In all such cities, a board, consisting of the judges of the circuit court of such city, or of the judicial circuit in which such city is situated, or a majority of the same, shall, on or before the first day of January, 1912, and every two years thereafter, cause to be published in some daily newspaper of said city a notice for at least ten days announcing and designating the time and place when and where the said board shall have a hearing to determine what newspapers in such cities are eligible to publish such notices under the provisions of the foregoing section. The publishers of newspapers desiring the right to publish such notices shall, upon or prior to the date of such hearing, file with said board a petition, verified by the affidavit of such publishers, directed to said board petitioning for such right and setting forth that such newspaper has the required circulation as set forth in the foregoing section. At the time and place so designated the said board shall determine, by such method as shall seem to it best, what newspapers so making application are eligible under the provisions of the foregoing section, and a record of the decisions of the board and a list of the newspapers so declared eligible shall be made in such court and in such manner as the board shall determine.