Update: Was able to reconstruct Wolff's data transformation from his systematic tables (e.g., Wolff 1880, p. 128) to his summary tables (e.g., Wolff 1880, p. 147) eventually. It's rather simple, but the headline above the compounds in the summary tables themselves is misleading.]
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.
The second Aschen-Analysen
In 1880, Wolff published a sequel to his Aschen-Analysen von land- und forstwitschaftlichen Producten. (See here and here for reconstructions concerning the data treatments of his first Aschen-Analysen.) Much of the second Aschen-Analysen is made up of the same data as those given in the first (Wolff 1871). However, the tables have been augmented with new data from 1870 to 1880, and their arrangement has changed. Or so Wolff (1880) claims in the preface.
As far as spinach is concerned, the second Aschen-Analysen contain no new data in its part I, but instead of separately listing the results of the two original analyses, the averages of these two analyses are given. The two original analyses were from 1st: Saalmüller (1846. "Analysen der Asche von Spinacea oleracea." Justus Liebigs Annalen der Chemie und Pharmacie 58: 389.) and 2nd: Richardson (1848. "Beiträge zur chemischen Kenntnis der Vegetabilien." Justus Liebigs Annalen der Chemie und Pharmacie 67(3), without page number [erroneously attached to the last separately listed article in that issue, see here.])
Here is an excerpt of the table from Wolff (1871, p. 101) listing the results separately:
Lines 51 and 52 list the results of Saalmüller (1846) and Richardson (1848) on spinach respectively.
And here is the excerpt from Wolff (1880, p. 128) giving the averages of the above:
Wolff's sundry summary tables contain a decimal error
That is, from p. 141 onward of the 1880 volume, Wolff gives the contents in parts per 1000 instead of parts per 100. While this does create a decimal error, it applies to all the items in the sundry tables, not just spinach and not just iron-content.]
From page 119 onward, Wolff (1880, pt. II) gave "Allerlei Uebersichts-Tabellen" (sundry summary tables). These form part II of the second Aschen-Analysen from 1880. The first Aschen-Analysen from 1871 also came in two parts with sundry summary tables forming part II, but for some reason spinach was not listed in these summary tables from 1871.
In 1880 spinach does occur in the summary tables. As Wolff mentioned somewhere before, the pure ash is now given as 164.8 parts in 1000 dry matter instead of 16.48 in 100. The line above the compounds still says "in 100 parts of the pure ash," but each value has been multiplied by the portion of pure ash in the dry matter. That is, the values are truly giving the contents of the compounds in 1000 parts of dry matter rather than in 100 parts of pure ash. This may be one of many errors of a decimal dimension that has then been transmogrified into the misplaced decimal point in the spinach-iron mythology.* However, this misleading heading in the table, above the values for the compounds, concerns all the values for all the vegetables and all the chemical compounds. It cannot be the legendary error that affected the iron content of spinach only, but no other compounds or other vegetables.
For example, 3.35% or 0.0335 was the average portion of Fe2O3 in the pure ash of spinach; 16.48% or 0.1648 was the average portion of pure ash in the dry matter. Hence the portion of Fe2O3 in the dry matter was: 0.0335 x 0.1648 = 0.00552 or 5.52 in 1000 parts dry matter. The values for the other compounds can be transformed similarly, or simply all values can be multiplied by the factor 1.648 to get from the values in the table at page 128 to the ones at page 147 in Wolff (1880). Wolff transformed the values for other vegetables similarly, only the factors were different depending on the average portion of pure ash in the dry matter.
As already discussed in a previous entry, this is an illegitimate transformation, because the ash contains oxygen and its value must be corrected accordingly. Given Wolff's chemical species (K2O, Na2O, CaO, MgO, Fe2O3, P2O5, SO3, SiO2, Cl) the ash contains 37.27% and Fe2O3 contains 30.06% oxygen. Correcting their values yields 0.1648 * 0.6273 = 0.1034 for the ash without oxygen, 0.0335 * 0.6994 = 0.0224 for Fe, and that in turn yields 0.1034 * 0.0224 = 0.0023 Fe in the dry matter or 2.3 Fe in 1000 parts dry matter. Wolff's 5.52 Fe2O3 in 1000 parts dry matter would instead yield 3.86 (= 5.52 *0.6694). Hence, if we ignore inaccuracies in Wolff's data due to the methods of the time, Wolff (1880, p. 147) was 1.7 times too high for Fe in spinach. Alas, his illegitimate data transformation affected all ash compounds for all vegetables and other products listed.
[* Footnote: Particularly egregious exemplars of this legend can be found here, here and here. The authors do not even get Wolff's name right. Where the title page of the original source reads: "Von Dr. Emil Wolff" (meaning "By Dr. Emil Wolff"), this is garbled into "by Erich von Wolf." That's three to four mistakes in trying to simply give the name of the author that is falsely blamed. The first name is completely different, the academic title is lost and the preposition made into an aristocratic title instead, and the last name lacks an 'f.' While it seems to be true that the king of Württemberg honored Wolff's scientific achievements by awarding him personal peerage at the end of his life, Wolff achieved his scientific publications as a regular guy. Hence, it is okay to write an obituary and title it "Emil von Wolff," but it's wrong to cite his publications as if he had belonged to nobility already. That's as wrong as stating that the "Leiden des jungen Werther" had been written by Johann Wolfgang von Göthe.]
Postscript
Although the 5.52 Fe2O3 in 1000 parts of Wolff (1880, p. 147) could be mistaken for the 0.5g Fe in 100g dry matter that Bunge (1892) has claimed Wolff to have given, Bunge has not taken this average value, because (1.) he spoke of one of two analyses, (2.) he mentioned that the analysis was based on data by Richardson (1848), and he calculated the content of 0.5g Fe rather than Fe2O3 in 100g dry matter (see here). Otherwise, it would have been a data handling error (mistaking Fe2O3 with Fe) just the same.
