Thank you for sharing your knowledge of migration to Scotland and for all the time you spend searching my family names.I am very grateful to you.I am currently recovering from foot surgery and dealing with a few other distractions.I hope in a few weeks to be able to followup on your excellent suggestions for further research.
Since my original posting I believe I have found one of the James and Sarah Davidson's sons (Hugh, John and James Davidson) that their father said moved to Scotland.Hugh is found in the 1861 census for Scotland on Ancestry:
1861 Scotland Census 1861 Scotland Census Name: Hugh Davidson Age: 30 Estimated Birth Year: abt 1831 Relationship: Lodger Gender: Male Where born: C Armagh, Ireland Registration Number: 651/1 Registration district: Airdrie Civil Parish: New Monkland County: Lanarkshire Address: 15 Mains Square Occupation: Ironstone Miner ED: 10 Household schedule number: 56 Line: 19 Roll: CSSCT1861_117 Household Members: Name Age Robert Blair 31 Margaret Catheral 36 William Catheral 44 Hugh Davidson 30
Ancestry.com. 1861 Scotland Census [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2006. Original data: Scotland. 1861 Scotland Census. Reels 1-150. General Register Office for Scotland, Edinburgh, Scotland.
Description: The 1861 Census for Scotland was taken on the night of 7/8 April 1861. The following information was requested: place, name, relationship to head of family, marital status, age, gender, profession, birthplace, and whether blind, deaf, and dumb.