Bigooms,
Your William was baptised on March 16, 1746, parents MICHAL ARMSTRANG/MARY SCOTT in Hairlawhole (Scotlands People/ OPR). The 1841 Census lists a 20 year old coal miner James at Priorshill 5. At Priorshill 3, a 70 year old shoemaker named William and Catherine, 60, and an 11 year old agricultural labourer (!) named William. Perhaps the latter were related to your husband, but were in a different house there.
Thomas was an elder brother of your husband's ancestor, John. Michal and Mary had him baptised on 20 Dec 1751. Thomas and wife Mary Wilson had a son baptised Michal on 15 Oct 1795. This must be Michael, farmer, aged 45, listed on the 1841 Census at Hairlawhole. Perhaps also of interest, on April 6, 1746 John Armstrang and Grizal Scott in Hairlawhill had a lawful daughter baptised (?) Nicholas. (on same page of OPR as first entry above).
Hairlawhill and Hairlawhole were different places, along with nearby Harelaw. You can navigate to them at
http://geo.nls.uk/roy/ where Roy's 1750's military maps are digitally accessible. There is also a Hairlawhagg and a Hairlaw Mill.
Hector of Harelaw was an Armstrong of the 16th century who famously sheltered the Earl of Northumberland, after the failed Rising of the Northern Earls, but was said to have later betrayed him.
Mosside