Karmarsch is an excellent example of the untrustworthiness of the writings of early academics and encyclopedias of industrial arts. Although he was the founder of the Hannover Institute of Technology, he seems to have had some serious problems with numbers. He left us with two descriptions of Nürnberg wires gauges, which as Latcham has showed, conflict with each other. Furthermore, Karmarsch not only misunderstood the placement of half gauges, getting them on the wrong side of their whole gauges in the zeros zone, but he also couldn't properly count the number of whole gauges between 4/0 and 11, coming up with 16 instead of 15. A more significant error, missed by Latcham, lies in his calculation of actual diameters. In his first description of 1828, he said that gauge 4/0 "has a metric number of 115, that is, there are 115 meters per half kilogram." He continued with, "the thinnest, gauge 11, for the same weight is exactly 28 times as long, since it's metric value is 3221." Actually, "exactly [genau]" 28 times 115 is only 3220, but that's a minor point. The big mistake probably lies in Karmarsch's conversion from metric units to Viennese Fuß and Pfund, from which he further calculated the actual diameters in Viennese Zoll, which Latcham converts yet again back into millimeters. After this long and circuitous route, Latcham arrives at the values of 0.753mm for gauge 4/0 and 0.142mm for gauge 11.
However, we get at totally different answer if we bypass all the mucking about with conversions, both regional and temporal. The value of the meter and kilogram have not changed since 1828, and if we calculate directly from Karmarsch's original hard data, we get totally different answers. The only thing we need to know is the density of iron (which we can safely assume has also not changed). The standard textbook values are 7.87Mg/m3 for pure iron and 7.70 for wrought iron. Martha Goodway measured the density of Vater iron wire and got a value of 7.69Mg/m3. So using a value of 7.70, we get values of 0.85mm for gauge 4/0 and 0.16mm for gauge 11. Even taking the higher density for pure iron would not alter these figures noticeably. These are significant errors, being about 13% in diameter. In practical terms, this would account for a tension differential of about 28% in musical instrument applications.
Obviously something has gone very wrong somewhere along the whole train of assumptions, conversions, and calculations. But what? Considering Karmarsch's track record, I suspect we can place the blame squarely on him, either in his "hard" data or his conversions. In any case, Karmarsch and his descriptions, riddled with errors, are totally worthless in helping us unravel Nürnberg gauge marks.