At any time after the filing of a petition for the annexation of any tract or tracts of land to an existing reclamation district and not less than thirty days prior to the time fixed by the order of the board of directors of such district for the hearing upon said petition, and not thereafter, a petition may be filed with the board of directors of such district wherein the proceedings for the annexation of any tract or tracts of land to such district is pending, signed by not less than the owners of fifty-one percent of the acreage of lands in the tract or tracts of land to be annexed to such district, exclusive of land in cities and villages, who have not signed the petition for the annexation of a tract or tracts of land to such district, protesting the annexation of such tract or tracts of land to such district. The protesting petition shall list each tract or tracts of land and the total acreage of each signer opposite his name.