That any person, or persons, who open the gate of any fence, or fences, of any person or persons, the same being private property, for the purpose of passing as aforesaid, [and] shall neglect to close the gate of any fence or fences after having opened the same, shall be subject to and responsible for the damage to the land, crop or grass of the owner, or owners, of such land, through such neglect; and such damage shall be appraised as provided by law.