On a further examination of your communication of the 29th ulto I observe that you state—“If two persons at two1 points of the same hemisphere, (as Greenwich and Washington, for example) observe the same celestial phenomenon at the same instant of time, the difference of the times marked by their respective clocks, is the difference of their longitudes, or the distance of2 their meridians”. This principle is perfectly correct, when referred to the center of the Earth under those meridians; but not so, when referred to the two points on its surface. This is evident in cases of occultations, and solar eclipses. For instance, the immersion of ♈ ♉, on the 12th of January, 1813, happened at 12h 43m 39Sec P.M. at Greenwich, and at the place of observation in Washington, at 5h 46m. 49S. P.M. appt time. The difference of these times, 6h. 56m. 50S. as marked by their respective clocks, would be = 104.° 12.′ 30″, of longitude; but we find by calculation, that the time at the center of the Earth under the meridian of Washington, when the immersion happened at Greenwich, was 7h 35m 49Sec nearly, which subtracted from 12h 43m 39Sec gives 5h 7m. 50Sec in time, = 76.° 57.′ 30.″ W. of Greenwich. The place of observation was 1.′ 49.″ 75.dec of longitude West of the Capitol.

Whatever, therefore, may be the kind of observation taken, and particularly any position of the Moon compared with that of another object, it is always to be understood, that reference should be had to the Center, and not to the surface of the Earth. The Nautical Almanac, or Connaissance des Tems, gives us the Moon’s longitude, latitude, right ascension, and declination, not as seen from the surface, but as viewed from the Center of the Earth, under the meridian of Greenwich, or Paris; and if we would find the difference of meridians, by either the Moon’s longitude or right ascension, we must, by having its apparent position at any instant of time, find its true place at the same moment.

I may not have clearly understood your meaning in this respect; if not, you will please to set me right in any communication you may hereafter make on this subject.

With regard to the object of exploring the western country, and ascertaining the latitude and longitude of its prominent points, I think the object worthy of your patriotism and enlightened views.—I am apprehensive that Congress will take no further measures to establish a first meridian at the seat of the national government. Having sent Copies of my report to the President, to various sections of the U.S. and to Europe, I expected, e’re this, to have been favored with the opinions of scientific men on the work, and that Congress would, in some way, or other, sanction what has been done by some declaratory act in relation to the result which has been found. As I have already been,3 and may be further disappointed in this expectation, I should willingly undertake the calculation of the latitude and longitude of places in the we[stern] region of the U.S. provided I could in every cas[e] be furnished with observations and data that could be relied on. It would not suit me now to travel there, or undergo the fatigues and hardships of an actual observer.