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 and every acre of land in the district shall represent one share and each owner shall be entitled to one vote in person or by proxy in writing duly signed for every acre of land owned by him in such district. The three persons receiving the highest number of votes shall be declared elected as supervisors. The landowners shall at such election determine the length of the terms of each supervisor so elected by them, which shall be, respectively, one, two and three years, and they shall serve until their successors shall have been elected and qualified. The State Department of Administration at any such meeting may represent the State and shall have the right to vote for supervisors or upon any matter that may come properly before the meeting to the extent of the acreage owned by the State in such district. Such vote may be cast by any person designated by the Board. At such meeting guardians may represent their wards, executors and administrators may represent estates of deceased persons and private corporations may be represented by their officers or duly authorized agents.