A Historical View of Kirchhoff's Black Body Universal Distribution Function $\left( K_{\lambda }\right) $

Stefan (1879) established experimentally that Kirchhoff's total emitted intensity $K=\int_{0}^{\infty }K_{\lambda }d\lambda =\sigma T^{4}$. Boltzmann (1884) derived this result from classical thermodynamic principles. V A Michelson (1887) first defined $K_{\lambda }=c_{1}\lambda ^{-6}T^{\frac{3}{2}}e^{-\left ( \frac{c_{2}}{\lambda ^{2}T}\right) }$. Weber suggested $K_ {\lambda }=c_{1}\lambda ^{-2}e^{\left[ c_{3}T-\left( \frac{c_ {2}}{\lambda ^{2}T^{2}}\right) \right] }$. Experimentally, Wien's displacement law required $\lambda _{m}T=b$. Paschen (1896) thus proposed $K_{\lambda }=c_{1}\lambda ^{-\gamma }e^{- \left( \frac{c_{2}}{\lambda T}\right) }$ with $5<\gamma <6$. Compatibility with Stefan-Boltzmann's Law led to the value $\gamma =5$ in Wien's solution. Planck's solution $\left( K_ {\lambda }=c_{1}\lambda ^{-\gamma }\left( e^{\left( \frac{c_{2}} {\lambda T}\right) }-1\right) ^{-1}\right) $ set $\gamma <5$. Rayleigh-Jeans' attempt $\left( K_{\lambda }=c_{1}\lambda ^{-4} Te^{-\left( \frac{c_{2}}{\lambda T}\right) }\right) $ is also noteworthy. From Michelson's first attempt, $\lambda T$ was placed in the denominator of the exponential part of the function. This did not change until Gall's derivation of the function $\left( K_{\lambda }=\sigma \frac{T^{6}}{b^{2}}\lambda e^{-\left( \frac{\lambda T}{b}\right) }\right) $ (http://meetings.aps.org/link/BAPS.2007.MAR.X21.4), based on emission as a decay process (sites.google.com/site/purefieldphysics), placed $\lambda T$ in the numerator. If temperature is defined as reciprocal wavelength then $T^{6}\lambda \equiv \lambda ^{-5}$. It is mathematically evident that the new location of $\lambda T$ is what finally allowed for the exact solution of Kirchhoff's Function with the original empirical constants $\left( \sigma ,b\right) $!