All warrants issued under the provisions of this chapter shall be presented by the owners thereof to the county treasurer, who shall indorse thereon the day of presentation for payment, with the additional indorsement thereon, in case of nonpayment, that they are not paid for want of funds; and no warrant shall draw interest under the provisions of this chapter until it is so presented and indorsed by the county treasurer. And it shall be the duty of such treasurer, from time to time, when he or she has sufficient funds in his or her hands for that purpose, to advertise in the newspaper doing the county printing for the presentation to him or her for payment of as many of the outstanding warrants as he or she may be able to pay: PROVIDED, That thirty days after the first publication of said notice of the treasurer calling in any of said outstanding warrants said warrants shall cease to bear interest, which shall be stated in the notice. Said notice shall be published two weeks consecutively, and said warrants shall be called in and paid in the order of their indorsement.