Antique Contraption! How & For What Would This Hardware Tool Have Been Used?

This is a true mystery that many people have tried to crack, but none have succeeded. I am hoping that you may be willing to help. I think that the closest theory is that it came from an early physics department from a college. The arch swivels 360 degrees to remain stationary at any angle. Hand painted on one of the cast iron legs reads, "PHY." and the #31576. The back includes a small metal clipboard with a series of numbers in white section at the bottom in photo #2. It also displays a series of numbers along the entire back of the large arch in increments of 10, as seen in the last photo. It measures 20.5 diameter sphere, 15.5" tall & 18.5" long. I just couldn't pass on this item at a local yard sale due to my intrigue; I would greatly appreciate any help on this one.
I have been doing more research; is this a mural ("wall") quadrant? A mural ("wall") quadrant was a large 90-degree arc attached to a north-south wall, with a sighting tool to measure the altitudes of stars and planets. See Tycho's wall quadrant...