Whenever an employee, whose position is not exempt from merit system requirements, and who has passed his probationary period as set forth in the rules of the Manager, is disciplined by dismissal, suspension of longer than five working days within any six month period, or demotion to a lower grade and salary, he may appeal to the Board, under rules set forth by the Board; and if his appeal meets the conditions of said rules, the Board shall hear his appeal within thirty days of the effective date of the disciplinary action. After hearing the evidence on which disciplinary action was based, and the employee explanation, the Board shall render a judgment, either to affirm, reverse, or modify the decision of the appointing authority; and such judgment shall be final. In hearing any appeal, the Board shall have the power to subpoena witnesses and require the production of records. The Board may also promulgate -such additional rules as may be required to carry out the provisions of this section.