156.

If we finally introduce the temperature $T$ from [eqn:(223)] (223), we get from the last equation, by taking account of the value [eqn:(268)] (268) of the factor of proportionality $p$, $𝖨=\frac{32{\pi }^{2}h{\nu }^3}{3c^3}\frac{1}{e^{\frac{h\nu }{kT}}-1}.\mathrm{\backslash Label}[eqn](273)\text{upshape (273)}$ Moreover the specific intensity $𝖪$ of a monochromatic plane polarized ray of frequency $\nu$ is, according to equation [eqn:(160)] (160), $𝖪=\frac{h{\nu }^3}{c^2}\frac{1}{e^{\frac{h\nu }{kT}}-1}\mathrm{\backslash Label}[eqn](274)\text{upshape (274)}$ and the space density of energy of uniform monochromatic unpolarized radiation of frequency $\nu$ is, from [eqn:(159)] (159), $𝗎=\frac{8\pi h{\nu }^3}{c^3}\frac{1}{e^{\frac{h\nu }{kT}}-1}.\mathrm{\backslash Label}[eqn](275)\text{upshape (275)}$ Since, among all the forms of radiation of differing constitutions, black radiation is distinguished by the fact that all monochromatic rays contained in it have the same temperature ([sect:93.] Sec. 93) these equations also give the law of distribution of energy in the normal spectrum, i.e., in the emission spectrum of a body which is black with respect to the vacuum.

If we refer the specific intensity of a monochromatic ray not to the frequency $\nu$ but, as is usually done in experimental physics, to the wave length $\lambda$, by making use of [eqn:(15)] (15) and [eqn:(16)] (16) we obtain the expression $E_{\lambda }=\frac{c^{2}h}{{\lambda }^5}\frac{1}{e^{\frac{ch}{k\lambda T}}-1}=\frac{c_1}{{\lambda }^5}\frac{1}{e^{\frac{c_2}{\lambda T}}-1}.\mathrm{\backslash Label}[eqn](276)\text{upshape (276)}$ This is the specific intensity of a monochromatic plane polarized ray of the wave length $\lambda$ which is emitted from a black body at the temperature $T$ into a vacuum in a direction perpendicular to the

surface. The corresponding space density of unpolarized radiation is obtained by multiplying $E_{\lambda }$ by ${\displaystyle \frac{8\pi }{c}}$.

Experimental tests have so far confirmed equation [eqn:(276)] (276).See among others H. Rubens und F. Kurlbaum, Sitz. Ber. d. Akad. d. Wiss. zu Berlin vom 25. Okt., 1900, p. 929. Ann. d. Phys. 4, p. 649, 1901. F. Paschen, Ann. d. Phys. 4, p. 277, 1901. O. Lummer und E. Pringsheim, Ann. d. Phys. 6, p. 210, 1901. Tätigkeitsbericht der Phys.-Techn. Reichsanstalt vom J. 1911, Zeitschr. f. Instrumentenkunde, 1912, April, p. 134 ff. According to the most recent measurements made in the Physikalisch-technische ReichsanstaltAccording to private information kindly furnished by the president, Mr. Warburg. the value of the second radiation constant $c_2$ is approximately $c_{2} = \frac{ch}{k} = 1.436\, \text{cm}\, \text{degree}.

\Label[eqn]{(277)}\tag*{\upshape (277)}$

More detailed information regarding the history of the equation of radiation is to be found in the original papers and in the first edition of this book. At this point it may merely be added that equation [eqn:(276)] (276) was not simply extrapolated from radiation measurements, but was originally found in a search after a connection between the entropy and the energy of an oscillator vibrating in a field, a connection which would be as simple as possible and consistent with known measurements.