The Mayor with the approval of Council shall appoint a board of five directors, chosen from the citizens at large of Greenbrier County with reference to their fitness for such office. The Directors shall hold office for five years from the first day of July following their appointment, and until their successors are appointed and qualified; provided that upon their first appointment under this article, a proportionate number shall be appointed for one year, for two years, for three years, for four years and for five years; and thereafter all appointments shall be for terms of five years. Vacancies in the Board shall immediately be reported by the Board to Council and filled by appointment in like manner, and if for an unexpired term, for the remainder of that term only. A Director may be removed for just cause in the manner provided by the bylaws of the Library Board. No compensation shall be paid or allowed any Director.