When any tract of land may be filed upon, platted and recorded as a townsite in accordance with the provisions of an act of congress or law of New Mexico, and no town or organization under the laws of New Mexico shall have been perfected by the inhabitants residing thereon, or the owners thereof, the same may be vacated by consent of all such inhabitants or owners and disposed of as the said inhabitants or owners shall agree: provided, that a statement, signed and certified to by a majority of said inhabitants or owners, setting forth the fact of the vacation of such townsite, be filed with the clerk of the county in which the same shall be situated. When any tract of land has been recorded as a townsite, or has been annexed as an addition to a townsite, any part or portion thereof may be vacated upon the written consent of all the owners of that part or portion which it is proposed to vacate: provided, that no expenditures of money have been theretofore made or incurred by said town for the improvement or benefit of said part or portion, and that the same is bounded in same [whole] or in part by exterior town lines, and that when so vacated a statement, subscribed by such owners, setting forth the facts of such vacation, together with an accurate description, map and plat of such part vacated shall be filed in the office of the county clerk of the county in which such town is situated.