Do I get a brownie or something nice if I can lead you close to this one? I'm just in a great mood as Janet and I have enjoyed a wonderful day as only retirees can.
The helmet Mark is not a mystery as much as it is a wonderful example.
If you read the article http://www.pickelhauben.net/articles/DepotMarks.htm#_ednref6
it might start to show the answer. Or maybe even confuse you more!
In peacetime, pre-war Germany equipment was issued by Army Corps. Each Corps had a small but very important supply unit called the Bekleidungsamt (BKA). Consider them clothing depots. It seems however, that 4 of the 25 Corps did not at first glance have an independent BKA. XVIII, XX, XXI and III Bavarian Corps seemed to have doubled on an older BKA.
VIII Corps in Coblenz seems to have picked up much of the slack in the missing BKAs. They did parts of XVIII Corps, parts of XXI Corps and assorted other units like the NCO school. II Corps picked up XX corps. XV picked up most of XXI Corps. XI Corps picked up Regiment 87 & 88 from XVIII Corps as well as both Eisenbahn Regiment 2 & 3. Mostly I Bavarian Corps but some of II Bavarian Corps picked up Bavarian III Corps.
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The source that I quote: Freidag, B., F?durch Heer und Flotte, Verlag Heer der Bergangenheit, Krefeld, 1914. Pg. 193.
In footnote 13 he goes on to explain the brigades that were covered by the 15th Corps 59, 62, 65 brigade. Infantry Regiment, 138, was part of the 42nd division 59th brigade.
So we have here an example of a helmet accepted by the 15th BKA and issued out to infantry Regiment, 138. You'll not find the BKA XXI, because as a force structure saving method. They didn't have one. One truly wonderful thing about this whole question is that I noticed that the map of corps areas in Das Deutsche Heer (text volume) is wrong. It shows a 1912 distribution and cites 1914.
What do you think do I get the obscure human prize?