[Enter trumpets, sounding; then two Aldermen, Lord Mayor, Garter, Cranmer, Duke of Norfolk with his marshal’s staff, Duke of Suffolk, two Noblemen bearing great standing-bowls for the christening-gifts; then four Noblemen bearing a canopy, under which the Duchess of Norfolk, godmother, bearing the child richly habited in a mantle, etc., train borne by a Lady; then follows the Marchioness Dorset, the other godmother, and Ladies.
There are no more uses of "alderman" in the play.
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aldermen usually represent city wards
Mary Whitney said she [Mrs. Parkinson] ought to have been the Alderman herself, as she was the better man.