and in such a sense we are justified _in regarding the disappearing work as the cause of the kinetic energy that arises_, and to designate this relation summarily as a transformation. By the inclusion of cases in which work is converted into kinetic energy the law of the conservation of work therefore becomes _the law of the conservation of the sum of work and kinetic energy_. We are thereby compelled to extend the concept of substance, which at first contains only work, to the sum of both magnitudes, and to introduce a new name for this enlarged concept. It will soon appear that all cases of imperfect machines, in which work disappears without giving rise to an equivalent amount of kinetic energy, can, with a corresponding enlargement of the concept, be likewise included in the law of conservation. For experience has shown that in such cases something else arises, heat, light, or electric force, etc. This generalized concept, which embraces all natural processes and permits the sum of all corresponding values to be expressed by a law of conservation, we call _energy_. The law in question, therefore, is: _In all processes the sum of the existing energies remains unchanged._ The principle of the conservation of work in perfect machines proves to be an ideal special instance of this general law. A perfect machine is one in which work changes into nothing but _work_ of another kind, and not into a different kind of energy. Then each side of the equation which expresses the general law of energy, namely, Energy that has disappeared = energy that has arisen, contains only the magnitude of the work, and expresses the law of the conservation of work. If, on the other hand, as in the case of the pendulum, the work increasingly changes part by part into kinetic energy, and _vice versa_, the equation during the first period is: Work that has disappeared = kinetic energy that has arisen, and during the second period in which the pendulum rises again, Kinetic energy that has disappeared = work that has arisen.