TABLE XII Differential Values of C ============+===============+===========+====================== | | | Random Orientation | | +-----------+---------- Class | Pure Classes | Observed | No. as | | | | Observed | Equal No. ------------+---------------+------------+-----------+---------- C_{7}–C_{7} | 0.00 | 0.00 | 0.00 | 0.00 C_{6} | 0.63 | 0.35* | 0.25 | 0.35 C_{5} | 1.10 | 0.70* | 0.58 | 0.70 C_{4} | 1.51 | 0.85 | 1.11 | 1.01 C_{3} | 1.84 | 1.42 | 0.87 | 1.28 C_{2} | 2.13 | 1.67 | 1.33 | 1.55 C_{1} | 2.39 | 2.01† | 1.54 | 1.83 C_{0} | 2.62 | 2.17† | 2.15 | 2.25 ------------+---------------+------------+-----------+---------- * Read from smooth curve in Fig. 6. The small numbers of observed E5 and E6 nebulae justify this procedure. The other values are the means actually observed. † N.G.C. 524 and 3998 are included as E0 and E1, respectively. Meanwhile, it is evident that, to a first approximation at least, the polar diameters alone determine the total luminosities of all elliptical nebulae, and the entire series can be represented by the various configurations of an originally globular mass expanding equatorially. A single formula represents the relation, in which the value of C is that corresponding to the pure type E0. From Table XII, this is found to be 2.62 mag. less than the value of C_{7} The latter is observed to be 12.75, hence $m_{T} + 5 log b = 10.13.$ (5) If this relation held for the spirals as well, the polar diameters could be calculated from the measured magnitudes. Unfortunately, it has not been possible to measure accurately the polar diameters directly, and hence to test the question, but they have been computed for the mean magnitudes of the Sa, Sb, and Sc nebulae as given in Table III, and the ratios of the axes have been derived by a comparison of these hypothetical values with the means of the measured maximum diameters. The results, 1 to 4.4, 1 to 5.7, and 1 to 7.3, respectively, although of the right order, appear to be somewhat too high. An examination of the photographs indicates values of the order of 1 to 5.5, 1 to 8, and 1 to 10, but the material is meager and may not be representative. The comparison emphasizes, however, the homogeneity and the progressive nature of the entire sequence of nebulae and lends some additional color to the assumption that it represents various aspects of the same fundamental type of system.