Page:Über die Energievertheilung im Emissionspectrum eines schwarzen Körpers.pdf/4

such that the homogeneous radiation under consideration is emitted preferentially by one constituent of the gaseous mixture.

The number of molecules having velocity between $v$ and $v+dv$ is proportional to the quantity

$v^{2}e^{-{\frac {v^{2}}{\alpha ^{2}}}}dv$

,

where $\alpha$ is a constant that can be deduced from the average velocity ${\bar {v}}$ through the equation

${\bar {v}}^{2}={\frac {3}{2}}\alpha ^{2}$

The absolute temperature is therefore proportional to $\alpha ^{2}$.

Now for radiation emitted by a molecule, of velocity $v$, it is completely unknown how the radiation depends on the state of the molecule. The view that the electric charges in the molecules can excite electromagnetic waves is nowadays generally accepted.

We hypothesize that each molecule emits radiation with a wavelength that depends only on the velocity and has intensity that a function of that velocity.

This conclusion can be reached by various special assumptions about the process of radiation, but since such assumptions are completely arbitrary for the time being, it seems to me safest at first to make the necessary hypothesis as simple and general as possible.

Since the wavelength $\lambda$ of the radiation emitted by a molecule is a function of $v$, $v$ should also be a function of $\lambda$

The intensity of radiation whose wavelength is between $\lambda$ and $\lambda +d\lambda$ is proportional to

1. The number of molecules that emit radiation in this range.

2. A function of the velocity $v$, and therefore also a function of $\lambda$.

That means,

$\varphi _{\lambda }=F(\lambda )e^{-{\frac {f(\lambda )}{\theta }}}$