Royal Damascus was a mark used by Ancien Etablisment Pieper of Herstal, Belgium, c. 1890-1914. T Barker is usually dismissed as "just another Belgian clunker", but with a silver escution and engraving, yours is probably better than the average utility shotgun from the period. I have heard that T Barker was a hardware outlet in California, but have no proof of that.
Damascus steel is made by folding a mild steel together with a high-carbon steel to make it stronger, and gives it a pretty pattern. Problem with Damascus barrels is that, while they work fine with low pressure black powder loads, modern smokeless shotshells are likely to cause the barrel to rupture, which is bad. If a shotgun has a Damascus barrel, it's very old and probably just a wall-hanger.
The use of damascus barrels on guns began to decrease pretty rapidly after 1900, although they were still fairly common up until the start of WWI. If you have a breech loading gun with damascus barrels it will probably date from 1875 - 1910. Most damascus barrels on U.S. guns seem to have actually made in Belgium. There is a lot of debate as to whether any damascus barrels for shotguns were actually made in the U.S. It seems likely there may have been small numbers produced in the U.S. However, Belgium had a large gunmaking trade at the time, with a lot of barrel makers specializing in damascus barrels, so it was generallly cheaper to import them than to make them.
Damascus steel barrels can usually be recognized by visible (if the metal is bare) "twists" or striations. Do NOT fire a gun that has a Damascus steel barrel unless it has been proof tested by a qualified gunsmith. For that matter, do not fire any old firearm, Damascus steel or not, unless you are certain that the barrel can withstand the higher pressures of modern gunpowder. Safety first: take it to a qualified gunsmith if there's any doubt. See the following links for examples of Damascus steel barrels: http://www.peterdyson.co.uk/acatalog/ORIGINAL_DAMASCUS_BARRELS.html http://www.griffinhowe.com/damascus_twist.cfm
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