Freed from the obscurities which prevented its being clearly perceived, his idea stands out to-day in all its imposing simplicity. Yet it must be acknowledged that if it was somewhat denaturalised by those who endeavoured to adapt it to the theories of mechanics, and if it at first lost its sublime stamp of generality, it thus became firmly fixed and consolidated on a more stable basis. The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the principle of the conservation of energy into mechanics, were far from useless. These illustrious physicists succeeded in giving a more precise form to its numerous applications; and their attempts thus contributed, by reaction, to give a fresh impulse to mechanics, and allowed it to be linked to a more general order of facts. If energetics has not been able to be included in mechanics, it seems indeed that the attempt to include mechanics in energetics was not in vain. In the middle of the last century, the explanation of all natural phenomena seemed more and more referable to the case of central forces. Everywhere it was thought that reciprocal actions between material points could be perceived, these points being attracted or repelled by each other with an intensity depending only on their distance or their mass. If, to a system thus composed, the laws of the classical mechanics are applied, it is shown that half the sum of the product of the masses by the square of the velocities, to which is added the work which might be accomplished by the forces to which the system would be subject if it returned from its actual to its initial position, is a sum constant in quantity. This sum, which is the mechanical energy of the system, is therefore an invariable quantity in all the states to which it may be brought by the interaction of its various parts, and the word energy well expresses a capital property of this quantity. For if two systems are connected in such a way that any change produced in the one necessarily brings about a change in the other, there can be no variation in the characteristic quantity of the second except so far as the characteristic quantity of the first itself varies--on condition, of course, that the connexions are made in such a manner as to introduce no new force. It will thus be seen that this quantity well expresses the capacity possessed by a system for modifying the state of a neighbouring system to which we may suppose it connected.