If the tax first levied shall prove insufficient to complete the improvement, the commissioners shall report the amount of the deficiency to the board of supervisors, and the board of supervisors shall thereupon make another levy on the property previously assessed for a sum sufficient to complete the improvement, which shall be collected in the same manner as the first levy. When any work has been begun under the provisions of this chapter, which shall not be completed and paid for out of the first or other levy, it shall be the duty of the board of supervisors to make such levy for its completion, and from year to year until it is completed, provided that the total levy shall in no case exceed the value of the benefits assessed on said property. The performance of such duty may be enforced by mandamus at the instance of any person or board interested.