Friday, 31 July 2015

Sources of the spinach-iron myth: Wolff (1871) & Bunge's (1892) bungle

[Click here to get all posts in this series.]

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.

Wolff (1871)
We begin with a collection of analyses of the compounds of ashes from various sources, including vegetables, published by Dr. Emil Wolff in 1871: Aschen-Analysen von landwirthschaftlichen Producten, Fabrik-Abfällen und wildwachsenden Pflanzen. Berlin: Wiegand & Hempel. [While Wolff (1871) is usually chosen as the starting point for the spinach-iron legend, he stood on the shoulders of others as well (see here).]

Wolff (1871, see table below) gave the content of substances as portions of 100 parts of the pure ash (In 100 Theilen der Reinasche). Pure ash, according to Wolff, was the raw ash (Rohasche) minus the sand and coal (Sand und Kohle) and minus the carbonic acid (Kohlensäure) in it (2nd to 5th column in the table below). Now that already gives me pause to wonder what coal and carbonic acid have to do in ash? I found no indication that the word Asche used to mean anything other than the remains of combustion. This coal-in-ash thing sounds like incomplete combustion to me. Anyway, the first of the Bemerkungen at page 1 of Wolff's publication is also important, because it explains that the amounts of raw or pure ash are again given as portions of 100 parts of dry matter unless otherwise mentioned.

As you can see from the table below (line 51 and 52), the portion of Fe2O3 in spinach was 2.1 or 4.6  parts respectively in 100 parts of pure ash [excuse me if the German decimal separator, a comma, slipped in sometimes]. And the amount of pure ash was given as 16.27 or 16.70 parts, respectively, of 100 parts of dry matter (as the first of the Bemerkungen at page 1 explained). One could state it simpler by saying that the mass of the pure ash equaled 16.27% (or 16,7% respectively) of the mass of the dry matter and that the mass of the Fe2O3 equaled 2,1% (or 4,6% respectively) of the mass of the pure ash in turn.

Page 101 of Wolff (1871). My red underlining.

Bunge (1892)*
Gustav Bunge (1892. "Weitere Untersuchungen über die Aufnahme des Eisens in den Organismus des Säuglings." Zeitschrift für Physiologische Chemie 16:173-186) said that he was prompted to measure the iron content of wild strawberries (footnote 2 at p. 180) and spinach (footnote 1 at p. 181), because of the strikingly high iron contents, which Wolff has given in his Aschenanalysen on the base of an analysis of Richardson. Bunge (1892, p. 181) concludes that Wolff's data were 15 times too high for strawberries and 16 times too high for spinach. Bunge's figure for the iron content in wild strawberries calculated from Wolff, though poorly legible, should read 0.14 Fe in 100 dry berries ("0,14 auf 100 trockener Beeren!" Bunge 1892, 180-181) as I will show below.  

[* Bunge was not really interested in the iron content of vegetables. His point of departure was the finding that the milk of mammals contained very little amounts of iron compounds, yet young mammals needed a lot of iron for the growing while suckling. The solution to this riddle was that mammals are born with a stock of iron compounds sufficient for the growing until they wean.]

Bunge (1892, footnotes at pp 180, 181). Footnote 2 from page 180 runs into page 181.
These footnotes leave no doubt that Bunge (1892) has treated data from the first Aschen-Analysen (Wolff 1871) and not from his second (Wolff 1880). Firstly, Bunge speaks of one of two analyses of spinach listed by Wolff. In 1880, however, Wolff had no longer given several lines of evidence but averages instead. Secondly, Bunge mentions that Wolff's data were based on an analysis by Richardson (Ann d. Chem. u. Pharm., Bd 67, Heft 3, 1848). Whereas Wolff (1871) referred to this at the bottom of each page (see above), Wolff (1880) no longer did so. Finally, the reconstruction below shows a neat fit between Wolff (1871) and Bunge (1892). 

Bunge's treatment of Wolff's data
Bunge took Wolff's data and calculate the iron content in the dry matter of a vegetable by correcting the data for the oxygen from the air in the iron-oxide. The logic is as follows:
Weight of fresh vegetables → get rid of water through desiccation → weigh of dry vegetables →  combust dried vegtables → subtract sand, coal and carbonic acid from raw ash to get the mass of the pure ash → subtract the part that is due to oxygen from the portion of Fe2O3** → calculate the iron content of the dry mass from the thus corrected data.   
One caveat about this logic is that part of the pure ash is also from oxygen from the air (e.g., in magnesia or calcium oxide). That is, the values for pure ash would also need to be corrected. As I will show below, Bunge has not done so.***

[** 30% of the mass of Fe2O3 stems from oxygen, which entered this product from the air during combustion. We know that from the atomic masses of Fe (55.85u) and O (16u). Hence 70% of the molecular mass of Fe2O3 (159.7u) stems from iron (55.85 times 2 = 111.7u) and 30% from oxygen (16u times 3 = 48u).
***As the prequel has shown, some of the original data used by Wolff did not measure the iron content as Fe2O3 but as FePO4 in the first place. That is, the oxygen has not been gained from the air during combustion, but the content of FePO4 has been mathematically transformed into an equivalent of Fe2O3. Nevertheless, if the portion of Fe2O3 is rid of oxygen mathematically, then the value for pure ash will need to be treated likewise.]

