This is only a guess and not made with any knowledge of water wheel power for a mill, but, from the picture, the end of the shaft looks like it is smaller and smoother than the rest of the shaft which makes me think that the end rode in, what today would be a bearing, but, not sure what it would have rode in back then. I am thinking that the center wood use to be the paddles that the water ran over and I am guessing the other end, that is buried, is also a shaft like the end that is exposed.

Just guessing and nothing more....