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 effect. These corrections have been mentioned in the Halley lecture (Hubble 1934b), but were not there discussed relative to the space curvature measurement. Part of the 1936 paper was concerned with the problem for the first time.
Hubble concluded that his observed log N(m) distribution showed a large departure from Euclidean geometry, provided that the effect of redshifts on the apparent magnitudes was calculated as if the redshifts were due to a real expansion. A different correction is required if no motion exists, the redshifts then being due to an unknown cause. Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift “represents a hitherto unrecognized principle of nature”. This viewpoint is emphasized (a) in The Realm of the Nebulae, (b) in his reply (Hubble 1937a) to the criticisms of the 1936 papers by Eddington and by McVittie, and (c) in his 1937 Rhodes Lectures published as The Observational Approach to Cosmology (Hubble 1937b). It also persists in his last published scientific paper which is an account of his Darwin Lecture (Hubble 1953).
From the beginning of his career Hubble was intrigued with the distribution of nebulae. His work on the problem began with his Ph.D. research (Hubble 1920), elementary as this now appears. He returned to the subject time and again with ever-increasing sophistication until the end of his career. He had even begun a major count programme anew in 1949 using the just-completed Palomar 48-inch Schmidt telescope (unpublished investigation) in an effort to use the modern magnitude scales then being set up photoelectrically. The aim was to investigate again from scratch the space curvature measurement.
In his paper of 1926 Hubble had used his estimate of the average space density of galaxies to calculate the space curvature of the static Einstein universe. This fact is of quite ironic interest because it was Hubble himself, more than anyone, who three years later set out the observational foundation for the non-static solutions to the Einstein field equations of gravity. His use, then, of a static model to calculate the space curvature shows that as late as 1926 he had believed in non-expanding models, despite the large velocities that had been observed by Slipher and the attempts by many astronomers to understand these velocities using particular cosmological models. Recall that the Friedmann non-static solutions had been discovered in 1922, evidently unknown at Mount wilson at the time. The next major observational development was the discovery of the redshift-distance relation in 1929.
d). The redshift-distance relations.
As is well known the Einstein field equations of gravity admit only three stationary solutions (Tolman 1929 and 1934 sections 133-145). By stationary is meant that the manifold is not expanding. The mathematical expression of this condition is that the coefficients of each of the spatial coordinates in the equation of the metric is not a function of time.
The two stationary solutions of historical importance are those of Einstein (1917) and of de Sitter (1916a, b; 1917), neither of which later proved to describe the true situation. Einstein’s did not because it contained matter but no redshift (it was truly static both in space and time). De Sitter’s did not because it had no matter, but curiously did have spectrum shifts (both red and blue) of test particles placed in the space which it described. This was due to a scandalous space-dependent factor in the metric coefficient of the time dimension , despite the static nature of the space coordinates.
The “de Sitter spectral shift effect” had been looked for by many astronomers (see Hubble’s history in his chapter V of The Realm of the Nebulae) without convincing success. Robertson (1928) had predicted a linear relation and believed he had found a suggestive effect that could be interpreted in this way. He had correlated Slipher’s redshifts with the distances he had estimated using apparent magnitudes. Robertson gave no details. His result was set out in a single paragraph in a highly theoretical paper, but he was clearly aware of the possibility of the Kr term in the velocity field and that the universe might not, after all, be static.
As with Hubble’s Cepheid paper 5 years before, and his space distribution paper to come 5 years in the future, Hubble’s (1929b) discovery paper of the expansion was written so convincingly that it was believed almost immediately. Despite its astonishing content and its few data points, Hubble must have been quite certain of the result. In the paper immediately preceding Hubble’s, Humason (1929) reported the very large (for the time) redshift for NGC7619 of 3779 km s[-1], far larger than any redshift known before. From this result Hubble must have been certain that a significant phenomenon was at hand.
All effort was then made at Mount Wilson to confirm and to extend the astounding possibility that the universe expands. By 1930 Humason (1931) had obtained redshifts of galaxies in clusters whose “velocities” were as high as 20,000 km s[-1]. In perhaps the most important paper on the series, Hubble and Humason (1931) showed beyond doubt (a) the existence of the effect, (b) that it was linear with distance, and (c) that the brightest members of clusters are predominantly E galaxies (a major discovery related to galaxy and cluster formation).
The work was extended to field galaxies soon thereafter (Hubble and Humason 1934), showing the generality of the phenomenon. By 1936 the work had been completed as far as it was to be done with the Mount wilson reflector, reaching redshifts of 40,000 km s[-1] for the Ursa Major No. 2 cluster (Humason 1936, Hubble 1936). Humason began the work again in 1949, using the Palomar 200-inch reflector, reaching 60,000 km s[-1] (Humason, Mayall and Sandage 1956) for the Hydra cluster, but was stopped from going further by the techniques of the time in the presence of the night sky air glow. Hubble (1953) symmarized the work finally in his Darwin Lecture.
(e). Other programmers.
The previous subsections have outlined the four major subjects in which Hubble’s results were dominant in the 1930s. But he produced other works of influence as well, the results of which are also part of modern astronomical culture.
(1). He solved the problem of the source of radiation and the nature of the spectra of diffuse nebulae, recognizing the difference between emission and reflection nebulae (Hubble 1922a, b), and proving that the source of radiation of reflection nebulae is an associated star. An elegant appreciation of the work is given by Greenstein (1951).
(2). The surface brightness profiles of E galaxies were measured accurately for the first time (Hubble 1930), providing the basic model from which later modifications and extensions of the profile laws would be derived by others.
