While this is most likely from the 1838 edition of Bradford's atlas and Walter's notes indicate that, the color palette doesn't match other copies available online that are defintely from that atlas. However, the colors also vary between those maps.
Different sources have different publication dates for this atlas. The Library of Congress uses information from the supplementary index to date it to 1843. This is a fine steel engraving typical of Archer's work.
While Cary's maps of this area are almost indistinguishable from one another, the size of the map and the date indicate this was most likely published in "A New Elementary Atlas". The 1813 version of this map appears to be quite rare.
This map was apparently copied from Morse's American Geography. However because there are no notes on the map and the north eastern boundary between the United States and British North America (specifically New Brunswick and Quebec) had been under negotiation at various times since 1783 we can't determine which edition of American Geography it was copied from. The topic of the north eastern boundary would have been of interest at this time as it was finally resolved in 1842.
The following note accompanies this map and is signed by Walter: "This chart was given to me September 20, 1995 by Dr. John E. Dornbach of Seabrook, Texas. This is one of the two charts carried by Col. John H. Glenn on the first U.S. manned orbital flight in the Project Mercury Gemini capsule Friendship 7, February 20, 1962. The three-orbit flight covered approximately 130,000 km. in 4 hours, 55 minutes. Dr. Dornbach was the person responsible for producing this chart for Aeronautical Chart and Information Center at that time. Later he was transferred to N.A.S.A. to produce the Lunar lander maps and ultimately became the Director of the Earth Resources branch at NASA. John Dornbach was a classmate of mine in the Geography Graduate School at Clark University, Worcester, Mass. in 1950-52. Walter K. Morrison."