That the petition provided for in the next preceding section shall describe the territory proposed for annexation to and incorporation into the improvement district by sections or subdivisions of sections, according to the government survey, or by metes and bounds, and state that the taxpayers residing within the area therein embraced desire to be incorporated into the improvement district, or state that the owners of the area therein embraced if there be no resident taxpayers within such area desire to be incorporated within the improvement district, which shall be specified by corporate name in the petition.