the appeal is, in the case of a property tax, brought within thirty days next after the date of authentication of the assessment list under section 70 (exclusive of the time requisite for obtaining a copy of the relevant entries therein) or, as the case may be, within thirty days of the date on which an amendment is finally made under section 72 and, in the case of any other tax, within thirty days next after the date of the receipt of the notice of assessment or of alteration of assessment or, if no notice has been given, within thirty days after the date of the presentation of the first bill or, as the case may be, the first notice of demand in respect thereof;

the amount, if any, in dispute in the appeal has been deposited by the appellant in the office of the Council.