I'm going to go out on a limb here and guess that this is our oldest wheel. It (or the soap) was patented in 1881 and I can't imagine this is too much older than that.
This measures 3.75 inches and is in somewhat bad shape. It stands to reason. It's a little game with advertisements for the Enoch Morgan's Sapolio soap products. Honestly, I can't figure out the dang game, but its interesting nonetheless. I don't know what desperate situation you'd find yourself in to resort to playing the Sapolio soap game.