U.S. Corps of Topographical Engineers

Finding the Way and Fixing the Boundary:

The Science and Art of Western Map Making,
As Exemplified by William H. Emory and his Colleagues
of the U.S. Corps of Topographical Engineers


Rollie Schafer

University of North Texas

Presented at

A Sesquicentennial Mexican War Symposium

October 2-3, 1997

Fort Gibson, Oklahoma

Under the Auspices of The Oklahoma State Historical Society


I thank Mr. Bruce Hunter of the Center for Remote Sensing and Land Use Analysis at the University of North Texas, who assisted with establishing modern coordinates of latitudes and longitudes for the locations visited by W.H. Emory and J.C. Frémont in their explorations. Mr. Don Erickson of Image Exploration (Denver, Colorado) is due special thanks for transforming the original observations and the modern latitudes and longitudes to a common datum (NAD 83) for use in this study.  Ms. Sandra Anderson deserves thanks for timely assistance with the manuscript while I was learning a new word processing program. Thanks also to Dr. William Faubion for assistance in understanding and recreating the technology of mid-19th century exploration and to Messrs. Robert Dorian, Robert Elsloo, Don Erickson, and Dr. Jim Ruster who assisted in the living history presentation that complemented the symposium. 


William H. Emory, an officer of the U.S. Corps of Topographical Engineers, served both on the war front in 1846 in Northern Mexico (soon to be the American Southwest) and, after the war, in the Mexican Boundary Survey that fixed the new border between the two countries. His 1846 narrative and those of other army topographers clearly illustrate the techniques and technology used in the field to determine longitude and latitude precisely, the foundation of accurate map making. Because Emory's detailed observational notes, including raw data, were published as appendices to his narratives, we can assess his topographical accomplishments quantitatively and compare them to his contemporaries and to modern standards. This paper describes the technology and methods used by the U.S. Corps of Topographical Engineers during the Mexican War period and the challenges they faced in making scientific measurements in the field.


At the start of the 1840s, almost none of Western North America had been mapped accurately. The situation changed materially during the decade of the 1840s with the expeditions of John Charles FrémontWilliam H. Emory, and their associates of the U.S. Corps of Topographical Engineers. The Mexican-American War of 1846-47 enlarged the territory of the United States by a third and provided a strong impetus for topographical exploration that ultimately set the modern boundaries of the continental United States. The postwar Mexican Boundary Survey and the Pacific Railroad Surveys of the 1850s filled in many of the remaining blank spaces on the map of the Western United States and intense exploration continued well into the last half of the 19th century. By 1876, even the most remote Colorado stream of any size appeared on a government map and may have been assigned a name (cf. Hayden, 1876).

To make an accurate map, one must fix landmarks and measure distances accurately, i.e., relate physical geographical features to precisely determined latitudes and longitudes. The technology used by the officers of U.S. Corps of Topographical Engineers in the 1840s and 50s was the best available at the time and the technology and techniques remained little changed into the 20th century, even until the 1980s when global positioning system (GPS) technology superseded methods based on sextants and chronometers. The army topographers of the 1840s typically used precision instruments made in England and France and mathematical tables published under the auspices of the British Admiralty, although some American instruments and publications were used too1. The army topographers trained at the only engineering school in existence in the United States at the time, the U.S. Military Academy at West Point, New York.2 This paper is about the technology, science, and art of fixing latitude and longitude in the field as accomplished by the army topographers, especially one of the topographical bureau's best practitioners, William H. Emory.

The Technology of Latitude and Longitude

Latitude may be determined most easily in the Northern Hemisphere by measuring the altitude of the North Star, Polaris. By the late 18th century, an instrument called the Octant was widely used for seagoing navigation, having supplanted earlier instruments such as the cross staff and back staff. The octant, typically made of ebony wood, was a framework in the form of a sector describing an eighth of a circle (45°) with a scale of boxwood or ivory divided into 90o along the margin of the curved surface (Figure 1). A moveable arm, the index arm, carried a mirror (index mirror) at its pivot end at the apex of the sector and a pointer at the opposite end, indicating a value on the 90o scale. A peep sight, later a low power telescope, revealed to the user a horizon glass through which was viewed the horizon on the left side through a clear glass and a reflected image from a silvered surface on its right half.

Through the principle of double reflection, the user was able to view, simultaneously, the horizon directly and the reflected image of a heavenly body, such as Polaris, reflected first by the index mirror, then by the half-silvered right side of the horizon glass. Once the horizon was exactly aligned with the star image, the altitude of the star above the horizon could be read off the 90o scale at the point indicated by the pointer at the end of the index arm. By the 19th century, a vernier scale was added to increase the accuracy of the system. If the observer measured the altitude of Polaris, the octant's reading gave the latitude directly.3

The sextant materially improved the accuracy of angle measurement. Based on a sixth of a circle (60o), the sextant's scale spanned 120o, enabling a larger angle measurement. Made of brass, the sextant was fitted with interchangeable telescopes, filters for solar and lunar work, a finely divided scale,4 and a magnifier to help the user to read the scale (Figure 1). Octants were relatively inexpensive, while the precision sextant was expensive. Mariners typically used the octant for routine observations, reserving the sextant for more careful determinations (Bennett, 1987). Meriwether Lewis carried both an octant and a sextant but most of his measurements seem to have been made with the octant (Thwaites, 1959). The importance of the sextant is indicated in William H. Emory's narrative of his 1846 expedition, Notes of a Military Reconnaissance (1848), when he details one of his party's civilian employees, W. H. Peterson, solely to the "charge of horizon box and cantina for sextants."

