A.   Appointment: The mayor is hereby authorized, with the approval of the city council, to appoint a board of nine (9) trustees for the library association, in accordance with the statutes in such case made and provided. (1925 Code § 37-3)
   B.   Terms Of Office: The trustees shall hold office, one-third (1/3) for one year, one-third (1/3) for two (2) years and one- third (1/3) for three (3) years from July 1 following their appointment, and at their regular meeting shall cast lots for their respective terms, and annually thereafter, the mayor shall, before July 1 of each year, appoint as before three (3) trustees to take the place of the retiring trustees, who shall hold office for three (3) years and until their successors are appointed. The mayor may, by and with the consent of the city council, remove any trustee for misconduct or neglect of duty. (1925 Code § 37-4)