And be it further enacted, That in case any Person or Persons shall think him, her, or themselves aggrieved by any Rate or Assessment to be made as aforesaid, it shall and may be lawful for them respectively to appeal to the Court of Mayor and Alderman of the said City, whose Decision shall be final and conclusive : Provided always, that Notice of such Appeal shall be left in Writing at the Office of the Town Clerk of the said City, within Ten Days after the Sum so rated and assessed shall be demanded ; and such Appeal shall be made to the next Court of Mayor and Aldermen of the said City, after such Notice shall be so left as aforesaid.