Update: corrected the reconstruction of Wolff's recalculation from Richardson's data.]
The old narrative
A misplaced decimal point caused the false reputation of spinach for being the vegetable that was richest in iron. Though still highly popular, this narrative is most likely wrong (see here). The decimal error probably never occurred in that stupidly simple way. Ignoring wrinkles in the narrative, such as that spinach is still rather rich in iron but that it cannot be assimilated well for other reasons, the new narrative can be stated most simply as follows.
The new narrative
The decimal error is a myth, it never occurred. The false reputation of spinach was due to unreliable methods or poor experimentation. That is, errors were inherent in experiments not data treatments (see here).
The complex history
Still, not everything about the spinach-iron legend is clear yet. In particular, nobody has yet thoroughly reconstructed where the original data came from, how they have been treated (mathematically) by the various researchers who wanted to reach comparability with their own data, and whether any mistakes were made in these data treatments. At the end of this series of reconstructing data handling, you will see that the whole research endeavour was full of data handling errors, though none as simple as a misplaced decimal point.
Retrieving original data from limbo
Wolff's Aschen-Analysen (1871) was itself a massive collection of data that he needed to treat in order to standardise them and reach comparability. Wolff's particular value of 4.60% Fe2O3 in the pure ash of spinach was based on an analysis of Richardson (see red underlined reference in the reproduced page 101 from Wolff 1871 below). But this reference, that both Wolff (1871) and Bunge (1892) gave for Richardson (1848), ends in a cul-de-sac.
At first sight, the Annalen der Chemie und Pharmacie 67(3) of 1848, Justus Liebig's journal by the way, has no such publication from Richardson—and neither do the other volumes and issues around that time. My first hunch was that the world of science was so small that authors could simply assume everybody knew who was meant and where to find it. As it turns out, my hunch was wrong. Richardson's data were a mere table appended by Justus Liebig to his Annalen der Chemie 67(3) of 1848 without giving it an own page number.
Unfortunately, Wiley has therefore not listed it as a separate publication, but buried it in a limbo by attaching it to the preceding paper by another author on another topic: C. List (1848) "Ueber das sogenannte Terpentinölhydrat." Justus Liebigs Annalen der Chemie 67(3): 362-376. Fortunately, Justus Liebig stated somewhere (I cannot remember where) that Richardson's publication consisted of a mere data sheet and was unceremoniously appended to the end of his journal. That's why I or anybody could conceive of downloading List (1848) in order to get Richardson (1848).
Reconstructing Wolff's treatment of Richardson's data
As far as I can tell, Richardson gave 8.67 parts "phosphorsaures Eisenoxyd" (FePO4) per 100 parts pure ash (see Richardson's 11th line for Chenopodaceae below). How does that relate to Wolff's 4.60 parts (in his line 52)? If we take Richardson's value and correct it for the proportion of iron in FePO4 (37.03%)* and recalculate it to the portion of iron in Fe2O3 (69.94%), we get: (8.67*0.3703)/0.6994 = 4.59. (By the way, doing this calculation instead for FePO4·2H2O yields 3.70 and for FePO4·4H2O yields 3.11.) That is, Wolff has taken Richardson's value for FePO4 in the pure ash and recalculated it as his value for Fe2O3 in the pure ash. No mistake in data handling yet (but see next entries).
*[Use the atomic weights for Fe = 55.85u, P = 30.97u, O = 16u to calculate the portion of the molecular mass that is due to iron.]
P.S.: What was Moleschott's treatment of Richardson's data?
Before Wolff treated Richardson's data, Jacob Moleschott (1859. Physiologie der Nahrungsmittel, ein Handbuch der Diätik. Zahlenbelege, 166) has written a book on dietetics. It falls into two parts. The main text runs from page 1 to 570. This is probably a rich source for people interested in the history of dietetics and nutrition. The "Zahlenbelege" after the main text is a collection of data with its own numbering running from page 1, again, to page 254.
At page 166 within the Zahlenbelege, Moleschott gave Richardson's value for the iron content of spinach as 0.93 parts Eisenoxyd in 1000 parts. But, as far as I can see, he did not specify whether the latter meant dry or fresh weight. So far, I could not reconstruct how Moleschott treated Richardson's data to get 0.94 in 1000.
The main text is interesting in so far, as Moleschott (1859, main text, 347) states:
"Fast immer enthalten die Triebe und Blätter mehr Kalk als Bittererde und oft auch wenig Eisen; eisenreich sind indess der Spinat und die Endivie, die unter den pflanzlichen nahrungsmitteln hinsichtlich des Eisengehalts nur dem Samen von Chenopodium quinona nachstehen, während die Artichocken und die Spargeln einen mittleren Eisengehalt führen.1"
"The shoots and leaves almost always contain more lime than magnesia and are often also low in iron; rich in iron, however, are the spinach and endive, which, among the vegetable foods, are inferior, in terms of the iron content, only to the seeds of Chenopodium quinona, while the artichokes and asparagus have an average iron content." [Footnote refers to his own data tables at end of book.] (my translation)P.P.S:
An encyclopaedia of Brockhaus (1852. Die Gegenwart. Eine encyklopädische Darstellung der neuesten Zeitgeschichte für alle Stände. Siebenter Band. Leipzig: F. A. Brockhaus) states at page 172: "Weiße Rüben enthalten nur eine geringe Menge von Eisen, Spinat dagegen viel."