"The OUTSTANDING FEATURE, however, is the possibility that the velocity-distance relation may represent the DE SITTER EFFECT, and hence that numerical data may be introduced into discussions of the general curvature of space."
Peacock (2013, ASPC 471, 3) latches onto Hubble's comment and goes on to describe how the de Sitter effect impacted both Lundmark and Hubble:
"For this reason, the correct redshift-distance relation is linear at lowest order. This was first demonstrated by Weyl (1923) ... This was also shown independently by Silberstein (1924) and Lemaitre (1927) ...""The picture that emerges from this study is thus that Hubble's 1929 work was perhaps more an exercise in validation of a linear D(z) than a discovery ... we can conclude that Hubble was influenced by the same theoretical prior as Lundmark in 1924 - and it is debatable which of these investigations achieved greater success in tracking down their quarry."
**The root of the problem is that dark energy - the only type of matter present in de Sitter's universe - is the one form of material that does not have any preferred rest frame. Thus, when one adds galaxies to a de Sitter universe, one has freedom how to distribute them, as there is no natural frame of reference. Today we would say that the problem with de Sitter's metric as he wrote it originally is that it was not in proper Robertson-Walker form, and in particular does not have a universal cosmic time. Lanczos (1922) was the first to find a transformation from static to R-W form.
As originally shown by de Sitter (1917, MNRAS, 78, 2), there are actually two effects at work in his metric. The first effect is that time seems to run slower at large r, causing distant objects to appear redshifted. However, this effect is only meaningful for objects at fixed coordinate distance, which are not on geodesics, and more importantly, the relation is quadratic between velocity and distance.
The second effect is found by considering the motion of an object that actually does follow a geodesic. In the general case such motion forms a hyperbola, and for those portions of the orbit where the object is close to the asymptotes, the velocity is nearly proportional to distance. All this was shown (at least implicitly) by de Sitter in 1917 and explicitly by Silberstein in 1924. Notably, his equations admit both positive and negative velocities. (That the velocity and distance are nearly proportional for the orbit of a single object is a property unique to the de Sitter universe; it would not hold for, say, a matter dominated expanding universe, even though the Hubble law would still be valid there.)
There are additional issues. Most importantly, the de Sitter metric doesn't tell us how to distribute objects on different geodesics. The latter form a multi-dimensional family of possible orbits (e.g., parametrized by the distance and velocity at the point of closest approach), and the distribution of objects along each orbit adds yet another dimension. It is the different choices that theorists made for this distribution that led to different predictions.
***In Tolman's model of "continuous entry", most galaxies would be on orbits that have large peculiar motions relative to the RW comoving spatial coordinates. Tolman did not address the question of homogeneity in this model - while the de Sitter universe itself is formally homogeneous (no preferred center), this particular galaxy distribution is not.
Weyl (1923, Raum Zeit, Materie; 1923, Phys. Zeitschr, 24, 230) invoked a hypothesis ("Weyl's principle") that matter is uniformly distributed across a set of geodesics that emanate from a common point in the infinitly disant past. Applying this principle to a de Sitter universe, most geodesics would be empty, and galaxies would only occupy receding branches of the hyperbolae such that only redshifted objects would be seen (and now with a strictly linear velocity-distance relation to first order). Weyl seems to have been the first to call attention to a velocity-distance relationship (even though it was implicit in de Sitter's 1917 paper). [Note, however, that Tolman, 1929, claims to be unable to follow Weyl's derivation!]
Eddington (1923, Math. Th. Rel., p. 161), like Weyl, also imagined that there could only be positive velocities, but his belief was based on the fact that the acceleration on a particle is always radially away from the origin and increases linearly with distance. He did not actually integrate the force law or derive a velocity-distance relationship, and he only considered particles that started at rest (but not at the same point, as Weyl did.) Eddington used the term "scatter" to describe the resulting motions.
[Lemaitre's paper came after Lundmark and was unknown to Hubble, so it did not have any influence on either.]
It is unclear whether Hubble had such clear preconceptions as Lundmark, but given that Hubble gave no equations for the effect and that he described it qualitatively ("a tendency of material particles to scatter") suggests that he was NOT trying to validate a linear D(z) prediction. Rather, his description of the scattering simply echoed both Eddington 1923 ("... there is the general tendency to scatter ...") and Tolman 1929 ("The tendency for particles to scatter ..."). The fact that Hubbble discussed the theoretical interpretation of his result only after all the observational results have been presented mirrors his approach to observational astronomy in general, and in later papers he would be even more cautious, presenting his results as being purely empirical.
Menzel (1929, PASP, 41, 224) actually thought Hubble's data agreed with theory: "Hubble has investigated the relation between the amount of shift and distance of the nebulae, and finds that the observations agree very well with the theoretical predictions." Doh! It is clear from Menzel's lead-in discussion that he was only considering the quadratic portion of the effect (which Hubble's data do not match).
Weyl's principle regarding geodesics was skewered and mocked by Silberstein, and while Silberstein may have had the better argument at the time, it is Weyl's principle that is in accord with our ideas regarding a Big Bang origin to the universe.
Peacock's assertion that "... it is debatable which of these investigations achieved greater success in tracking down their quarry" will be disposed of in another essay.