The Treasurer of State, Secretary of State, Auditor of State, and Attorney-General shall perform such duties as may be prescribed by law; they shall not hold any other office or commission, civil or military, in this State or under any State, or the United States, or any other power, at one and the same time; and in case of vacancy occurring in any of said offices, by death, resignation or otherwise, the Governor shall fill said office by appointment for the unexpired term.