Hi Ken (don't know if that is your actual name but it will do!)
Many thanks for replying on this.
Also thanks to the others who have responded. To Carol (Cazza47) I had looked previously at that link, and have gone back and spent some time digging further into this. Although it is around the right date, the father James McA came from Greenock, Scotland and there are a couple of other 'unnamed' births around that period, with him as father and Ann Gilliland as mother, they are all within Belfast city over a period of a few years and that doesn't easily tie in with James being a salt miner at Carrickfergus, and probably farming this land before salt mining started on it.
If the Millar connection is correct, Henry would have had a brother Robert born in 1874, who may have died at age 5 (this may be a different branch of the family). also, if Annie Millar is the correct mother, this makes a lot of sense.
My wife's aunt is Anna Leana (originally McAllister or McAlister) still living in Carrickfergus, daughter of Samuel and Mary J McClean. I'm in Scotland and what I've got from her are anecdotes / snippets of information rather than any comprehensive background. However she recalls strong connections with the salt mines, including family deaths there.
Apart from the mystery of Henry's birth date (I wonder if he was the son of perhaps a sister of James, but brought up within James's family?), I am trying to figure out the Saunderson connection. At least one document shows James as 'James Saunderson McAlister' and Henry's son Samuel was 'Samuel Sa(u)nderson McAlister'. I've seen one family tree showing James's mother as 'Fanny Saunderson' but I can find nothing to substantiate this.
Also, I've only found birth records for 5 children of Henry and Eliza/Lizzie Kirk, although there may be children to subsequent marriages?
Earlier records show James as a 'labourer'. Later records indicate 'salt miner'. Henry's occupation throughout is shown as 'tailor' and this ties in with family knowledge - I'm told his tailor's shop in Ballycarry is now a butcher's shop...
Any light you can throw on any of these questions would be very welcome!
Regards
Jim