232 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1913. 



searches, the most general equation of an electromagnetic system, 

 based upon the ether, electrons, and matter, by a suitable choice of 

 parameters can be reduced to the Hamiltonian form of the equations 

 of mechanics. The aj)plication of the methods of probability and 

 statistical mechanics, especially the theorem of Liouville (which is 

 a consequence of the Hamiltonian form), leads us, then, to consider 

 as applicable to the ether the theorem of the equipartition of energy 

 which also brings us out with Rayleigh's formula. 



In order to escape from this blind alley and obtain the earlier 

 formula, Planck invented the hypothesis of the discontinuity of en- 

 ergy or quanta.^ According to this hypothesis, the molecular resona- 

 tors can not exchange energy with the surrounding medium except 

 in whole multiples of the same elementary quantity (quantum), %? 

 an amount proportional to the frequency of the resonator. The con- 

 stant h would be a universal constant. We will not explain here the 

 various forms given to the theory by Planck himself, Sommerfeld, 

 Einstein, H. Poincare, and others (see articles cited, note 4, p. 231). 

 We will pass over all the consequences which have been deduced from 

 this hypothesis (theory of specific heats by Einstein, etc.), except 

 those which are purely electromagnetic.^ 



It appears that we need not give up for the free ether the equations 

 and ordinary laws of electromagnetics or the dynamics of the free 

 electron. The modification of the electromagnetic theory which we 

 must make, if necessary, relates only to the relations between matter 

 and the ether; that is to say, with regard to electrons not free, to 

 emissions and absorption of energy, or perhaps to emission alone, 

 which must then be considered as discontinuous. 



Brillouin" thinks that there is a loophole of escape: Planck's 

 theory rests upon an arbitrary hypothesis with regard to strictly 

 monochromatic resonators having xqyj little physical basis. In 

 giving these up, the complication of the reasoning rapidly increases, 

 but Brillouin thinks that we can probably come out with Planck's 

 formula without recourse to quanta. The result would, however, 

 be inconsistent with the general theory of Lorentz previously men- 

 tioned. Possibly we may hope to reach more precise knowledge of 

 the mechanism of absorption about which we know practically noth- 

 ing, and thence get a loophole for escape. This doubtless will hap- 

 pen in the future. 



There is another domain than that of radiation, wherein the elec- 

 tronic and quanta theories are clearly inconsistent, that of the prop- 

 erties of the metals. According to the electronic theory, the thermal 

 and electrical conductivities of the metals, as well as many other of 



^ See the recent article by J. Perrin In the Revue for Nov. 15, 1912. 

 2 These consequences have been resumed in a notable course of lectures given thig year 

 at the Collf^so de France by Langevin. 



« Brillouin, Comptes Rendus, vol. 150, pp. 124, 301, 1913. 



