Wyo. Stat. § 41-4-302
The said board shall prepare a notice, setting forth the date when the engineer will begin a measurement of the stream, and the ditches diverting the water therefrom, and a place, and a day certain, when the superintendent of the water division in which the stream to be adjudicated is situated, shall begin the taking of testimony as to the rights of the parties claiming water therefrom. Said notice shall be published in two (2) issues of a newspaper having general circulation in the county in which such stream is situated, the publication of said notice to be at least thirty (30) days prior to the beginning of taking testimony by said division superintendent, or for the measurement of the stream by the state engineer, or his assistant; and the superintendent taking such testimony shall have the power to adjourn the taking of evidence from time to time, and from place to place; provided, all places appointed and adjourned to by the superintendent shall be so situated, as related to the streams, as shall best suit the proper convenience of the persons interested in the determination of such priorities and appropriations.
W.S. 41-4-302