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. N.G.C. 6822, a curiously faithful miniature of the Clouds, serves to bridge the gap between them and the smaller objects, such as N.G.C. 4214 and 4449. In these latter, a few individual stars emerge from an unresolved background, and occasional isolated spots give the emission spectrum characteristic of diffuse nebulosity in the galactic system, in the Clouds, and in N.G.C. 6822[12] These features are found in other irregular nebulae as well, notably in N.G.C. 1156 and 4656, and are just those to be expected in systems similar to the Clouds but situated at increasingly greater distances. The system outlined above is primarily for the formal classification of photographic images obtained with large reflectors and portrait lenses. 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. [Illustration: PLATE XIV Irregular Nebula N.G.C. 4214 Direct photograph with 100-inch reflector March 18, 1925. Scale 1 mm = 3″.3 Slitless spectrogram at primary focus of 100-inch reflector, March 19, 1925] PART II. STATISTICAL STUDY OF EXTRA-GALACTIC NEBULAE THE DATA The most homogeneous list of nebulae for statistical study is that compiled by Hardcastle[13] containing all nebulae found on the Franklin-Adams charts. These are uniform exposures of two hours on fast plates made with a Cooke astrographic lens of 10-inch aperture and 45-inch focal length. The scale is 1 mm = 3′. The entire sky is covered, but since the plates are centered about 15° apart and the definition decreases very appreciably with distance from the optical axis, the material is not strictly homogeneous. Moreover, the published list suffers from the usual errors attendant on routine cataloguing; for instance, four conspicuous Messier nebulae, M 60, M 87, M 94, and M 101, are missing. In general, however, the list is thoroughly representative down to about the thirteenth photographic magnitude and very few conspicuous objects are overlooked. It plays the role of a standard with which other catalogues of the brighter nebulae may be compared for completeness, and numbers in limited areas may be extended to the entire sky.