Strange - that theodolite doesn't look "weird" or the wrong way up to me, because it's invisible!
Something's barred the pictures from my computer, but only for this thread. l can view the rest of the Gallery easily enough.
Reading about the strange divisions and your idea it may have been a military instrument, if so, perhaps for artillery range-finding? I don't know much about guns, but I wonder if those units facilitate ballistics calculations, in which case it may have been issued originally with specially-written, trig-derived, tables?