I don't know a think about surveyor's tools, or the process of using them, but I really like this "make do: version, with hand-drawn angles and rotating head equipped with a level and a slightly bent metal wire pointer. From what I can tell Steber Mfg Co. Chicago was a company that produced light fixtures, and I believe it's just the branded metal plate that was repurposed as a mount here.  The level works and the arm turns all the way around, and while I'm not exactly sure what, it might be it seems surely this must be useful now for something! But also, to my eye at least, great looking enough just to hang on the wall, and perhaps impetus to invent some game or code or measuring system to go along with it!

8 1/2" w x 7 1/4" t x 5" d. I believe this likely dates to the 1950s or so and is good condition--sound, stable and very sturdy.