13. Whenever any person, having failed to sign the maps and papers, or to give in his objections in writing within the time prescribed by the notification or by the special notice mentioned in the last preceding section, shall, at any time before the Collector has finally confirmed the boundaries for the purposes of the survey, prefer any subsequent objection against the correctness of any maps or papers in respect of which notification or notice was issued, the Collector shall require him to deposit the estimated costs of any further inquiry which it may be necessary to make in respect of his objection; and, if the said person shall fail to deposit such costs within the time specified by the Collector, he shall be deemed for all purposes of this Act to have admitted the correctness of the said maps and papers. If the costs of any inquiry which may be deemed necessary be deposited, the Collector shall make such further inquiry at the expense of the person so objecting; and, if the objection shall seem to the Collector not to be well-founded, he may pass such order as he shall think fit in respect of the recovery from the objector of any sum expended by the Collector on the inquiry in excess of the sum deposited, and of any necessary expenses incurred by any other persons on account of such inquiry: Provided that no person so making an objection after the prescribed time shall, under any circumstances, be entitled to recover the expenses which he is required to deposit before any further inquiry is made in respect of such subsequent objection.