Whenever it may become necessary for the owner or owners of a mill to construct a mill ditch, when the same is to be constructed in whole or in part over the land of another owner, and the said owner does not permit the construction of said ditch, then and in that event, the owner of the mill and the owner of the land over which the ditch is to pass shall apply to the justice of the peace [magistrate], of the precinct asking him to appoint three arbitrators or assessors, each party shall name one and the justice [magistrate] shall name the third, but if the landowner refuses to name one then the justice [magistrate] shall name two and the owner of the mill one.