Much of what Lewis and Clark had to do in terms of their own mapmaking was to ascertain the accuracy of Indian information by doing what we call today "ground truthing"--checking Indian data against their own visual observations--and "celestial reckoning," using the instruments they carried for the purpose of fulfilling Jefferson's instructions to "take [careful] observations of latitude & longitude." To fulfill these tasks they used instruments: spirit and telescopic levels, several compasses including a surveyor's compass or circumferentor with extra needles and even a magnet to "polarize" them, a sextant, a "Hadley's quadrant" or octant, rods and chains, telescopes, artificial horizons, drafting instruments, a very early version of a measuring tape, and a clock or chronometer. They also used books and tables giving the daily locations of sun, moon, and planets for use in computing geographical position after obtaining sightings of these "celestial objects." The two most important groups of items of the Lewis and Clark Expedition, if cost is the measure, were mapping instruments and gifts for native peoples: these were the tools of empire, necessary in establishing a claim to place and space and defending that claim through trade,
Both Lewis and Clark were reasonably proficient in the use of these instruments and for 28 months, as long as the Expedition was on the move, a part of the daily routine was the measurement of latitude and longitude and the calculation of course, time, and distance of travel. Even during those times when Lewis and Clark were fixed in location for lengthy periods of time, such as at Fort Mandan and Fort Clatsop, the "mathematical instruments" saw almost daily use, weather permitting.
In this, the captains followed Jefferson's instructions to the letter and throughout the Expedition made the two basic types of geographical observations their sponsor had requested: (1) daily measurements of local features, taken continually during a day's travel; and (2) the more abstract measurements of latitude and longitudinal position, usually made by astronomical observation when and where atmospheric conditions allowed, but most commonly at camp during the night. Their guides were the moon and the stars.