THE FORMS OF ENERGY. Ill 



the motions occur. When and only when this condition is fulfilled, the 

 work done against the forces in moving from one configuration to another 

 will be independent of the mode in which the change is effected, and for 

 each configuration there will be a . definite amount of kinetic energy. 

 The loss of kinetic energy in any change is thus recoverable on changing 

 back again, so that we can assume that potential energy is gained equal 

 to the kinetic energy lost. A system of this kind is termed a " con- 

 servative system," and the forces are termed "conservative forces." 

 The experimental basis, then, of the assertion that the sum of the 

 potential and kinetic energies of a system is constant is the observation 

 that the forces depend solely on the configuration. 



Probably no system is exactly conservative. But the planets and 

 the sun form a system in which we have not as yet been able to detect 

 any departure from conservation of kinetic + potential energies, in 

 the comparatively short time over which astronomical observations have 

 extended, and it gives us the best illustration of such a system. Even 

 in the solar system, however, there are tidal effects which depend on 

 the velocity of the bodies producing them, and we know that they must 

 decrease the sum total of the kinetic and potential energies though we 

 have not actually observed the decrease. If we include comets in the 

 system, there appear to be some cases of observed decrease and diminu- 

 tion of orbits. 



We continually use stores of potential energy in practical life to 

 obtain work. Thus we use a head of water to turn a turbine or a water- 

 wheel. We wind up a clock-weight to keep a clock going, and so on. 

 But we can never use the potential energy directly. We must always 

 allow the body or system to move in the direction of the forces acting, 

 and convert the potential in the first place into kinetic energy, and 

 thus get work from the kinetic energy. It would be absurd to attempt 

 to get energy from a reservoir of water without allowing the water to 

 run down hill, or to attempt to keep a clock going from the potential 

 energy of the weights without allowing them to fall. 



Heat Energy. In almost all cases of motion with which we are 

 concerned on the surface of the earth, the forces are not conservative. 

 We generally find friction of some kind coming into play, some force 

 opposed to the motion. If a body is projected along a horizontal table 

 its kinetic energy gradually disappears, work being done against the 

 friction. When the body comes to rest, the whole of the kinetic energy 

 is lost without any gain of potential energy, for there is no tendency 

 on the part of the body to return to its original position. But a new 

 phenomenon is observed. The body and the table are both slightly 

 heated. This appearance of heat is illustrated by the familiar experi- 

 ment of rubbing a button on a table and then applying it to the skin, 

 when the heating is found to be quite appreciable. In Sir Humphry 

 Davy's celebrated experiment, ice was melted by rubbing together two 

 pieces in a vacuum. Kinetic energy was continually supplied to the ice. 

 It disappeared in doing work against friction and heat appeared in the 

 melting of the ice. Many other examples of the appearance of heat on 

 the loss of kinetic energy by friction, will occur to the reader. In all 

 these cases the kinetic energy has disappeared, and there is no means 

 of regaining it by allowing the body to retrace its path. It has, there- 