Latitude determination on land requires a different approach than at sea because on land, the true horizon cannot be seen. Therefore, an artificial horizon is necessary to supply a point of reference to substitute for the missing horizon. Artificial horizons used by army topographers typically employed a pool of mercury in a wooden or iron pan set on the ground.5 The mercury formed a self-leveling, reflective surface perfectly tangent to the Earth's surface. Most artificial horizons were provided with a tent-shaped cover with optically flat glass windows arranged at 90o to protect the liquid surface from disturbance by the wind. In use, the observer arranged the artificial horizon on the ground such that the reflection of the star, such as Polaris, could be seen on the mercury surface. The octant or sextant was then used to view simultaneously the image of the star reflected in the mercury through the left (clear) half of the horizon glass and the double reflected image of the star through the right (silvered) surface of the horizon glass. In this method, the observer effectively measured the combined angle from the horizon downward to the star's reflection in the mercury plus the angle from the horizon upward to the star in the heavens. Dividing by two gave the altitude of the star and if the star was Polaris, the operation of dividing by two gave the latitude directly.6

Use of the artificial horizon required some care to isolate it from the effects of wind and ground-borne vibrations. Topographer Lieutenant Amiel Weeks Whipple in his narrative of the Pacific Railroad Survey of the 35th parallel (Whipple, 1857) recommended elaborate precautions for observations:7

Upon arriving at camp, usually from 3 to 5 p.m., a firm stool, about two and a half feet high will be placed on solid ground, from whence a clear view of the heavens, and particularly of the meridian, can be obtained. A trench from one and a half to two feet will be dug surrounding the stand [of the instrument being used], about eighteen inches from the point beneath the centre, leaving an isolated column of earth, free from the vibratory motion communicated by the ordinary movements of the men and animals about camp. There should be a platform for the observer north and south of the stand, resting entirely outside the trench. It must be recollected that the value of the observations greatly depends upon the isolation of the instrument. Hence a flat rock should never be selected as a foundation, in case the observer is obliged to stand upon the same himself. Cooking-fires should be at least 300 feet distant, and to the leeward, that the smoke may not vitiate the results.

Topographer William Emory encountered an unusual nuisance in using an artificial horizon at a camp of the Army of the West on November 12, 1846 near the junction of the Gila and Salt Rivers, near present-day Phoenix, Arizona (Emory, 1848):

My camp was selected on the side towards the village, and the constant galloping of horses rendered it difficult for me to take satisfactory observations, which I was desirous of doing, as it is an important station. When I placed my horizon on the ground, I found that the galloping of a horse five hundred yards off affected the mercury, and prevented a perfectly reflected image of the stars, and it was in vain to hope for these restless Maricopas to keep quiet. News got about of my dealings with the stars, and my camp was crowded the whole time.

Longitude was a problem solved only in the 19th century after the invention of accurate, portable clocks or chronometers that could be carried on sea or land without running erratically. Gaining or losing time was permissible if the rate of gain or loss was constant. Chronometers also helped in determining latitude by using stars other than Polaris or by using the planets and the Earth’s moon.

Chronometers came in two forms. The box chronometer contained a clock about four inches in diameter, mounted in gimbals to lessen the effects of movement on the clockwork. The pocket chronometer was a much smaller watch, which could either be carried in a padded box or on one's person. The principal advantage of the pocket chronometer was its convenient size and ultimate portability. The published accounts of western exploration devote considerable attention to the problem of timekeeping and protecting the time keeping machines: Emory (1848) described his chronometers and their adventures:stage

"We left Washington on the 6th of June, unable to procure a pocket chronometer, or telescope of power sufficient to observe eclipses; but through your intercession, and by the kindness of the Chief of Hydrography, U.S.N., we were provided with two excellent box chronometers, No. 783 and No. 2075, by Parkinson and Frodsham, and we received from the bureau two of Gambey's 8-1/2 inch sextants. Crossing the Alleghanies [sic] the stage capsized with us, and placed the chronometers in great danger, but the prudence of Mr. Bestor, who carried them in a basket on his arm, saved them from destruction. Their rates were changed very materially by the accident, but subsequent observations showed no other injury had been incurred. Elaborate observations for time and rate were made at St. Louis; from which place being tolerably well established in geographical position, it was intended to carry the longitude by chronometer, but, on reaching Fort Leavenworth, the chronometers were again found to have changed their rates materially, owing to the peculiarly unsteady and jarring motion of the steamer upon which we ascended."

By the time of the Mexican War, longitude was most accurately determined by comparing the time at the base meridian running through Greenwich, England (to which the chronometer could be set) to local time determined astronomically. On sea or land, local noon could be determined by measuring the maximum altitude of the sun as it crossed the sky (called "shooting the sun" or a "noon sight" in later parlance). However, the most accurate determinations of local time were made by observing the transit (crossing) of certain of the brighter stars in the southern sky across the local north-south meridian at night.

All army topographers used the technique of double altitudes 8 in which a series of measurements were made before, during, and after the expected time of transit of a star or other body across the local north-south meridian. As the transit time neared, the observer noted the altitude measurements gradually increasing as the star approached the meridian. For a brief time the altitude measurements changed but slowly, if at all, then began decreasing after the star had passed the meridian. Interpolation of the series of timed observations between measured altitudes of nearly equal value was used to estimate the actual time of meridian transit. While the method of double altitudes yielded an estimate of local time, it was much more accurate in practice than trying to measure the exact instant of maximum altitude and it also avoided certain instrumental errors.

Computation. Astronomical tables of transits and other data (called ephemeris), computed for the base meridian of Greenwich and other meridians, were published by the British admiralty in the Nautical Almanac. Local observations of transits at a meridian distant from Greenwich were compared with the time of transit at the base meridian of Greenwich, carried in the field by the chronometer. Such calculations were made in the field but were refined later by experts called computers. Civilian employees, such as Norman Bestor who accompanied Emory on the 1846 expedition, often helped with these calculations in the field. However, other civilian experts refined the calculations for publication. Emory (1848) credited his computers:

The astronomical observations, in number, were computed, in the first place, by myself and Mr. Bestor, and subsequently by Professor J.C. Hubbard. The results, as given in the appendix, are the final computations of Professor Hubbard, whose well-earned reputation as a computer entitles his work to entire confidence.9 These observations establish the geographical position of 52 points, extending from Fort Leavenworth to the Pacific, most of which lie in regions before undetermined.

Because chronometers were not perfect timekeepers, it was necessary to check them against an astronomical clock. Three such clocks were available: (1) eclipses or occultations of Jupiter's four Galilean moons by the planet's disk; (2) occultations of fixed stars by the Earth's moon; and (3) measurement of the motion of the Earth's moon against the backdrop of fixed stars.

