92\%$ of population-$a$ are enhanced in nitrogen, while only $\sim 8\%$ are N-poor.

We find that all the aforementioned stellar populations exhibit average proper motions consistent with each other within 1$\sigma$.

Kinematics of stellar populations with different metallicities {#sec:fe subpop}
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Spatial distribution of Multiple Populations {#subsec:spatial}
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In the following, we extend to the sample of Fe-poor and Fe-rich stars of $\omega\,$Centauri and M22 the procedure based on the two-dimensional Binned Kernel Density Estimate [@wand2015] used by @cordoni2019 to analyse the spatial distributions of stellar populations in seven Type I GCs.

Due to crowding, stellar proper motions from GAIA DR2 are not available for most of the stars in the central regions of $\omega\,$Centauri. To increase the number of studied stars of $\omega\,$Centauri cluster members, we included in the analysis those stars that have membership probabilities larger than $90\,\%$ according to @bellini2009.

Results for $\omega\,$Centauri are illustrated in the upper panels of Figure \[fig:spatial\] where we show the density plots of the Fe-poor (left) and Fe-rich (right) stars by using orange and blue colors, respectively. The contours are determined by smoothing the data-points with a Gaussian kernel of fixed size. The size is chosen with the criterion of minimizing 