In cities of fifty thousand inhabitants or more, in addition to the three commissioners of public works to be elected as provided in § 5-31-210, the mayor and the chairman of the committee on water supply, if there be such a committee, shall be ex officio commissioners of public works. In such cities such commissioners of public works shall serve without compensation. The board of commissioners of public works in any such city shall fill any vacancy occurring in the commission by appointment for the unexpired term, appointment to be made by the remaining commissioners, except in the case of an ex officio member of the commission.