I'm very grateful for the replies again.
Dorrie - the William Davies, the shale miner whom you found in the 1881,1891 and 1901 censuses, born c1855 in Airdie, Lanarkshire seemed that he must be him. I have now been able to find him in FindMyPast in 1891 and 1901, but not in 1881 for some reason. However, there seems to be something odd. In the 1891 census William is a coal miner, still living in Airdrie - he seems to be the same one, with his wife Agnes. The oil works records list a William Davies, a tenant in 1888, 1889 and 1892, in their housing, actually in Pumpherston, not Uphall. It would be odd for William to go home and become a coal miner for one year. Does the 1881 census record him in Uphall? If it does he must have done.
Don