Instead of a prudential committee now required by law to be elected, the Bradford Academy and Graded School District at its first annual meeting shall elect three Trustees, as follows:  one for the term of one year, one for the term of two years, and one for the term of three years; and at all subsequent annual meetings, vacancies caused by the expiration of the term of office of Trustees shall be filled by the election of Trustees for the term of three years each; and all vacancies caused by resignation, death, removal from the District, or other cause, shall be filled at an annual or special meeting duly warned for that purpose, for the unexpired term of such Trustees only. Such Trustees shall have all the powers and perform all the duties of a prudential committee, and shall choose one of their number to be President, and shall appoint a Secretary of the Board of Trustees, who shall hold office for the term of one year and until their successors are chosen and appointed. All other officers of the District shall be elected in the manner prescribed by law.