Hi Sheila and Chiad,
I've had a look backwards and forwards on Ancestry through the latter part of the century for William and Barbara.
I couldn't find anything on the Davis angle, so I'm putting that aside for the time being.
It would seem that Barbara Davidson, nee Hardy was present in Ayr in 1861 and 1871. No records exist for her either after this period, either as Davidson, or with another surname (say that William Davidson, her husband, not present in the census, had died and she had remarried).
I then went backwards and forwards on William Davidson, spouse to Barbara, and children born to this couple. I wondered if they had all emigrated. William and Barbara Davidson's last child Jeanie, was born in Ayr and I found her as a servant in the 1891 census. So no complete family emigration.
I'm supposing that Barbara died and had a closer look at William Davidson. Based on 1861 census, William Davidson, was born in Portpartrick, 1833. As Barbara has disappeared from the census, I checked for William Davidson with his details.
I found a William Davidson working as a dairyman, with these birth details with Agnes Davidson in 1881.
It would seem he had remarried, as his daughter Mary (to Barbara) was still living with him.
So I did some checking and I found a marriage record on IGI:
Information removed due to copyright violation. See http://www.rootschat.com/forum/copyright.php for more details
RootsChat must deal with any breach of copyright by its members. If this is the same William Davidson, this would give us a death date for Barbara as between 1871 and 1874.
In the 1881 census with William and Agnes Davidson, is William Davidson, born 1861, Ayr.
I went forward and William Davidson doesn't appear on any other census after 1881. However Agnes (still with Mary, daughter of Barbara) is now head indicating that William has died before the 1891 census.
Using the dates of the birth of William and Agnes's last child, and 1891 census, I narrowed his death between (1885 - 1891).
I checked on SP and found William's Death Certificate which gives us the following information:
William Davidson, Dairyman, 35 Kyle Street, Ayr, 54 years, died of Brights Disease and dropsy on 16th April 1888. His spouse is Agnes McLeod and his parents are William Davidson, deceased, Cattle Dealer and Mary Gray (?spelling), deceased. It gives his daughter Mary as Witness (wouldn't it have been great if it had been William Randolph Davidson?!)
Send me a pm with your email address and I'll send it on.
Now the names of Barbara Davison (similar to Davis as on her marriage certificate) and William Davidson
(did it give an occupation of William Randolph Davidson's marriage certificate? - yes miner mmm) and the fact both are deceased, link to William Randolph Davidson's marriage in 1893.
But, if this Barbara and William Davidson are the parents to William Randolph Davidson, then William senior's occupation on his marriage certificate would have recorded him as "dairyman" as opposed to "miner", don't you think?
So we're left with several options:
this is the wrong family for William Randolph Davidson;
there are two Davidson families living in and around Ayr, dairymen and miners and I've got the Death Cert for the wrong man.
Or, if going by occupations, I've traced the wrong man...
or William could have been delivering coal and milk...
No easy answers here!!!