FOECE 689 



tirely analogous to that of which I spoke at the end of the paragraph 

 containing my reflections on the principle of inertia. But as a matter 

 of fact the difficulty is artificial. Provided that the future indica- 

 tions of our instruments can only depend on the indications which 

 they have given us, or that they might have formerly given us, such is 

 all we want, and with these conditions we may rest satisfied. 



Energy and Thermo-Dynamics 



Energetics. The difficulties raised by the classical mechanics have 

 led certain minds to prefer a new system which they call Energetics. 

 Energetics took its rise in consequence of the discovery of the prin- 

 ciple of the conservation of energy. Helmholtz gave it its definite 

 form. We begin by defining two quantities which play a fundamental 

 part in this theory. They are kinetic energy, or vis viva, and potential 

 energy. Every change that the bodies of nature can undergo is regu- 

 lated by two experimental laws. First, the sum of the kinetic and 

 potential energies is constant. This is the principle of the conserva- 

 tion of energy. Second, if a system of bodies is at A at the time t , and 

 at B at the time t i} it always passes from the first position to the 

 second by such a path that the mean value of the difference between 

 the two kinds of energy in the interval of time which separates the 

 two epochs, t and t is a minimum. This is Hamilton's principle, and 

 is one of the forms of the principle of least action. The energetic 

 theory has the following advantages over the classical. First, it is 

 less incomplete that is to say, the principles of the conservation of 

 energy and of Hamilton teach us more than the fundamental princi- 

 ples of the classical theory, and exclude certain motions which do not 

 occur in nature and which would be compatible with the classical 

 theory. Second, it frees us from the hypothesis of atoms, which it 

 was almost impossible to avoid with the classical theory. But in its 

 turn it raises fresh difficulties. The definitions of the two kinds of 

 energy would raise difficulties almost as great as those of force and 

 mass in the first system. However, we can get out of these difficulties 

 more easily, at any rate in the simplest cases. Assume an isolated 

 system formed of a certain number of material points. Assume that 

 these points are acted upon by forces depending only on their relative 

 position and their distances apart, and independent of their velocities. 

 In virtue of the principle of the conservation of energy there must 

 be a function of forces. In this simple case the enunciation of the 

 principle of the conservation of energy is of extreme simplicity. A 

 certain quantity, which may be determined by experiment, must re- 

 main constant. This quantity is the sum of two terms. The first 

 depends only on the position of the material points, and is inde- 

 pendent of their velocities; the second is proportional to the squares 



