ON THE CONSERVATION OF FORCE. 291 



with considerable velocity. It is the velocity of the water, 

 exerting an impact against the float-boards, which acts in this 

 case, and which produces the motive power. 



Windmills, which are used in the great plains of Holland 

 and North Germany to supply the want of falling water, afford 

 another instance of the action of velocity. The sails are driven 

 by air in motion by wind. Air at rest could just as little 

 drive a windmill as water at rest a water-wheel. The driving 

 force depends here on the velocity of moving masses. 



A bullet resting in the hand is the most harmless thing in 

 the world ; by its gravity it can exert no great effect ; but when 

 fired and endowed with great velocity it drives through all ob- 

 stacles with the most tremendous force. 



If I lay the head of a hammer gently on a nail, neither its 

 small weight nor the pressure of my arm is quite sufficient to 

 drive the nail into the wood ; but if I swing the hammer and 

 allow it to fall with great velocity, it acquires a new force, 

 which can overcome far greater hindrances. 



These examples teach us that the velocity of a moving mass 

 can act as motive force. In mechanics, velocity in so far as it 

 is motive force, and can produce work, is called vis viva. The 

 name is not well chosen ; it is too apt to suggest to us the force 

 of living beings. Also in this case you will see, from the in- 

 stances of the hammer and of the bullet, that velocity is lost, as 

 such, when it produces working power. In the case of the 

 water-mill, or of the windmill, a more careful investigation of 

 the moving masses of water and air is necessary to prove that 

 part of their velocity has been lost by the work which they 

 have performed. 



The relation of velocity to working power is most simply 

 and clearly seen in a simple pendulum, such as can be con- 

 structed by any weight which we suspend to a cord. Let M, Fig. 

 43, be such a weight, of a spherical form ; A B, a horizontal 

 line drawn through the centre of the sphere ; P the point at 

 which the cord is fastened. If now I draw the weight M on 

 one side towards A, it moves in the arc M a, the end of which, 

 a, is somewhat higher than the point A in the horizontal line, 

 u 2 



