If the city or incorporated town has no city engineer or public works commissioner, or city solicitor, then the mayor or chief executive of such city or town shall appoint 2 members, each to be appointed for a term of 3 years and removable for cause by the appointing authority upon written charges and after public hearing, who, with the presiding officer of the zoning commission, shall constitute the board of adjustment for such city or town. Vacancies shall be filled for the unexpired term of any member whose term becomes vacant.
22 Del. C. § 322