Should an appeal be taken on any part of such judgment, and the municipality elect to proceed with the improvement, the clerk shall certify such appealed portion, from time to time, in the manner above mentioned, as the judgment is rendered thereon, and the warrant accompanying such certificate in each case shall be authority for the collection of so much of such assessment as shall be included in the portion of the roll thereto attached. The warrant in all cases of assessment, under this Act, shall contain a copy of such certificate of the judgment describing lots, blocks, tracts and parcels of land assessed so far as they shall be contained in the portion of the roll so certified, and the respective amount assessed on each lot, block, tract or parcel of land, and shall be delivered to the officer authorized to collect such special assessment. The collector having a warrant for any assessment levied to be paid by installments may receive any or all of the installments of such assessment, but if in part only, then in their order.