The failure of the small, but respectable, banking-house of Messrs. Hector and Co., of Petersfield, of which some mention was made in the City on Saturday, appears, unfortunately, to be confirmed. The liabilities of the concern are estimated at 30,000l. The effect of the failure of the Chichester Old Bank, recently made public, on the local interests of the neighbourhood, was, from all accounts, greatly mitigated by the seasonable interference of some members of the Lennox family, and other influential residents of that part of the country; but, although Messrs. Hector and Co. are said to be sanguine as to the payment of a good dividend, we do not hear that they have as yet been able to make any arrangement that can be attended with present benefit or relief to the holders of their notes, and creditors generally.