PROFESSOR IN BERLIN 351 



Leibniz had defined the work-equivalent as whatever in 

 Nature could be employed as motive force, or (to give us at 

 the same time a measure of it) could lift a weight ; and he 

 gives as the measure of work the product of the weight, and 

 the height to which it is raised. We call this the potential 

 energy of the weight, because in falling it is able to do this 

 work ; it is in this way, as was said above, that potential energy 

 is reckoned for all other forces and any given path of the 

 body affected, only that the force must be replaced by its 

 component in the direction of the path. Leibniz, however, had 

 already pointed out the second principal form of the work- 

 equivalents of ponderable bodies, namely the vis viva of the 

 moving masses, or the kinetic energy, and finds its value equal 

 to half the product of the mass into the square of the velocity. 



The Law of the Conservation of Kinetic Energy stated that 

 in any given aggregate of natural bodies, on which only such 

 forces act as proceed from fixed centres, the sum of the actual, 

 or kinetic, and the potential energy is constant. It was only 

 when men began to investigate the work-equivalents which 

 must be gained or lost if imponderables are to be brought 

 into play, that Robert Mayer and Helmholtz became convinced 

 of the universal validity of the Law of Energy for all natural 

 processes of the non-living as of the living world, and thus 

 arrived at the Law of the Conservation of Energy. But it is 

 the task of physics to refer the phenomena of nature back to 

 the simplest laws of mechanics, which gave rise to the 

 important question how mechanics itself is constituted in its 

 simplest presentation, and what, as Hertz expresses it, are its 

 ultimate and simplest laws, which every natural motion obeys, 

 which admit of no motion that is excluded by our present 

 experience, and from which, as from the true principles of 

 mechanics, the whole science of mechanics can be purely 

 deductively developed without further appeal to experience. 



The discovery of the Law of the Conservation of Energy 

 made a coherent structure of theoretical mechanics possible. 

 The concept of force retreated into the background ; mass and 

 energy emerged as the given indestructible physical quantities. 

 The energy present proved to consist of two parts, one of which, 

 the kinetic energy, bears in all cases the same relation to the 

 velocities of the masses in motion ; the other, the potential energy, 



