The radiation of multipoles formed by putting together elementary dipoles is investigated according to the classical theory and wave mechanics. It turns out that the radiations are of two kinds:

The first part has the same frequency as the dipoles and is present only if the multipole structure is present even without vibration.

The second part is always present. If $n$, the order of the multipole, is even then the frequencies are $2\nu$, $4\nu$, up to $n\nu$. If $n$ is odd then the frequencies are $\nu$, $3\nu$, up to $n\nu$.

The relative intensities of subsequent multipoles are proportional to the square of the ratio: dipole amplitude to wave-length, as has been found in other cases. This calculation would apply to the infrared radiation of molecules.

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