The timing of occultations of Jupiter's moons by the disk of the planet were computed and published in the Nautical Almanac 10 and other publications.11 Since the occultations of Jupiter's satellites appear simultaneously to distant observers anywhere on earth because of Jupiter's great distance from the Earth, a telescope of sufficient power could be used to check the chronometer against the astronomical clock. Emory complained at several points in his Notes of a Military Reconnaissance (1848) that the "inferior telescope" he carried lacked sufficient magnification and resolving power for this purpose:

The instruments with which I was furnished were not those, perhaps, which I would have selected; at the same time there was nothing for me to regret, except the absence of a good portable telescope, with which occultations of the fixed stars by the moon, and the immersions of Jupiter's satellites, could have been observed, and a few pocket chronometers.

Even with a good telescope, observing Jupiter and its satellites was tedious after traveling overland all day. Frémont (1846) remembered waiting for occultations along the Boise River in the narrative of his second expedition:

Sitting by the fire on the river bank, and waiting for the immersion of the satellite, which did not take place until after midnight, we heard the monotonous song of the Indians, with which they accompany a certain game of which they are very fond. Of the poetry we could not judge, but the music was miserable.

Frémont's scientific aide, Charles Preuss, remembered the same incident, although differently (Gudde and Gudde, 1958):

Half-past ten in the evening. I am sitting all alone by the fire to watch till twelve o'clock, when an immersion of satellites will occur. To tell the truth, I wish the dear Lord had not attached any satellites to Jupiter. One can lose one's mind over it. These immersions occur so often that one forgets how to sleep.

The second astronomical clock, that of observing occultations of fixed stars by the Earth's moon was limited to only part of the month when the moon was visible and during those infrequent instances when occultations of relatively bright stars occurred at night. More useful was a third method, the system of lunar distances, in which the observer used an octant or sextant to measure the angle between the limb of the moon and certain fixed stars. Because the moon moves among the fixed stars along a mathematically predictable path, its motion can be used as a timekeeper. Indeed, the sextant was initially developed to improve the accuracy of angle measurement sufficiently to make the method of lunar distances practicable. The Royal Observatory at Greenwich was established to make the precision observations necessary to develop an accurate lunar method. Lunar tables, published by several sources, enabled the observer in the field to determine the time at Greenwich. However, use of lunars, as the method was often called, was complicated by the fact that the moon is much closer to the earth than distant Jupiter and its moons. Parallax between Greenwich and the observer in the field in Western America required additional computing such as that done by Professor Hubbard for Emory.

Equipment Carried by Major Expeditions

Sextants, artificial horizons, and chronometers were indispensable and were carried by each of the major topographic expeditions of the Mexican War period. Later expeditions, such as those of the Mexican Boundary Survey and the Pacific Railroad Surveys, also used transit instruments and theodolites that were harder to transport but superior for the work. In most cases, the explorers elected to take more than one of each instrument. The best-equipped of the early expeditions, Stephen H. Long's expedition to the Rocky Mountains in 1819-20, carried two sextants, two artificial horizons, two chronometers, plus a reflecting circle. The reflecting circle or repeating circle was a more elaborate angle measuring device than the sextant and could be used to measure very large angles. Long complained about the quality of his English reflecting circle, but Frémont carried very high quality reflecting circles made by Gambey of Paris on both his first and second expeditions. Frémont in 1842 carried one Gambey's sextant and Emory carried two Gambey's sextants, which he described as, "made by the celebrated Gambey, of Paris."12  Lieutenant A.W. Whipple (1857) on the 35th parallel railroad survey and John Pope on the 32nd parallel railroad survey used Gambey's sextants (Pope, 1854).

Technically, the Gambey "sextants" were quintants. The quintant, based on a sector that is a fifth of a circle (72o), enabled a wider angle of measurement (144o) than the sextant (120o) — an advantage in measuring celestial altitudes using an artificial horizon. The U.S. government purchased two dozen Gambey's theodolites in the 1840's (Warner, 1990) and probably a number of Gambey's quintants.13

Other Measurements and Equipment

Altitude. Barometers were essential for determining altitude above sea level and were carried by all the expeditions. However, the long columns of mercury were difficult to manage without breakage. Preuss lamented the loss of a barometer on the 1842 Frémont expedition to South Pass on the continental divide, then added his editorial comments on Frémont's efforts to salvage their box chronometer:

A barometer, not the best one though, has gone wrong. The bad road between here and Laramie killed it. We left the large chronometer in Laramie; Frémont succeeded in making it run again and he was jubilant when he heard the ticking and tick-tocking. In comparing we found, however, that every twenty-four hours it went wrong by about one hour. Oh, you American blockheads!

The mountain barometer was a form of barometer specially constructed for portability but the earlier expeditions often carried barometers meant to hang on a wall in a fixed location within a building. Frémont described his repair of the broken barometer noted by Preuss (Frémont, 1846):

As soon as the camp was formed, I set about endeavoring to repair my barometer. As I have already said, this was a standard cistern barometer, of Troughton's construction. The glass cistern had been broken about midway; but as the instrument had been kept in a proper position, no air had found its way into the tube, the end of which had always remained covered.14 I had with me a number of vials of tolerably thick glass, some of which were of the same diameter as the cistern, and I spent the day in slowly working on these, endeavoring to cut them of the requisite length; but, as my instrument was a very rough file, I invariably broke them. A groove was cut in one of the trees, where the barometer was placed during the night, to be out of the way of any possible danger, and in the morning I commenced again. Among the powder horns in the camp, I found one which was very transparent, so that its contents could be almost as plainly seen as through glass. This I boiled and stretched on a piece of wood to the requisite diameter and scraped it very thin, in order to increase to the utmost its transparency. I then secured it firmly in its place on the instrument, with strong glue made from a buffalo, and filled it with mercury, properly heated. A piece of skin, which had covered one of the vials, furnished a good pocket, which was well secured with strong thread and glue, and then the brass cover was screwed to its place. The instrument was left some time to dry; and when I reversed it, a few hours after, I had the satisfaction to find it in perfect order; its indications being about the same as on the other side of the lake before it had been broken. Our success in this little incident diffused pleasure throughout the camp; and we immediately set about our preparations for ascending the mountains.

