I have studied the Drummond family tree again and I can provide further information from it:
The William Gott who married Mary Bee on 28th June 1803, mentioned in an earlier posting, was the son of Esther Drummond and William Gott. William and Esther are shown as having 2 children - Elizabeth born ? and William born 1780.
The marriage of William Gott and Mary Bee resulted in 8 children - Isabel b ?, William b 15 Oct 1809, Elizabeth b 18 Oct 1811, John b 1814, James b 1815, Mary b 1819, Esther b 17 Dec 1821 and Dorothy b 28 Oct 1823.
Esther Drummond's second marriage to John Dobbs produced one child - also called John.
There is no indication on the tree as to who William Gotts parents were.
Whereas Arthur Appleton's book only seems to mention James Drummond and Elizabeth Armstrong as having 3 children, the tree shows 7 children.
My gr gr grandmother was Alice Drummond who was b 1808 at Lamesley, however I have been any connection back to James Drummond of Biddick.