Where the commissioners of any district organized under the provisions of this article shall adopt an ordinance prescribing land-use regulations in accordance with the provisions of Section 69-27-37, they shall further provide by ordinance for the establishment of a board of adjustment. Such board of adjustment shall consist of three (3) members, each to be appointed for a term of three (3) years, except that the members first appointed shall be appointed for terms of one (1), two (2), and three (3) years, respectively. The members of each such board of adjustment shall be appointed by the State Soil and Water Conservation Committee, and shall be removable, upon notice and hearing, for neglect of duty or malfeasance in office, but for no other reason, such hearing to be conducted jointly by the State Soil and Water Conservation Committee and the commissioners of the district. Vacancies in the board of adjustment shall be filled in the same manner as original appointments, and shall be for the unexpired term of the member whose term becomes vacant. Members of the State Soil and Water Conservation Committee and the commissioners of the district shall be ineligible to appointment as members of the board of adjustment during their tenure of such other office. The members of the board of adjustment shall receive no compensation for their services but shall be entitled to expenses, including travelling expenses, necessarily incurred in the discharge of their duties. The commissioners shall pay the necessary administrative and other expenses of operation incurred by the board, upon the certificate of the chairman of the board.