Every grant, deed, conveyance, lease or contract hereafter made to any person, firm or corporation over and across any state lands for the purpose of right-of-way for any logging and/or lumbering railroad, private railroad, skid road, flume, canal, watercourse or other easement to be used in the hauling of timber, stone, mineral or other natural products of the land and the manufactured products thereof and all necessary machinery, supplies or materials to be used in transporting, cutting, manufacturing, mining or quarrying any or all of such products, shall be subject to the right of the state, or any grantee or successor in interest thereof, owning or hereafter acquiring from the state any timber, stone, mineral, or other natural products, or any state lands containing valuable timber, stone, mineral or other natural products of the land, of having such timber, stone, mineral or other natural products, and the manufactured products thereof and all necessary machinery, supplies or materials to be used in transporting, cutting, manufacturing, mining or quarrying any or all of such products transported or moved over such railroad, skid road, flume, canal, watercourse or other easement, after the same is or has been put in operation, upon paying therefor just and reasonable rates for transportation or for the use of such railroad, skid road, flume, canal, watercourse or other easement, and upon complying with just, reasonable and proper rules affecting such transportation, which rates, rules and regulations shall be under the supervision and control of the utilities and transportation commission of the state of Washington.