Each board of law library trustees shall meet regularly each month on such day as it shall appoint, but if it appoint no day, it shall meet on the first Tuesday after the first Saturday of each month, and any board may meet at such other times as it may appoint, at a place to be designated for that purpose. The president of the board may call a special meeting at any time for the transaction of necessary business. A majority of the members constitutes a quorum for business, and an affirmative vote of a majority of the members is required to exercise the powers of the board.