When the whole or any portion of the improvement authorized by this Charter passes through or by a public wharf, market space, park, cemetery, structure for the Fire Department, water works, school building, infirmary, market house, work house, hospital, house of refuge, bridge, gas works, public prison, court house, church or any other public structure or public grounds within said corporation and belonging to said corporation or to the County, State or any church, association, or eleemosynary institution, the Council may authorize the proper proportion of the estimated cost and expense of the improvement to be certified to the clerk of the county court of Kanawha County, and it shall be the duty of these persons having charge of the fiscal affairs of any such property or institution to make proper arrangements for the payment of such assessments when due and payable.