Edwin Hubble

“ By applying corrections to C, the nebulae can be reduced to a standard type and then a single formula expresses the relation for all nebulae from the Magellanic Clouds to the faintest that can be classified. When the minor diameter is used, the value of C is approximately constant throughout the entire sequence. The coefficient of log d corresponds with the inverse-square law, which suggests that the nebulae are all of the same order of absolute luminosity and that apparent magnitudes are measures of distance. ”

“ 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. ”

“ Very few can be classified from the Franklin-Adams plates; for this purpose photographs on a much larger scale are required. Until further data on the individual objects are available, Hardcastle’s list can be used only for the study of distribution over the sky. This shows the well-known features—the greater density in the northern galactic hemisphere, the concentration in Virgo, and the restriction of the very large nebulae to the southern galactic hemisphere.
Fortunately, numerical data do exist in the form of total visual magnitudes for many of the nebulae in the northern sky. ”

“ The results are given in Table X, where the actual ellipticities, listed in the first column, are followed across the table by the percentages which, on the assumption of random orientation, will be observed as having the various apparent ellipticities. The bottom row will be seen to show the percentages of apparent ellipticities observed in an assembly of nebulae in which the numbers for each actual ellipticity are equal and all are oriented at random. ”

“ The numbers of the barred spirals are too limited to inspire confidence in the results, but among the normal spirals there is conclusive evidence that the highly tilted and edge-on nebulae are fainter for a given diameter than those seen in the round. A study of the individual images indicates that the effect is due very largely to dark absorption clouds, which become more conspicuous when the nebulae are highly tilted. ”

“ The characteristic feature of extra-galactic nebulae is rotational symmetry about dominating non-stellar nuclei. About 97 per cent of these nebulae are regular in the sense that they show this feature conspicuously. The regular nebulae fall into a progressive sequence ranging from globular masses of unresolved nebulosity to widely open spirals whose arms are swarming with stars. The sequence comprises two sections, elliptical nebulae and spirals, which merge into each other. ”

“ If an outer belt of absorption is assumed, which, combined with the known inner clouds, obscures extra-galactic nebulae to a mean distance of 15° from the galactic plane, the value derived for the density of space must be increased by nearly 40 per cent. ”

“ The numbers of nebulae to different limiting magnitudes can be used to test the constancy of the density function, or, on the hypothesis{44} of uniform luminosities, to determine the distribution in space. The nebulae brighter than about the tenth magnitude are known individually. ”

“ The form most nearly related to the elliptical nebulae has a large nuclear region similar to E7, around which are closely coiled arms of unresolved nebulosity. Then follow objects in which the arms appear to build up at the expense of the nuclear regions and unwind as they grow; in the end, the arms are wide open and the nuclei inconspicuous. ”

“ About 3 per cent of the extra-galactic nebulae lack both dominating nuclei and rotational symmetry. These form a distinct class which can be termed “irregular.” The Magellanic Clouds are the most conspicuous examples, and, indeed, are the nearest of all the extra-galactic nebulae. ”

“ Fig. 4.—Relation between luminosity and diameter among nebulae at the end of the sequence of types—Sc and SBc nebulae.
The correlation of the data is very closely represented by the formula
This falls between the two regression curves derived from least-square solutions and could be obtained exactly by assigning appropriate weights to the two methods of grouping. The nature of the data is such that a closer agreement can scarcely be expected. ”

“ For each instrument, however, there is a limiting size and luminosity below which it is impossible to classify with any confidence. Except in rare instances, these small nebulae are extra-galactic, and their numbers, brightness, dimensions, and distribution are amenable to statistical investigation. For cataloguing purposes, they require a designating symbol, and the letter “Q” is suggested as convenient and not too widely used with other significations.
PLATE XIV
Direct photograph with 100-inch reflector March 18, 1925. ”

“ Normal spirals.—All regular nebulae with ellipticities greater than about E7 are spirals, and no spirals are known with ellipticities less than this limit. At this point in the sequence, however, ellipticity becomes insensitive as a criterion and is replaced by conspicuous structural features which now become available for classification. Of these, practically speaking, there are three which fix the position of an object in the sequence of forms: (1) relative size of the unresolved nuclear region; (2) extent to which the arms are unwound; (3) degree of resolution in the arms. ”

“ This indicates an approximately uniform density of space, of the order of one nebula per 1017 cubic parsecs or 1.5×10–31 in C.G.S. units. The corresponding radius of curvature of the finite universe of general relativity is of the order of 2.7×1010 parsecs, or about 600 times the distance at which normal nebulae can be detected with the 100-inch reflector. ”

“ The data for the Magellanic Clouds are taken from Shapley’s investigations. The absolute magnitudes of the remaining nebulae were derived from Holetschek’s apparent magnitudes and the distances as determined at Mount Wilson, where the stellar magnitudes were also determined. M 32 is generally assumed to be associated with the great spiral M 31, because the radial velocities are nearly equal and are unique in that{37} they are the only large negative velocities that have been found among the extra-galactic nebulae. M 101 has been added to the list on rather weak evidence. ”

“ The change from ellipsoidal to lenticular figures, noticeable in the later-type nebulae, would affect the results in the proper direction, as would also a progressive shortening of the polar axis. The discrepancies, however, are second-order effects, and since they may be due to accidental variations from random orientation, a further discussion must await the accumulation of more data. ”

“ The extra-galactic nebulae form a homogeneous group in which numbers increase rapidly with diminishing apparent size and luminosity. Four are visible to the naked eye;2 41 are found on the Harvard “Sky Map”;3 700 are on the Franklin-Adams plates;4 300,000 are estimated to be within the limits of an hour’s exposure with the 60-inch reflector.5 These data indicate a wide range in distance or in absolute dimensions. ”

“ No positive evidence of absorption by inter-nebular material, either selective or general, has been found, nor should we expect to find it unless the amount of this material is many times that which is concentrated in the systems. ”

“ The agreement is very suggestive in view of the wide field covered by the data, and Jeans’s theory might have been used both to interpret the observations and to guide research. It should be borne in mind, however, that the basis of the classification is descriptive and entirely independent of any theory.
Elliptical nebulae.—These give images ranging from circular through flattening ellipses to a limiting lenticular figure in which the ratio of the axes is about 1 to 3 or 4. ”

“ New magnitudes were thus obtained for 85 individual nebulae and from these were derived mean correction tables applicable to the entire list. The revised magnitudes are used throughout the following discussion. Hopmann’s corrections extend to about 12.0 mag., and have been extrapolated on the assumption that they are constant for the fainter magnitudes. The errors involved are unimportant in view of selective effects which must be present among the observed objects near the limit of visibility. ”

“ It is based on the assumption that luminous material in the spirals has about the same coefficient of emission as the material in the galactic system. Öpik computed the ratio of luminosity to mass for our own system in{43} terms of the sun as unity, using Jeans’s value23 for the relative proportion of luminous to non-luminous material. The relation is
The application of this method of determining orders of masses seems to be justified, at least in the case of the later-type spirals and irregular nebulae, by the many analogies with the galactic system itself. ”