PETERSFIELD, April 21.—The London and Portsmouth mail, that runs through this town, will cease running in a few days. The Portsmouth and Gosport letter bags will be sent to Southampton from London by the South Western Railway, and conveyed to Portsmouth by a cross-road mail. The London letter bags for Petersfield, Ripley, Godalming, Guildford, and Cobham, will be dropped at Esher, and sent to the different towns by mail carts.