The Supervisors representing the city and its inhabitants under the previous charter shall be and remain such Supervisors for the balance of the terms for which they were severally elected or appointed and until their successors are appointed or assume such office, in accordance with the provisions of this Charter. The first appointive Supervisors appointed under this Charter, shall be appointed and confirmed during the month of March in 1963 and shall assume office at the organizational meeting of the Eaton County Board of Supervisors in the following month of April.