Section 2. If the mayor acts as presiding officer of the board of aldermen, he shall not vote in meetings of said board nor in conventions of the two branches of the city council. The board of aldermen may elect one of its number as president, who shall, in the absence of the mayor, preside at meetings of the board. This section shall apply to every city, notwithstanding any special law enacted prior to April twenty-ninth, eighteen hundred and eighty-two.