How did Lewis and Clark measure distances on their historic "Voyage of Discovery" from 1804 to 1806? William Clark was the primary cartographer of the expedition, according to Journal editor Dr. Gary Moulton "working with crude and unreliable instruments and with no apparent training," yet doing "a masterful job." Clark was primarily concerned with the "direction of travel from point to point, the number of miles covered between the points, and the daily mileage accumulation."
Volume One of The Journals of the Lewis and Clark Expedition, Lincoln: University of Nebraska Press, 1983, edited by Gary E. Moulton, is an oversize atlas which reproduces all the maps drawn during the expedition. This book is a fine source of geographical information as it was known to the explorers.
Capt. Lewis indicated in his lists of expedition equipment that they carried quite a few surveying instruments, but all of them were far more useful for short rather than long-distance measuring. These included a "two pole chain" (33 feet long), a "log line reel" which measured the rate of boat travel (these measurements were affected by river currents), compasses, quadrants, sextants, and a chronometer. Early in the second year, the chronometer ran down, which further complicated things by making it impossible to determine longitude. Gary Moulton notes that: some of these scientific instruments may have been used in establishing distances between widely separated points, but for routine measuring it seems likely that the explorers used estimates or the time-honored method of 'dead reckoning.' The fact that various journals give differing mileage figures for the same area traversed supports such a conclusion. John J. Peebles, who has examined the route of the explorers in Idaho, found that for river travel the journalist's mileages are generally short of true figures, while for land travel the reverse holds. Exaggerations of land mileage figures occur more often when the party traveled over difficult terrain. In fact, the mileage estimates are of little help in determining specific geographic points or expeditionary campsites. Journal entries and geographic landmarks on the maps are more reliable guides. Clark, then, probably based his mileage figures on the time of travel or his skill and experience as an outdoorsman (see page 4 of Volume One).
Moulton theorizes that Clark relied on compass readings for his "courses." His compass traverse notes are at the beginning of nearly every journal entry. According to Moulton, Clark "probably employed the route traverse method, taking bearings at each turn of the trail or bend in the river and plotting those shifts on his maps.... For his mapping Clark was probably taking 'back sightings' or 'back azimuths,' giving his bearing from north or south in degrees. After traveling forward some miles, Clark would turn and take an azimuth reading from his previous point of sighting. This procedure was necessary because he could not always determine his next point of observation. In converting back azimuths to forward readings, Clark may have become confused occasionally, and some of his readings may seem turned around because they reflect the direction he was looking rather than the direction that he had traveled."
Whether or not all the readings were correct, the feat of merely recording them all and making maps which can still be followed today, while exploring unknown territory, for a total of over 8,000 miles, is an extraordinary one by anyone's reckoning. If you would like to read more about Lewis and Clark and the subject of geography, you may be interested in the following books:
Allen, John Logan. Passage Through the Garden: Lewis and Clark and the Image of the American Northwest. Urbana: University of Illinois Press, 1975.
Jackson, Donald, ed. Letters of the Lewis and Clark Expedition, with Related Documents, 1783-1854. Urbana: University of Illinois Press, 1962.
Moulton, Gary E., ed. Volume One of The Journals of the Lewis and Clark Expedition, Lincoln: University of Nebraska Press, 1983.
Wheat, Carl I. Mapping the Trans-Mississippi West, 1540-1861: Volume 2 - From Lewis and Clark to Fremont, 1804-1845. San Francisco, 1958.