Per the 1868 proof act the diameters given are the actual weight of a ball of which that many would weigh one pound. The actual marking by the proof house was done with a series of plug gages. The 13/1 etc "Tween" sizes were not used prior to 1887, thus a bore marked 13 could be anywhere from just accepting a .710" plug to just not accepting a .729" one (12 gauge). The Gunmaker himself could bore it to any size which he deemed desirable, the proof house just marked it as to what gage plug it accepted. I don't really see much confusion there.
