For instantaneousness of observation, the equatorial has great advantage over the circle or sextant; for being truly placed in the meridian beforehand, the telescope may be directed sufficiently in advance of the moon's motion, for time to note its place on the equatorial circle, before she attains that point. Then observe, until her limb touches the cross-hairs; and in that instant direct the telescope to the star; that completes the observation, and the place of the star may be read at leisure. The apparatus for correcting the effects of refraction and parallax, which is fixed on the eye-tube of the telescope, saves time by rendering the notation of altitudes unnecessary, and dispenses with the use of either a time-keeper or portable pendulum. I have observed that, if placed in a desert where neither meridian nor latitude is yet ascertained, the equatorial enables the observer to find both in a few hours. For the latitude, adjust by the cross-levels the azimuth plane of the instrument to the horizon of the place. Bring down the equatorial plane to an exact parallelism with it, its pole then becoming vertical. By the nut and pinion commanding it, and by that of the semi-circle of declination, direct the telescope to the sun. Follow its path with the telescope by the combined use of these two pinions, and when it has attained its greatest altitude, calculate the latitude as when taken by a sextant. For finding the meridian, set the azimuth circle to the horizon, elevate the equatorial circle to the complement of the latitude, and fix it by the clamp and tightening screw of the two brass segments of arches below. By the declination semicircle set the telescope to the sun's declination of the moment. Turn the instrument towards the meridian by guess, and by the combined movement of the equatorial and azimuth circles direct the telescope to the sun, then by the pinion of the equatorial alone, follow the path of the sun with the telescope. If it swerves from that path, turn the azimuth circle until it shall follow the sun accurately. A distant stake or tree should mark the meridian, to guard against its loss by any accidental jostle of the instrument. The 12 o'clock line will then be in the true meridian, and the axis of the equatorial circle will be parallel with that of the earth. The instrument is then in its true position for the observations of the night. To the competence and the advantages of this method, I will only add that these instruments are high-priced. Mine cost thirty-five guineas in Ramsden's shop, a little before the Revolution. I will lengthen my letter, already too long, only by assurances of my great esteem and respect. TO ---- NICHOLAS. MONTICELLO, December 11, 1821.