Authorization, composition, terms, chairperson, vacancies and compensation. A Board of Appeals is hereby authorized to be established. The word "Board," when used in this chapter, shall be construed to mean the Zoning Board of Appeals. The Board shall consist of seven members appointed by the Mayor of the City of Lexington, by and with the consent of the City Council of the City of Lexington. The members of said Board shall serve respectively for the following terms (or until their respective successors are appointed and qualified): one for one year, one for two years, one for three years, one for four years, one for five years, one for six years, and one for seven years, for the first seven appointed; and five years each for those following the first seven appointed. One of the members of the Board shall be designated by the Mayor of the City of Lexington as Chairperson, until his/her successor is appointed. Such Chairperson, or, in his/her absence, the Acting Chairperson, may administer oaths and compel the attendance of witness. The Mayor of the City of Lexington shall have the power to remove any member of said Board for cause and after a public hearing. Vacancies upon said Board shall be filled for the unexpired term of the member whose place has become vacant, in the manner herein provided for the appointment of such member. All members of the Board shall serve without compensation.