I agree with checking with the Polk county clerk for a birth record, but it is highly likely you won't find one. Let me know if you need help with that. I do live in Polk county.
Otherwise a baptism/christening record would be your next best chance. I don't think Arthur was buried in Polk county, at least not in the cemeteries I've photographed. Sometimes a burial will give you a clue as to what church or denomination they were a member. Hope that helps.