It's part of a parasol or umbrella. There was an item about these in Mark Parker's column in the June 2006 issue of Western & Eastern Treasures. I couldn't find it online, but here's a quote from it:
Actually, it’s part of the hardware from an old umbrella, and the notches are where the ribs or stretchers were held in place. The ribs of an umbrella’s canopy fit into what’s called a “top notch”; and the stretchers, the shorter lengths that attach the ribs to the shaft, are connected to a “runner,” the piece that moves up and down the umbrella shaft when the canopy is opened or closed. Quite a few of these turn up in Civil War camps, and many relic hunters refer to them as “parasol braces.”