Delegation of state tax powers permits officers to exercise subordinate duties, subject to conditions and excluding appellate authorities. The provision permits officers of State tax, subject to conditions and limitations imposed by the Commissioner, to exercise powers and discharge duties conferred by the Act and to act for subordinate officers; the Commissioner may delegate his powers to subordinates subject to conditions, while an Appellate Authority is expressly precluded from exercising the powers or duties of any other State tax officer.