The notice shall be in writing and signed by the co-owner who performed or caused to be performed the assessment work. It shall be served upon the delinquent co-owner personally by the sheriff of the county in which the mine is situated, if the delinquent co-owner is within the county. If the delinquent co-owner can be found in any other county, then the notice shall be served by the sheriff of that county. If the delinquent co-owner cannot be found within the state, or if at the time of giving the notice the delinquent co-owner is without the state, service of the notice shall be made by publication thereof in the weekly newspaper published in the county nearest to where the mine is situated. If there are two or more papers published in the county at the same distance from the mine, the co-owner giving notice may elect in which paper the notice shall be published. If no weekly newspaper is published within the county, service of the notice shall be made by publication in any other weekly newspaper within the state published nearest the mine. The notice shall be published at least once a week for a period of 90 days after the first publication.