The state university shall be under the management and control of a board of trustees, which shall consist of two members from the congressional district in which the university is located, one from each of the other congressional districts in the state, the superintendent of education, and the governor, who shall be ex officio president of the board. The members of the board of trustees as now constituted shall hold office until their respective terms expire under existing law, and until their successors shall be elected and confirmed as hereinafter required. Successors to those trustees whose terms expire in nineteen hundred and two shall hold office until nineteen hundred and seven; successors to those trustees whose terms expire in nineteen hundred and four shall hold office until nineteen hundred and eleven; successors to those trustees whose terms expire in nineteen hundred and six shall hold office until nineteen hundred and fifteen; and thereafter their successors shall hold office for a term of twelve years. When the term of any member of such board shall expire, the remaining members of the board shall, by secret ballot, elect his successor; provided, that any trustee so elected shall hold office from the date of his election until his confirmation or rejection by the senate, and, if confirmed, until the expiration of the term for which he was elected, and until his successor is elected. At every meeting of the legislature the superintendent of education shall certify to the senate the names of all who shall have been so elected since the last session of the legislature, and the senate shall confirm or reject them, as it shall determine is for the best interest of the university. If it reject the names of any members, it shall thereupon elect trustees in the stead of those rejected. In case of a vacancy on said board by death or resignation of a member, or from any cause other than the expiration of his term of office, the board shall elect his successor, who shall hold office until the next session of the legislature. No trustee shall receive any pay or emolument other than his actual expenses incurred in the discharge of his duties as such.