Having in the last communication I had the honor to make to you, explained the motive which induced me to transmit sundry astronomical calculations for the use of the University of Virginia, the inclosed is offered to their acceptance, thro’ you, for the purpose of promoting the knowledge of a branch of science, which, if properly attended to, may hereafter be beneficial to the American community, in ascertaining with precision, the longitude of such points as may be considered material, particularly those within my native state, for which, it will be confessed, I have always had, and still retain a partiality. I am well aware, that much study and labor are required to make any person a master of this subject; and that few in any country, comparatively speaking, turn their attention to it; but I shall not think myself unprofitably employed, to aid those few, while I have leisure, at such seminaries of learning in the United States, as I may prefer, with rules and process founded upon correct principles, which may be interesting for them to know, and may, at some future period, be usefully applied. Another reason which more immediately concerns myself, has led to this communication. Not having time, during the last fall and winter, to examine and revise the calculation founded on the solar eclipse of August, 1821, and suspecting that some errors might exist in the elements, especially in the Moon’s parallaxes, the work has been undertaken, and the results are tested by such methods and process of computation, as cannot fail to ensure their accuracy.