thats actually in stupendous condition for being a detector find, and just in general, great stuff. As far as falls city goes, that means falls city indiana and i believe this ax was a transitional piece from sometime after 1906 and before 1930, because TT acquired the kelly name in 1930. Of course this could be after TT stopped using the kelly works name, sometime in the 50s maybe, which would explain the great condition. A third option is, like the Kelly works axes, these axes could have been available concurrently with the kelly works axes from 1904-ww2ish, but because they were made here, they were marked falls city
why it's not marked "Perfect" or "Kelly Perfect", i have no idea. it's quite certainly machine made in my opinion, because the eye has no tool marks and the walls are a uniform thickness.
I think the reason yours was tossed aside is you can clearly see the bit is bent to one side, which would make it an absolute b&%#@ to use, so someone probably chucked it off into the woods