Whenever the city council, or the proper legislative body of any city, shall deem it necessary to condemn or appropriate private property and to assess the cost thereof against property in a benefit district, said legislative body shall enact an ordinance setting forth the general nature or purpose of the use to which such private property is to be put and declare it to be necessary to take and appropriate private property therein described for such purpose and define the limits of a benefit district within which private property shall be deemed benefitted or assessed to pay for such improvements, and the time and mode of payment of such assessment and the penalty for failure to pay the same when due.