Unless otherwise expressly fixed or provided by law, the heads of the departments hereinabove enumerated shall each select and appoint his or their respective subordinates, and may at any time remove a subordinate and appoint his successor; and the subordinate shall perform such duties as shall be prescribed by the said head or heads of his department. Unless as to a particular subordinate, some other form of oath is prescribed by law, every subordinate shall take and subscribe an oath well and faithfully to perform all the duties incumbent upon him, which oath shall be filed in the office of the secretary of state.