The mayor shall designate one member as chairman, who shall also act as secretary. Two members shall be a quorum for the transaction of business. If a member ceases to be a resident of the city for which he is appointed or becomes unable to perform his official duties, there shall be a vacancy in the board. All vacancies shall be filled by the mayor for the remainder of the unexpired term in the manner provided for an original appointment.
Mass. Gen. Laws ch. 138, § 6