TABLE X ========+=========================================== Actual | Apparent +---------+--------+--------+--------+------ | E0 | E1 | E2 | E3 | E4 --------+---------+--------+--------+--------+------ E7 | 0.055 | 0.111 | 0.114 | 0.116 | 0.121 E6 | .059 | .123 | .126 | .133 | .148 E5 | .067 | .140 | .148 | .166 | .216 E4 | .079 | .169 | .190 | .250 | 0.312 E3 | .100 | .225 | .299 | 0.376 | E2 | .145 | .378 | 0.477 | | E1 | 0.300 | 0.700 | | | E0 | 1.000 | | | | +---------+--------+--------+--------+------ Total | 1.805 | 1.846 | 1.354 | 1.041 | 0.797 | 0.226 | 0.231 | 0.169 | 0.130 | 0.100 --------+---------+--------+--------+--------+------ ========+===================================== Actual | Apparent --------+---------+--------+--------+--------- | E5 | E6 | E7 | Total --------+---------+--------+--------+--------- E7 | 0.132 | 0.164 | 0.187 | 1.000 E6 | .187 | 0.224 | | E5 | 0.263 | | | +---------+--------+--------+--------- Total | 0.582 | 0.388 | 0.187 | 8.000 | 0.073 | 0.049 | 0.023 | 1.000 --------+---------+--------+--------+--------- From this table and the actual numbers in the observed classes as read from a smoothed curve, the numbers of each actual ellipticity mingled in the observed classes can be determined. For instance, the four nebulae observed as E7 represent 0.187 of the total number of actual E7. The others are distributed among the observed classes E0 to E6 according to the percentages listed in Table X. Six nebulae are observed as E6, but 3.6 of these are actually E7. The remaining 2.4 actual E6 nebulae represent 0.224 of the total number of that actual ellipticity, the others, as before, being scattered among the observed classes E0 to E5. Table XI gives the complete analysis and is similar to Table X except that the percentages in the latter are replaced by the actual numbers indicated by the observations. Finally, the mean values of C_{7} – C_{e} are calculated from the numbers of nebulae in the various columns of Table XI together with the values of C_{7} – C_{e} for the pure classes as derived from formula (4). The results are listed in the fourth column of Table XII following those for the pure and the observed classes. In determining the observed values, N.G.C. 524 and 3998 are included as E0 and E1, although in Table I they are listed as peculiar, because they are obviously much flattened nebulae whose minor axes are close to the line of sight.