van Maanen's critics err! Object image sizes are not the limiting factor regarding the precision in astrometrically locating salient points on astronomical plates, for example, the centroids of object images.

According to the History of Leander McCormick Observatory web page, in 1916, the Gaertner Single Screw Measuring Engine allowed an operator to read positions down to about 0.003 arcseconds on plates taken with a 40 inch telescope (HPA) Van Maanen used a 60 inch telescope for the majority of his work. (MA21)

Figure 1 shows that position measurements can be made down to dimensions much less than the diameter of blurred stellar images. Figure 1a represents a section of an early photographic image, and Figure 1b represents the image taken a suitable number of years later. It should be obvious that delta X and delta Y can be much smaller than the atmospherically blurred diameters of the stellar images.

Figure 1
Illustration of Astrometric Measurements Smaller than Atmospheric Seeing Limit

Present day. - CCD astrometry has demonstrated 1 milliarcsecond positional accuracy (Monet et al. 1992). This level of precision means that proper motions of distant objects can be determined on time scales of 10 years or less. ( MD&SP) (CCD photography does not get rid of atmospheric blurring. It allows you digitally dig into the fuzzy stuff without the mechanical idiosyncrasies of the measuring engines.)

There are unresolved differences of opinion about the results of Knut Lundmark's re-reading of van Maanen's plates for M33. Listed here are two quotes from recent critics of van Maanen's "rotations."

In his section on "The Island Universe Theory," Kurtiss Gordon ( GK02) says:

    "Although his results correlated well with van Maanen's with respect to both
    direction and relative size of proper motion, the absolute scale of Lundmark's
    proper motions was less than 1/10 as large as those van Maanen had measured."

An "Anonymous Critic" (IU) says:

    "The Swedish astronomer Knut Lundmark also acquired evidence that van Maanen's
    evidence was faulty. He was allowed to remeasure the very same plates used by
    van Maanen to determine the motion of M33. In 1924 he found completely different
    results, namely that there was no measurable rotation of M33's image in the five
    year interval between the plates. In other words, van Maanen's claims were completely
    bogus. Lundmark told some of his colleagues privately of his results. He also published
    a paper to the same effect in 1925, but it was either too obscure or too polite to cause
    many other astronomers to notice."

The following table shows a comparison of van Maanen and Lundmark's measurements of motions in M33.

Table added 26 Oct 2003.

Readers may read Lundmark's obscure 1926 report (LK26) in the Astrophysical Journal.
[Added 05 October 2003; updated 26 October 2003.]

See Gustav Holmberg's article Astronomy in Sweden 1860-1940, Uppsala Newsletter: History of Science nr 26 (1997), for a commentary on Lundmark's work on spiral nebulae. (Comments are in the fourth and third paragraphs from the end.) [Added 27 September 2003]

Michael Hoskin summarizes the warfare between Hubble and van Mannen (HM97). He says: "The van Maanen problem became acute as the Dutchman pointedly persevered with his comparisons of pairs of photographs of spirals, concluding in every case that the nebula was rotating at a speed that made it physically impossible for it to be an island universe."

The warfare seemingly ended in 1935, with Hubble winning. Hoskin reports "A compromise was imposed, and in 1935 readers of the Astrophysical Journal were no doubt intrigued to find there a two-page paper by Hubble delicately outlining his conclusions, immediately followed by a two-page paper by van Maanen, conceding that 'it is desirable to view the motions [the rotations in the spirals] with reserve.'

The author would hope that Hoskin's purpose was to encourage readers to read the papers for themselves, because although what he says about the papers is true, may be misleading. Hoskin makes it sound as though Hubble demolished van Maanen's findings and that van Maanen's new tests put him in his proper place. That's not quite like it was!

Hubble's four paragraphs and single ambiguous tabular summary (HE35) offers no substantive data to back his claim for non-rotations. He fails to explain the relation between his total observed displacements and what he calls extrapolated rotations. The text reads as though he vectorially added the motion vectors of individual nebular points to get his total observed displacements. (Such a process would, in fact, tend toward zero, but the result would be meaningless.) In three cases he relates negative total observed displacements to positive extrapolated rotations (which were supposedly of a much smaller order than the values van Maanen had been "finding."). In four other cases null values for total observed displacements are related to positive extrapolated rotations. It is very hard to tell just what Hubble was reporting, other than that he still didn't like fast nebular rotations. [This paragraph will in all likelihood come to be toned down.]

In regard to van Maanen's supposed declaration of surrender (MA35), he stated "The measures give motions for both nebulae [M33 and M74] in the same direction as those found for the spirals measured previously; but the value of M33, mean of 114 nebular points, is considerably smaller (+0.013 milliarcsec as compared with +0.020 milliarcsec) than that found before. " The phrase considerably smaller was the politically correct thing to say, and was probably part of the imposed settlement. On the other hand his new smaller value for M33's rotation was a hefty 65% of his 1921 measure. (Reading between the lines is encouraged.)

This writer has not had opportunity to do a good literature search to compare current findings on spiral nebula rotations, compared to those reported by van Maanen, but is of the opinion that the findings will match up just fine. If they do, then the constant rotation curves for spiral nebulae, a.k.a. "galaxies" can most likely be explained in terms of plasma dynamics.

Present day. - CCD astrometry has demonstrated 1 milliarcsecond positional accuracy (Monet et al. 1992). This level of precision means that proper motions of distant objects can be determined on time scales of 10 years or less. (MD&SP) (CCD photography does not get rid of atmospheric blurring. It allows you digitally dig into the fuzzy stuff without the mechanical idiosyncrasies of the measuring engines.)