EXTRA-GALACTIC NEBULAE[1] By EDWIN HUBBLE Transcriber’s Note: This etext was produced from: The Astrophysical Journal, Vol. LXIV, pp. 321-369, 1926. The plain text version of this ebook includes mathematical formulae in TeX notation. These formulae are enclosed between dollar signs. The HTML version includes the same formulae rendered in their original form. ABSTRACT This contribution gives the results of a statistical investigation of 400 extra-galactic nebulae for which Holetschek has determined total visual magnitudes. The list is complete for the brighter nebulae in the northern sky and is representative to 12.5 mag. or fainter. _The classification_ employed is based on the forms of the photographic images. About 3 per cent are irregular, but the remaining nebulae fall into a sequence of type forms characterized by rotational symmetry about dominating nuclei. The sequence is composed of two sections, the elliptical nebulae and the spirals, which merge into each other. _Luminosity relations_.—The distribution of magnitudes appears to be uniform throughout the sequence. For each type or stage in the sequence, the total magnitudes are related to the logarithms of the maximum diameters by the formula, $m_{T} = C - 5 \log d,$ where C varies progressively from type to type, indicating a variation in diameter for a given magnitude or vice versa. 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. This hypothesis is supported by similar results for the nuclear magnitudes and the magnitudes of the brightest stars involved, and by the small range in luminosities among nebulae whose distances are already known. _Distances and absolute dimensions_.—The mean absolute visual magnitude, as derived from the nebulae whose distances are known, is –15.2. The statistical expression for the distance in parsecs is then $\log D = 4.04 + 0.2 m_{T},$ where m_{T} is the total apparent magnitude. This leads to mean values for absolute dimensions at various stages in the sequence of types. Masses appear to be of the order of 2.6×10^8 ☉.