Sec. 5. (a) The board of trustees of Vincennes University shall from time to time:
(1) elect and appoint a professor of divinity, of law, and of physic, whenever:
(A) the board of trustees considers it necessary for the good of Vincennes University; or
(B) the progressed state of education in Vincennes University may require;
(2) agree with them for their salaries; and
(3) point out the duties of the professors.
(b) The professors elected and appointed under this section shall be considered to be members of the faculty of Vincennes University. Professors hold their appointments at the pleasure of the board of trustees of Vincennes University.