_It involves the Law of Equivalence._—Here we may be content with noticing that the law of the conservation of energy involves the existence of relations of equivalence between the different varieties. A certain quantity of a given energy, measured, as we have seen, by the product of two factors, is equivalent to a certain fixed quantity of quite a different form of energy into which it may be converted. The laws which govern energetic transformations therefore contain, from both the qualitative and the quantitative points of view, all the connections of the phenomena of the universe. To study these laws in their detail is the task that physics must take upon itself. The conversion one into the other of the different forms of energy by means of equivalents is only a possibility. It is subject, in fact, to all sorts of restrictions, of which the most important are due to the second principle. § 8. CARNOT’S PRINCIPLE. ITS GENERALITY. The second fundamental principle is that of the transformations of equilibrium, or of the conditions of reversibility, or again, Carnot’s principle. This principle, which first assumed a concrete form in thermodynamics, has been very widely extended. It has reached a degree of generality such that contemporary theoretical physicists such as Lord Kelvin, Le Châtelier, etc., consider it the universal law of physical, mechanical, and chemical equilibrium. Carnot’s principle contains, as was shown by G. Robin, d’Alembert’s principle of virtual velocities, and according to physicists of to-day, as we have just remarked, it contains the laws peculiar to physico-chemical equilibrium. The application of this principle gives us the differential equations from which are derived numerical relations between the different energies, or the different modalities of universal energy. _Its Character._—It is very remarkable that we cannot give a general enunciation of this principle which by its revealing power has changed the face of physics. This is because it is less a law, properly so called, than a method or manner of interpreting the relations of the different forms of energy, and particularly the relations of heat and mechanical energy. _Conversion of Work into Heat and Vice-versâ._—The conversion of work into heat is accomplished without difficulty. For example, the hammering of a piece of iron on an anvil may bring it to a red heat. A shell which passes through an armour plate is heated, and melts and volatilizes the metal all round the hole it has made. By utilizing mechanical action under the form of friction all energy can be converted into heat. The inverse transformation of heat into work, on the contrary, cannot be complete. The best motor that we can think of, and _à fortiori_ the best we can realize, can only transform a third or a fourth of the heat with which it is supplied.