Dear Kate
Thank you so much for that extremely useful information - the plot now thickens as there were no matches for BRIGLEY but a handful or so for BIGLEY.
The English censuses vary too, and this makes searching for people very difficult, and matching who was related to whom!
Yet I had looked at a different search engine on another Irish site and not found 'Bigley', only Brigley.
I suspect that it was more a question of local variation, and maybe a question of times being a period when so many people emigrated from Ireland, maybe there were none left. OR maybe their name changed from ERSE {and I have no idea how Bigley or indeed Brigley would have been spelled in Erse} when they went to an English language zone such as Britain or America.
Just thinking out loud!
Thank you again - it has set me wondering who is right?
Best wishes
IMISON