The Mayor shall preside at all meetings of the City except freeman's meetings, with the power of moderator in town meetings, and at meetings of the City Council. The Mayor, together with the aldermen shall constitute a Board of City Council and shall have the management of the affairs of the corporation and the necessary powers for that purpose, and in addition thereto all the powers of selectmen, and shall establish pounds. Said City Council shall hold a meeting on a stated day of each month, to be determined by that body, and oftener at the call of the Mayor. In case of the absence, resignation, or inability from any cause of the Mayor, the duties of the Office shall devolve on the senior Alderman, chosen by City Council, for the remainder of the Mayor's official term. The Mayor and aldermen shall, ex officio, have and exercise all the powers and authority of justices of the peace.