Frémont was so concerned about the barometer because he was about to make the first attempt in history to measure the height of a peak in the Rocky Mountains using a barometer. We have both Frémont's and Preuss's narratives of the attempt to scale the mountain that Frémont thought was the tallest in the Wind River range. Frémont's words convey romance and exhilaration, Preuss's pure misery. Curiously, Frémont neglects to tell us about using the barometer on the peak.

Both Frémont and Emory carried Bunten siphon barometers of French manufacture. Emory got his from the medical department because they were in charge of recording atmospheric phenomena that were supposed to influence health and disease. Emory wrote:

At Fort Leavenworth, through the liberality of the medical department, I was furnished with a siphon barometer, by Bunten, No. 515, the comparison of which, with the standard at Paris is given in the subjoined note.

Emory (1848) took care to publish the maker's specifications because the barometer's performance was critical in determining altitudes. Emory's Bunten barometer made it all the way to San Diego and was left there in the care of Lieutenant William H. Warner who was instructed to continue the meteorological observations. Lieutenant Whipple's (1857) narrative of the Pacific Railroad Survey of the 35th parallel contains an extensive discussion of barometric observations and the puzzlement they created. The concept of moving pressure fronts and the relationship between atmospheric pressure and weather was not yet understood.

Magnetic Dip and Magnetic Deviation. Several of the expeditions cited here carried a dip needle for measuring the vertical component of the Earth's magnetic field, which was related to magnetic variation, the deviation of a compass in the horizontal plane from true north. The azimuth compass and the circumferentor (or surveyor's compass) could be used to determine the magnetic deviation by measuring the sun's location at local noon. Magnetic deviation is the difference between true north and magnetic north indicated by a compass. Meriwether Lewis carried both a circumferentor and an azimuth compass and reported measuring the magnetic deviation. Stephen H. Long carried a dip needle but Frémont carried none. Emory (1848) requisitioned a dip needle but never received it and never mentioned any regrets at the omission. Emory was scientifically well informed and almost certainly knew that measuring magnetic dip was a superfluous exercise.

An early hope was that magnetic dip could provide a unique signature for every point on Earth, thus solving the problem of longitude. However, no such unique magnetic signatures exist, and the idea should have been laid to rest in the late 18th century when it was realized that magnetic variation changes over time as the Earth's magnetic field evolves.

DistanceOdometers or viameters were mounted on wagon wheels for measuring distance by registering the number of wheel revolutions. William Emory noted using an odometer on his trip to the Pacific and his concern about the safety of his equipment when the Army of the West's wagons were sent back after the party turned westward, climbing out of the Rio Grande valley south of Socorro, New Mexico:

October 14. — We parted with our wagons, which were sent back under charge of Lieutenant Ingalls, and in doing so, every man seemed to be greatly relieved. With me it was far otherwise. My chronometers and barometer, which before rode so safely, were now in constant danger. The trip of a mule might destroy the whole. The chronometers, too, were of the largest size, unsuited to carry time on foot or horseback. All my endeavors, in the 24 hours allowed me in Washington to procure a pocket chronometer, had failed. I saw then, what I now feel, the superiority of pocket over large chronometers for expeditions on foot or horseback. The viameter for measuring distances, heretofore attached to the wheel of the instrument wagon, was now attached to the wheel of one of the small mounted [sic] howitzers.

Photography became a prominent feature of the Powell and Hayden expeditions in the latter part of century, but there were earlier attempts by John Mix Stanley during the 1853-54 Pacific Railroad Survey of the 35th parallel (Whipple, 1857) and S.N. Carvalho on Frémont's fifth and last expedition (Jackson and Spence, 1970). Although Frémont did not mention it in his famous 1843 narrative, he had a daguerreotype machine with him in 1842. We are indebted to Charles Preuss for his diary entry for the events of August 2, 1842, at Independence Rock (Gudde and Gudde, 1958):

Yesterday afternoon and this morning Frémont set up his daguerreotype to photograph the rocks; he spoiled five plates that way. Not a thing was to be seen on them. That's the way it often is with these Americans. They know everything, they can do everything, and when they are put to a test, they fail miserably. Preuss continued in his entry for August 5: Today he said the air up here is too thin; that is the reason his daguerreotype was a failure. Old boy, you don't understand the thing, that is it."

The entry for August 11 completes the story:

Today Frémont again wanted to take pictures. But the same as before, nothing was produced. This time it was really too bad, because the view was magnificent.

Thus we learn from Preuss that an army topographer was in the field in Western America in 1842 with a daguerreotype machine trying to take photographic images within four years after Daguerre in France and Talbot in England made public their inventions of photography. The financial records of the expeditions of both 1842 and 1843-44 indicate the purchase of Daguerreotype apparatus from a New York physician and chemist, Dr. James R. Chilton.15 Since Frémont did not report using his Daguerreotype equipment, he probably failed, although Daguerreotypes from the second expedition, now lost, may have been used to prepare lithographs for Frémont's Reports and his Memoirs (Jackson and Spence, 1970).

Equipment Apparently Not Used

Lewis and Clark in 1804-07, Long in 1819-20, and Whipple in 1853-54 carried surveyor's chains, which were typical for surveying estates and farm land, but not a wilderness. The omission of surveyor's chains and related equipment from the other expeditions, such as Frémont's and Emory's, meant to discover large scale features of geography is not surprising. However, the author finds no mention of the plane table and alidade, devices for sketching topography in the field, although many sketches were made in preparation for the maps to come in publications after the expeditions. Emory recognized the importance of such sketches:

From Santa Fé to the Pacific, I was aided by First Lieutenant W.H. Warner, of the topographical engineers, and Mr. Norman Bestor; all of whom deserve notice for the zeal and industry with which they performed their duty. Whilst with me, Lieutenant Peck made the topographical sketches; after he left, they were made by Lieutenant Warner.


Frémont (1846) published a Table of Latitudes and Longitudes, Deduced from Observations Made During the Journey, for his first expedition but only a Table of Distances Along the Road Travelled by the Expedition in 1843 and 1844. By contrast, Emory (1848) published extensive appendices, including a Table of Meteorological Observations (appendix no. 3), a Table of Geographical Positions (appendix no. 4), and 205 pages of Astronomical Observations(appendix no. 5), which laid out all of his raw data on latitudes and longitudes and his calculations for time and sextant index error. The astronomical appendix takes up roughly half of Emory's (1848) publication. The positions and Emory's fixes start at Fort Leavenworth (June 21, 1846) and end at San Diego (December 23, 1846).

