Wherever, on a hearing by the court, or before a jury, the amount of any assessment shall be reduced or cancelled, so that there shall be a deficiency in the total amount remaining assessed in the proceeding, the court shall have the power, in the same proceeding, to distribute such deficiency upon the other property in the district assessed, in such manner as the court shall find to be just and equitable, not exceeding, however, the amount it will be benefited by said improvement. In case any portion of such deficiency be charged against such property not represented in court, a new notice, of the same nature as the original notice, shall be given in like manner as the original notice, to show the cause why the assessment, as thus increased, should not be confirmed, and the owners of or parties interested in such property shall have the right to object in the same form and with the same effect as in case of the original assessment, and the court shall have the same power to dispose thereof.