This book is extremely rare.  

The reasons are: 

1) the copies still in existence worldwide are only about six!  And 

2) the map of The Middle States shows a small city on the Allegany River called “Hamilton”.  This is actually the location of the city of Olean, NY.  

3) this is the last edition prior to the changes with Texas.  In this edition, Texas is not even mentioned in the brief description for Mexico.  The boundary line on the maps show the current US Southwest still being a part of Mexico.  Interestingly, the author's description of the people of Mexico are brief and quite insulting!  It states:  ..."The white people of the country are very wicked and indolent.  The Indians are numerous, and ignorant, though they are said to be very fond of music.  They usually go naked."  And, also, ..."The mint or place for coining money in Mexico, is the richest in the world."  

As for the map that should be showing Olean, NY, this is the only map of New York I have ever seen with Olean being called Hamilton.  

There was a Hamilton, NY, in Eastern New York State.  

This was evidently unknown to the early residents of Olean.  Olean was founded in 1804 by people with connections to the American Revolution, in particular, Alexander Hamilton, who owned property about 30 miles East of Olean, in Belvidere, NY, near Belfast, NY.    However, just after Olean was founded, Hamilton was shot and killed in his famous duel with Aaron Burr.  The people of Olean wanted to change the name of this new village from Olean to Hamilton.  When they communicated this intention to the postal officials in Rochester, NY, they replied that this was not a good idea.  They pointed out that Olean had just been registered as the name for this new settlement and to try to change it would only result in confusion.  

The early settlers of Olean did try to commemorate the memory of Alexander Hamilton by naming a river landing south of the city center “Hamilton Point”.  The name never caught on.

The minister author of this little book for children evidently did not get the notice of the failure to change the name.  Thus, in his map he does not mention Olean.  Instead he marks the location as Hamilton.

I wish to repeat that I have never seen another map ever substitute Hamilton for Olean.  Never!

Thus, this book is rather unique.  

The World Cat shows only six book copies to actually exist in all editions.  It does not locate any copies of this  Fourth Edition anywhere.

Google books does have a copy of this Fourth Edition available for free on line.

The book is:  

A GEOGRAPHY FOR CHILDREN. By H. N. Brinsmade, A.M.

Embellished With Numerous Engravings Illustrating The Subjects, and Ten Neatly Engraved Maps.

FOURTH EDITION.

HARTFORD:

Published By H. F. Sumner & Co.

1835. 

124 pages.

The book measures approximately 4 ⅝ by 5 ½ inches.

There is occasional scattered foxing.

The covers are worn and darkened from age.  There is a section of the front cover missing (about 2 by 1 ¾ inches).  The blank front end page is has about a third of the bottom of the page missing.

This copy belonged to David O. Lyon, Esquire of Bloomington,  Mc Lean County.

This David O Lyon may have become a minister and moved from Bloomington.

As for the author, we thank Wikipedia for the following biography:

Dr. Horatio N. Brinsmade was the son of Thomas C. and Elizabeth Brinsmade, and was born at New Hartford, Conn., Dec. 18, 1798. He received his preparation for college at Phillips' Academy, Andover, Mass., from John Adams, and was graduated from Yale College in September 1822. He united with the Congregational church of his native town, New Hartford, upon profession of his faith, at seventeen years of age. Immediately after leaving Yale, he entered the Princeton Seminary, where he remained nearly one year, after which he went to Hartford, Conn., and studied theology about two years under the Rev. Joel Hawes, D.D., teaching also in the Deaf and Dumb Asylum in that city from May 1823 until December 1831. He was licensed by the North Congregational Association of Hartford in June 1824, and was ordained by the same body as an Evangelist June 1, 1828. He supplied the North Congregational church in Hartford a part of the years 1827 and 1828, preaching also for other churches in the vicinity during the most of his residence in Hartford.

In Dec 1831, he left Hartford and began to preach at Collinsville, Hartford Co., Conn. At this place a Congregational church was organized in August 1832, which he served until Nov. 1834. At the latter date he began to preach at Pittsfield, Mass., where he was installed pastor of the First Congregational church Feb. 11, 1835. Here he labored with great popularity and success for six and a-half years, and was released Sept. 9, 1841, having accepted a call to the Third Presbyterian church of Newark, N.J. Over this new charge he was installed Sept. 23, 1841, and here he labored with large acceptance and usefulness for twelve years. On Oct. 9, 1853, he was released by the Presbytary of Passaic. His next pastorate was over the First Congregational church of Beloit, Wis., where he was installed Feb. 10, 1854, and closed seven highly successful years of labor, Jan. 1, 1861. From Beloit, he returned to Newark, N. J., where he commenced labors with a mission of the Third Presbyterian church, as a result of which the Wickliffe Presbyterian church was organized by the Presbytery of Passaic, May 14, 1865. He continued to serve this young church as stated supply until April 15, 1867, at which date he was duly installed as its pastor, from which pastoral relation he was released by Newark Presbytery April 17, 1872. He continued, however, to reside in Newark, preaching often, useful in many ways to the church and the community, honored and beloved by all around him, until his death. This event will occurred Jan. 18, 1879, in the 81st year of his age. His voice was heard in exhortation and prayer a few days previously in the meetings held during the week of prayer, with no abatement of its natural force. His death was sudden, probably of heart disease, but all with him was light, and peace and joy in believing.

Dr. Brinsmade was thrice married. First, at Farmington, Conn., to Maria S., daughter of the Rev. Joseph Washburn, Sept. 29, 1825. Secondly, at Collinsville, Conn., to Amelia, daughter of Alexander Collins, April 29, 1833. Thirdly, at Great Barrington, Mass., Jan. 1, 1866, to Anna M., daughter of George Warner. His last wife survives him, but he has buried all his children, four in number.

Dr. Brinsmade was one of the best of men, and one of the most faithful and useful of pastors. His preaching was always with earnestness and love. He spent and was spent in the service of Christ. Having travelled extensively in Europe and the East, he had broad and intelligent views. He was faithful, affectionate, devout. The law of love was the rule of his life. He made the impress of his piety and fidelity of all who came within the reach of his influence.