Wherever any artesian conservancy district has heretofore been organized or may hereafter be organized, under and pursuant to Chapter 97 of the New Mexico Session Laws of 1931 [73-1-1 to 73-1-13 and 73-1-16 to 73-1-23 N.M. Stat. Ann.], or amendments thereto, such conservancy district may be given the same rights, power and authority as to all underground waters within the boundaries of such conservancy district as have been or may hereafter be conferred upon such district by said legislative act, and amendments thereto, as to artesian waters; provided, however, the boundaries of such underground waters have been reasonably ascertained and the same, or a substantial portion thereof, have been beneficially appropriated for private, public, domestic or irrigation purposes and are subject to appropriation, as provided by Chapter 131 of the New Mexico Session Laws of 1931 N.M. Stat. Ann. § 72-12-1 to 72-12-10, or amendments thereto, and provided further it is determined that said underground waters, or a substantial portion thereof, are derived from the artesian basin, or basins, included, or to be included in such district, and that the same are so closely related to such artesian waters that they can be effectively conserved by said district.