ii6 PHYSICS 



energy respectively), the mean energy of a resonator must be i.346Xio~ 16 XT erg, 

 where T is the absolute temperature. Now, according to Maxwell's equations, the 

 mean energy of a resonator exposed to a radiation of frequency v and intensity S r is 



C 

 ?T"^X S y , where C is a constant. By combining these two results, we get S,, = C'Tj> 2 . 



This result is obviously contradicted by experience, since it crowds the radiant energy 

 into the shorter wave-lengths and makes the total radiation integrated over the whole 

 spectrum infinite. 



The only solution of this difficulty seems to be that proposed by Planck, who as- 

 sumes that molecular oscillators are incapable of continuous radiation, but accumulate 

 energy up to a certain amount proportional to their frequency, and then throw off the 

 whole of that amount at once. The " quantum" thus thrown off : is hv ergs, where v 

 is the frequency in revolutions or complete vibrations per second, and h is the universal 

 " action constant," amounting to 6.5sXio' 27 erg-seconds. 



This is a grave departure from the postulate of the equi-partition of energy which 

 has hitherto governed the dynamical theory of heat. The resonators of highest fre- 

 quency obtain the greatest share of the incident energy. They absorb it without 

 loss by radiation until the time has come to emit the whole of 'it. Radiation is as 

 " chaotic " as are the molecular motions in a gas. The " temperature " of radiation is 

 that of the emitting body, and its entropy is derived from the logarithm of the proba- 

 bility of its state just as it is in the case of a gas. 



A difficulty arises as regards the aether, to which the energy of radiation is com- 

 municated by means of its pressure. The aether, with its infinite freedom, cannot be 

 in equilibrium with an oscillator having only two degrees of freedom. Einstein 1 sought 

 to overcome this difficulty by supposing that light itself is propagated in discrete " cells " 

 or quanta, which have a fixed and definite volume, and simply increase their mutual 

 distances as they proceed outward into space. This, as Lehmann suggests, may 

 account partly for the twinkling of stars, and even for their visibility at enormous dis- 

 tances. A discrete structure of light has also been suggested by Sir J. J. Thomson, on 

 the basis of some photoelectric experiments, and by Sir J. Larmor in his Bakerian 

 lecture (1909). 



c 2 h i 



" Natural " Units. Planck's radiation formula is S\= y C /,/I,\T _ > where 



SA is the energy in ergs per cm 2 of radiating black surface at the absolute temperature 

 T C, the radiation being of wave-length Xcm; c is the velocity of light in cm/sec, h 

 is the " action constant," and k is the atomic gas constant expressed in ergs per degree, 

 its value being i.346Xio" 16 . If h, k, c and the constant of gravitation (G = 0.66X10^) 

 are each made unity, we obtain " natural " units for length, mass, time, and temperature 

 which may be held ,in reserve for future use in case the C.G.S. system is ever to 'be 

 superseded. 



Atomic Heats. Planck's law, which for large wave-lengths resolves itself into Lord 

 Rayleigh's, while for short wave-lengths it gives Wien's law, has been found to cover 

 the whole range of infra-red spectroscopy, and E. Baisch (1911) has confirmed it down 

 to 330 nn. The Stefan-Boltzmann law of total radiation and Wien's displacement 

 law are simple deductions from it. It is therefore likely to become an important datum 

 of physics. Whether the more speculative parts of Planck's theory arc adopted or not, 

 it is certain that its general method is fruitful. It has already led to some important 

 results, and has become a valuable guide in physical and chemical investigations. 



Thus, according to the older kinetic theory, the mean energy of an atom per degree 

 of freedom must be Xi.346Xio~ 16 erg per degree. In a solid body, whose atoms 

 possess 6 degrees of freedom (3 kinetic and 3 potential), each atom must have six times 

 that amount of mean energy. In one gram atom, or 0.64+ io 24 atoms, the energy is, 

 therefore, 5.955 calories per degree. This figure, embodied in the law of Dulong and 

 Petit, only applies to fairly high temperatures, and even at these it fails in carbon, 



1 Physikalische Zeilschrift, io, p. 185, 1909. 



