The City Clerk shall forthwith set such matter for hearing before the Council at a subsequent regular meeting and shall cause notice thereof to be given to the applicant not less than five days prior to such hearing, unless such notice is waived in writing by the applicant. At such hearing the appellant shall show cause on the grounds specified in the notice of appeal why the action excepted to should not be approved. The Council may continue the hearing from time to time, and its findings on the appeal shall be final and conclusive in the matter.
('63 Code, § 1-4.03)