Emory took special care by making repeated observations at each point along the way in order to gain the utmost accuracy from his technology. A typical night's observations included multiple observations of time, latitude, and longitude — never fewer than seven in each category and usually nine, thirteen or more. He preferred odd numbers, but why is not clear. Certain key geographical points called for a maximum effort. For example, Emory wrote of his extended stay in Santa Fe:

The latitude of Santa Fé, determined by 52 circum-meridian altitudes of alpha aquilae, 23 of beta aquarii, and 36 altitudes of polaris out of the meridian, is N. 35o 44' 06". The longitude, by measurement of 8 distances between MAlpha Aquilae and the K[moon], and 8 between M Antares and the K [moon], is respectively 7h. 04m. 14s. 7 and 7h .04m. 22s.4. The mean of which is 7h. 04m. 18s. and the longitude brought by the chronometer from the meridian of Fort Leavenworth is 7h. 04m. 05s.5 — (See Appendix No.4.) 

The place of observation was a court near the northeast corner of the public square. The latitude may be considered fixed; but satisfactory as the longitude may appear, I should, nevertheless, have greatly multiplied the number of lunar distances, had I not been in daily expectation of receiving a transit instrument, with which a set of observations on moon culminating stars could have been made at this important geographical point. 
The mean of all the barometric readings at Santa Fé indicates, as the height of this point above the sea, 6,846 feet, and the neighboring peaks to the north are many thousand feet higher.

Emory was right on with his elevation measured with the Bunten barometer. The actual value is within fifty feet of Emory's measurement. For astronomical observations, Emory preferred multiple observations. He clearly grasped the merit of averaging repeated measurements to achieve greater statistical significance, although the science of statistics was yet to be defined. The author believes that this scientific approach was the product of Emory's technical training at West Point and the deep strain of common sense his writings reveal.

The author used Emory's narrative to determine some of the locations where he measured the latitude or both the latitude and longitude. If Emory's observing time was limited to an overnight camp or the location was relatively unimportant, Emory often measured the latitude, but not the longitude. In this study, Emory's data for several points that could be located were compared with modern geodesic measurements. The modern latitudes and longitudes for Emory's locations are shown in Table 1 and were obtained from 1:24,000 scale (7.5 minute series) topographic maps published by the United States Department of the Interior Geological Survey.

In order to compare the astronomical observations for latitude and longitude with modern map positions, all data were converted to a common datum, North American Datum 1983 (NAD 83).  The astronomical observations were converted to NAD 83 through a method of approximation.  Two correction factors, xi and eta were generated for each position using DEFLEC96, a National Geodetic Survey program. The NAD 83 coordinates were then computed using the following equations:

Geodetic latitude = astronomic latitude - (correction for xi)

Geodetic longitude = astronomic longitude + (correction for eta) / cos astronomic longitude

    The modern latitudes and longitudes were measured by placing individual topographic maps on a commercial digitizing table (Calcomp 9100), indexing them, and determining the putative locations of Emory's observations using ERDAS software, version  Locations provided by the software in Universal Transverse Mercator (UTM) format were converted to degrees, minutes, and seconds on NAD 27 and then converted to NAD 83 for direct comparison with Emory's data.  A similar exercise was performed using selected locations in Frémont's 1842 data (Table 2).  The level of accuracy of modern technology (within 20 meters) is undoubtedly far more accurate than the author's guesses as to the location of Emory and Frémont's camps, although in most cases the guesses were highly informed by these officers' respective narratives.

Some of Emory's camps and observation points could be located precisely on modern topographical maps, such as the Santa Fe location noted above. Other points required careful interpretation or flat out guesswork. For example, the location of Emory's Camp 38 at Cimarroncito Creek ("Cimmaron Citon," according to Emory) in northeastern New Mexico was taken as the point where the modern road (State Highway 21) to the Philmont Scout Ranch Headquarters crosses Cimarroncito Creek. However, given the topography and the intertwining nature of the old Santa Fe Trail at this point, the actual location of Camp 38 could have been as much as four or five miles to the east but, since Emory did not measure longitude here, the guess does not matter. Franzwa's Maps of the Santa Fe Trail (1989) helped to locate the trail and the camp positions. Also included in Table 1 are the two longitudes that Emory published in his narrative but did not measure himself: Fort Leavenworth (measured by J.N. Nicollet) and San Diego (measured by a Captain Belcher).

All of Emory and Frémont's latitudes are very close to the measurements made with modern geodesic methods. Of the latitudes measured by Emory, the largest error among the sample locations is the measurement for Santa Fe which differs by approximately 02' 56" from the modern measurement, or about 5.4 kilometers (3.4 statute miles). The level of error in Emory's Santa Fe latitude measurement is surprising, considering the number of measurements that he made at Santa Fe and his obvious interest in getting it right, as suggested by the quotation cited above. Likewise, Emory labored hard to determine the latitude of San Diego where he also used the public square as his observation point and was more accurate, missing by about 280 meters (9 seconds error). The other five of Emory's latitude observations are in the same range of accuracy, including the observations at Fort Leavenworth (six seconds error), Diamond Spring (11  seconds error), the Bend of the Arkansas (less than one second error), Bent's Fort (24 seconds error), and Cimarroncito Creek (five seconds error) (Table 1). The errors in terms of linear distance are only about 198 meters, 334 meters, 12 meters, 724 meters, and 150 meters for the five positions, respectively (Table 3).

The two longitudes measured by Emory cited here were taken at Bent's Fort on the Arkansas, where he erred by about 24 minutes of longitude or about 36 kilometers [23 miles] and Santa Fe, where he erred by about fifty-two minutes of longitude or about 80 kilometers [49 miles]. The author attributes this error to the inherent difficulties of the lunar method and carrying Greenwich time in Emory's two box chronometers. However, Emory had help in making errors. His calculations gave the longitude of Bent's Fort as 103o 25' 45", but the narrative's Table of Geographical Positions (Appendix No. 4) gives the Bent's Fort longitude as 103o 01' 00". Emory provides the explanation in a footnote:

*Note.— this longitude of Bent's Fort is the result of the improved method of computation adopted by Professor Hubbard. The longitude, deduced by me from the same data, and communicated to the Chief of the Bureau of Topographical Engineers in an official report, dated Santa Fé, September 1, 1846, was 103o 25' 45". As this longitude was published at the time by the bureau, this explanation becomes necessary. My confidence in Professor H. induces me to adopt his determination. It is the only point where any great difference exists. W.H.E.

