The state engineer or division engineer shall rate the measuring flume and weirs referred to in sections 37-84-112 to 37-84-117, and the original notes of such rating, together with a complete table compiled therefrom, shall be filed as a part of the records of the office of the state engineer, and the state engineer shall supply the division engineer of the division in which such measuring flumes or weirs are located with a copy of such rating table, which shall be used by him in measuring water flowing to and from such natural stream.