(3). He began the detailed study of the stellar content of the nearby galaxies. Besides the identification and measurements of Cepheids and very bright irregular variables in members of the Local Group, he made the unprecedented identification of globular clusters in M31 (Hubble 1932), starting an activity that occupies many present-day astronomers.
(4). He discussed the sense of rotation of the spiral arms in individual galaxies. The most important papers, in which the solution of the problem was set out by identifying the near sides of galaxy images by the dust lane asymmetries, are Hubble (1935, 1943) and a paper with Mayall (Hubble and Mayall 1941).
(5). In a most important paper, Baade and Hubble (1939) found the nature of the Sculptor and Fornax dwarf E galaxies that had been announced by Shapley in 1938. Their discovery of RR Lyrae stars provided Baade with the crucial clue to his eventual population concept (cf. Sandage 1986 for a review).
An Assessment. The principal surprises in rereading Hubble’s papers from the vantage point of 1989, after the discoveries of the Gamow, Alpher, Herman 3 K radiation, the development of radio astronomy, the discovery of how to age-date the stars, and the invention of the new cosmology of grand unification, are (1) the nature of Hubble’s methods, and (2) those central items that he hardly discussed but which seem so much a part of the cosmology that he pioneered.
(1). Hubble’s methods were largely inductive – nearly pure Baconian. His usual procedure was to assemble massive data sets from which he generalized to reach conclusions of wide scope that had continuing applications in further advances. Occasionally he did employ analytical methods such as in his analysis of the source of the light from diffuse nebulae (Hubble 1922b), his analysis of the flattening distribution of E galaxies (Hubble 1926b), his use of the Emden gravitationally bound gas sphere in understanding the luminosity of E galaxies (Hubble 1930), and his analysis of the galaxy counts for the space curvature (Hubble 1936c using the formalism of Tolman). But the method used in his most important papers – those papers that convincingly changed a field – was that of nearly pure Baconian induction. His success was remarkable, and his proportionate influence nearly unparalleled in modern astronomy.
(2). The most curious impression we are left with is his lack of comment on the significance of the redshift phenomenon, which is surely one of the most important discoveries in science. In none of his writings did Hubble comment on the central importance that the form of the redshift-distance law is linear. This single feature is most crucial for the standard model. Heckmann (1942) was perhaps the first to emphasize the singular significance of the linear form.
A linear velocity field has two fundamental properties; (a) each observer sees the identical form and expansion rate from any vantage point, and (b) it is the only velocity field that permits all points in the manifold to be “together” at some time in the past. Discovery of the linear form is usually taken to be as important as the discovery of the expansion itself if the phenomenon has any relevance to “the creation of the universe”. But hardly any hint of this appears in Hubble’s writings, despite his discovery of the linearity. There is also a lack of discussion of how the expansion relates to “beginnings” – a topic emphasized so strongly in modern cosmological writings. We simply do not know if Hubble was impressed with his discovery in these ways.
The second puzzling omission is a lack of emphasis on the meaning of the numerical value of the expansion rate (i.e. the Hubble constant). In an expanding model with a singular point, the inverse Hubble rate is related to the age of the model, the exact function depending on the deceleration. Credence that we are dealing in the redshift phenomenon with an aspect of “a creation event” requires that the “Hubble time”, obtained from the inverse “Hubble constant”, be the same as the “age of the universe” determined in other ways. We are so used to talking in this way that it is surprising to see none of this in Hubble’s writings.
Of course, it is true that the three types of cosmological time scales were not well known in Hubble’s time. These are (a) the Hubble time, (b) the age of our Galaxy via its oldest stars, and (c) the age of the oldest chemical elements. The method to age-date the stars had to await the understanding of the Sch?nberg-Chandrasekhar (1942) limit as a departure of evolving stars off the main sequence of the Hertzsprung-Russell diagram, an understanding that came only by the developments in stellar evolution in the early 1950s. The age of the chemical elements, although known in principle in about 1910 by Rutherford based on the first understandings of radioactivity, was not worked out in detail until, also, the decade of the 1950s. What we take for granted in the current work that is organized to test the agreement of the three time scales to within say 20 per cent was not possible in Hubble’s time. Nevertheless, it remains a curiosity that Hubble did not strongly emphasize the problem publicly, or, if at all, even privately to himself.
There was, of course, the embarrassment that the inverse of the Hubble expansion rate (i.e. the Hubble time) was only two billion years on Hubble’s 1930 to 1953 distance scale whereas the Earth was believed to be a bit older than three billion years even in 1936. It was left to the inventors of the steady state cosmology to emphasize this discrepancy of time scales, pointing out that any of the Friedmann models (sans cosmological constant) that were used to espouse a “beginning” could not be true.
The influence of Hubble was so great that errors in his 1930/1936 distance scale were considered to be out of the question in his time. The discrepancies began to appear only when the 200-inch Palomar reflector was put into operation in late 1949 by the heroic and largely unheralded two-year effort by I. S. Bowen. Baade began obtaining data which showed that Hubble’s scale must be modified. We now know that the scale must be stretched by a factor of a least 5, more likely by a factor a bit larger than 10. But it must be fairly pointed out that some astronomers, not believing that the problem of the distance scale has been solved by the results of the 200-inch programme from 1950 to 1980, have suggested that the value of the Hubble constant can be determined to the satisfaction of the sceptics only by the future use of the Hubble Space Telescope. For this one suspects that Hubble might have been pleased