5866 | Sa | .48 | 11.76 | 11.51 7331 | Sb | +0.95 | 11.82 | 10.93 Means | | +0.509 | 11.60 | 11.90 -------+------------+---------+----------------+--------------- The low value for Sa-SBa is due to N.G.C. 5866, for which the magnitude difference of 0.06 is certainly in error, and the high value for Sc and SBc, to M 51, for which the difference of 3.98 mag. is not representative. The latter is accounted for in part by the fact that the m_{T} refers to the combined magnitude of the main spiral and the outlying mass, N.G.C. 5195. When these two cases are discarded, the final mean becomes 1.52 ± 0.05, and the average residual, 0.52 mag., is consistent with the probable errors of the magnitude determinations. The small numbers of objects within each class are insufficient for reliable conclusions concerning slight variations along the sequence. From the constancy of m_{n} – m_{T}, the relation expressed by formula (6) necessarily follows, the small difference in the constant being accounted for by the different methods of handling the data. [Illustration: Fig. 9.—Relation between nuclear magnitudes and diameters. The nebulae have been reduced to the standard type by applying corrections to the magnitudes.] The parallelism of the two curves representing formulae (2) and (6) indicates that the regular extra-galactic nebulae, when reduced to the standard type, are similar objects. The mean surface brightness is constant, and the luminosity of the nucleus, as measured by Hopmann, is a constant fraction, about one-fourth, of the total luminosity of the nebulae. If there is a considerable range in absolute magnitude and hence in actual dimensions, the smaller nebulae must be faithful miniatures of the larger ones. ABSOLUTE MAGNITUDES OF EXTRA-GALACTIC NEBULAE Reliable values of distances, and hence of absolute magnitudes, are restricted to a very few of the brightest nebulae. These are derived from a study of individual stars involved in the nebulae, among which certain types have been identified whose absolute magnitudes in the galactic system are well known. The method assumes that the stars involved in the nebulae are directly comparable with the stars in our own system, and this is supported by the consistency of the results derived from the several different types which have been identified.