Besides the myth busted in this paper, that the actually later work of Rayleigh could have influenced Planck, there is another incorrect myth, that Planck has introduced the "constant of Planck" in his publication from 1900, where he presented the deduction of the Planck formula from the supposition that the emission and absorption of electromagnetic radiation are quantized.

This frequently seen claim is also wrong. Planck has introduced the constant of Planck and he has also computed its value with excellent precision for that time (4% relative error) in an earlier work published in 1899:

Max Planck, "Ueber irreversible Strahlungsvorgaenge", "Sitzungsberichte der koeniglich preussischen Akademie der Wissenschaften zu Berlin. Jahrgang 1899", pp. 440-480.

There Max Planck has presented deductions of the formulae previously established by Wien for the blackbody radiation, where he replaced the empirical constants of Wien with functions of other universal constants and of the new universal constant introduced by him.

Already Maxwell, a quarter of century earlier, had shown that it is possible to determine the units for all physical quantities with a single arbitrary choice (in his example, the wavelength of the yellow light emitted by sodium vapor).

In 1899, Planck has shown that the law of blackbody radiation provides an additional relationship between the units of length, time and energy, which, together with the previous relationships considered by Maxwell, can determine the units of all physical quantities without any arbitrary choice.

So at the end of this work from 1899, where the constant of Planck has been introduced, he has also presented the system of natural units known now as the Planck units.

Nevertheless, the system of Planck units cannot be used as the base of a practical system of units, because the uncertainty of measuring the Newtonian constant of gravitation is huge. This makes useless one of the equations that connect the units of length, time and energy.

Because of that, any practical system of units must contain a single arbitrary choice of a unit, which in the case of SI is the frequency of a certain hyperfine transition of the cesium-133 atom, while all the other units result from this choice by adopting conventional values for the universal constants, except for the Newtonian constant of gravitation, which must be measured experimentally (some constant determining the intensity of the electromagnetic interaction, e.g. the fine structure constant, must also be measured experimentally, but for that the uncertainty is extremely low).

BTW, another extremely frequent incorrect claim about the constant of Planck is that it is a quantum of action. This is very wrong, it is a quantum of angular momentum (the ratio between energy and frequency is an angular momentum, like also the ratio between their integrals, i.e. between action and plane angle). The origin of the mistake is the fact that many follow the suggestions of the recent SI brochures (there was a resolution adopted by vote that the unit of plane angle is not a base unit, which is equivalent with establishing by vote that 2 + 2 = 5), and they omit the unit of plane angle in the dimensional formulae, in which case it appears that the unit of action is the same with the unit of angular momentum, but they are not the same, as any attempt to change the unit used for plane angles would demonstrate, e.g. between radians and degrees or cycles.

The original constant of Planck corresponds to plane angles measured in cycles, while the so-called h bar is the same constant converted to correspond with plane angles measured in radians.