In all cases where partition fences are erected as one-half (½) of the partition fence between proprietors or possessors of adjoining lands, or where the fence may be hereafter erected by the agreement of the parties in interest or other lawful manner, the proprietors of the fences in either of the cases erected, their heirs, successors, or assigns, shall hold and improve the fences without molestation; and shall be forever afterwards excused from making other fence on such dividing line in all cases whatever, except by the special agreement of the parties to the contrary; and all agreements which shall be made relating to the partition fences shall be registered in the office of the town clerk in the town where such lands shall lie.