Before the Expedition left its winter quarters at Camp Dubois in May 1804, Lewis had obtained some of the more reliable maps and data available concerning Western geography. The most important geographical information regarding the location of the Mandan village came from the celestial observations David Thompson took on 10 January 1798. Lewis had received these coordinates from Thomas Jefferson and may not have known who took the celestial observation or how reliable they might be (the trading companies tried to keep Thompson's maps and data for themselves). Lewis knew that Jefferson had obtained the coordinates from a British source, and Lewis may have had reason to suspect that the coordinates had been altered before coming into Jefferson's hands. Whether this is the case or not, Lewis certainly wanted to have data of his own taking to compare in order to verify or refute these other coordinates.
In the early 1800s there were several means of obtaining one's longitude—all involved comparing the correct time at your location with that at Greenwich. Before telegraphy this required using a chronometer or reliable watch to obtain the time for a celestial event and comparing that time to the Greenwich time for that event as given in the Nautical Almanac. Some of the more common celestial events whose times could be used were: an eclipse of the moon; immersions or emersions of Jupiter's satellites; occultations of stars or asteroids by the moon; and distance of the moon from the sun or one of eight or ten stars (Lunar Distance Observation). Most of these methods worked better in theory than in application to persons untrained or inadequately trained in taking the observations or making the calculations.
Lewis's mainstay observation for longitude was the Lunar Distance Observation, though here at Fort Mandan a fortuitous eclipse of the moon presented him with another opportunity, and this observation would have given him his best longitude—if he had calculated it correctly.
Eclipse of the Moon, 14-15 January 1805
The 1805 Nautical Almanac noted that a total eclipse of moon would begin on 14 January at 18:42 hours Greenwich Apparent Time. Astronomers at that time, however, began their day at noon, so 18:42 hours meant, not 6:42 pm as it would today, but 6:42 in the morning. Using Thompson's longitude of 101°14'24" West would place Fort Mandan about 6h 45m earlier than Greenwich. This meant that the eclipse would begin about midnight local time 14-15 January. Lewis, however, was not sure he could trust Thompson's longitude, and this necessitated his going outside to start his observations perhaps as much as an hour before time so as not to miss the beginning of the eclipse.
The temperature was bitterly cold. The high temperature for 14 January was about 8° below zero and the temperature was 10° below zero at sunrise on the 15th. Lewis had nothing more than the telescopic eyepiece from his sextant to observe the eclipse, and the chronometer to time it. The sky was partly to mostly cloudy, and Lewis was unable to see the beginning of the eclipse. He was, however, able to time four of the five principal elements of the eclipse: 1) the commencement of total darkness, 2) the middle of the eclipse, 3) the end of total darkness, and 4) the end of the eclipse. Now all he had to do is obtain the correct time from his wayward chronometer.
Lewis had taken an Equal Altitudes observation of the sun on 22 December and had calculated that his chronometer was 39m 37.6s slow on local mean time (I calculate 39m 43.4s). He, however, needed another Equal Altitudes observation as soon after the eclipse as possible to find the chronometer's error then and, from it, the chronometer's daily rate of loss. Lewis took an Equal Altitudes observation on the 15th but he was unsatisfied with it because, 1) owing to the cold, he had to use a leveled mirror as an artificial horizon and 2) clouds moved in during the afternoon and interfered with two of the three measurements he had to take.
Lewis made another Equal Altitudes observation on 20 January and calculated that the chronometer was 1hr 15min 20.3sec slow on Local Mean Time. Lewis, however, must have thought that this observation also was unsatisfactory for he did not use the times from it to calculate the longitude from the eclipse. Fortunately he didn't use the chronometer error he derived from that observation because he had miscalculated the chronometer error. The chronometer's actual error on Local Mean Time 1hr 05m 43.6s slow, not 1hr 15m 20.3 s slow. If Lewis had calculated the chronometer error correctly for this observation he could have continued with his eclipse calculations because the observation actually was reliable.
Lewis, on 28 January, made yet another Equal Altitudes observation. From this observation he calculated that his chronometer was 1hr 11m 12.2s slow on Local Mean Time (I get 1 hr 11m 18.8s slow). Using this latest Equal Altitudes observation and that for 22 December, Lewis calculated his chronometer's daily rate of loss and from that determined how slow his chronometer would have been on Local Mean Time during the eclipse. Comparing the corrected Mean Time for the end of total darkness and that the end of the eclipse with the times given in the Nautical Almanac he derived a longitude of 99°22'45.3" from the time for the end of total darkness and 99°26'45" from the time for the end of the eclipse. The average of these two longitudes, however, puts Fort Mandan at 99°24'45" West or too far east by 1°52'! Where did Lewis go wrong?
1. The main reason the longitude Lewis derived was so far east of the actual longitude is that he made his time comparisons with those given in the Nautical Almanac using his calculated Local Mean Times. The times in the Nautical Almanac were given in Greenwich Apparent Time. For the later elements of the eclipse there was a difference of 9m47s between Mean Time and Apparent Time; that is, it was necessary to subtract 9m47s from Mean Time to convert it to Apparent Time (or add 9m47s to Apparent Time to obtain Mean Time). At 4 minutes per degree of longitude, this time difference of 9m47s moves Lewis's calculated average longitude 2°27' farther west to 101°51'45" West.
2. Lewis also made a mistake in how he determined his chronometer's error. He might have discovered this if he had recalculated the times of his observations and made a plot (graph) of the chronometer's rate of loss. From this plot he could have obtained more nearly correct times for the elements of the eclipse. These corrected times, however, move his longitudes about 20' farther east. Subtracting this error of 20' from 101°52' gives an average longitude of 101°32' west for Fort Mandan or about 15' west of its actual location.
Funded in part by a grant from the National Park Service, Challenge-Cost Share Program.