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In the mid-1820s, banks became the first businesses in Great Britain and Ireland to be allowed to form freely on an unlimited liability joint-stock basis. Walter Bagehot warned that their shares would ultimately be owned by widows, orphans, and other impecunious individuals. Another hypothesis is that the governing bodies of these banks, constrained by special legal restrictions on share trading, acted effectively to prevent such shares being transferred to the less wealthy. We test both conjectures using the archives of an Irish joint-stock bank. The results do not support Bagehot's hypothesis.