PRINCIPLES OF MATHEMATICAL PHYSICS 621 



account for any derogation whatever to the principle of Mayer; it 

 responds in advance not only to the objection of Curie, but to all 

 the objections that future experimenters might accumulate. This 

 new and unknown energy would serve for everything. This is just 

 what I have said, and we are thereby shown that our principle is 

 unassailable by experiment. 



And after all, what have we gained by this coup de pouce ? 



The principle is intact, but thenceforth of what use is it? 



It permitted us to foresee that in such or such circumstance we 

 could count on such a total quantity of energy; it limited us; but 

 now where there is put at our disposition this indefinite provision of 

 new energy, we are limited by nothing; and as I have written else- 

 where, if a principle ceases to be fecund, experiment, without con- 

 tradicting it directly, will be likely to condemn it. 



This, therefore, is not what would have to be done, it would be 

 necessary to rebuild anew. 



If we were cornered down to this necessity, we should moreover 

 console ourselves. It would not be necessary to conclude that science 

 can weave only a Penelope's web, that it can build only ephemeral 

 constructions, which it is soon forced to demolish from top to bot- 

 tom with its own hands. 



As I have said, we have already passed through a like crisis. I 

 have shown you that in the second mathematical physics, that of 

 the principles, we find traces of the first, that of the central forces; 

 it will be just the same if we must learn a third. 



When an animal exuviates, and breaks its too narrow carapace to 

 make itself a fresh one, we easily recognize under the new envelope 

 the essential traits of the organism which have existed. 



We cannot foresee in what way we are about to expand; perhaps 

 it is the kinetic theory of gases which is about to undergo develop- 

 ment and serve as model to the others. Then, the facts which first 

 appeared to us as simple, thereafter will be merely results of a very 

 great number of elementary facts which only the laws of chance 

 make cooperate for a common end. Physical law will then take an 

 entirely new aspect; it will no longer be solely a differential equation, 

 it will take the character of a statistical law. 



Perhaps, likewise, we should construct a whole new mechanics, 

 of which we only succeed in catching a glimpse, where inertia increas- 

 ing with the velocity, the velocity of light would become an impass- 

 able limit. 



The ordinary mechanics, more simple, would remain a first approx- 

 imation, since it would be true for velocities not too great, so that we 

 should still find the old dynamics under the new. 



We should not have to regret having believed in the principles, 

 and even, since velocities too great for the old formulas would always 



