I think he was arguing from a shared celtic background between Ireland and the Island (a concept that was at that time in vogue) - thus he looked at the names current in Ireland of the 10th century assuming that these names would have continued in the gaelic speaking masses - the patronymics becoming surnames under the Norman (and later English) model.

However that was late 19th C - (my comment was written some 6 years ago - we still await a new published theory !)