136 THEORY OF WORK AND ENERGY. [CHAP. VIII. 



reversed in sense when the relative motion of the points of contact 

 is reversed in sense. Since the friction always acts so as to 

 oppose slipping, the work done by the friction in any displace 

 ment is negative (or zero), and thus friction in a system never 

 increases the kinetic energy. Systems in which we recognise the 

 action of forces always tending to diminish the kinetic energy 

 without producing an equivalent in potential energy are said to be 



153. Conservation of Energy. In any system every 

 increase in the kinetic energy can be regarded as produced by 

 forces which do work, and every decrease by forces against which 

 work is done. In a conservative system every increase of kinetic 

 energy is accompanied by a diminution of potential energy, and 

 conversely. In such a system the total energy, as well as the total 

 mass, remains always the same, and all motions are processes in 

 which redistributions of the energy among the parts of the system, 

 or else transformations of the energy, from kinetic to potential or 

 from potential to kinetic, take place. 



In a conservative system let E be the total energy. Let T be 

 the kinetic energy, and W the work-function, in any position. 

 The equation of energy can be written 



showing that the kinetic energy is a one-valued function of the 

 quantities that define the position of the system. 



The principle of the Conservation of Energy is a principle 

 which asserts that the occurrence of dissipative forces in the 

 formulation of the laws which govern any phenomenon is invari 

 ably due to an imperfect analysis of the circumstances. The 

 suggestion is that when the circumstances are completely analysed, 

 and the motions of all the parts of the system are allowed for, the 

 total kinetic energy will be found to be in every case a function of 

 position only, as it is in the case of a system moving under con 

 servative positional forces. This is the same thing as saying that 

 for a system isolated from the action of external bodies, or under 

 such external actions only as can be represented by conservative 

 positional forces, there is a constant total energy, some part of 

 which is at any instant kinetic energy, and the remainder potential 

 energy. 



