The presiding officer of the county board with the advice and consent of the county board shall appoint a board of appeals consisting of 5 members and may appoint 2 alternate members, the 5 members to serve respectively for the following terms: one for one year, one for 2 years, one for 3 years, one for 4 years and one for 5 years; and the alternate members to serve respectively for 4 years and 5 years. The successor to each member so appointed shall serve for a term of 5 years. Alternate members, if appointed, shall serve as members of the board only in the absence of regular members, with the alternate member who has the greatest amount of time remaining in his or her term to have priority over the other alternate member in determining which alternate member shall serve in the absence of a regular member. In counties of less than 1,000,000 population the presiding officer of the county board with the advice and consent of the county board may appoint an additional 2 members to serve for a term of 5 years. At the end of the term of the 2 additional members, the county board may provide for the appointment of successors in the same manner or may allow the board of appeals to revert to a membership of 5. One of the members so appointed shall be named as chairman at the time of his appointment, and in case of vacancy the appointing power shall designate a chairman. All members of a board of appeals shall be residents of separate townships at the time of their appointments, except that in counties containing fewer than 5 townships, or fewer than 7 townships if the county board has provided for the appointment of 2 additional members, that limitation shall not be applicable. The appointing authority shall have the power to remove any member of the board for cause, after public hearing. Vacancies shall be filled by the appointing authority for the unexpired term of any member whose place has become vacant. The members of the board of appeals shall be compensated on a per diem basis with a mileage allowance for travel, the amounts to be determined by the county board. All meetings of the board of appeals shall be held at the call of the chairman and at such times and places within the county as the board may determine. The chairman, or in his absence the acting chairman may administer oaths and compel the attendance of witnesses. All meetings of the board shall be open to the public. The board shall keep minutes of its proceedings, showing the vote of each member upon every question, or if absent or failing to vote, indicating such fact, and shall also keep records of its examinations and other official actions. Every rule, regulation, every amendment or repeal thereof, and every order, requirement, decision or determination of the board shall immediately be filed in the office of the board and shall be a public record. In the performance of its duties the board of appeals may incur such expenditures as are authorized by the county board.