## 4 The Results
Looking at the results of the test statistics (Tables 13 and 14), we can see that for any group except the 11 Virgo cluster, the distribution of the angle \(\eta\) cannot be seen to significantly deviate from the values of the statistics predicted for random distributions. For the \(\delta_{D}\) angle distributions, the largest deviation from the random distribution is observed for the 15 and 31 groups, but the effect is statistically marginal. As a result, we could conclude that when we analyzed the spatial orientation of galaxies inside 18 Tully groups of galaxies belonging to the Local Supercluster, taking into account their morphological type and FP correction, we do not find any significant alignment. This result indicates that the orientation of galaxies in the studied Tully groups is random. The observational effect generated by the process of deprojection of galaxies from their optical images (Kenyon, 1972) makes it much harder to find real alignment during analysis of the spatial orientation of galaxies in clusters, but can be analyzed in more detail. For each \(\delta_{D}\) angle for each cluster, we computed the \(\Delta_{11}\) parameter, describing the galactic axes' alignment with respect to a chosen cluster pole, divided by its formal error \(\sigma(\Delta_{11})\). It is called the \(s\) parameter, \(s\equiv\Delta_{11}/\sigma(\Delta_{11}))\)(Kenyon, 1972). The idea is to change the position of the coordinate system's pole along the entire celestial sphere. Thus, the main plane of the system also changes its position. For each such instantaneous coordinate system, we now compute the parameter \(s\). The positive value of this coefficient means predominance of the normal perpendicular to the main plane, i.e., directed to the pole of the instantaneous coordinate system. The resulting maps can be also analyzed in terms of their correlations of their maxima with the important points on the maps. In the Figure 11, we present analysis for Cluster 12 (Ursa Major Cloud). We choose this cluster because his position is far from the center of the Local Supercluster (i.e., Virgo Cluster), and thus avoids the possible influence of global alignment within the Local Supercluster In the left panel of this figure (i.e., for original inclination angles from NBG Catalogue), we observe strong maxima that correlate well with the direction of the line of sight. In this figure, we also mark other important points, such as the three possible poles of the cluster. There are three possible poles because [PERSON]'s catalog gives the affiliation (or not) of each galaxy in the catalog to galaxy groups, as well as spherical coordinates and independent distances for each galaxy. This means that we can obtain a three-dimensional spatial distribution of galaxies belonging to each studied group in terms of their Cartesian coordinates. Assuming a Gaussian distribution of positions in the cluster, we can thus fit the ellipsoid of covariance, and, thus, the directions of the three axes of the ellipsoid in space, which is a more general solution than adopting a simplified model, in which galaxy clusters are ellipsoids of rotation. The positions of these axes of the ellipsoid uniquely determine the positions of the three possible poles of the cluster. However, the observed maxima are not correlated with them. It is easy, on the right panel (i.e., for the situation when we take into account their morphological types when calculating inclination angles and apply Fouque and Paturel corrections), to see that these maxima disappear. This confirms our opinion that the originally observed effect was not the result of a real alignment, but an effect related to not taking into account the real flattening of galaxies depending on their morphological types and the Fouque and Paturel correction. We would like to point out that the discussed method makes it possible to find even a weak alignment of galaxies in clusters. The example of cluster 15 illustrates this.