". . . you will take [careful] observations of latitude & longitude"
–Thomas Jefferson, Instructions to Meriwether Lewis, 20 June 1803
Thomas Jefferson was as interested in the methods and equipment for "ascertaining by celestial observation the geography of the country" as with any other single aspect of the Expedition. He played an important role in making sure that Lewis purchased the proper equipment and learned how to use it before he left for the West. He also insisted that observations be conducted with accuracy, would be redundant, would be comprehensible to others, and that sufficient copies of all observations would be made to guarantee against the possible loss of one or more sets. As faithfully as they could, the captains complied with the President's wishes.
For Lewis and Clark, as for so many of their predecessors and contemporaries, calculating latitude was far simpler than calculating longitude. In the northern hemisphere, latitude may be derived by measuring the angle made between the North Star and the horizon. Crude instruments to obtain this angle have existed for thousands of years and by the time of Lewis and Clark, instruments like the sextant and octant, only slightly less precise than those available to us, were in use.
Latitude may also be calculated by measuring the altitude of the sun, moon, or certain planets and stars above the horizon on known days and reading latitude from tables designed for that purpose. It was not much more difficult for the captains to measure these altitudes with a sextant or octant and to calculate latitude using one of the three ephemerides or astronomical almanacs they carried. These contained tables showing the daily position of celestial bodies such as the sun, the moon, and key stars. Calculating latitude gave Lewis and Clark few problems and their readings were accurate to within a fraction of a degree.
Longitude can be calculated using either time or astronomical observation. Calculating longitude by chronometer is based on the fact that any point on the earth's surface moves through a complete circle of 360 degrees once in a 24-hour period; during 1 hour, any point on the earth's surface moves through an east-to-west 15° arc of a full circle. If time can be fixed along any meridian of longitude, then longitudinal distance can be determined by comparing time at that meridian with local time, usually based on the point at which the sun reaches its zenith.
All this seems quite simple. Why, then, were the captain's longitudinal observations so prone to error? The answer is also simple: they did not have, as we do, reliable battery-powered watches with quartz movements. When their chronometer ran down, it had to be re-calibrated on local time, which required them to make observations to determine the sun's zenith or local "noon" and then setting the chronometer by estimating the Expedition's current longitudinal position. Over the course of their journey, the small incremental errors produced by this procedure became larger ones.
There were other methods of calculating longitude available to them, using astronomical observation. But many astronomical readings had to be acquired over the course of a night in order to obtain sufficiently precise data to determine longitude. It was asking a lot for men exhausted by the rigors of their daily trek, to spend three or four hours in the cold and damp of a mountain night taking sightings of the moon and stars, recording observations, and making calculations by firelight. It was only natural that errors would exist in data obtained in this manner. Even the most skilled astronomer or surveyor would have been hard pressed to make highly accurate observations under such circumstances.