Partial payments on contracts shall be made, from time to time, to the contractor as the work progresses, based upon estimates made by the superintendent of construction, setting forth the relative value of work done, and by him approved at the time of estimate, as compared with the total contract price. All such estimates shall be approved by the department. At no time before the completion of the work, and final approval thereof by the court, shall any payment or payments be made in excess of eighty per centum (80%) of the estimated value of work done, and approved by the superintendent of construction. If, by the report of the inspectors, it appears that said bridge has been built in conformity with the terms of the contract and specifications, and such report is approved by the court, payment shall be made of all the contract price not previously paid. Upon approval of any estimate by the department, or upon approval by the court of the report of the inspectors finding that the bridge has been built in conformity with the terms of the contract and specifications, as the case may be, it shall become the duty of the Auditor General to draw a proper warrant upon the State Treasurer in accordance with the foregoing, payable out of the appropriation specifically made for such purpose.