THE VALUE OF SCIENCE 44 1 



quantity of energy; it limited us; but now that this indefinite provi- 

 sion of new energy is placed at our disposal, we are no longer limited 

 by anything; and, as I have written in 'Science and Hypothesis,' if 

 a principle ceases to be fecund, experiment without contradicting it 

 directly will nevertheless have condemned it. 



Future Mathematical Physics. This, therefore, is not what would 

 have to he done; it would be necessary to rebuild anew. If we were 

 reduced to this necessity, we could moreover console ourselves. It 

 would not be necessary thence to conclude that science can weave only 

 a Penelope's web, that it can raise only ephemeral structures, which it 

 is soon forced to demolish from top to bottom 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 central forces; it will be 

 just the same if we must know a third. Just so with the animal that 

 exuviates, that breaks its too narrow carapace and makes itself a fresh 

 one, under the new envelope one will recognize the essential traits of 

 the organism which have persisted. 



We can not 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 would be merely resultants of a 

 very great number of elementary facts which only the laws of chance 

 would make cooperate for a common end. Physical law would then 

 assume an entirely new aspect; it would no longer be solely a differ- 

 ential equation, it would take the character of a statistical law. 



Perhaps, too, we shall have to construct an entirely new mechanics 

 that we only succeed in catching a glimpse of, where, inertia increasing 

 with the velocity, the velocity of light would become an impassable 

 limit. The ordinary mechanics, more simple, would remain a first 

 approximation, since it would be true for velocities not too great, so 

 that the old dynamics would still be found 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 be only excep- 

 tional, the surest way in practise would be still to act as if we continued 

 to believe in them. They are so useful, it would be necessary to keep 

 a place for them. To determine to exclude them altogether would be to 

 deprive oneself of a precious weapon. I hasten to say in conclusion 

 that we are not yet there, and as yet nothing proves that the principles 

 will not come forth from out the fray victorious and intact. 1 



1 These considerations on mathematical physics are borrowed from my 

 St. Louis address. 



