THE ETHER AND MATTER POINCARE. 203 



currents. A magneton is then a wlihl of electrons antl so our atom 

 gains and gains in complexity. 



Wo now come to something still better because it permits us to 

 estimate the complexity of the atom, the theory which Debierne 

 announced near the end of this series of meetings. It relates to an 

 explanation of the law governing radioactive transformations. The 

 law is very simple. It is exponential. Its very form suggests at 

 once the principles of statistics. We recognize the earmarks of 

 chance. This chance does not here relate to the fortuitous encounters 

 of atoms and other exterior bodies. Its causes lie withui the interior 

 of the atom itself. I wish to be understood to refer not only to the 

 cause relating to this chance but to something yet deeper. Other- 

 wise we would find external conditions, the temperature, for mstance, 

 having an effect upon the coefficient of the exponent. Now that 

 coefficient is remarkably constant, indeed Curie proposed to use it 

 as a measure of absolute time. 



The chance which rules the transformations which we are consider- 

 ing lies whoUy within the atom. That is, the atom of a radioactive 

 bodyis a universe withui itseh* and a world subject to chance. But if 

 we consider a little further, when we talk of probabilities we think of 

 gi'eat numbers of tilings. A closed world made up of a few elements 

 would obey laws more or less complicated but they would not be 

 those we consider when we deal with statistics. Then it must foUov/ 

 that an atom is a very complex world. It is true that a closed world, 

 at least one nearly closed, would be at the mercy of any exterior 

 perturbations to which we might subject it. Since the atom is sub- 

 ject to tliis statistical law there is consequently an internal thermo- 

 dynamics of the atom and we can talk of the internal temperature of 

 it. But, mark, this temperature has no tendency to get into equilib- 

 rium with the temperatin-e without; it is as if the atom were shut up 

 witliin a perfectly adiathermic shell. It is precisely because it is 

 thus closed, because its functions are so shai'ply limited and guarded 

 by this impervious shell that the atom is so individual. 



At fu'st, this complexity of the atom docs not seem oil'ensive; it 

 seems as if we would not be embarrassed by it. But a little reflection 

 brings dillicultics not apparent at first. When we counted the atoms 

 we really did not count their numbers dii-ectly but then* degrees of 

 freedom of movement, and wo implicitly assumed that each atom 

 had three degi-ees of such freedom. This also accounted for the 

 observed specific heats. But each new complexity must introduce a 

 new degree of freedom and we become troubled in our count of the 

 atoms. This difliculty did not escape the attention of the originators 

 of the theory of the equipartition of energy. They were astonished 

 at the number of the lines in tlie spectra, but, seehig no way of escape 

 from theij- diliiculties, they bohlly passed them by. 



