I have the honor of receiving your letter of the 12th January by Mr. Freeman; I am extremely glad of his arrival, as no time ought now to be lost; the waters will begin to fall with the advancement of our Summer. Mr. Freeman is well qualified for the geographical part of the Expedition, but he did not seem fond of astronomical observation when I knew him on the line of demarkation, but I presume he has had occasion to improve himself since that time: I am much pleased that he brings with him a good Chronometer, we will endeavour to have it here for 10 or more days before the boats arrive, to enable us to ascertain its rate of going by the help of my astronomical Clock and Celestial observation; if it be found to go well, the longitudes may be ascertained as frequently and as easily as the latitudes.

I am greatly obliged by Doctor Barton’s observations and the new proposed methods for finding the Longitudes: I observe that all those methods suppose an asistant; and altho’ Mr. Patterson speaks of his last method as requiring only one person with a sextant, yet it appears that some species of a time piece is indispensible to enable him to bring into order his lunar distance and the altitudes of the two bodies, so that the whole may be referred to the same instant of time. This method has been taught not only by Mackay but by Mansfield.

With respect to my own method by the moon’s greatest altitude near the meridian requiring neither assistant nor time-piece, having lately for the first time seen Mackay’s treatise on the longitude, I there find one of his problems for finding the longitude is deduced from the moon’s meridian altitude; I at first supposed myself anticipated in my proposed method, but upon examination I find the subject treated much too lightly and no investigation given of the Correction for the meridian altitude, altho’ it is acknowledged that the greatest altitude is not on the meridian; for this reason perhaps Mackay treats the method as not susceptible of accuracy, & moreover he requires to have his apparent time previously known from the supposed longitude, which is not necessary by my method. As I consider myself only a Tyro in astronomy, I shall be glad to learn the objections which will be made to this method by Persons of eminent talents: In my own hands the results have been uniformly satisfactory.

I am much pleased to observe Mr. King’s Copy of the Map of the Washita so much resembling my own that they might be taken for Copies of each other; they would perhaps have been perfectly so, had I not contracted a little the Scale to accommodate it to the Map which is preparing by La–fon of Louisiana. Mr. Briggs has returned from the 33d degree of Latitude on the Missisippi, & he has favored me with some of his observations, but I have not yet found time to make Calculations, tho’ I already see that we shall remove Mr. Ellicott’s Missisippi farther East so as to leave more space between that and the Washita. as soon as I shall ascertain the Correction I will do myself the pleasure of forwarding it.—

I have the honor to be with perfect respect and attachment Your most Obedient Servant