The references to the literature are not claimed to be in any way complete, and are intended to serve only for a preliminary orientation.
[1] G. Kirchhoff, Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. _Gesammelte Abhandlungen._ Leipzig, J. A. Barth, 1882, p. 597 (§ 17).
[2] H. Hertz, _Ann. d. Phys._ 36, p. 1, 1889.
[3] _Sitz.-Ber. d. Preuss. Akad. d. Wiss._ Febr. 20, 1896. _Ann. d. Phys._ 60, p. 577, 1897.
[4] _Sitz.-Ber. d. Preuss. Akad. d. Wiss._ May 18, 1899, p. 455.
[5] L. Boltzmann, _Sitz.-Ber. d. Preuss. Akad. d. Wiss._ March 3, 1898, p. 182.
[6] W. Wien, _Ann. d. Phys._ 58, p. 662, 1896.
[7] According to Wien’s law of the distribution of energy the dependence of the energy _U_ of the resonator upon the temperature is given by a relation of the form:
[Illustration: upper U equals a dot e Superscript negative b divided by t.]
Since
[Illustration: StartFraction 1 Over upper T EndFraction equals StartFraction d upper S Over d upper U EndFraction,]
where _S_ is the entropy of the resonator, we have for _R_ as used in the text:
[Illustration: upper R equals 1 colon StartFraction d squared upper S Over d upper U squared EndFraction equals minus b upper U.]
[8] According to Wien’s displacement law, the energy _U_ of the resonator with the natural vibration period ν is expressed by:
[Illustration: upper U equals nu dot f left parenthesis StartFraction upper T Over nu EndFraction right parenthesis.]
[9] _Ann. d. Phys._ 1, p. 719, 1900.
[10] O. Lummer und E. Pringsheim, _Verhandl. der Deutschen Physikal. Ges._, 2, p. 163, 1900.
[11] H. Rubens and F. Kurlbaum, _Sitz.-Ber. der Preuss. Akad. d. Wiss._ Oct. 25, 1900, p. 929
[12] It follows from the experiments of H. Rubens and F. Kurlbaum that, for high temperatures, _U_ = _cT_. Then, in accordance with the method quoted in [7]:
[Illustration: upper R equals 1 colon StartFraction d squared upper S Over d upper U squared EndFraction equals minus StartFraction upper U squared Over c EndFraction.]
[13] Put
[Illustration: upper R equals 1 colon StartFraction d squared upper S Over d upper U squared EndFraction equals minus b upper U minus StartFraction upper U squared Over c EndFraction,]
then by integration,
[Illustration StartFraction 1 Over upper T EndFraction equals StartFraction d upper S Over d upper U EndFraction equals StartFraction 1 Over b EndFraction log left brace 1 plus StartFraction b c Over upper U EndFraction right brace]
whence the radiation formula,
[Illustration: upper U equals b c colon left parenthesis e Superscript negative b divided by upper T Baseline minus 1 right parenthesis.]
Cf. _Verhandlungen der Deutschen Phys. Ges._ Oct. 19, 1900, p. 202.
[14] Cf. W. Nernst und Th. Wulf, _Verh. d. Deutsch. Phys. Ges._ 21, p. 294, 1919.
[15] For the absolute value of the energy is equal to the product of the inert mass and the square of light velocity.
[16] _Verhandlungen der Deutschen Phys. Ges._ Dec. 14, 1900, p. 237.
[17] Generally, if _k_ be the first radiation constant, the mean kinetic energy of a gas molecule is:
[Illustration: upper U equals three halves k upper T]
If we put, therefore, _T_ = _U_, then _k_ = ⅔. In the conventional [absolute Kelvinian] temperature scale, however, _T_ is defined by putting the temperature difference between boiling and freezing water equal to 100.
[18] Cf. for example L. Boltzmann, Zur Erinnerung an Josef Loschmidt, _Populäre Schriften_, p. 245, 1905.
[19] E. Rutherford and H. Geiger, _Proc. Roy. Soc._ A. Vol. 81, p. 162, 1908.
[20] Cf. R. A. Millikan, _Phys. Zeitschr._ 14, p. 796, 1913.
[21] The evaluation of the probability of a physical state is based upon counting that finite number of equally probable special cases by which the corresponding state is realized; and in order sharply to distinguish these cases from one another, a definite concept of each special case has necessarily to be introduced.
[22] A. Einstein, _Ann. d. Phys._ 17, p. 132, 1905.
[23] A. Einstein, _Ann. d. Phys._ 22, p. 180, 1907.
[24] M. Born und Th. v. Karman, _Phys. Zeitschr._ 14, p. 15, 1913.
[25] P. Debye, _Ann. d. Phys._ 39, p. 789, 1912.
[26] W. Nernst, _Phys. Zeitschr._ 13, p. 1064, 1912
[27] A. Eucken, _Sitz.-Ber. d. Preuss. Akad. d. Wiss._ p. 141, 1912.
[28] O. Sackur, _Ann. d. Phys._ 36, p. 958, 1911.
[29] H. Tetrode, _Proc. Acad. Sci. Amsterdam_, Febr. 27 and March 27, 1915.
[30] J. Franck und G. Hertz, _Verh. d. Deutsch. Phys. Ges._ 16, p. 512, 1914.
[31] Ph. Lenard, _Ann. d. Phys._ 8, p. 149, 1902.
[32] E. Ladenburg, _Verh. d. Deutschen Phys. Ges._ 9, p. 504, 1907.
[33] R. A. Millikan, _Phys. Zeitschr._ 17, p. 217, 1916.
[34] E. Warburg, Über den Energieumsatz bei photochemischen Vorgängen in Gasen. _Sitz.-Ber. d. Preuss. Akad. d. Wiss._ from 1911 onwards.
[35] N. Bohr, _Phil. Mag._ 30, p. 394, 1915.
[36] A. Sommerfeld, _Ann. d. Phys._ 51, pp. 1, 125, 1916.
[37] F. Paschen, _Ann. d. Phys._ 50, p. 901, 1916.
[38] P. Epstein, _Ann. d. Phys._ 50, p. 489, 1916.
[39] P. Debye, _Phys. Zeitschr._ 18, p. 276, 1917.
[40] E. Wagner, _Ann. d. Phys._ 57, p. 467, 1918.
[41] P. Ehrenfest, _Ann. d. Phys._ 51, p. 327, 1916.
