Where a person has chosen to let his land lie open, if he shall afterwards enclose or use such land, or portion thereof, for agricultural, horticultural, grazing or livestock purposes, he shall refund to the adjoining owner a just proportion of the value of the partition fence adjoining such lands, or portion thereof, enclosed or so used that shall have been made by such adjoining owner, regardless of whether or not such fence at the time is a lawful fence.