1 8 abstracts: physics 



for the corresponding range of conditions, which covers those most 

 usual in calorimetry. The results, however, are sufficient to serve as a 

 practical guide in calorimeter designing. For the dimensions tested, 

 the transmission of heat by convection in horizontal layers was a little 

 over twice that in vertical. W. P. W. 



PHYSICS. — The necessary physical assumptions underlying a proof of 

 the Planck radiation law. F. RussELL v. Bichowsky. Phys. 

 Rev. 11: 58-65. January, 19 18. 



In order to prove Planck's radiation law by means of the quantum 

 theory, only two physical assumptions need be made: first, that energy 

 is absorbed or radiated by a radiating system in quanta of hv; second, 

 that a radiating system has the statistical properties of a perfect gas, 

 i. e., that Maxwell's distribution law holds for the distribution of the 

 local values of the energy among the coordinates defining the state of 

 the radiating system. (The usual auxiliary assumptions, such as 

 Planck's oscillators or Larmor's regions of equal probability, are not 

 only unnecessary but misleading.) 



Although these two assumptions are sufficient for deriving the Planck 

 radiation law, both of them, and particularly the latter, are very dubious, 

 it being almost unthinkable that a radiating system can have the statis- 

 tical properties of a perfect gas and yet not have the equipartition law 

 hold. For these and other reasons it seems necessary to give up at 

 least the second of the quantum hypotheses and to assume that the 

 distribution of energy in a radiating system does not obey Maxwell's 

 law — ^that is, to assume that in a radiating system the distribution 

 of the local values of the coordinates is a function not only of the energy 

 of the system but also of some other variables. If we do this and as- 

 sume, for definiteness, that the distribution of the local values of the 

 generalized momenta is a function not only of the total energy E of 

 the system but also of the Helmholtz free energy A, and further assume 

 that the total energy of a radiating system cannot be less than a cer- 

 tain limiting value Eq {E^ turns out to equal hv), we can, following 

 the methods of Gibbs and Ratnowsky, derive in a very simple manner 

 the Planck radiation law, and moreover we can do this without assum- 

 ing discreteness of radiant energy, without contradicting classical 

 mechanics (equipartition does not hold for systems of this kind), with- 

 out discarding infinitesimal analysis or without contradicting thermo- 

 dynamics or the direct experimental evidence of the photoelectric 

 effect that the hv law holds only as a limiting case. 



