FORCE 693 



laws from which it was deduced, in the same way that Newton's law 

 has survived the laws of Kepler from which it was derived, and 

 which are no longer anything but approximations, if we take pertur- 

 bations into account. Now why does this principle thus occupy a kind 

 of privileged position among physical laws? There are many reasons 

 for that. At the outset we think that we cannot reject it, or even 

 doubt, its absolute rigor, without admitting the possibility of perpetual 

 motion; we certainly feel distrust at such a prospect, and we believe 

 ourselves less rash in affirming it than in denying it. That perhaps 

 is not quite accurate. The impossibility of perpetual motion only 

 implies the conservation of energy for reversible phenomena. The 

 imposing simplicity of Mayer's principle equally contributes to 

 strengthen our faith. In a law immediately deduced from experi- 

 ments, such as Mariotte's law, this simplicity would rather appear to 

 us a reason for distrust ; but here this is no longer the case. We take 

 elements which at the first glance are unconnected; these arrange 

 themselves in an unexpected order, and form a harmonious whole. 

 We cannot believe that this unexpected harmony is a mere result of 

 chance. Our conquest appears to be valuable to us in proportion to the 

 efforts it has cost, and we feel the more certain of having snatched its 

 true secret from Nature in proportion as Nature has appeared more 

 jealous of our attempts to discover it. But these are only small rea- 

 sons. Before we raise Mayer's law to the dignity of an absolute prin- 

 ciple, a deeper discussion is necessary. But if we embark on this dis- 

 cussion we see that this absolute principle is not even easy to enunciate. 

 In every particular case we clearly see what energy is, and we can give 

 it at least a provisory definition ; but it is impossible to find a general 

 definition of it. If we wish to enunciate the principle in all its gen- 

 eiality and apply it to the universe, we see it vanish, so to speak, and 

 nothing is left but this there is something which remains constant. 

 But has this a meaning? In the determinist hypothesis the state of 

 the universe is determined by an extremely large number n of par- 

 ameters, which I shall call a*j, a' 2 , x 3 . . . xn. As soon as we know 

 at a given moment the values of these n parameters, we also know 

 their derivatives with respect to time, and we can therefore calculate 

 the rallies of these same parameters at an anterior or ulterior moment. 

 Tn other words, these n parameters specify n differential equations of 

 the first order. These equations have n 1 integrals, and therefore 

 there are n 1 functions of .r,, .r 2 , # :i , . . . xn, which remain con- 

 stant. If we say then, there is something which remains constant, we 

 are only enunciating a tautology. We would be even embarrassed to 

 decide which among all our integrals is that which should retain the 

 name of energy. Besides, it is not in this sense that Mayer's principle 

 is understood when it is applied to a limited system. We admit, then, 

 that p of our n parameters vary independently so that we have only 



