Ron, If it looks like R{?] NORRI[?] ,There was a John Norris listed in B'ham, England 1829, 1830 and 31. This is from Kauffman's book.
Also, there were 2 makers named "NORRIS" in Ohio around the time that rifle may have been made. William, Brown co.,1841-54 and R W, Miami Co.,1851-54.
That "perch belly" stock looks Ohioish to me. Just my 2 cents worth.
Jim