Section 33. There shall be a board of trustees of the state library, consisting of the president of the senate, the speaker of the house of representatives and the state secretary, who shall be trustees ex-officiis, and four other persons appointed by the governor, of whom one shall be appointed annually for a four year term commencing June first of the year of appointment. An ex-officio member of the board may designate another person to serve in his place by notice in writing to the librarian. Any person so designated shall serve until such member ceases to be a member of the board ex-officio or until sooner removed by such member by notice in writing to the librarian stating the reasons for removal. The board shall elect from its membership a chairman to serve for a term of one year. The librarian shall serve as clerk to the board. Four members of the board, or their designees, shall constitute a quorum for the conduct of the official business of the board.