On the presentation of a petition signed by one-fourth of the electors, as shown by the vote at the next preceding city election, of any city acting under a special charter or act of incorporation, to the governing body of the city, asking that the question of the amendment of the special charter or act of incorporation be submitted to the electors of such city, the governing body shall immediately propose sections to amend the charter or act of incorporation, and shall submit the amendment, as requested, at the first ensuing city election. At least ten days before the election, the mayor of the city shall issue a proclamation setting forth the nature and character of the amendment, and shall cause the proclamation to be published in a newspaper published in the city, or, if there be none, the mayor shall cause the amendment to be posted in five public places in the city. On the day specified, the proposition to adopt the amendment shall be submitted to the electors of the city for adoption or rejection, in the manner provided by the general election laws.