TABLE XII
Differential Values of C
| Class | Pure Classes | Observed | Random Orientation | |
|---|---|---|---|---|
| No. as Observed | Equal No. | |||
| C7–C7 | 0.00 | 0.00 | 0.00 | 0.00 |
| C6 | 0.63 | 0.35* | 0.25 | 0.35 |
| C5 | 1.10 | 0.70* | 0.58 | 0.70 |
| C4 | 1.51 | 0.85 | 1.11 | 1.01 |
| C3 | 1.84 | 1.42 | 0.87 | 1.28 |
| C2 | 2.13 | 1.67 | 1.33 | 1.55 |
| C1 | 2.39 | 2.01† | 1.54 | 1.83 |
| C0 | 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 C7 The latter is observed to be 12.75, hence
| (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.
From the dynamical point of view, the empirical results are consistent with the general order of events in Jeans’s theory. Thus interpreted, the series is one of expansion, and the scale of types becomes the time scale in the evolutionary history of nebulae. In two respects this scale is not entirely arbitrary. Among the elliptical nebulae the successive types differ by equal increments in the ellipticity or the degree of flattening, and among the spirals the intermediate stage is midway between the two end-stages in the structural features as well as in the luminosity relations.
One other feature of the curves may be discussed from the point of view of Jeans’s theory before returning to the strictly empirical attitude. The close agreement of the diameters for the stages E7 and Sa suggests that the transition from the lenticular nebula to the normal spiral form is not cataclysmic. If the transition were gradual, however, we should expect to observe occasional objects in the very process, but among the thousand or so nebulae whose images have been inspected, not one clear case of a transition form has been detected. The observations jump suddenly from lenticular nebulae with no trace of structure to spirals in which the arms are fully developed.
If the numerical data could be fully trusted, the SBa forms would fill the gap. Among these nebulae, the transition from the lenticular to the spiral with arms is gradual and complete. It is tempting to suppose that the barred spirals do not form an independent series parallel with that of the normal spirals, but that all or most spirals begin life with the bar, although only a few maintain it conspicuously throughout their history. This would also account for the fact that the relative numbers of the SBa nebulae are intermediate to those of the lenticular and of the Sa. The normal spirals become more numerous as the sequence progresses, while the numbers of barred spirals, on the contrary, actually decrease with advancing type.