Lewis took meridian altitude observations on 11 November 1804, 13 January and 26 January 1805 (as he calculated them). The latitudes he calculated differed from each other by less than 1 arc minute; their average was 47°21' 24". Although this average was about 4' north of that which Thompson obtained (47°17' 22"), Lewis must have felt his observations were satisfactory.
Lewis, however, did not realize that both he and Clark persistently made a mistake in their calculations from all observations obtained with both the sextant and the artificial horizon. The proper procedure was to subtract the sextant's index error (usually 8' 45") from the observed angle, then divide the result by two, because using the artificial horizon doubled the observed angle. Lewis and Clark, unfortunately, first divided the observed angle by 2, then subtracted the sextant's index error. This meant that their calculations produced altitudes that were too low by an average of 4'22Ω", and thus made their calculated latitudes too far north by that same amount.
Lewis's observations, calculated correctly, yield an average latitude of 47°16' 54" N, not 47°21' 24". The latitude for Fort Mandan usually given in the Journals is 47°21' 47"" ; this was for the observation made on 26 January. Lewis must have thought that the observation on this date was more reliable than the others.
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