Hopefully William and Elizabeth are related in some way. On the 1860 Census for Davidson County it lists in William B. Adcock's (age 42)household: Sarah (age 33) wife, daughters Mary E. 15, Nancy L 13 and sons Green V. 9, John W. 6 and William B. 1. It doesn't say anything about the William B. being a JR but bet he was. I will keep searching and posting.