FOECE 695 



is reduced to mere tautology; since, in each particular case, and pro- 

 vided we do not wish to extend it to the absolute, it has a perfectly 

 clear meaning. This subtlety is a reason for believing that it will last 

 long; and as, on the other hand, it will only disappear to be blended 

 in a higher harmony, we may work with confidence and utilize it, 

 certain beforehand that our work will not be lost. 



Almost everything that I have just said applies to the principle of 

 Clausius. What distinguishes it is, that it is expressed by an in- 

 equality. It will be said perhaps that it is the same with all physical 

 laws, since their precision is always limited by errors of observation. 

 But they at least claim to be first approximations, and we hope to 

 replace them little by little by more exact laws. If, on the other hand, 

 the principle of Clausius reduces to an inequality, this is not caused 

 by the imperfection of our means of observation, but by the very nature 

 of the question. 



General Conclusions on Part III. The principles of mechanics are 

 therefore presented to us under two different aspects. On the one 

 hand, there are truths founded on experiment, and verified approxi- 

 mately as far as almost isolated systems are concerned; on the other 

 hand, there are postulates applicable to the whole of the universe and 

 regarded as rigorously true. If these postulates possess a generality 

 and a certainty which falsify the experimental truths from which they 

 were deduced, it is because they reduce in final analysis to a simple 

 convention that we have a right to make, because we are certain before- 

 hand that no experiment can contradict it. This convention, however, 

 is not absolutely arbitrary; it is not the child of our caprice. We 

 admit it because certain experiments have shown us that it will be 

 convenient, and thus is explained how experiment has built up the 

 principles of mechanics, and why, moreover, it cannot reverse them. 

 Take a comparison with geometry. The fundamental propositions of 

 geometry, for instance, Euclid's postulate, are only conventions, and it 

 is quite as unreasonable to ask if they are true or false as to ask if the 

 metric system is true or false. Only, these conventions are convenient, 

 and there are certain experiments which prove it to us. At the first 

 glance, the analogy is complete, the role of experiment seems the same. 

 We shall therefore be tempted to say, either mechanics must be looked 

 upon as experimental science and then it should be the same with 

 geometry; or, on the contrary, geometry is a deductive science, and 

 then we can say the same of mechanics. Such a conclusion would 

 be illegitimate. The experiments which have led us to adopt as more 

 convenient the fundamental conventions of geometry refer to bodies 

 which have nothing in common with those that are studied by geo- 

 metry. They refer to the properties of solid bodies and to the propa- 

 gation of light in a straight line. These are mechanical, optical expe- 

 riments. In no way can they be regarded' as geometrical experiments. 