Emory should have stuck by his own calculations, but perhaps the inclusion of the footnote reflects his skepticism. Without Professor Hubbard's correction, Emory's longitude is only 18 second of longitude off the modern measurement, which is the equivalent to missing by less than half a kilometer.  Professor Hubbard's recalculation increased Emory's error to the equivalent of 36 kilometers (Table 3).

The longitude that Emory gives for Fort Leavenworth was measured by J.N Nicollet, who was Frémont's mentor. This measurement is off by about 10 minutes of longitude or about 15 kilometers. The measurement published by Emory for San Diego was done by a Captain Belcher, who is further identified in the Table of Geographical Positions (Appendix No. 4) as Sir Ed. Belcher. Presumably he is a captain of the Royal Navy, but the author has not confirmed this point. Belcher missed San Diego’s longitude by about a minute of longitude (about 1.5 km), a full order of magnitude (ten times) better than Nicollet’s measurement for Fort Leavenworth, (and 24 times better than Emory's measurement for Bent’s and 53  times better than Emory's longitude for Santa Fe as recalculated by Professor Hubbard).

The errors in the two longitude measurements by Frémont cited here are substantially less than those of  Emory and comparable to Nicollet, but inexplicably, the average error of Frémont's latitude measurements is about thirteen times that of Emory's average. Nevertheless, all three of the latitude measurements by Frémont cited here are much less than two minutes of latitude and all are well under four kilometers by linear measure (Table 3).

Emory's measurement for Bent's Fort was recalculated incorrectly by Professor Hubbard, adding a substantial error. Frémont's work was also degraded by others after the fact. Frémont's 1843 Map to Illustrate an Exploration of the Country lying between the Missouri River and the Rocky Mountains, on the line of the Nebraska or Platte River, which was compiled by Charles Preuss, has a major defect of longitude, as though the whole frame of reference was shifted westward by about 50 minutes of longitude. Frémont's published longitude of Fort Laramie is W 104o 47' 43" but the map coordinates place the fort at about W 105o 20' 22", which is a linear difference of about 69 kilometers (43 miles). The 1843 report was hurried into production through the intercession of Senator Thomas Hart Benton, Frémont's father-in-law (Goetzmann, 1959), and perhaps the rush to publication contributed to the error. Discrepancies in this famous map have been noticed at least once before (Dellenbaugh, 1914). Longitudes in Frémont's later maps of this area, Map of an Exploring Expedition to the Rocky Mountains in the Year 1842 and to Oregon and California in the Years 1843-44 (1845) and Topographical Map of the Road from Missouri to Oregon (1846, in seven sections) are much more accurate.16

Emory and Frémont contributed a unique record of exploration through their narratives, but especially the maps created from their astronomical observations and topographical sketches done under trying conditions in the field. Frémont's maps aided the Oregon and Mormon emigrants and provided a new frame of reference for American geography. Emory's efforts set the stage for the Mexican Boundary Survey, of which he became leader. The collective efforts of these and other topographers created the modern geographic outline of the United States that each of us has carried in our brains since we were small children at school.

to References


sextant and octant

Figure 1. Octant and Sextant

This illustration in Bowditch's New American Practical Navigator (1868) pictures the octant (left) and sextant (right). The octant, inexpensive and widely used on land and sea for astronomical measurements, was usually made of ebony wood with a scale of boxwood or ivory. The moveable arm, the index arm (labeled D) carried a mirror (index mirror, F) at its pivot end at the apex of the sector. A pointer at the opposite end of the index arm indicated the measured angle in degrees along the 90o scale (B-C). The user viewed the half-silvered horizon glass (G) through a peep sight (K). Through the principle of double reflection, the user simultaneously viewed the horizon through the unsilvered left half of the horizon glass and the reflected image of a heavenly body, such as Polaris, reflected first by the index mirror, then by the half-silvered right side of the horizon glass. Some octants, such as the one illustrated, carried a second horizon glass (H) and a second sighting vane (L) for an alternative form of sighting called a back observation.

The sextant (right) materially improved the accuracy of angle measurement. Based on a sixth of a circle (60o), the sextant's scale spanned 120o, enabling a larger angle measurement than the octant. Usually made of brass, the sextant was fitted with interchangeable telescopes that fitted into a receptacle (K), filters for solar and lunar work (D & E), and a finely divided scale (A-A) with a vernier scale to improve accuracy.


Table 1



Emory's Measurement 
(converted to NAD 83)

Modern Determination 
(on NAD 83)


Fort Leavenworth

W Long. 94o 44' 03.8"*  
N Lat. 39o 21' 14.7"

W Long. 94o 54' 49"  
N Lat. 39o 21' 21"

- 10' 45.2"  
- 00' 06.3"

Camp 9,  
Diamond Spring

W Long. Not Measured  
N Lat. 38o 36' 52.2"W

Long. 96o 45' 43"  
N Lat. 38o 37' 03"

- 00' 10.8"

Camp 14,  
Bend of Arkansas

W Long. Not Measured  
N Lat. 38o 21' 19.6"

W Long. 98o 45' 20"  
N Lat. 38o 21' 20"

- 00' 0.4"

Camp 30,  
Bent's Fort 

W Long. 103o 01' 04"  
N Lat. 38o 02' 50.5"

W Long. 103o 25' 46"  
N Lat. 38o 02' 27"

- 24' 42"  
+ 00' 23.5"

Camp 38,  
Cimarroncito Creek

W Long. Not Measured  
N Lat. 36o 27' 52.2"

W Long. 104o 56' 49"  
N Lat. 36o 27' 57"

- 00' 04.8" 

Santa Fe  
NE Corner of Plaza 

W Long. 105o 03' 45.1"  
N Lat. 35o 44' 10.49"

