A petition addressed to the county board praying for the incorporation of a district, signed by or on behalf of at least fifty percent of the owners of the land within the proposed district may be filed with the county clerk. The petition shall define the boundaries of the proposed district and shall state (1) that the lands within such boundaries are without an adequate water supply; (2) that the construction and maintenance of ponds or reservoirs or pipelines or wells or check dams or pumping installations, or any other facility for water storage, transportation or utilization, or that the construction and maintenance of any combination of such projects is necessary for the improvement of the area; and (3) that such improvement or works will be conducive to and will promote the public health, convenience and welfare.