Time to get back to the Planck. To re-start the discussion, here's a relevant statement by another famous German physicist:
Boltzmann’s principle interprets entropy in terms of the probability of states and expresses it in the terse formula
S = k log W.So it stands carved out on Boltzmann’s memorial in the Central Cemetery in Vienna, floating in the clouds over his majestic bust.It is immaterial that Boltzmann himself never wrote down the equation in this form. This was first done by Planck … . The constant, k, was also introduced by Planck and not by Boltzmann. Boltzmann only referred to the proportionality between S and the logarithm of the probability of a state. The designation ‘Boltzmann’s principle’ was advocated by Einstein for …W = exp(S/k)in which S was considered to be known empirically, the quantity W being the unknown for which an expression was sought.
--Arnold Sommerfeld,
Thermodaynamics and Statistical Mechanics, English translation, Academic Press
© 1956, fifth printing 1967, page 213. (But, you'd need to know k to calculate W... . Never mind!)
And below, a couple of relevant drawings from the time of Planck's discovery.
Taken from the book Statistical Physics by Bernard Lavenda, here's a figure showing the actual experimental results Planck used when was trying to fit his theory to the data, and eventually of course succeeded:
And here's the device, not exactly box-like but more cylinder-like (see bottom part of drawing), used to experimentally produce the radiation whose energy spectrum is plotted above. You know how you have to swing a hand-held spectrometer back and forth to view the spectrum of a visible light source, or at least you've seen how a prism disperses visible light. This black-body cylindrical cavity is on wheels so the stationary spectrum analyzer equipment can get measurements from the full spectrum, which in this case is in the infrared region. From a September 2016 American Journal of Physics article about Planck.
