CARLISLE and ANNAN.—The City of Carlisle and Royal Victoria three times a week. J. D. Thomson, Agent, 13, Water-street. LANCASTER.—The John O’Gaunt. John Hadwen, Atherton’s Buildings, Dale-street. WHITEHAVEN.—Steam packets sail three times a week during the summer months, and twice a week during the winter months, with passengers and goods. W. Dowson, Agent, 8, Goree Piazzas. WORKINGTON and MARYPORT.—The Union sails once a week during the winter, and twice a week during the summer months. J. D. Thomson, Agent, 13, Water-street. POST OFFICE. DELIVERY OF LETTERS.—The First Delivery commences at 8 a.m., and the Office continues open till the arrival of the London Mail, (per Grand Junction Railway,) 10.55 a.m. The letters comprised in this delivery are those of the over-night Birmingham Mail (with a bag from Manchester and a foreign bag from London); the Holyhead and Carlisle Mails (with bags from Edinburgh and Glasgow); and the Dublin Packet. 2nd DELIVERY—Commences about 9 a.m., with the first Manchester Mail per Railway; bringing also bags from Rochdale, Halifax, Bradford, Leeds, and York. 3rd DELIVERY—Commences about 10.45 a.m., and includes the letters by the 2nd Manchester Mail per Railway, with a bag from Newton. 4th DELIVERY—Commences about 12 noon, (and continues until about 3.40 p.m.,) in which are included bags from Birmingham, Walsall, Wolverhampton, Penkridge, Stafford, Newcastle, Nantwich, Middlewich, Northwich, Preston Brook, Warrington, Eccleshall, Stone, Towcester, Northampton, London, Bristol, Exeter, Falmouth; and the letters from Portugal, North and South America, and the West Indies, are also included in this delivery. 5th DELIVERY—Commences about ¼ past 1, p.m., and includes the letters brought by the Bristol Mail. 6th DELIVERY—Commences about 4 p.m., and includes letters brought by the 3rd Manchester Mail, per Railway. 7th DELIVERY—Commences about 4.50 p.m., and includes bags from Birmingham, Wolverhampton, Stafford, Warrington, Prescot. 8th DELIVERY—Commences ten minutes past 6 p.m., with the letters by the Lancaster Mail, from Ormskirk and Maghull. 9th DELIVERY—Commences at ¼ past 7, p.m. It includes the letters of the 4th Manchester Mail, per Railway, with Bags from York and Leeds. 10th DELIVERY—Commences about 7.30 p.m. and includes bags from Birmingham, Walsall, Wolverhampton, Penkridge, Stafford, Newcastle, Nantwich, Middlewich, Northwich, Preston Brook, Warrington, and Prescot. _The Delivery closes finally at 9 p.m._; _on Sundays at 8 p.m._ There are Three Deliveries within the Town by Letter Carriers, every day (except Sunday); the first delivery to commence about 8, a.m.; the second about 12; the third about 5, p.m. On Sundays, only the first, at 8, a.m. When any delay occurs in the arrival of the Mails, a corresponding delay will, of course, occur in the delivery. The office is closed on Sundays from 9, a.m., until 1.30, p.m., and finally at 8, p.m. DESPATCH OF LETTERS.