I think Archibald Douglas Waddell was born on 17 March 1799 in Airdrie. I wonder if Elizabeth Rymer was born on Tortola as her aunt Elizabeth was. Her father William had a plantation there and when she married Joseph Gilchrist in 1819, Blackwood's magazine noted that she was the only daughter of the late William.
I can't find any note of the marriage yet, nor any sign of the family, although Elizabeth was dead by 1864 when her son James Gilchrist (my g4 grandfather) died. Alexander Waddell was a witness on James death certificate and noted as his half brother.