Should the owner or operator of any private railroad, skid road, flume, canal, watercourse or other easement operating over lands acquired since the fifteenth day of June, 1911, or hereafter acquired, from the state, as in the previous sections provided, fail to agree with the state, or any grantee thereof, as to the reasonable and proper rules, regulations and charges, concerning the transportation of timber, mineral, stone, sand, gravel or other valuable materials, from lands contiguous to, or in proximity to, the lands over which such private railroad, skid road, flume, canal, watercourse or other easement, is operated, for transporting or moving such valuable materials, the state, or such person, firm or corporation, owning and desiring to have such valuable materials transported or moved, may apply to the state utilities and transportation commission and have the reasonableness of the rules and regulations and charges inquired into, and it shall be the duty of the utilities and transportation commission to inquire into the same and it is hereby given the same power and authority to investigate the same as it is now authorized to investigate or inquire into the reasonableness of rules, regulations and charges made by railroad companies, and it is authorized and empowered to make any such order as it would make in an inquiry against a railroad company, and in case such private railroad, skid road, flume, canal, watercourse or easement, is not then in use, may make such reasonable, proper and just rules and regulations concerning the use thereof for the purposes aforesaid as may be just and proper, and such order shall have the same force and effect, and be binding upon the parties to such hearing, as though such hearing and order was made affecting a common carrier railroad.