Hi Grandma Sheila
Just thought I'd update the search here with the bonus bit of information that I emailed to you yesterday

WILLIAM DAVIDSON
(note no Randolph at this stage)b. 14 November 1860 43 Carrick Street, Ayr, Ayrshire
Parents:
William Davidson (Coachman)
Barbara Davidson maiden name Hardy
Then there was his marriage in 1893 to Mary Black that we have already. There's a wee problem here tho' because his mother, although shown as 'Barbara Davidson' on hte Register has her maiden name shown as 'Davison'.
Seems we could be getting there although we're still not out of the woods yet!
Regards
Chiad Fhear