Hi Fred,
Are you referring to use on long rifles or any classes of guns? If the latter, octagon to round barrels were used since the 16th century. The kind we are familiar with are referred to as "Spanish form" because Spanish gunsmiths made made the finest barrels in the world during the 17th and 18th centuries and they almost universally made them octagon to round. Most were smooth bore barrels for fowling guns. French, Germanic, Dutch, Belgian, Italian, British, etc all used octagon to round barrels on many guns, again primarily on fowling guns. They were also used on American-made fowling guns and smooth rifles. I think there exists guns by Haines, Beck, and Oerter with octagon to round barrels but I do not recall clearly. Certainly, they were common on New England fowlers and some rifles. They also were used on our first military rifle, the 1803 Harper's Ferry, and the later "Common " rifle.
dave