In the 1870 census for Davidson County, TN, there is a Thomas and Catherine Edging and they have a daughter named Martha A. (age 17). Living next door to the Edging family is a William Green (age 23). The 1880 census shows that enumerated in the household of William Green and wife Martha is Thomas and Catherine Agent and they are listed as mother-in-law and father-in-law. Martha A Edging had married William Green and her mother and father were living with them. My own grandfather spelled his name "Agent" but was a Edging. If you say the name just right you can hear either name. My grandfather could neither read nor write. I can only assume this is the case here.