Whenever one or more proprietors of lands in this state, the corners and boundaries of whose lands are lost, destroyed, or are in dispute, or who are desirous of having said corners and boundaries permanently re-established, and who will not enter into an agreement as provided by section one of this act, it shall be lawful for said proprietor or proprietors that they shall cause a notice, in writing, to be served on the owner or owners of adjacent tract or tracts, if known, and residing in this state; or if not known or not residing in this state, by publishing in a public newspaper published in such county, and if no newspaper shall be published, then by posting up in four different public places in said county a written or printed notice to the effect that, on a return day named therein, which shall not be later than sixty days from the date of such notice, he, she or they will make application to the circuit court of the county in which said lands are situated, for the appointment of a commission of surveyors to make survey of and to permanently establish said corners and boundaries, which notice shall be posted up at least four weeks before the time appointed for said application, and one of said notices shall be in the precinct or township in which said corners and boundaries are situated. If personal service is had on the owner or owners of adjacent lands the same shall be made at least ten days prior to the day of application named in the notice and if notice is given by publication in a newspaper the same shall be published therein once each week for three successive weeks, the first publication to be at least four weeks before the day of application named in the notice.