(translation into Russian) M.Planck, Izbrannye Trudy, Nauka, M. (1975) 249.
(translation into English) The Old Quantum Theory, ed. by D. ter Haar, Pergamon Press (1967) 79.
The interesting result of long wave length spectral energy measurements which were communicated by Mr. Kurlbaum at today's meeting, and which were obtained by him and Mr. Rubens, confirm the statement by Mr. Lummer and Mr. Pringsheim, which was based on their observations that Wien's energy distribution law is not as generally valid, as many supposed up to now, but that this law at most has the character of a limiting case, the simple form of which was due only to a restriction to short wave
lengths and low temperatures... ... Following this suggestion I have finally started to construct completely arbitrary expressions for the entropy which although they are more complicated than Wien's expression still seem to satisfy just as completely all requirements of the thermodynamic and electromagnetic theory. I was especially attracted by one of the expressions thus constructed which is nearly as simple as Wien's expression and which deserves to be investigated since Wien's expression
is not sufficient to cover all observations. We get thisexpression by putting fracd2SdU2 = fracU( + U). It is by far simplest of all expressions which lead to S as a logarithmic function of U-which is suggested from probability considerations - and which moreover reduces to Wien's expression for small values of U. Using the relation fracdSdU = frac1T and Wien's "displacement'' law (the expression
of Wien's displacement law is simply S = f(U/), where is the frequency of the resonator, as I shall show elsewhere) one gets a radiation formula with two constants: E = fracC-5expc/ T - 1, which, as far as I can see at the moment, fits the observational data, published up to now, as satisfactory as the best equations put forward
for the spectrum, namely those of Thiesen, Lummer-Jahnke, and Lummer-Pringsheim. (This was demonstrated by some numerical examples.) I should therefore be permitted to draw your attention to this new formula which I consider to be the simplest possible, apart from Wien's expression, from the point of view of the electromagnetic theory of radiation.
Related references See also M. Planck Am. Physik. 1 (1900) 730;
M. Thiesen, Verhandl. Dtsch. phys. Ges. 2 (1900) 67;
M. Planck, Annalen der Physik. Leipzig 1 (1900) 719;
Analyse data from O. Lummer and E. Jahnke, Annalen der Physik. Leipzig 3 (1900) 288;
O. Lummer and E. Pringsheim, Verhandl. Dtsch. phys. Ges. 2 (1900) 174;
Discovery of a new formula for the energy spectrum of the black body radiation, Planck's radiation law.