64.

The numerical value of the constant $a$ is obtained from measurements made by F. Kurlbaum.F. Kurlbaum, Wied. Annalen, 65, p. 759, 1898. According to them, if

we denote by $S_t$ the total energy radiated in one second into air by a square centimeter of a black body at a temperature of $t°\mathrm{C}.$, the following equation holds $S_{100} - S_{0} = 0.0731\, \frac{\text{watt}}{\text{cm}^{2}} = 7.31 × 10^{5}\, \frac{\text{erg}}{\text{cm}^{2}\, \text{sec}}.

\Label[eqn]{(79)}\tag*{\upshape (79)}$ Now, since the radiation in air is approximately identical with the radiation into a vacuum, we may according to [eqn:(7)] (7) and [eqn:(76)] (76) put $S_t=\pi K=\frac{ac}{4}(273+t{)}^4$ and from this $S_{100}-S_0=\frac{ac}{4}({373}^4-{273}^4),$ therefore $a=\frac{4\times 7.31\times {10}^5}{3\times {10}^{10}\times ({373}^4-{273}^4)}=7.061\times {10}^{-15}\frac{\text{erg}}{{\text{cm}}^3{\text{degree}}^4}.$

Recently Kurlbaum has increased the value measured by him by $2.5$ per cent.,F. Kurlbaum, Verhandlungen d. Deutsch. physikal. Gesellschaft, 14, p. 580, 1912. on account of the bolometer used being not perfectly black, whence it follows that $a=7.24·{10}^{-15}$.

Meanwhile the radiation constant has been made the object of as accurate measurements as possible in various places. Thus it was measured by Féry, Bauer and Moulin, Valentiner, Féry and Drecq, Shakespear, Gerlach, with in some cases very divergent results, so that a mean value may hardly be formed.

For later computations we shall use the most recent determination made in the physical laboratory of the University of BerlinAccording to private information kindly furnished by my colleague H. Rubens (July, 64 1912). (These results have since been published. See W. H. Westphal, Verhandlungen d. Deutsch. physikal. Gesellschaft, 14, p. 987, 1912, Tr.) $\frac{ac}{4}=\sigma =5.46·{10}^{-12}\frac{\text{watt}}{{\text{cm}}^2{\text{degree}}^4}.$ From this $a$ is found to be $a=\frac{4·5.46·{10}^{-12}·{10}^7}{3·{10}^{10}}=7.28·{10}^{-15}\frac{\text{erg}}{{\text{cm}}^3{\text{degree}}^4}$ which agrees rather closely with Kurlbaum's corrected value.