During the construction period of any public works job, the urban county engineer or his assistant assigned to lay out, supervise and inspect such construction work shall measure and determine the accurate quantities of all items of construction which may not be seen or accurately measured at a later date; and a record of such measurements and quantities shall be kept on file in the office of the urban county engineer for use in calculating quantities to be used in the final estimate. Promptly upon the completion of any public works job, the urban county engineer or his assistant in charge of such work shall measure and determine the actual quantities of all items comprising such job according to methods and standards employed in good engineering practice and shall incorporate all such items and quantities in the final estimate.