If any person go or be upon any public land, and cut, fell, or otherwise injure any tree thereon or commit any other trespass on such land, the damages for such trespass shall not be assessed at less than the sum of two dollars ($2.00) per acre for each acre in every subdivision of forty (40) acres of land upon which any trespass was committed by the defendant, besides the statutory damages prescribed for trespass committed as to any tree or timber thereon. All such damages may be recovered in one (1) and the same action, and the secretary of state may institute suits for the recovery of any timber taken contrary to law; but this shall not apply to a person renting public land and having the license of the secretary of state to take trees or timber from contiguous woodland for fuel and the like.