W Long. 105o 56' 15"  
N Lat. 35o 41' 15"

- 52' 29.9"  
+ 02' 55.5"

Camp 120,  
San Diego

W Long. 117o 10' 48.7"**  
N Lat. 32o 45' 06.9"

W Long. 117o 11' 50"  
N Lat. 32o 45' 16"

- 01' 01.3"  
- 00' 09.1"

*Measurement by J.N. Nicollet, not Emory. **Measurement by Captain E. Belcher, not Emory


Table 2


Location Frémont's Measurement  
(converted to NAD 83)
Modern Determination 
(on NAD 83)
July 2,  
Junction of N. & S. Platte
W Long. 100o 49' 45.9"  
N Lat. 41o 05' 09"
W Long.100o 40' 37.5"  
N Lat.41o 07' 00"
+ 09' 08.4"  
- 01' 51" 
July 13-16,  
Fort Laramie
W Long. 104o 47' 56.4"  
N Lat. 42o 12' 14.9"
W Long. 104o 31' 49"  
N Lat. 42o 11' 59"
+ 16' 07.4"  
+ 00' 15.9" 
Sept. 25, Platte,  
mouth of Loup fork
W Long. Not Measured  
N Lat. 41o 22' 13.6"
W Long. 97o 19' 18"  
N Lat. 41o 24' 07"
- 01' 53.4" 


Table 3

BY EMORY (1846) AND FRÉMONT (1842)


Location Error in Measurement Equivalent In Meters
Fort Leavenworth W Long. - 10' 45.2"  
N Lat. + 00' 06.3"
14,935 m east*  
198 m north
Camp 9, Diamond Spring N/A  
N Lat. - 00' 10.8"
334 m south
Camp 14, Bend of Arkansas  N/A  
N Lat. - 00' 00.4"
12.4 m south
Camp 30, Bent's Fort W Long. - 24' 42"  
N Lat. + 00' 23.5"
35,953 m east  
724 m north
Camp 38, Cimarroncito Creek  N/A  
N Lat. - 00' 04.8" 
150 m south
Santa Fe, NE Corner of Plaza W Long. - 52' 29.9"  
N Lat. + 02' 55.5"
79,935 m east  
5,440 m north
Camp 120, San Diego W Long. - 01' 01.3"  
N Lat. - 00' 09.1" 
1,563 m east**  
282 m south

*Measurement by J.N. Nicollet, not Emory. **Measurement by Captain E. Belcher, not Emory.



Location Error in Measurement Equivalent in Meters
July 2, Junction of N. & S. Platte W Long. + 09' 08.4"  
N Lat. - 01' 51"
13,033 m west  
3,475 m south
July 13-16, Fort Laramie W Long. + 16' 7.4"  
N Lat. + 00' 15.9" 
8,695 m west  
2,746 m north
Sept. 25, Platte, mouth of Loup fork N/A  
N Lat. - 01' 53.4" 
3,520 m south



Bennett, J.A. 1987 The Divided Circle. A History of Instruments of Astronomy, Navigation and Surveying. Phaidon - Christie's Ltd., Oxford, pp. 136-137.

Bowditch, Nathaniel 1848 The New American Practical Navigator: Being an Epitome of Navigation, Containing All the Tables Necessary to be Used with the Nautical Almanac in Determining Latitude, and the Longitude by Lunar Observations, and Keeping a Complete Reckoning at Sea; etc. E.&G.W. Blunt, Boston, 458 pp.

Bowditch, Nathaniel 1868 The New American Practical Navigator: Being an Epitome of Navigation, Containing All the Tables Necessary to be Used with the Nautical Almanac in Determining Latitude, and the Longitude by Lunar Observations, and Keeping a Complete Reckoning at Sea; etc. U.S. Government Printing Office, Washington, D.C., 460 pp.

Bowditch, Nathaniel 1984 American Practical Navigator. An Epitome of Navigation Originally by Nathaniel Bowditch, LL.D. Volume 1, Defense Mapping Agency Hydrographic/Topographic Center, Washington, D.C., pp. iv-vi.

Dellenbaugh, Frederick S. 1914 Frémont and `49: The story of a remarkable career and its relation to the exploration and development of our western territory, especially of California. New York.

Emory, William H. 1848 Notes of a Military Reconnaissance from Fort Leavenworth in Missouri to San Diego, in California. 30th Congress, 1st session, Senate Document No. 7.

Franzwa, Gregory M. 1989 Maps of the Santa Fe Trail. The Patrice Press, St. Louis, Missouri, 196 pp.

Frémont, John C. 1845 Report of the Exploring Expedition to the Rocky Mountains in the Year 1842, and to Oregon and North California in the Years 1843-`44. Washington, D.C. U.S. Congress. Senate. 30th Cong., 1st sess, 1848, S. Exec. Doc. 7.

Hayden, F.V. 1876 Annual Report of the United States Geological and Geographical Survey of the Territories, Embracing Colorado and Parts of Adjacent Territories; being a Report of Progress of the Exploration for the Year 1874. U.S. Government Printing Office, Washington, D.C., 515 pp.

Goetzmann, W.H. 1959 Army Exploration in the American West: 1803-1863. University of Nebraska Press, Lincoln.

Gudde, Erwin G. and Elisabeth K. Gudde 1958 Exploring with Frémont. The Private Diaries of Charles Preuss, Cartographer for John C. Frémont on His First, Second, and Fourth Expeditions to the Far West. University of Oklahoma Press, Norman, pp. 32 and 35.

Haswell, C. H. 1889 Mechanic's and Engineer's Pocket-Book of Tables, Rules, and Formulas Pertaining to Mechanics, Mathematics, and Physics:  Including Areas, Squares, Cubes, and Roots, etc.;  Logarithms, Hydraulics, Hydrodynamics, Steam and the Steam Engine, Naval Architecture, Masonry, Steam Vessels, Mills, etc.;  Limes, Mortars, Cements, etc.; Orthography of Technical Words and Terms, etc.,etc. Fifty-third Edition, Harper& Brothers Publishers, Franklin Square, New York.

Jackson, Donald and Mary Lee Spence (eds.) 1970 The Expeditions of John Charles Frémont. Vol. 1, Travels from 1838 to 1844. University of Illinois Press, Urbana, 854 pp.

