In conformity to the act of Congress of the United States, entitled "An act for the encouragement of learning by securing the copies of Maps, Charts and Books to the proprietors of such copies during the times therein mentioned;" and also of the act entitled "An act supplementary to an act entitled an act for the encouragement of learning by securing the copies of Maps, Charts and Books, to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraving and etching historical and other prints." Attest, WILLIAM KEY BOND, CLERK. ADVERTISEMENT. The writer of the following work is said to be a resident of the Miami country. After reading Captain Symmes's numbers, and hearing some of his lectures, he wrote the work, it seems, in the first place without the idea of publication; but afterwards corrected and enlarged it, and left it with a friend of Captain Symmes for publication, sometime in the autumn of the year 1824. The nett profits were then, as now, to be paid to Captain Symmes, towards enabling him to promote and establish his principles: but owing to the absence of the author, and other circumstances, it has remained unpublished till now. The author has chosen to present the work anonymously; and has obtained the promise of Captain Symmes to forbear criticising it in manuscript,――reserving any remarks or corrections, he may wish to make, for future publication. Some _errors of the press_ will doubtless be discovered; as (in the absence of both Compiler and Theorist) there was no _proof-reader_ at hand, sufficiently versed in the New Theory, at all times, to detect them. THE PUBLISHERS. _Cincinnati, April, 1826._ To the Public. The following little treatise, was written in the autumn of the year eighteen hundred and twenty-four; when from the urgency of my common avocation, and from a desire to remain _incognito_, the manuscript was placed in the hands of a friend of Captain Symmes for publication. As it was not my intention to seek a publisher, or make advances to facilitate its progress, I left the country for a considerable length of time, without paying any further attention to the subject. Various difficulties intervening, delayed the publication, until _subsequent events_, have destroyed my chief inducement; which was, that these speculations, compiled from a cursory examination of facts, should go forth as a harbinger, merely, and not "_follow in the wake_," of public investigation. THE AUTHOR. _March, 1826._ Preface.