Pursuant to Article 16, § 271 of the Town Law of the State of New York, the Town of Barton shall appoint five members to such Planning Board which shall include one full voting agricultural member and designate the chairperson thereof. The terms of members of the Planning Board shall be for terms so fixed that the term of one member shall expire at the end of the calendar year in which such members were initially appointed. The terms of the remaining members shall be so fixed that one term shall expire at the end of each calendar year thereafter. At the expiration of the term of each member first appointed, his or her successor shall be appointed for a term which shall be equal in years to the number of members of the Board.