Eileen Starr
"Beginning at the mouth of the Missouri, you will take observations of latitude and longitude, at all remarkable points on the river & especially at the mouths of rivers, at rapids, at islands & other places & objects distinguished by such natural marks & characters of a durable kind, as that they may with certainty be recognized hereafter."
Lewis made these measurements using astronomical observations. He used a quadrant, a sextant, and an octant, along with artificial horizons, a circumferentor (a surveying compass), and a chronometer. He determined latitude by using a sextant to measure the altitude of the sun at local noon, when the sun was directly south. An octant was used when the sun's altitude was greater than what could be read with a sextant. The latitude was obtained from the sun's altitude using astronomical tables that gave the altitude of the sun at noon for every day of the year at specified places on the earth.
To find longitude, a timepiece or watch called a chronometer was used. Longitude could be determined if the time of a celestial event was known. All observers on Earth see celestial events such as an eclipse of the moon, at the same instant. But the local time, sundial time, of the event is different, depending on the observer's location. One person might see the eclipse at 9 PM local time such as in the Pacific Time Zone. Someone else, on the eastern seaboard, would observe the same eclipse at midnight. The longitude of any two places on earth is related to the difference in time. The key was knowing the time in England, and this was found by using a chronometer, a five inch timepiece, that kept Greenwich time. Longitude was found by determining the difference in time between the two locations. However, the chronometer was difficult to reset in the field, which caused the accuracy of Lewis' observations to be open to question.
Another astronomical method of determining longitude during the early 19th century was to determine equal altitudes of the sun. In this method, a series of altitude observations were made at times when the sun was at the same height above the horizon when viewed both east and west of the meridian, and the time of each observation was noted. The times were then averaged to determine the time of local noon that was then compared to Greenwich time.
Longitude could also found by observing the distance between the moon, planets and stars. A table of moon and star positions told the time of the event at the Prime Meridian. The Captains knew the time of the event as seen from their location. The difference in time determined their longitude. This method did not require an accurate timepiece.
The Nautical Almanac and Astronomical Ephemeris contained the predicted angular distances between the moon and sun, and eight bright zodiacal stars - Alpha Aquilae, Alpha Arietis, Aldebaran, Pollux, Regulus, Antares, Spica and Alpha Pegasi, plus the star Fomalhaut. The positions were given for eight times during the day. Proportional logarithms were given in Maskelyne's Requisite Tables to calculate the angular separation at times other than those given.
The astronomical tables gave values of the position of the moon and other celestial objects as viewed from the center of the earth. A number of tedious spherical trigonometric calculations, termed "clearing the distance" were necessary to adjust the table information for their location on the earth's surface. Corrections for parallax and the refraction of light were needed, as well as the position of the center of the sun or moon. A number of different methods were used to clear the distance, and all gave slightly different values for longitude. All calculations of longitude required the knowledge of the latitude of their position.
There were a number of reasons for errors in their measurements. There were considerable errors in the published lunar distance tables. At the time of the Lewis and Clark expedition, the mean error in the tables for celestial latitude was 13 seconds, with a maximum of 80 seconds. The mean error for celestial longitude was 27 seconds, with a maximum of 87 seconds.
On January 14-15, 1805, while at Fort Mandan, in current North Dakota, Lewis observed an eclipse of the moon. The time of the eclipse was given in the Astronomical Almanac. However, clouds obscured the beginning of the eclipse. Lewis recorded the end of total darkness, and the end of the eclipse. However the resulting longitude for Fort Mandan, using this information, was in error by over two degrees, placing the fort about 70 miles too far to the east, and 4.6 miles too far south. The slowness of the chronometer and poor weather conditions may have contributed to the error.
There were many errors in their measurements for various reasons. The figures used to determine latitude do not include an adjustment for the equation of time. The determination of longitude using the distance of the moon from another celestial object required solving a number of equations using spherical trigonometry. It was easy to miscalculate. Although the standard error of each instrument was known, each was affected by the expansion or contraction of metal or wood due to changes in temperature. Lewis included instrument error in his calculations but not error due to the temperature. The weather was also often uncooperative. Clouds interfered with many of the observations, as at Fort Mandan.
The Journals of Lewis and Clark report many astronomical observations to determine latitude and longitude. However, in a short final report to Jefferson, written upon their return to St. Louis, Captain Lewis gives the latitude of only seven important locations on their journey. Significantly, the only longitude mentioned is that of the mouth of the Columbia, no doubt reflecting Lewis' lack of confidence in his other longitude measurements. At these seven locations, Lewis' latitude readings were either too far north or too far south showing that a systematic error was not present. The errors in latitude range between 3.5 miles at Travelers Rest, near Lolo, Montana, and 47 miles for the Great Falls of the Missouri. The only longitude reading, at the mouth of the Columbia, placed this feature too far west by at least 42 miles.
Conclusion:
The Corps of Discovery, following Jefferson's orders, did make latitude and longitude measurements at all remarkable points along the Missouri. Considering the instruments and tables that they had to work with, the latitude and longitude measurements were remarkably accurate, and provided the approximate locations of Jefferson's durable "natural marks & characters" found in the lands secured by the Louisiana Purchase, and of the lands located farther west. The accuracy of their work, as written in their journals has made it possible to recognize most of the places and objects they discovered.