,)S APPLIED MATHEMATICS 



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

 and reaction; and the law of least action, which would appear, it 

 is true, not as experimental verities, but as theorems, and of which 

 the enunciation would have at the same time a something more pre- 

 cise and less general than under their actual form. 



It is the mathematical physics of our fathers which has familiar- 

 ized us little by little with these divers principles; which has taught 

 us to recognize them under the different vestments in which they 

 disguise themselves. One has to compare them to the data of ex- 

 perience, to find how it was necessary to modify their enunciation 

 so as to adapt them to these data; and by these processes they 

 have been enlarged and consolidated. 



So we have been led to regard them as experimental verities; 

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

 rather an embarrassment, since it made the principles partake of its 

 hypothetical character. 



The frames have not therefore broken, because they were elastic; 

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

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

 traits of the sketch which they traced. 



Are we about to enter now upon the eve of a second crisis? Are 

 these principles on which we have built all about to crumble away 

 in their turn? For some time, this may well have been asked. 



In hearing me speak thus, you think without doubt of radium, 

 that grand revolutionist of the present time, and in fact I will come 

 back to it presently; but there is something else. 



It is not alone the conservation of energy which is in question; 

 all the other principles are equally in danger, as we shall see in pass- 

 ing them successively in review. 



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 

 directly to 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 attraction depended only on the distance. 

 it seems that all these phenomena 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 describe in the retrograde sense this 

 same elliptic orbit which it describes in the direct sense, if the initial 

 conditions of its movement had been reversed. On this account, if 

 a physical phenomenon is possible, the inverse phenomenon should 

 be equally so, and one should be able to reascend the course of 

 time. 



