Within 60 days after a county board of a single county qualified as an Authority under the provisions of Section 170-10 shall adopt a resolution or ordinance providing for an Authority, the county board chairman, with the advice and consent of the county board, shall appoint 3 members of the board for an initial term expiring the second June first after appointment; and 3 members of the board for an initial term expiring the third June first after appointment; and 3 members of the board for an initial term expiring the fifth June first after appointment, and until their successors have been appointed and qualified. At the expiration of the term of any member, the county board chairman, with the advice and consent of the county board, shall appoint his successor in like manner for a term of 5 years from the first day of June of the year in which they are appointed, except in case of an appointment to fill a vacancy.
     The Board of Authorities comprised of combinations of counties, as provided in Section 170-10, shall be appointed in the following manner: memberships for the Board shall be apportioned among the member counties, as nearly as possible, according to the proportion each county’s assessed valuation, as equalized by the Department of Revenue, of all real property located within the county bears to the total assessed valuation, as equalized by the Department of Revenue, of all real property located within the Authority. The initial terms of such appointees for each such county shall then be determined by lot. Each such county chairman, with the advice and consent of his respective county board, shall then appoint the members allotted to him in the manner provided in this Section.