Section 13. If unenclosed land is afterward enclosed or used for depasturing, the occupant or owner shall pay for one half of each partition fence standing upon the line between it and the enclosed land of any other occupant or owner, the value thereof, as determined in writing by the fence viewers; and if thereupon such occupant or owner neglects or refuses, for thirty days after demand, to pay one half of the value, the proprietor thereof may maintain an action of contract therefor and for the costs of ascertaining the same; but the occupant or owner of unenclosed land on the island of Nantucket used only for depasturing shall not be subject to this section.