THE EXPANDING UNIVERSE — HUBBLE 125 



is such that gravitational assemblages maintain their identities. In 

 other words, material bodies or groups and clusters of nebulae do not 

 themselves expand but maintain their permanent dimensions as their 

 neighbors recede from them in all directions. 



Several types of expanding universes are possible, and some of 

 them can be further specified by the nature of the curvature, whether 

 it is positive or negative. In fact, the particular universe we inhabit 

 could be identified if we had sufficiently precise information on three 

 measurable quantities, namely, the rate of expansion, the mean 

 density of matter in space, and the spatial curvature at the present 

 epoch. Recent empirical investigations have been directed toward 

 these problems, and the results will be briefly described in the remain- 

 ing section of this discussion. 



COMPARISON OF THEORY AND OBSERVATIONS 



We may begin with two results which are thoroughly consistent 

 with the theory. The first result concerns the assumption of homo- 

 geneity ; the second, the conclusion that groups maintain their dimen- 

 sions as the universe expands. 



The distribution of nebulae has been studied in two ways. The first 

 information came from sampling surveys at Mount Wilson and at the 

 Lick Observatory. Small areas, systematically scattered over the sky, 

 were studied with large telescopes. Thus the nebulae that were 

 counted lay in narrow cones penetrating to vast distances. These 

 surveys established large-scale homogeneity over the three-quarters of 

 the sky that could be studied from the northern latitudes of the ob- 

 servatories involved. 



Later, the Harvard College Observatory, with the help of its south- 

 ern station, has furnished counts of the nebulae extending over large 

 areas but made with moderate-size telescopes. In other vrords, these 

 nebulae are scattered through wide cones penetrating to moderate dis- 

 tances. Shapley, in his reports, has stressed or perhaps overstressed, 

 the familiar, small-scale irregularities of distribution, but analysis of 

 such published data as are adequately calibrated agrees with the earlier 

 conclusion. In fact, the mean results from the two quite different 

 methods of study are sensibly the same. This fact reemphasizes the 

 large-scale homogeneity of the observable region. 



The second result is derived from a study of the Local Group. Our 

 own stellar system is one of a dozen nebulae that form a loose group, 

 more or less isolated in the general field. These neighboring systems 

 furnished the first clues to the nature of the nebulae and the scale of 

 internebular distances. They are so near that their brightest stars 

 could be recognized and compared with similar stars in our own sys- 

 tem. Radial velocities of the members of the Local Group, listed in 



