Hi,
Octagon to round barrels were largely copied from the Spanish. In fact, octagon to round barrels with a wedding band were called "Spanish form" during the 17th and 18th centuries. The design allowed great breech strength but relative light weight. It evolved from their heavy muskets during the 16th century. The heavies had to fire a ball with enough power to penetrate hardened armor breast plates of heavy cavalry. The Spanish used octagon breeches to handle the force but lightened the barrels considerably by turning them round for most of the length, and I mean turning them round. They were forged round, the octagon was hammered then filed, and then the rest of the barrel was slimmed by turning on a lathe and cutting the soft iron with firmer chisels and files. Anyway, the Spanish made the best smooth bored barrels in the world during the 17th, 18th, and early 19th centuries and most other nations tried to copy their styling. It really did not have anything to do with sight radius. I don't know why Germanic makers preferred octagon and swamped octagon barrels over round or Spanish form for their rifles. They did use them on fowlers but rifles tended to have "squared" (old term for octagon) barrels. Maybe they were concerned about higher breech pressures from rifles and stuck with octagon all the way. Perhaps the flats made fitting and adjusting front and rear sights easier. But they mostly made barrels that were quite short so the idea of a long sight radius did not matter very much (except perhaps for some special target guns). With respect to accuracy, the most accurate muzzleloading rifles ever (Whitworth, Gibbs, Rigby, etc) had round barrels. I don't think the shape of the barrels mattered just its quality.
Deepcreekdale, no hand gonnes did not have octagon barrels exclusively. In Europe, gun barrels were called barrels because the earliest iron barrels were made like cooper's barrels. Staves were welded into a round tube and then iron hoops were added for strength. The first octagon or square barrels of which we know were cast in bronze or brass and it was not until well into the 15th century that iron octagon barrels without hoops start showing up. Moreover, many of the early cast gonnes were round not octagon.
dave
