776. During the 6 months prescribed for the publication his or her authors, may appear at the Registrar's office and bid an increase over the sum, price, or other consideration or value, if any, mentioned in the title, and have his or her bid received, provided the increase be equal to at least 1/10 of the whole price, sum or other consideration, and the bidder offers, besides, to refund to the applicant all his or her costs and lawful disbursements, giving him or her security to that effect in the ordinary manner, or depositing for that purpose a sufficient sum, according to the discretion of the Court or Judge, reserving the subsequent completion of the precise amount.