In making the reassessment the street superintendent shall first deduct from the amount appropriated by the legislative body the estimated cost of the reassessment proceedings. If the estimate for any reason exceeds the actual cost thereof, then the excess of the fund reserved for the payment of costs shall revert to the fund from which the appropriation was made. If the estimate proves to be insufficient to meet the costs of the reassessment, the legislative body shall appropriate such additional sums as may be necessary to meet the excess costs and expenses thereof.