p.227. Notes and Queries. "ARCHIBALD HAMILTON. - I shall be greatly obliged to any correspondent who will assist me in identifying the Archibald Hamilton who married Margaret, daughter and eventually heiress of Colonel James Maxwell of Drumbeg, County Down. The inscription on their tomb in Drumbeg states that he died "February, 1725, aged 80" (? 75)years, and his wife died in January, 1736.They had inter alias James Hamilton, who assumed the name of Maxwell (according to injunction contained in the will of his uncle, Arthur Maxwell of Drumbeg, who died "2nd day of January, 1720, aged 74 years", old tomb), and married Letitia ....... (?).He died in 1751, leaving at least one son, Arthur Hamilton Maxwell, who inherited all his property, and died in 1757 ; and I wish to ascertain the names of all his younger children." Query was from Wm. Jackson Pigott, Manor House, Dundrum, Co. Down.
I have not looked further into the lineage of Arthur Hamilton Maxwell, sorry.