Wolff's data for wild strawberries were 5.89 parts Fe2O3 in 100 parts pure ash and 3.40 parts pure ash in 100 parts dry matter (see data for Fragaria vesca in Wolff 1871, p. 127). Correcting these data for the fact that only 70% of the mass of iron oxide is from iron yields: 100 x 3.40% x 4.12% = 0.14 as stated in Bunge's footnote 2 at page 180 (see above, Bunge 1892, footnote 2, p. 180). That Bunge gave the content calculated for wild strawberries without unit seems to be mere whim. Likewise, taking the higher value of Wolff's data on spinach, 4.60 parts Fe2O3 in 100 parts pure ash, and correcting for the oxygen in it yields: 100g x 16.70% x 3.22% = 0.538g. This corresponds to Bunge's statement that, according to one of the two analyses given in Wolff "100gr. der trockenen Blätter" would contain "einen halben Gramm Eisen" (see above, Bunge 1892, footnote 1, p. 181).

The correspondence between the calculation in the previous paragraph and the figures given by Bunge (1892, p. 180, footnote and p. 181, footnote 2) suggest that Bunge did just the same calculations, that is, he multiplied the portion for iron (corrected) times the portion of pure ash (not corrected) times the 100 parts dry weight that Wolff started with. If, however, the portion of pure ash was not corrected for oxygen in its compounds (for example, magnesia oxide), his calculations were necessarily too high.

Can we check how much Bunge was too high? Yes! Look at line 52 in the table from Wolff reproduced above. Wolff gave portions for the following compounds: KO, NaO, CaO, MgO, Fe2O3, PO5, SO3, SiO2 and Cl. And the portions of these compounds add up to 101. That is, the pure ash was supposed to consist of these compounds and the sum is slightly higher than 100 due to rounding. Unfortunately, some of the chemical species given by Wolff do not exist. Potassium oxide comes as K2O, sodium oxide as Na2O, phosphor oxide has several species (e.g., P4O6, P4O10) none of which corresponds to the one given by Wolff, sulfur trioxide is a gas, and Cl does not exist as such. One would also expect silicon oxide to belong to the sand that has been subtracted from the raw ash in order to get the pure ash, but that may have been a matter of method and grain size.

What a mess! Anyway, let's just take Wolff's chemical species for granted, even though they seem strange, and correct the portion of pure ash accordingly. The percentage of the mass that is due to oxygen in these compounds would be: 29% for KO, 41% for NaO, 29% for CaO, 40% for MgO, 30% for Fe2O3, 72% for PO5, 60% for SO3, 53% for SiO2 and 0% Cl. That yields the following corrected portions of these compounds: 6.88 for K, 23.10 for Na, 9.31 for Ca, 3.17 for Mg, 3.22 for Fe, 3.34 for P, 3.72 for S, 1.49 for Si and 0% Cl. That sums up to 54,14 (instead of 100) meaning that 45.86% of the pure ash were made up of oxygen from the air. Hence the 16.70 parts pure ash given by Wolff (see line 52 in the table above) would reduce to 9.04 parts per 100 parts dry matter. The estimation of the iron content in 100g dry matter would go down to (100g x 0.0904 x 0.0322 =) 0.29g.

In his own analysis, Bunge (1892, p. 181, main text) found 0.0016g Fe in 4.8893g dry matter of spinach equal to 0.0327g in 100g dry matter.**** Comparing this against the content that he had calculated from Wolff's data, he concluded Wolff's data to be 16 times too high (our check: 0.538g/0.0327g = 16.44). In comparison with this, the estimate calculated from Wolff's data with corrected value for the pure ash would no longer be 16 times too high, but roughly 9 times too high (0.29/0.0327 = 8.87).

[****Bunge (1892, p. 174) found his value of 0.0327 or 32.7mg in 100g dry matter corroborated in a similar value of 39.1mg/100g dry matter that he cited from Boussingault (1872. "Du fer contenue dans le sang et dans les aliments." Comptes Rendus de l'Académie des Sciences 74: 1353-9). Boussingault (1872) gave 0.0045g for "Feuilles d'épinards" at page 1356 and the specification at page 1355 that his values were "Fer exprimé à l'état métallique dans 100 grammes de matière." The text above Boussingault's table specifies that his values are for the fresh matter as consumed. Bunge (1892) stated at p. 173 that he has transformed values for fresh matter to dry matter according to J. König (1889. "Chemie der menschlichen Nahrungsmittel."). That, in turn, implies that König has given a water content of 88.49%.] 

Almost half (9/16) of the discrepancy, that Bunge found, between his own experimental findings and Wolff's data were due to Bunge's false treatment of Wolff's data. In particular, Bunge forgot to rid the value for the pure ash from the oxygen gained during combustion from the air. The same should be true for the value for wild strawberries, which Bunge thought were 15 times too high. But I will leave the fun of getting a periodic table of elements and doing the calculation to the reader.