# Astronomy Edwin Hubble Essay Research Paper THE — страница 4

the form of the luminosity function, provided that the objects are distributed homogeneously in distance. With this knowledge, the early aim of Hubble’s work on counts was to determine the numerical value of the coefficient of the magnitude term. In the first discussion in his remarkable 1926 paper, Hubble shows that the data then known were consistent with the required value of 0.6, indicating homogeneity (his equation 10 from Table XVII of Hubble 1926b). He used data from the standard sources of counts then available, including the classical work on galaxy distribution by Seares (1925) – a generally neglected major discussion of what is now known as Hubble’s zone of avoidance. But it was clear that the data could be fundamentally improved and carried to fainter magnitudes by using the enormous power of the 100-inch reflector. Building on the experience of his Ph.D. work, Hubble began a massive observing programme to do just that. The results began to appear in a series of papers that was to culminate in 1936 in the attempt to measure the curvature of space. In his first paper, Hubble (1931) gives no hint of the direction which the problem would take toward the curvature determination when he teamed with R.C. Tolman in 1935. The 1931 announcement was simply an abstract of preliminary results from his new survey of galaxy counts made with the Mount Wilson telescopes. The detailed paper on the distribution appeared three years later (Hubble 1934a). As in the Cepheid work ten years earlier, this paper was so thoroughly convincing that it brought the problem of the mean galaxy distribution, which by then was more than 100 years old, to a close. The paper has become a classic. Its power lies in the large amount of new data presented, and in Hubble’s straightforward, seemingly simple analysis of them – a trait characteristic of much of Hubble’s work. After presenting the data and the technical methods of reducing the material to “uniform plate conditions”, Hubble treats (1) the distribution in galactic latitude outlining the “zone of avoidance”, recovering Seares’ (1925) prior result, (2) the extinction in the poles (the famous cosecant distribution of the counts which has so confused modern discussions; see Noonan 1971 for a critique), (3) the tendency to cluster, based on the nature of the count residuals, field-to-field, the residuals being Gaussian in log N(m) rather than in N(m) itself, (4) the space density of galaxies, (5) the mean mass of galaxies, and (6) the mean density of matter in space of the order of 10[-30] g cm[-3]. Curiously, no mention of space curvature was made in this paper nor in the account of his Halley lecture (Hubble 1934b), although it was to be the major theme from then on. Hubble’s interest in what Gauss and Karl Schwarzschild called experimental geometry can be traced to his collaboration with Tolman that must have begun in 1934. Their joint paper (Hubble and Tolman 1935), sets out how galaxy counts, conceptually, could be used to find the curvature of space by direct measurement. The principle is to determine if the volume encompassed within various “distances”, appropriately defined, increases at the rate of r[3], or more rapidly or more slowly than this Euclidean value. The observational problem is complicated by the delicate corrections required to the data for the effects of redshifts, etc. But the grandeur of the conception and the carrying out of the programme still provokes the modern reader, despite the fact that the attempt failed because of large errors in the magnitude scales and what we now know to be the overwhelming effects of galaxy evolution in the look-back times. The technical aspects of the methods need not be discussed here (cf. Sandage 1988 for that) nor the criticisms of them. More useful is a chronicle of Hubble’s progress in the curvature programme following his initial collaboration with Tolman. The problem still remains as a principal goal of observational cosmology. But because of the effects of galaxy evolution, galaxy counts are no longer considered to be the main source of data with which to solve it. Rather, we now attempt, in one way or another, to measure the deceleration of the expansion from which spatial density can be derived and hence the curvature from Einstein’s relativity equations. Hubble’s (1936c) major paper discussing his attempt contains two fainter points on the N(m) count curve determined at Mount Wilson plus the important N(m) additional data point from Mayall’s (1934) Ph.D. survey. A principal part of the analysis centres on the effects of red shifts on the observed N(m) distribution and the corrections required due to the redshift

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