Before the board of supervisors will be authorized to take action under Sections 19-5-53, 19-5-55, a petition containing the names of not less than one hundred contestants in the county must be on file in the office of the chancery clerk of the county on or before the first Monday of January, in the year in which the premiums are to be offered. Publications of the premiums must be made on or before the 15th day of February in the year in which they are to be offered.