THE PRINCIPLES OF ENERGY 47 



department of science we deal with, the behaviour of material 

 bodies that " obey " Newton's laws of motion. There is no 

 friction; bodies are perfectly rigid or perfectly elastic, and 

 everything happens in an ideal world where all events can be 

 described strictly mathematically. We do not consider heat at 

 all, and energy is always mechanical, and is either potential or 

 kinetic. There is no dissipation, and all transformations are 

 reversible ones. In such circumstances " energy " is an entity 

 that can be denned as above. 



Potential and Kinetic Energy. 



Sometimes available energy seems to vanish, although it is not 

 converted into unavailable energy, or dissipated. Thus a grand- 

 father's clock has stopped because its weights have run down, 

 and we proceed to wind up the latter, but do not start the pen- 

 dulum. In doing so we have expended muscular work, which is 

 measured by the masses of the weights and the distance through 

 which they have been raised. But the clock doesn't " go " 

 until the pendulum is given an initial swing, and we have thus 

 to account for the energy which we have expended. Now the 

 system, clock and weights, and the earth, is in a different state 

 from what it was before the weights were wound up, for the 

 latter are now some 5 feet further away from the centre of the 

 earth than they were when the clock had run down, and they are 

 therefore free to fall. So long as the clock is not started, the 

 weights possess potential energy that is, energy of position 

 relative to something else. When the clock is started the weights 

 begin to descend, and the potential energy begins to transform 

 into kinetic energy, which is the energy of a mass in motion. 

 Call M the mass of the weights and V the velocity with which 

 they fall, and we get |MF 2 =the kinetic energy developed. 

 During the time of fall the potential energy decreases, and the 

 kinetic energy passes into the unavailable form, for the friction 

 of the wheels, etc., generates heat, which is radiated away. 

 When the weights have reached the bottom of the case they are 

 no longer free to fall, and the system contains no more potential 

 energy that is available for doing work at least, so far as the 

 clock itself is concerned. 



Think about a mixture of oxygen and hydrogen in the pro- 

 portions of one molecule of the former and two of the latter ; this 

 system contains potential chemical energy. It will remain a 



