You have often gratified me by your astronomical communications, and I am now about to amuse you with one of mine. but I must first explain the circumstances which have drawn me into a speculation so foreign to the path of life which the times in which I have lived, more than my own inclinations have led me to pursue.

I had long deemed it incumbent on the authorities of our country to have the great Western wilderness beyond the Missisipi explored, to make known it’s geography, it’s natural productions, it’s general character and inhabitants. two attempts which I had myself made formerly, before the country was ours, the one from West to East, the other from East to West, had both proved abortive. when called to the administration of the General government, I made this an object of early attention, and proposed it to Congress. they voted a sum of 5000.D. for it’s execution, and I placed Capn Lewis at the head of the enterprise. no man, within the range of my acquaintance, united so many of the qualifications necessary for it’s succesful direction. but he had not recieved such an Astronomical education as might enable him to give us the geography of the country with the precision desired. the Missouri and Columbia, which were to constitute the tract of his journey, were rivers which varied little in their progressive latitudes, but changed their longitudes rapidly and at every step. to qualify him for making these observations, so important to the value of the enterprise, I encouraged him to apply himself to this particular object, and gave him letters to Doctr Patterson and mr Ellicott requesting them to instruct him in the necessary processes. those for the longitude would of course be founded on the lunar distances. but as these require essentially the aid of a time keeper, it occurred to me that during a journey of 2. 3. or 4. years, exposed to so many accidents as himself and the instrument would be, we might expect with certainty that it would become deranged, and in a desert country, where it could not be repaired. I thought it then highly important that some means of observation should be furnished him, if any could be, which should be practicable and competent to ascertain his longitudes in that event. the Equatorial occurred to myself as the most promising substitute. I observed only that Ramsden, in his explanation of it’s uses, and particularly that of finding the longitude at land still required his Observer to have the aid of a timekeeper. but this cannot be necessary. for the margin of the equatorial circle of this instrument being divided into time by hours, minutes & seconds, supplies the main functions of the time keeper, and for measuring merely the interval of the observations, if such as not to be neglected, a portable pendulum, for counting by an Assistant, would fully answer that purpose. I suggested my fears to several of our best astronomical friends, and my wishes that other processes should be furnished him, if any could be, which might guard us ultimately from disappointment. several other methods were proposed, but all requiring the use of a time keeper. that of the Equatorial being recommended by none, and other duties refusing one time for protracted consultations, I relinquished the idea for that occasion. but, if a sound one, it should not be abandoned. those deserts are yet to be explored, and their geography given to the world and ourselves with a correctness worthy of the science of the age. the acquisition of the country before Capt Lewis’s departure facilitated our enterprise. but his time keeper failed early in his journey. his dependance then was on the compass, & log line, with the correction of latitudes only, and the true longitudes of the different points of the Missouri, of the Stony mountains, the Columbia, and Pacific, at it’s mouth, remain yet to be obtained by future enterprise.

The circumstance which occasions a recurrence of the subject to my mind at this time particularly is this. our legislature, some time ago, came to a determination that an accurate map should be made of our state. the late John Wood was employed on it. it’s first elements are prepared by maps of the several counties. but these have been made by chain and compass only, which suppose the surface of the earth to be a plane. to fit them together, they must be accomodated to it’s real spherical surface; and this can be done only by observations of Latitude and Longitude, taken at different points of the area to which they are to be reduced. it is true that, in the lower and more populous parts of the state, the method of lunar distances by the circle, or sextant and timekeeper, may be used; because those parts furnish means of repairing or replacing a deranged timekeeper. but the deserts beyond the Alleganey are as destitute of resourse in that case, as those of the Missouri. the question then recurs Whether the Equatorial, without the auxiliary of a time-keeper, is not competent to the ascertainment of longitudes at land, where a fixed meridian can always be obtained? and Whether indeed it may not, every where at land, be a readier and preferable instrument for that purpose? to these questions I ask your attentions: and to shew the grounds on which I entertain the opinion myself, I will briefly explain the principles of the process, and the peculiarities of the instrument which give it the competence I ascribe to it. and should you concur in the opinion, I will further ask you to notice any particular circumstances claiming attention in the process, and the corrections which the observations may necessarily require. as to myself, I am an astronomer of theory only, little versed in practical observations, and the minute attentions and corrections they require. I proceed now to the explanation.

A Method of finding the longitude of a place at land, without a time keeper.

If two persons, at different points of the same hemisphere, (as Greenwich and Washington, for example) observe the same celestial phaenomenon, 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 between their meridians. to catch with precision the same instant of time for these simultaneous observations, the moon’s motion in her orbit is the best element; her change of place (about a half second of space in a second of time) is rapid enough to be ascertained by a good instrument with sufficient precision for the object. but suppose the Observer at Washington, or in a desert, to be without a time keeper; the Equatorial is the instrument to be used in that case. again we have supposed a cotemporaneous Observer at Greenwich. but his functions may be supplied by the Nautical Almanac, adapted to that place, and enabling us to calculate for any instant of time the meridian distances there of the heavenly bodies necessary to be observed for this purpose.

The Observer at Washington, chusing the time when their position is suitable, is to adjust his Equatorial to his meridian, to his latitude, and to the plane of his horizon, or if he is in a desert where neither meridian, nor latitude is yet ascertained, the advantages of this noble instrument are, that it enables him to find both in the course of a few hours. thus prepared, let him ascertain by observation the right ascension of the moon from that of a known star, or their horary distance; and, at the same instant, her horary distance from his meridian. her right ascension at the instant thus ascertained, enter with that the Nautical Almanac, and calculate, by it’s tables, what was her horary distance from the meridian of Greenwich at the instant she had attained that point of right ascension, or that horary distance from the same star. the addition of these meridian distances if the moon was between the two meridians, or the subtraction of the lesser from the greater, if she was on the same side of both, is the difference of their longitudes.

This general theory admits different cases, of which the Observer may avail himself, according to the particular position of the heavenly bodies at the moment of observation.

for instantaneousness of observation the Equatorial has great advantage over the Circle or Sextant: for being truly placed in the mereidian beforehand, the telescope may be directed sufficiently in advance of the moon’s motion for time to note it’s 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 compleats the observation, and the place of the star may be read off 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, it’s pole then becoming vertical. by the nut & pinion commanding it, and by that of the semi-circle of declination, direct the telescope to the sun. follow it’s path with the telescope by the combined use of these two pinions, and when it has attained it’s greatest altitude, calculate the latitude as when taken by a sextant.

For finding the Meridian, set the Azimuth circle to the horison, elevate the Equatorial circle to the complement of the Latitude, and fix it by the clamp & 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 & 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 it’s loss by any accidental jostle of the instrument. the 12. aclock line will then be in the true meridian, & the axis of the Equatorial circle will be parallel with that of the earth. the instrument is then in it’s true position for the observations of the night. to the competence & the advantages of this method, I will only add that these instruments are high-priced. mine cost 35 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.