De Sitter (1930) - The "Other" Velocity - Distance Paper

The Royal Astronomical Society Meeting

When historians recount the story leading to the discovery of the expanding universe (e.g., Nussbaumer, 2013, ASPC, 471, 25), the narrative often includes references to two particular events that happened at this time. The first was the publication by Hubble (1929, PNAS, 15, 168) of his paper in which he demonstrated a linear relation between the velocity and distance of galaxies based entirely on observational data. The second event took place ten months later at the January 10, 1930 meeting of the Royal Astronomical Society (Observatory 53, 37), wherein de Sitter said, "I will begin by showing a slide illustrating the relation between the velocities of the spirals and their distances. You will see that the correlation is represented by a straight line ... The question now arises - how can we account for the linear connection between the velocities and the distances? I am not sure that I can ..."

It is the discussion of this slide by de Sitter and Eddington that triggered a series of events that might properly be called the discovery of the expanding universe. Lemaitre read the report of the RAS meeting and immediately sent a note to Eddington, pointing to a paper he had written three years previously (1927, Annales de la Societe Scientifique de Bruxelles, A47, 49) on a model of an expanding universe. Eddington had forgotten about it, and de Sitter had never even seen it. Upon reading it, both Eddington and de Sitter realized immediately that it provided a natural explanation for the relation that de Sitter had shown on his slide, and the idea that we live in an expanding universe became quickly accepted (e.g., de Sitter 1930, PNAS, 16, 474: "The dynamical solution of the field equations thus is found to account for the expansion of the universe, which is observed in the radial velocities of the extragalactic nebulae.")

This gives rise to the question - what was on the slide that de Sitter showed in the first place? One might have the impression that he was showing the diagram from Hubble's paper. However, that was not the case. de Sitter did say that he was using distances from Hubble, Lundmark, and Shapley. But what was he showing, exactly?

De Sitter Writes A Paper

Almost certainly he was showing a version of Figure 10 from a paper that he would publish a few months later (1930, BAN, 5, 157). This figure was created by de Sitter himself and showed the velocity distance relation for many of of the same galaxies used by Hubble (1929) and, earlier, by Lundmark (1924). The figure also showed that the relation is linear, just as Hubble's did. However, this gives rise to the question - from where did de Sitter get his data?

The answer is given in Table 13. The galaxies were largely the same ones used by Hubble, but de Sitter had added several objects with new radial velocities that had just been obtained by Humason (in part based on spectra taken by Pease), including three objects in the Coma cluster. These objects increased the velocity range by a factor seven.

For distances, de Sitter reverted to the old practice of trying to use entire galaxies as standard candles and rulers. The data he used were taken from the lists of Hubble (1926, ApJ, 64, 321). De Sitter improved on the old method in one important way: his calibration of the magnitude-distance relation depended on morphological type (thus making him one of the first to make use of Hubble's still-new morphological classification system).

However, de Sitter still had the challenge of calibrating the distances, which was complicated by the fact that he needed a different calibration for each morphological class. He did this in Table 11. De Sitter culled distances from several sources, but the two most important ones were Lundmark (1927, Ark. Mat. Astr. Fys, 20B) and Hubble (1929). The latter reference is familiar - it is Hubble's list of distances measured using the brightest star method. However, Lundmark's distances appeared a full two years before Hubble's. Most curiously, the distances derived by Lundmark were in reasonable accord with Hubble's (and in fact, had many of the same galaxies in common). Had de Sitter relied on Lundmark's distances alone, he could still have constructed a credible velocity-distance relation. Which leads to the next question - from where did Lundmark get his distances?

Lundmark Misses An Opportunity

The answer, for the most part, is ... Hubble (1926). Sort of. Hubble had collected most of the data on brightest stars in his first paper, but he didn't actually turn them into distances. It was Lundmark who took the obvious next step and did so in the 1927 paper. Lundmark also added some galaxies which he felt had been resolved into stars using data from Lick and Mt Wilson. Had de Sitter been paying attention, he would have realized that many of Lundmark and Hubble's distances were based on much the same data. Indeed, had Lundmark been paying attention, he could have made a velocity-distance diagram that was nearly as good as Hubble's and beaten him by two years.

