Any entryman under sections 321 to 323, 325, and 327 to 329 of this title who shall show to the satisfaction of the Secretary of the Interior or such officer as he may designate that he has in good faith complied with the terms, requirements, and provisions of said sections, but that because of some unavoidable delay in the construction of the irrigating works intended to convey water to the said lands, he is, without fault on his part, unable to make proof of the reclamation and cultivation of said land, as required by said sections, shall, upon filing his corroborated affidavit with the land office in which said land is located, setting forth said facts, be allowed an additional period of not to exceed three years, within the discretion of the Secretary or such officer, within which to furnish proof as required by said sections of the completion of said work.