The supplemental assessment shall be made and collected, and notice thereof shall be given in the same manner, as nearly as may be, as in the case of the original assessment. The superintendent of streets shall prepare and file with the supplemental assessment, a diagram showing the lots or parcels of land deemed by him to have been benefited by the acquisition. The superintendent of streets shall assess upon the said several lots or parcels of land shown in said diagram, the additional acquisition cost, in proportion to the estimated benefits to be received by each of said several lots or parcels of land.