If there is any suplus remaining at the close of the last contract year under any proceedings, such surplus shall be used as follows:
(a) If new proceedings are started within one year after the close of the last contract year, such surplus shall be applied toward a reduction of the first installment of the new assessment. Such part of the surplus as was collected from each zone or subdivided zone shall be applied to reduce the installment levied against that zone or subdivided zone.
(b) If new proceedings are not started within the one-year period or if one or more zones or subdivided zones are omitted for any reason from the new proceedings any such surplus shall become and remain a part of the general funds of the city.