694 SCIENCE AND HYPOTHESIS 



n p relations, generally linear, between our n parameters and their 

 derivatives. Suppose, for the sake of simplicity, that the sum of the 

 work done by the external forces is zero, as well as that of all the 

 quantities of heat given off from the interior: what will then be the 

 meaning of our principle ? There is a combination of these n p rela- 

 tions, of which the first member is an exact differential; and then this 

 differential vanishing in virtue of our n p relations, its integral is a 

 constant, and it is this integral which we call energy. But how can it 

 be that there are several parameters whose variations are independent ? 

 That can only take place in the case of external forces (although we 

 have supposed, for the sake of simplicity, that the algebraical sum 

 of all the work done by these forces has vanished). If, in fact, the 

 system were completely isolated from all external action, the values of 

 our n parameters at a given moment would suffice to determine the 

 state of the system at any ulterior moment whatever, provided that we 

 still clung to the determinist hypothesis. We should therefore fall 

 back on the same difficulty as before. If the future state of the system 

 is not entirely determined by its present state, it is because it further 

 depends on the state of bodies external to the system. But then, is it 

 likely that there exist among the parameters x which define the state 

 of the system of equations independent of this state of the external 

 bodies? and if in certain cases we think we can find them, is it not 

 only because of our ignorance, and because the influence of these 

 bodies is too weak for our experiment to be able to detect it? If the 

 system is not regarded as completely isolated, it is probable that the 

 rigorously exact expression of its internal energy will depend upon 

 the state of the external bodies. Again, I have supposed above that 

 the sum of all the external work is zero, and if we wish to be free 

 from this rather artificial restriction the enunciation becomes still 

 more difficult. To formulate Mayer's principle by giving it an abso- 

 lute meaning, we must extend it to the whole universe, and then we 

 find ourselves face to face with the very difficulty we have endeavored 

 to avoid. To sum up, and to use ordinary language, the law of the 

 conservation of energy can have only one significance, because there is 

 in it a property common to all possible properties; but in the deter- 

 minist hypothesis there is only one possible, and then the law has no 

 meaning. In the indeterminist hypothesis, on the other hand, it 

 would have a meaning even if we wished to regard it in an absolute 

 sense. It would appear as a limitation imposed on freedom. 



But this word warns me that I am wandering from the subject, and 

 that I am leaving the domain of mathematics and physics. I check 

 myself, therefore, and I wish to retain only one impression of the 

 whole of this discussion, and that is, tnat Mayer's law is a form subtle 

 enough for us to be able to put into it almost anything we like. I do 

 not mean by that that it corresponds to no objective reality, nor that it 



