In the years between 1871 and 1914, the military establishment of Germany consisted of four separate armies, each of which belonged to one of the states of the Empire large enough to qualify as kingdoms: Prussia, Bavaria, Saxony, and Württemberg. The 21 smaller states of the Empire also possessed armies. However, in the course of the formation of the Empire, these grand duchies, principalities, and free cities had, by means of a series of unequal treaties, grafted their military forces onto those of Prussia.
The largest, by far, of the four royal armies of the Second Reich was that of Prussia. In 1914, 19 of the 25 peacetime army corps of the German Empire belonged to the Prussian contingent. Of the six remaining army corps, three hailed from Bavaria, two from Saxony, and one from Württemberg.
The degree of autonomy enjoyed by each of the three smaller royal armies was, to a large degree, a function of its size. Bavaria possessed its own general staff, its own uniforms, and its own system for numbering units and formations. Württemberg and Saxony, however, had none of those things. Thus, while the uniforms of a handful of regiments in the armies of Saxony and Württemberg retained distinctive features left over from the years before 1871, most soldiers in the service of those kingdoms dressed in a manner that closely resembled that of their Prussian counterparts. (This was particularly true when, on the very eve of the First World War, the German armies replaced their brightly colored “regimentals” with field gray uniforms.)
The separate battalions, regiments, brigades, divisions, and army corps of the Bavarian Army were numbered in a separate series. Thus, the 1st Bavarian Pioneer Battalion, the 1st Bavarian Field Artillery Regiment, the 1st Bavarian Cavalry Brigade, the 1st Bavarian Infantry Division and the I Bavarian Army Corps could easily be distinguished as belonging to the Kingdom of Bavaria. The units and formations of Saxony and Württemberg, however, usually bore two numbers. Thus, for example, the 139th Infantry Regiment was also the 11th Royal Saxon Infantry regiment, while the 26th Infantry Division was also the 2nd Royal Württemberg Infantry Division.
Most units of the Prussian Army also bore two numbers. However, rather than showcasing membership in one of the smaller armies of the Empire, the subsidiary name linked the unit to a particular province of the Kingdom of Prussia, one of the two imperial states (Alsace and Lorraine), a historical region, or a city.
Units and formations affiliated with the Grand Duchy of Baden occupied a place between that of the armies of the smaller kingdoms and that of the other elements Prussian contingent. While the Grand Duchy dissolved its war ministry when it joined the German Empire in 1871, it provided most of the component units of the XIV Army Corps: nine out of ten infantry regiments, three out of four cavalry regiments, and all field artillery, fortress artillery, and pioneer units.
Sources:
Wilhelm von Voß, editor, von Löbell’s Jahresberichte über die Veränderungen und Fortschritte im Militärwesen , (Berlin: E.S. Mittler, 1913), Volume 40, pages 1-24
Eike Mohr, Heeres- und Truppengeschichte des Deutschen Reiches und seiner Länder 1806 bis 1918 eine Bibliographie, (Osnabrück: Biblio Verlag, 1989), pages 769-780
For Further Reading: Captain James Moncrieff Grierson, The Armed Strength of the German Empire, (London: Her Majesty’s Stationery Office, 1888)
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I find the patchwork nature of the German Empire to be very fascinating. Reminds me of pre-Civil War US, or the Holy Roman Empire.