How did de Sitter's diagram compare with Hubble's? Since de Sitter treated galaxies as standard candles and rulers, his distances were worse, and even with the split by morphological type, the diagram showed nearly the same raggedness as did Lundmark's six years earlier. However, de Sitter had one big advantage - more velocities had been measured by Humason in the intervening months and reported either in the Journals or in the Mt. Wilson Annual Report, and de Sitter shamelessly added them to his diagram (much to Hubble's annoyance). In particular, three were galaxies in the Coma Cluster, which dominated the slope of the v-D relation.

Finally, there is this cryptic comment in the paper: "It has been remarked by SEVERAL ASTRONOMERS that there appears to be a linear correlation between the radial velocities and the distances." It is certainly true that several astronomers had previously floated the idea that there might be a correlation between radial velocities and distances, but this idea tended to be diluted by saying it could be a correlation with some other property (e.g., galaxy mass, such as would arise if the cause were a gravitational redshift.) Hubble was the first to positively state that the correlation was linear.


De Sitter, like Hubble (1929), did not provide citations for any of the redshifts (aside from three latecomers that he added after the paper was essentially finished.) Of the numerous historians who are harshly critical of Hubble for such an oversight, not a single one has commented on de Sitter's equally egregious omission. [Only rarely does anyone notice that Hubble and Humason (1931, ApJ, 74, 43), which is the report of the full investigation, gave full credit to the "pioneer work of V. M. Slipher".]

By the time of Hubble's 1929 paper, several investigators (e.g., Shapley & Shapley, Wirtz, and Lundmark) had already noted the possibility of a correlation between velocity and distance (or some other parameter that would correlate with distance) but no one had demonstrated it with the precision or significance that Hubble had done. Still, it is probably the case that few found even Hubble's work completely convincing. The highest velocity was only 1000 km/s. Hubble himself actually sat on the paper for over a year (Smith, 1979, JHA, 10, 133) hoping to get additional redshifts of more distant galaxies that would verify the validity of the relation. It was only when the redshift of NGC 7619 was obtained that he felt confident enough to publish, even though he didn't include it in the plot just yet. Skepticism is probably what drove Shapley and de Sitter to make their own versions of the diagram as well. De Sitter, in particular, benefited greatly from the availability of higher redshift galaxies recently measured at Mt. Wilson going to over 7000 km/s and making the reality of the relation far more apparent. While some would like to give credit for discovery of the linear velocity-distance relation to Lundmark or Lemaitre, both did their work before the higher velocity redshifts were available, and so in retrospect neither could have made a convincing case at the time.

It is somewhat curious that the velocity-distance relation, whether Hubble's version or de Sitter's, did not lead to the immediate concept of an expanding universe. It was the linking up of the velocity-distance relation with Lemaitre's 1927 paper in 1930 that broke the fixation on static models and thus best qualifies as the moment of "discovery." This event occurred a full year after Hubble's 1929 paper was published. Thanks to de Sitter having stolen Hubble and Humason's thunder, the state of the data behind the v-D relation was considerably advanced over what Lemaitre had available back in 1927 or even what Hubble used in his paper. Indeed, in spite of Hubble's irritation, it was probably de Sitter's version of the v-D relation that had the greater immediate impact at the time. In the 1931 translation of his 1927 paper, Lemaitre added a citation to de Sitter, but not to Hubble. When Lemaitre cut out his own initial determination of the Hubble constant (perhaps costing himself receiving some credit for having done so), he probably did so because he thought it was superseded by De Sitter's work, not Hubble's. (Nussbaumer and Bieri, 2011, arXiv:1107.2281 explicitly noted this fact and wrote - "He certainly meant no offence to Hubble by not mentioning his 1929 publication, which in 1931 was outdated by de Sitter's thorough investigations.")

De Sitter's moment in the sun was fleeting, however. Hubble and Humason would write their followup paper in 1931 (just after Lemaitre's translated paper appeared), measuring redshifts of more distant galaxy clusters, and rendering de Sitter's work "outdated".

Lemaitre's 1927 paper seems to be the first to have applied the term "expansion of the universe" to extragalactic nebulae. (Campbell had applied the term to B stars back in 1911. Wirtz described the "expansion of the system of spiral nebulae" in 1922. Regarding the B stars, Ralph Wilson in 1927, AJ, 38, 7, said, "... the existence of such a phenomenon ... if real, would indicate an EXPANDING UNIVERSE.") Would Lemaitre's paper have had the same impact in 1927 if it had, say, been published in English in MNRAS as it did in 1930 when it was linked up with de Sitter's diagram? An interesting question.