I received a follow-up by you on my Dec. 2003 query.Sorry about the delay in answering, but computer problems and other interests have delayed things somewhat.
You surmised that my John M. Mathis's father might be the brother of your Nancy Caroline Mathis, daughter of James H. and Sally Jones Mathis.
I received a note from Vineta Wingate where she made a guess that a James H. Mathis might be the father of James M., William F., nd John M. Mathis.Also, James H.probably died in the Civil War (Union Army}. (See Genforum for Carroll County, AR, Message 542.) .
Also, in clicking around in rootsweb.com, I found a picture of a man named James Henry Mathis, and another picture of the James Mathis family.The central gentleman in the family picture appears to be the same man as in the single picture.
If these observations are right, then a major road block in my research could be resolved somewhat.i.e., James H. Mathis and Sally Jones could be the parents of my John McConnell, William F., and James H. Mathis.