A Theory of the Spatial Distribution of Galaxies.

A theory of the spatial distribution of galaxies is built, based on the following four main assumptions: (i) galazies occur only in clusters; (ii) the number of galazies varies from cluster to cluster, subject to a probabilistic law; (iii) the distribution of galaxies within a cluster is also subject to a probabilistic law; and (iv) the distribution of cluster centers in space is subject to a probabilistic law described as quasi-uniform. The main result obtained is the joint probability generating function ON1, N2(tl, t2) of numbers N1 and N2 of galazies visible on photographs from two arbitrarily placed regions 1 and c taken with fized limiting magnitudes and , respectively. The theory ignores the possibility of light-absorbing clouds. The function ON1, N2(t1, t2) is ezpressed in terms of four functions left unspecified, which govern the details of the structure contemplated. Methods are indicated whereby approzimations to these functions can be obtained and whereby the general validity of the hypotheses can be tested.