Page:Über die Energievertheilung im Emissionspectrum eines schwarzen Körpers.pdf/2

 1. Maxwell's law of the distribution of velocities for a large number of molecules is also valid for solid bodies.

2. The period of oscillation $$\tau$$ of a molecule, when excited, depends on the velocity of the molecule, by the equation:

$ \tau = \frac{4\varrho}{v} $

where $$\varrho$$ is a constant. (This assumption results from a certain idea about the modes excitation of the radiation.)

3. The intensity of the radiation emitted by a molecule is proportional to the number of molecules having the same period of oscillation. It is an indefinite function of temperature, and also an unknown function of kinetic energy, which, by a further assumption, is then restricted to a power of $$v^2$$.

The law which Michelson obtains from these assumptions for a given wavelength $$\lambda_m$$ at maximum energy is: $ \lambda_m = \frac{\mathrm{const}}{\sqrt\theta} $
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Where $$\theta$$ denotes the absolute temperature. This law, however, leaves the total emission as a function of temperature undetermined.

I have now endeavored to utilize Michelson's fortunate idea of using Maxwell's law of the distribution of velocities as the basis of the law of radiation, but reduce the number of hypotheses which have been put forward, because our complete ignorance of the cause of the radiation makes these particularly uncertain, by using the results obtained by Boltzmann and myself in a purely thermodynamic way.

The remaining hypotheses still leave some uncertainty in their theoretical justification, but offer the advantage that their results can be compared directly with experiment, for a wide range of values.