620 APPLIED MATHEMATICS 



even find anything analogous to the roots of those transcendental 

 equations to which so many problems of mathematical physics con- 

 duct us: that of the vibrations of an elastic body of any form, that 

 of the Hertzian oscillations in a generator of any form, the problem 

 of Fourier for the cooling of a solid body. 



The laws are simpler, but they are of wholly other nature, and to 

 cite only one of these differences, for the harmonics of high order 

 the number of vibrations tends toward a finite limit, instead of 

 increasing indefinitely. 



That has not yet been accounted for, and I believe that there we 

 have one of the most important secrets of nature. Lindemann has 

 made a praiseworthy attempt, but, to my mind, without success; 

 this attempt should be renewed. Thus we shall penetrate, so to say, 

 into the inmost recess of matter. And from the particular point of 

 view which we to-day occupy, when we know why the vibrations 

 of incandescent bodies differ from ordinary elastic vibrations, why 

 the electrons do not behave themselves like the matter which is familiar 

 to us, we shall better comprehend the dynamics of electrons and 

 it will be perhaps more easy for us to reconcile it with the princi- 

 ples. 



Suppose, now, that all these efforts fail, and after all I do not 

 believe they will, what must be done? Will it be necessary to seek 

 to mend the broken principles in giving what we French call a coup 

 de pouce f That is evidently always possible, and I retract nothing 

 I have formerly said. 



Have you not written, you might say if you wished to seek a 

 quarrel with me, have you not written that the principles, though of 

 experimental origin, are now unassailable by experiment because 

 they have become conventions? And now you have just told us the 

 most recent conquests of experiment put these principles in danger. 

 Well, formerly I was right and to-day I am not wrong. 



Formerly I was right, and what is now happening is a new proof 

 of it. Take, for example, the calorimeter experiment of Curie on 

 radium. Is it possible to reconcile that with the principle of the 

 conservation of energy? 



It has been attempted in many ways; but there is among them 

 one I should like you to notice. 



It has been conjectured that radium was only an intermediary, 

 that it only stored radiations of unknown nature which flashed 

 through space in every direction, traversing all bodies, save radium, 

 without being altered by this passage and without exercising any 

 action upon them. Radium alone took from them a little of their 

 energy and afterward gave it out to us in divers forms. 



What an advantageous explanation, and how convenient! First, 

 it is unverifiable and thus irrefutable. Then again it will serve to 



