In case of the absence of the Mayor from the City or his or her inability to serve, the President of the Board of Aldermen shall act as Mayor. It shall be the duty of the Mayor to give the City Clerk due notice of the absence of the Mayor from the City and of his or her return, and said City Clerk shall duly notify the President of the Board of Aldermen. In case of the absence from the City or inability to serve of the President of the Board of Aldermen, the Board of Aldermen shall designate one of their number to act as Mayor.