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In 1756 following France's successful siege of the strategic British base of Minorca he was appointed Governor of Minorca a position he held until 1758 and then again between 1760 and 1762.
One of them, John Armstrong, uncle of Andrew, was Governor of Minorca and author of a history of the island in 1752.
Lieutenant-General George Carpenter, 1st Baron Carpenter (10 February 1657 – 10 February 1731) was a British soldier who served as Governor of Minorca and as Commander-in-chief of all the forces in Scotland.
Bayly married firstly Caroline Paget, daughter of Brigadier General Thomas Paget (died 1741), Governor of Minorca, and Mary Whitcombe, in 1737.
##Brigadier General Thomas Paget (died 1741), Governor of Minorca, married Mary Whitcombe; their daughter Caroline Paget (died 7 February 1766) married in 1737 Sir Nicholas Bayly, 2nd Baronet