M40 was acurately measured and described by Messier. Nevertheless, observers since William Herschel were unable to identify this pair. Only in 1966, John Mallas found that it is identical to the double star Winnecke 4 (Mallas 1966).
M47 was missed because Messier did a sign error during the reduction of positional data. As Messier states, he computed the position of this cluster from the differences to the star 2 Puppis (2 Navis in Messier's time), but mistook the sign of the right ascension difference. This fact was recognized by T.F. Morris of the Royal Astronomical Society of Canada (RASC) in 1959 (Morris 1959). Previously, John Herschel had given the wrong position a number in his General Catalogue, GC 1594, and following him, J.L.E. Dreyer a NGC number, NGC 2478, although at that position there's no object at all.
M48 was first identified with NGC 2548, without any further discussion, by Oswald Thomas in his 1934 book Astronomie (Thomas 1934). This case is not so obvious as M47, but as (the same astronomer) T.F. Morris pointed out in 1959 (Morris 1959), the only object matching Messier's description in this celestial area is NGC 2548, which is now generally recognized as M48. This cluster lies at the same right ascension, but about 2.5 degrees south of Messier's position. The reasons for this error will probably remain obscure unless Messier's lost observing books of this period should come to light one day. A look at that position in a chart of Messier's time reveals that this may well be a "charting" or "grid" error: Messier's position is about the same distance south of the northern-next declination line, as the cluster is from the southern-next. Unidentified, M48 (NGC 2548) had been independently rediscovered by Johann Elert Bode before 1782, and by Caroline Herschel in 1783.
M91 was much more difficult to reconstruct; finally, Messier had measured the position of this galaxy from the previously discovered M89, but thought he had used M58, as the amateur astronomer William C. Williams of Fort Worth, Texas had found out and thus identified M91 with NGC 4548, now generally accepted and quite safe (Williams 1969). Previously, it had been assumed that M91 might be the 12 mag galaxy NGC 4571, the nearest to Messier's position - unlikely but not totally impossible. Many sources also held the version that it was actually a comet that fooled Messier - even more unlikely with regard to the fact that Messier was the comet specialist of his time, and Owen Gingerich had brought up the hypothesis that it might be a duplicate observation of M58.
M102 finally could not be cleared up with certainty up to now. At last, there are still two possibilities open: It may be a duplication of M101, as its discoverer Pierre Méchain believed when he wrote a letter to Bernoulli in Germany two years later, on May 6, 1783, but on the other hand, its description in Messier's catalog (which was actually Méchain's description) matches well with NGC 5866. Moreover, it may be that Charles Messier has observed this object when measuring the position of M102 which he wrote by hand into his personal copy of the catalog, but did a data reduction error again, plotting it exactly 5 degrees west (preceding) of its true position in right ascension (at its latitude, an angular distance of about 3 deg). The present author has discussed this topic and thinks it depends on taste to believe which was erroneous: the observation or the letter, or if Messier's possible (or probable?) observation justifies the designation "M102" for this object.
To summarize: M40 was simply not correctly identified by observers after Messier for about 200 years, despite its correct description and position. The other four missing Messier objects were probably missed because of errata of Messier in data reduction, in detail one sign error (for M47), one mistaken comparison object (for M91) and one or, probably, two "grid" errors, i.e. the declination of M48 was perhaps wrongly determined within the coordinate grid, while the RA of M102 is almost exactly 5 degrees off, which is the grid tick width in the charts he used (see e.g. this example) and can thus be explained by wrong looks or labels.
Last Modification: April 26, 2013