I also descend from the same Adams line. As I've read and have been told (need to verify with Morgan County records), James' father C.H. (Hugh) was the son of Hugh Adams, who married Ruth Paton. One of C.H.'s sisters was my ggg-grandmother, Charity Adams. She married a German fellow named Frederick Miller. (Her sister Mary Jane also married a Miller - August Miller, and the Millers may have been brothers).
In case you wanted more family data... Charity and Frederick were married 10 APR 1845 (Indiana State Library L-M Marriages Through 1850). They had four daughters: Ruth, Elizabeth, Isabelle and Mary Jane. My gg-grandmother Ruth Miller m. Samuel Moore. My grandmother, Glenna Pearl Moore Blankenship was raised by Ruth and Samuel (her grandparents). The name Charity was given to Ruth and Samuel's first daughter, who died as an infant. The name Ruth was used frequently in the family, last given to my mother. Do you see some of the Adams' given names used often in your line?
I see another posted message from you saying you will be taking a trip to Morgan Co. Have you gone yet? If not, I'm not sure where most of the Adams' settled, but Charity and Frederick Miller were in Jackson Township (SE corner of the county). My gg-grandmother Ruth Miller Moore and her sister Elizabeth Miller Lake and the families they were associated with are buried in the church graveyard next to the Mount Nebo Community Church about four miles east of Martinsville on Highway 252. I'm not sure if Charity Adams Miller is there, as I didn't know about her the last time I went to Morgan County.
Going back further on the Adams line, your C.H. was son of Hugh and Ruth Paton. Hugh was son of David and Polly Kephart. I've been told David's line is from Ireland. Have you heard contrary to this?
If you've already make your trek to Morgan County, what interesting Adams info did you find?