If any person, being requested to do so, will not contribute his proper share of the work and furnish the requisite materials suitable for a party fence, or pay the value of his share, the person desiring to build the fence may erect or construct the whole of it, of a proper and suitable kind, being a lawful fence, and may thereafter apply, in writing, to a justice of the peace, who shall appoint three (3) impartial freeholders of the neighborhood to view the fence and determine what amount should be paid by the person who has failed to contribute.