The holders of title, or evidence of title, representing a majority of the acreage of any body of land within any irrigation district, may file with the board of directors of the district a petition in writing, praying for the construction of any improvement necessary or expedient for the efficient irrigation of the lands, including facilities for the recharge of ground water basins. The petition shall in a general way describe the proposed improvement and shall describe the tracts, or body of land, owned by the petitioners, and shall contain a description of the exterior boundaries of the land for which the proposed improvement is to be constructed, and describing therein any lands that are to be excepted from the benefit or use of the proposed improvement. The petition shall also contain an agreement on the part of the petitioners that the cost of construction of the improvement shall constitute a lien upon the lands within the exterior boundaries of the land described in the petition, except the lands that are therein excepted from the benefit or use of the proposed improvement, and that the lands shall be assessed for and pay the cost of the improvement. The petition shall be deemed to give assent of the petitioners to construction of the improvement and shall authorize the assessment of the cost of such improvement upon and against the lands described in the petition and not specifically therein excepted. The petition shall be acknowledged in the same manner that conveyances of land are required to be acknowledged.