342 POPULAR SCIENCE MONTHLY 



energy and that of masses, and the equality of action and reaction, and 

 the law of least action, which appeared, it is true, not as experimental 

 truths, but as theorems; the enunciation of which had at the same 

 time something more precise and less general than under their pres- 

 ent form. 



It is the mathematical physics of our fathers which has familiarized 

 us little by little with these various principles; which has habituated 

 us to recognize them under the different vestments in which they dis- 

 guise themselves. They have been compared with the data of experi- 

 ence, it has been seen how it was necessary to modify their enunciation 

 to adapt them to these data ; thereby they have been extended and con- 

 solidated. Thus they came to be regarded as experimental truths; the 

 conception of central forces became then a useless support, or rather 

 an embarrassment, since it made the principles partake of its hypo- 

 thetical character. 



The frames then have not broken, because they are elastic; but 

 they have enlarged; our fathers, who established them, did not labor 

 in vain, and we recognize in the science of to-day the general traits of 

 the sketch which they traced. 



Chapter VIII. The Present Crisis of Mathematical Physics 

 The New Crisis. — Are we now about to enter upon a third period? 

 Are we on the eve of a second crisis ? These principles on which we have 

 built all, are they about to crumble away in their turn? This has 

 been for some time a pertinent question. 



"When I speak thus, you no doubt think of radium, that grand 

 revolutionist of the present time, and in fact I shall come back to 

 it presently ; but there is something else. It is not alone the conserva- 

 tion of energy which is in question; all the other principles are 

 equally in danger, as we shall see in passing them successively in 

 review. 



Camot's Principle. — Let us commence with the principle of Carnot. 

 This is the only one which does not present itself as an immediate 

 consequence of the hypothesis of central forces; more than that, it 

 seems, if not to directly contradict that hypothesis, at least not to 

 be reconciled with it without a certain effort. If physical phenomena 

 were due exclusively to the movements of atoms whose mutual at- 

 traction depended only on the distance, it seems that all these phe- 

 nomena should be reversible; if all the initial velocities were reversed, 

 these atoms, always subjected to the same forces, ought to go over 

 their trajectories in the contrary sense, just as the earth would de- 

 scribe in the retrograde sense this same elliptic orbit which it de- 

 scribes in the direct sense, if the initial conditions of its motion had 

 been reversed. On this account, if a physical phenomenon is possible, 



