All lands exclusive of timber lands and mineral lands which will not, without irrigation, produce some agricultural crop, shall be deemed desert lands, within the meaning of sections 321 to 323, 325, and 327 to 329 of this title, which fact shall be ascertained by proof of two or more credible witnesses under oath, whose affidavits shall be filed in the land office in which said tract of land may be situated.

The determination of what may be considered desert land shall be subject to the decision and regulation of the Secretary of the Interior or such officer as he may designate.