Even reduced to the most modest proportions, the principle of the conservation of energy retains, nevertheless, a paramount importance; and it still preserves, if you will, a high philosophical value. M.J. Perrin justly points out that it gives us a form under which we are experimentally able to grasp causality, and that it teaches us that a result has to be purchased at the cost of a determined effort. We can, in fact, with M. Perrin and M. Langevin, represent this in a way which puts this characteristic in evidence by enunciating it as follows: "If at the cost of a change C we can obtain a change K, there will never be acquired at the same cost, whatever the mechanism employed, first the change K and in addition some other change, unless this latter be one that is otherwise known to cost nothing to produce or to destroy." If, for instance, the fall of a weight can be accompanied, without anything else being produced, by another transformation--the melting of a certain mass of ice, for example--it will be impossible, no matter how you set about it or whatever the mechanism used, to associate this same transformation with the melting of another weight of ice. We can thus, in the transformation in question, obtain an appropriate number which will sum up that which may be expected from the external effect, and can give, so to speak, the price at which this transformation is bought, measure its invariable value by a common measure (for instance, the melting of the ice), and, without any ambiguity, define the energy lost during the transformation as proportional to the mass of ice which can be associated with it. This measure is, moreover, independent of the particular phenomenon taken as the common measure. § 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS The principle of Carnot, of a nature analogous to the principle of the conservation of energy, has also a similar origin. It was first enunciated, like the last named, although prior to it in time, in consequence of considerations which deal only with heat and mechanical work. Like it, too, it has evolved, grown, and invaded the entire domain of physics. It may be interesting to examine rapidly the various phases of this evolution. The origin of the principle of Carnot is clearly determined, and it is very rare to be able to go back thus certainly to the source of a discovery. Sadi Carnot had, truth to say, no precursor. In his time heat engines were not yet very common, and no one had reflected much on their theory. He was doubtless the first to propound to himself certain questions, and certainly the first to solve them.