\Delta \alpha \ln \left(\frac{\nu_2}{\nu_1}\right)$$

The residual signal power caused by the spectral index variation $\sigma^2_{\rm VAR}= \Delta \alpha^2 (\ln\nu_2 /\nu_1)^2
\sigma^2_{\rm MAP2} $. For the frequencies 31.5 and 53 GHz the residual RMS is smaller than $0.52 \Delta \alpha \sigma_{\rm MAP2}$. It can be seen that the less is Galactic radiation contribution, the less is the residual RMS on the more high frequency radio map.

It is evident the most Galactic radiation is concentrated near the Galaxy plane and near its center. If the spatial spectrum is represented in Galactic coordinate system the most power may be found in the components with $m=0$ for the even multipoles (Galaxy plane) and with $m=1$ for the odd multipoles (Galaxy center). So if we exclude this components the influence of the spectral index variation may be reduced drastically. At the same time this procedure does not break the multipoles orthogonality.

Table \[tab\_gal\] shows some results obtained after the spectrum analysis from $l_{min} =2$ to $l_{max}=25$.

In addition one may find at the last row the difference between 53 GHz map and the 31 GHz map scaled with a spectral index $\alpha
= -2.15$ after spatial filtering. Data are represented in antenna temperatures. One 