# Latitude

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The morning of the 16th dawned "Clear and butifull," but "the wind was hard from the S W." At noon Clark took advantage of the conditions and made an observation of the sun's altitude for latitude. He used the sextant and artificial horizon:

I took a meridian altitude with sextant 50°36'15"; the shaking image below

Clark's "shaking image" most likely refers to the image of the sun reflected from the artificial horizon. The artificial horizon—in this case a tray nearly filled with water—was set in a shallow excavation so that the water surface was at or slightly below ground level. A wind screen or housing then was placed over the tray, but not touching it, to help reduce the effect of wind on the water surface. Nevertheless, the strong southwest wind must have produced a slight oscillation of the water surface, causing the image to shake. In spite of that, Clark's observation at Station Camp was one of his best.

## Table 3. Comparison of Latitudes, Captains versus Recalculated

 Latitude that Clark calculated from his Meridian Altitude of the Sun 1805 November 16 46˚19'11.1" Latitude recalculated from Clark’s Meridian Altitude of the Sun 1805 November 16 46˚15'47.3" Difference 00˚04'23.8"

The difference of 4' 24" between the recalculated latitude and that which Clark calculated comes from the incorrect method he and Lewis used to calculate latitude from an observation using the sextant and artificial horizon. The captains subtracted the index error of 8'45' after they divided the observed angle by two; they should have either: 1) subtracted the sextant error before they divided by two or 2) subtracted half the error after dividing by two. This error makes the captains' calculated sextant-artificial horizon latitudes too far north by an average of 4' 22½" (5 statute miles).

As interpreted from Clark's maps and from the expedition's courses and distances, Station Camp was at 46°14' 47" North Latitude—just 1 arc minute south the latitude recalculated from Clark's meridian observation. A latitude error of 1 arc minute (1.15 statute miles) from a sextant observation was within the normal limits of accuracy for that time. This shows that, despite the "shaking image," Clark's observation was a good one. Note, however, that if an index error of +6' 45" is used for the sextant instead of +8' 45", it produces a latitude of 46°14' 48" for this observation—just 1 arc second north of the actual latitude.

## Sextant Error

Having introduced, in the paragraph above, the suggestion about a different index error for the sextant, this seems like a opportune place to discuss its index error. All celestial observations that Lewis and Clark took with their sextant, except the Equal Altitudes observation, need to be adjusted for the sextant's index error. Whereas an index error of a minute or so, when using an artificial horizon, does not greatly affect the latitude, magnetic declination or even the time calculated for that observation, it makes a substantial difference in the calculated longitude. From November 1803 when the expedition was at the mouth of the Ohio River until November 1805 on the Pacific, the captains recorded that the sextant index error was 8' 45" subtractive. That is, the sextant read too high by 8' 45" and that amount had to be subtracted from all observations. A sextant's index error, however, rarely remains the same for a long time, and most navigators routinely check the index error of their instruments. Lewis may have done so, but never recorded any change in the sextant's index error until February 4, 1806. On that date he gave its index error as 5' 45" subtractive (too high). Longitudes calculated from observations the captains made at the mouth of Kansas River, Fort Mandan, Marias River, Three Forks, Fortunate Camp and Clearwater Canoe Camp suggest that if the sextant's index error had changed, it had not changed significantly. Although calculated longitudes generally are too far east of the actual longitude by 15—20 arc minutes this may result as much from observing error as from the sextant's index error. Beginning at the mouth of the Snake River, however, the longitude calculated from the captains' observations seem to indicate that the sextant's index error had changed, perhaps by an arc minute or more. Unfortunately, without reliable chronometer times the true index error cannot be ascertained.

Funded in part by a grant from the National Park Service's Challenge-Cost Share Program