All railroad companies desiring the use of any railroad bridge built in accordance with the provisions of sections 491 to 494 and 495 to 498 of this title, shall be entitled to equal rights and privileges relative to the passage of railway trains or cars over the same and over the approaches thereto upon payment of a reasonable compensation for such use; and in case of any disagreement between the parties in regard to the terms of such use or the sums to be paid all matters at issue shall be determined by the Secretary of Transportation upon hearing the allegations and proofs submitted to him.