  In this article we present and study a scaling law of the $m\Gamma_m$ CMB
Fourier spectrum on rings which allows us (i) to combine spectra corresponding
to different colatitude angles (e.g. several detectors at the focal plane of a
telescope), and (ii) to recover the $C_l$ power spectrum once the $\Gamma_m$
coefficients have been measured. This recovery is performed numerically below
the 1% level for colatitudes $\Theta> 80^\circ$ degrees. In addition, taking
advantage of the smoothness of the $C_l$ and of the $\Gamma_m$, we provide
analytical expressions which allow to recover one of the spectrum at the 1%
level, the other one being known.
