PRINCIPLES OF MATHEMATICAL PHYSICS 617 



wear itself out in 1250 years; you see that we are at least certain 

 to be settled on this point some hundreds of years from now. While 

 waiting our doubts remain. 



In the midst of so many ruins what remains standing? The prin- 

 ciple of least action has hitherto remained intact, and Larmor appears 

 to believe that it will long survive the others; in reality, it is still 

 more vague and more general. 



In presence of this general ruin of the principles, what attitude 

 will mathematical physics take? 



And first, before too much perplexity, it is proper to ask if all this 

 is really true. All these apparent contradictions to the principles are 

 encountered only among infinitesimals; the microscope is necessary 

 to see the Brownian movement; electrons are very light; radium is 

 very rare, and no one has ever seen more than some milligrams of 

 it at a time. 



And, then, it may be asked if, beside the infinitesimal seen, there 

 be not another infinitesimal unseen counterpoise to the first. 



So, there is an interlocutory question, and, as it seems, only 

 experiment can solve it. We have, therefore, only to hand over the 

 matter to the experimenters, and, while waiting for them to deter- 

 mine the question finally, not to preoccupy ourselves with these dis- 

 quieting problems, but quietly continue our work, as if the princi- 

 ples were still uncontested. We have much to do without leaving 

 the domain where they may be applied in all security; we have 

 enough to employ our activity during this period of doubts. 



And as to these doubts, is it indeed true that we can do nothing 

 to disembarrass science of them? It may be said, it is not alone 

 experimental physics that has given birth to them; mathematical 

 physics has well contributed. It is the experimenters who have seen 

 radium throw out energy, but it is the theorists who have put in 

 evidence all the difficulties raised by the propagation of light across 

 a medium in motion; but for these it is probable we should not have 

 become conscious of them. Well, then, if they have done their best 

 to put us into this embarrassment, it is proper also that they help us 

 to get out of it. 



They must subject to critical examination all these new views 

 I have just outlined before you, and abandon the principles only 

 after having made a loyal effort to save them. 



What can they do in this sense? That is what I will try to ex- 

 plain. 



Among the most interesting problems of mathematical physics, 

 it is proper to give a special place to those relating to the kinetic 

 theory of gases. Much has already been done in this direction, but 

 much still remains to be done. This theory is an eternal paradox. 

 We have reversibility in the premises and irreversibility in the con- 



