Wherever, on a hearing by the court, or before a jury, the amount of any assessment is reduced or cancelled, so that there is a deficiency in the total amount remaining assessed in the proceeding, the court may, in the same proceeding, distribute this deficiency upon the other property in the district assessed, in such manner as the court finds just and equitable, not exceeding, however, the amount such property will be benefited by the specified improvement.
     In case any portion of this deficiency is 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. The owners of or parties interested in such property have the right to object in the same form and with the same effect as in case of the original assessment, and the court has the same power to dispose thereof.