I herewith transmit you, a demonstration, of a Theory of due East and West lines, which was published in the Enquirer, on the 20th of may 1815, by myself, under the signature of, a Citizen of Richmond.

I know, that it would be sufficient for you, to have only the proposition stated, as I at first gave it, to the public on the 25th of February 1815: But confess, that I have the vanity to wish you, when at liesure, to read my demonstration, which is original, as it relates to myself, being deduced from the doctrine of the Sphere and the properties of the Earth. Besides, I think it important, in developing the principles of Mapping, and may account for many irregularities, in Surveying and Navigation, which have usually been ascribed1 to the variation of the needle and other causes. My object in the demonstration, was not only to refute the reasoning of my opponents, but to illustrate the subject, so that it might be understood by surveyors and other readers unacquainted, or but slightly acquainted, with the Mathematics. Hence it appears in a language and manner not strictly scientifical. But such as it is, without farther Apology, I present it to your consideration, and if it should afford you any Satisfaction, it will be but a very small return, for that which I have long enjoyed in the perusal of your Notes.

With salutations of sincere respect, and the Kindest wishes, I remain a citizen of Richmond, and an Emigran[t] from the Banks of the Mountain stream,—O—my—chu[m]