By an order made on Saturday, but journalized to-day, the Postmaster General has established a letter carrier arrangement for the City of New York to be called the "United States City Despatch Post" for the conveyance of letters from one part of the city to another subject to a charge on each letter of three cents, under the 20th section of the Act of 1836, and authorizes you to employ Alex. M. Greig, nominated by you as letter carrier, other carriers are to be appointed from time to time as may be required, and you are requested to nominate for that purpose. And you are also authorized to obtain the necessary fixtures, pouches, boxes, labels, stamps, etc, at not exceeding $1,200.00 for the whole and to appoint a clerk to superintend said establishment at not exceeding $1,000 per annum. You will be pleased to report the date of commencement of this arrangement. Very respectfully, Your obedient servant, S. R. HOBBIE, _First Ass't P. M. General_. JOHN LORIMER GRAHAM, _Postmaster, New York_. In another number of the same paper we have the text of the following notice concerning the same post. UNITED STATES CITY DISPATCH POST. Hours of delivery every day (Sundays excepted) at the principal office, upper P. O. Park and lower P. O. Merchants Exchange. Letters deposited before 8, 12, 3 and at the stations before 7, 11 and 2 will be sent out for delivery at 9, 1 and 4. Letters to be sent free must have a free stamp attached to them, which can be purchased at the upper and lower Post Offices and at all the stations. The charge will be 36 cents per dozen, 2 dols. 50 cents per hundred. All letters intended to be sent forward to the General Post Office for the inland mails must have a free stamp attached to them. Letters not having a free stamp will be charged 3 cents on delivery. JOHN LORIMER GRAHAM, P. M. _New York, June, 1843._