", and has a great velocity, it has an immense power of destroy- 

 ing ; and if it has lost its velocity, it is quite a harmless thing. The 

 great power it has depends only on its velocity. In the same sense, 

 the velocity of the air, the velocity of the wind, is motive power ; for 

 it can drive windmills, and by the machinery of the windmills it can 

 do every kind of mechanical work. Therefore you see that also velo- 

 city in itself is a motive force. 



Take a pendulum which swings to and fro. If the pendulum is 

 raised to the side, the weight is raised up ; it is a little higher than 