Pope, John 1854 Report of Exploration of a Route for the Pacific Railroad, Near the Thirty-Second Parallel of Latitude, from the Red River to the Rio Grande. U.S. Congress. House., 33rd Cong. 1st sess., 1854. H. Doc. 129, pp. 5-6.

Thrower, Norman J.W. 1990 William H. Emory and the Mapping of the American Southwest Borderlands. Terrae Incognitae, 22: 41-92.

Thwaites, Reuben Gold (ed.) 1959 Original Journals of the Lewis and Clark Expedition 1804-1806. Antiquarian Press Ltd., New York.

Warner, Deborah Jean 1990 Gambey's American Customers. Rittenhouse. The Journal of the American Scientific Instrument Enterprise, 4(3): 65-78.

Whipple, A.W. 1856 Report of Explorations for a Railroad Route, Near the Thirty-Fifth Parallel of North Latitude from the Mississippi River to the Pacific Ocean. In Pacific Railroad Reports, Vol 3, Pt. II.



1For example, Emory (1848) reported carrying two copies of Haswell's Tables.  First published in 1845 by Harper and Brothers, Haswell's Tables was a 19th century equivalent of the modern Handbook of Chemistry and Physics, a compilation of measures and scientific data of all kinds.

2The U.S. Naval Academy dates from 1845, with a four-year curriculum instated in 1851.

3At sea, both the refraction of the Earth's atmosphere and the observer's height above the sea on the ship's deck required mathematical correction of the altitude read from the instrument's scale. Correction factors were provided in nautical texts and tables, such as Bowditch's New American Practical Navigator and the Nautical Almanac published by the British Admiralty.

4A great advance in accuracy came through precision dividing engines that marked the scales on sextants and other astronomical instruments with great accuracy. Such scales were usually inscribed on an inlay made of a contrasting metal such as silver, German silver, or even gold on the finest instruments.

5Alternatively, a pool of refined molasses or another viscous liquid was used, but mercury was superior for its highly reflective and non-wetting qualities. Front surface mirrors or black glass were also used as artificial horizons, although this system required careful leveling.

6Unlike measurement at sea using the natural horizon, measurement on land with an artificial horizon needed no mathematical corrections to compensate for atmospheric refraction or the observer's height (on the deck of a ship) above the surface of the Earth. However, even on land, very precise measurement had to take account of the small circle that Polaris describes from the perspective of the earthbound viewer as Planet Earth turns on its axis.

7Whipple's description of preparations preceded a discussion of measuring magnetic dip as well as using a transit instrument or an artificial horizon to determine latitude and longitude.

8The term equal altitudes was used when the sun's transit was used to regulate a chronometer.

9Emory identified Hubbard elsewhere in the narrative as, "a very accurate young computer, attached to the observatory at Washington." Emory referred to the Naval Observatory, which had just opened in Washington, D.C. in 1844.

10During this period the Nautical Almanac was published by the British Admiralty. The British Nautical Almanac first appeared in 1767 and the first American Ephemeris and Nautical Almanac appeared in 1855. Shortly thereafter, the ephemeris section was dropped and the first American Nautical Almanac appeared in 1858. Its tables were always under constant improvement but the tables of lunar distance hung on until 1912. The current Nautical Almanac is published jointly by H.M. Nautical Almanac Office, Royal Greenwich Observatory and by the Nautical Almanac Office, United States Naval Observatory, with British and American editions published separately in the U.K and the U.S.A. The modern Almanac is very different than that published in the 1840s because the methods used and computing systems have changed radically.

11The students at West Point and the topographical officers in the field certainly had access to the excellent handbook of methods by Nathaniel Bowditch, The New American Practical Navigator, known then and now as Bowditch. Bowditch's handbook started as a knock-off American edition of John Hamilton's British handbook, The Practical Navigator, which had appeared in 1798 as a thirteenth edition. For the new American edition, published in 1799, Bowditch corrected some errors in the tables and added a chapter on "The Method of Finding the Longitude at Sea," which was his new lunar distance method. When the third American edition appeared in 1802, the publisher named Bowditch as the author and renamed the much- revised book The New American Practical Navigator. The original publisher sold the copyright to the newly-organized U.S. Navy Hydrographic Office in 1867 and the 1868 edition and subsequent editions have been published by the federal government. The author was much assisted in this research by reading period and contemporary editions of Bowditch (Bowditch, 1848, 1868, and 1984).

12Gambey's quality equalled or excelled that of the English makers, and he sold a large number of instruments of various types to Americans (Warner, 1990). The author owns a Gambey instrument that operates smoothly and effectively, despite its age of 150 years.

13A Gambey's reflecting circle and a quintant are present in the collection of the National Museum of American History. The quintant is marked USCAGS No. 61 (for U.S. Coast and Geodetic Survey) and may be viewed in a small museum at the headquarters of the National Oceanic and Atmospheric Administration at Rockville, Maryland. The author owns an identical Gambey's quintant marked USCRGS No. 16. A third Gambey's quintant, located by the author in private hands in a replacement U.S. Navy box, is marked "Not for Navigational Use" on the arc below the scale, which probably indicates that the quintants were restricted to hydrographic and land surveying.

14The barometer's tube could be blocked by a diaphragm and thumbscrew adjustment for transport to prevent flow of the mercury in and out of the tube when jarred. Fremont considered himself lucky because the most minute amount of air within the tube would defeat accurate measurements. Today mercurial barometers are filled under vacuum and heated to drive out the least residue of air.

15Fremont paid $78.25 on May 6, 1842 for "1 set of Daguerreotype apparatus, 25 polished Daguerreotype plates, and one pocket microscope. He paid an identical amount for "Daguerreotype apparatus" for his second expedition, plus another $68.16 in a separate entry for more "Daguerreotype apparatus." All the purchases were from Dr. Chilton (Jackson and Spence, 1970; pp. 145 and 379).

16Excellent reproductions of these maps were published in a companion to the three volumes on Fremont's expeditions edited by Jackson and Spence (1970).


The author is Vice Provost for Research and Professor of Neuroscience at the University of North Texas, P.O. Box 310979, Denton, Texas 76203; the author's e-mail address is Schafer@UNT.EDU.

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