Within thirty days after any drainage district shall have been organized and established under the provisions of this article the circuit clerk of the court organizing such district shall call a meeting of the owners of real estate or other property situate in such district, at a day and hour specified, in some public place in the county in which the district was organized, for the purpose of electing a board of three supervisors, to be composed of owners of real estate in such district, two of whom at least shall be residents of the county or counties in which such district is situate, or some adjoining counties. Notice of such meeting shall be given by such clerk by causing publication thereof to be made as a Class II legal advertisement in compliance with the provisions of article three, chapter fifty-nine of this code, and the publication area for such publication shall be each county in which lands of the district are situate. The last publication shall be at least ten days before the day of such meeting. The landowners, when assembled, shall organize by the election of a chairman and a secretary of the meeting who shall conduct the election. At such election each owner shall be entitled to one vote in person or by proxy for every acre of land or mile of right-of-way owned by him in such district, and the three persons receiving the highest number of votes shall be declared elected as supervisors. Such supervisors shall immediately by lot determine the terms of their office, which shall be respectively one, two and three years, and they shall serve until their successors shall have been elected and qualified.