I don't know anything about Martha Adams but I'm always looking for connections to my Adams family who came from Coweta to Dallas Co., AR about 1847. This was Absalom Adams, son of Jesse and Casey Posey Adams. They also had a daughter named Nellie who was born in 1818 and nothing else is known about her.
So where in Arkansas did your Martha Adams end up? I took it that you meant that Adams was her maiden name, not a married name, correct?