Gun appears that it could have been made somewhat past the time that silver or brass inlays, or patchbox were routinely used, thus it is a plain rifle. It nonetheless has a pleasing slender profile and a relatively long barrel. While it doesn't have high ornamentation, the maker nonetheless used nice maple plank wood for the stock. The wrist has a stepped appearance, a feature of the far W. PA and Ohio region guns in later guns with this look. The triggerguard has a spur and double spurs on the rear of the guard bow. I think that Davidson, (lock plate), may have been a gun maker, or parts supplier in Cincinatti, if memory serves. Gun probably made in the middle of the 1800s, (1845-1870). Original cost of the rifle would not have been high, perhaps $12.00 at the time, or even less.
f you can, take a look at Shelby Gallien's two volumes on "Kentucky Gunmakers" and you will learn as much as is known of these pieces. Better yet, purchse the books and then set out to find some of these attractive arms from the heart of America. And, by the way, this rifle would fit right in with those in Shelby's books. Hope that his this helps some.
Dick