152, 153] . CONSERVATION OF ENERGY. 137 



Cases in which the mechanical description of the motion, 

 according to the principles laid down in Chapters V. and VII., 

 requires the assumption of motional forces can only be brought 

 under the principle by supposing that the motions of the centres 

 of inertia of parts of the system, motions of rotation of these parts, 

 and strains effected in them, are not all the motions of which such 

 systems are capable. In the Chapters referred to we assumed 

 that bodies might be treated as continuous, and, on that assump- 

 tion, there cannot be any motions of bodies other than those 

 mentioned. There are however very many phenomena which 

 suggest that natural bodies are of discontinuous structure, and, on 

 this assumption, the mechanical descriptions, assuming continuity, 

 would be first approximations in which volumes of a certain order 

 of smallness are treated as infinitesimal, This can be expressed in 

 another way by saying that the motion of a particle is motion of 

 translation only, and that in the mechanical description of the 

 motion of a body portions of finite size are treated as particles. 

 Such a treatment affords an adequate description of many 

 motions. 



When we wish to retain the method of treatment by assump- 

 tion of continuity, and at the same time to adopt the Principle of 

 the Conservation of Energy, we make a compromise by imagining 

 that there are forms of energy which are neither kinetic nor 

 potential, that processes can be imagined by which quantities of 

 energy in any form can be transformed into equal quantities of 

 energy in any other form, and that in particular any form of 

 energy can be transformed into mechanical potential energy. Now 

 mechanical potential energy of a system in any position is 

 measured by the amount of work which would be done by the 

 forces of the system if the system passed from that position into a 

 certain standard position. 



We are thus able to make the following definition : 



The energy of a system in any state is its capacity for doing 

 work, and is measured by the amount of potential energy the 

 system would possess if all its energy were transformed into 

 mechanical potential energy. 



The Principle of the Conservation of Energy is then the state- 

 ment that the energy of a system is a quantity which can be 



