During the Expedition's stay at the junction of the Missouri and Marias River in 1805, Meriwether Lewis took three observations of the sun at noon (June 3, 9, and 10) to determine the latitude of the junction. He took each of these observations with his octant. Why didn't he use the more precise sextant to take them? The main reason was that the sun's noon (meridian) altitude was greater than 60°. Even if the sun's noon altitude had been less than 60°, however, Lewis still would have used the octant on June 3 and 9.
Altitude: At noon on June 3 at the mouth of Marias River, the altitude of the sun's center was 64°25' above the horizon and would increase until the summer solstice. Lewis had to use an artificial horizon to measure the sun's altitude, and the artificial horizon doubled the angle to be measured. Lewis's sextant could measure a maximum angle of a little more than 120°; the sun, thus, was too high at noon to use the sextant.
June 3 and 9: On these days Lewis took Equal Altitudes observations of the sun with the sextant to determine his chronometer's error on Local Time at noon. He always left the sextant's index arm locked at the altitude he had measured in the morning until he had completed the afternoon observations. Consequently, the sextant was not used for noon observations when Equal Altitude observations were taken even if the sun's noon altitude was less than 60°.
Lewis therefore used the octant to take his observations of the sun's noon altitude at the mouth of Marias River, and he took those observations by the "back method." Lewis called it the "back method" not because he stood with his back to the sun, measuring its altitude from the opposite horizon as he would have done at sea in a back observation, but because he used the peep sight and horizon glass on the octant's back limb.
What's a "back limb?"
The octant had a simple A shape. It was designed to be held in the observer's right hand while operating the index arm with its index mirror using the left hand. The fore limb of the octant was the limb closest to the observer's eye during a normal observation. When looking at the octant's working face the fore limb was to the right – the back limb was to the left, on the other side of the A.
An observation by the back method was more difficult for most people than the fore method because it required holding the octant in the left hand. Using an artificial horizon – with either water or a mirror as a reflecting surface – while taking an observation by the back method made the operation even more difficult because the observer had to be positioned close to the artificial horizon. This meant kneeling or sitting on the ground, a rock, a fallen tree trunk, or a stump, while facing the artificial horizon and the sun. The observer then tried to match the reflection of the sun from the artificial horizon with the reflection of the sun from the index mirror. It took skill and patience to make an accurate observation.
The methods of calculating a latitude from a meridian observation of the sun made with the octant by the back method were described for the latitude observations taken at the Mouth of Kansas River, and will not be described here. It is necessary, however, to point out a mistake that Lewis made throughout 1805 with his octant-derived latitude calculations.
Historians and students of the Expedition who are familiar both with the whereabouts of the Expedition and with detailed maps have noted that some of the Expedition's latitudes (especially those in 1805) fall about 30 miles too far south of the actual latitude1. Few people, however, have recalculated the Expedition's latitudes from their meridian observations. The comparisons below show, however, that Lewis's meridian observations at the mouth of Marias River (except, maybe on the 10th) were as good as his rather imprecise octant would allow. The fault lies not in his observations but in his using an erroneous index error to make his calculations.
In his detailed description of his scientific instruments on 22 July 1804, Lewis wrote that the octant's index error in the back observation was 2°11'40.3"".2 During 1805 he incorrectly used an index error of 2°40'3 for all his octant observations except on August 19 and 20 when he appears to have used an octant error of 2°30'. To Lewis's credit, he discovered his mistakes while at Fort Clatsop and recalculated some of his more important observations. It appears, however, that he did not inform Clark of these corrections because it is the latitudes that Lewis calculated in 1805 that appear on Clark's later maps – not the latitudes Lewis recalculated in 1806 while at Fort Clatsop.
The average of Lewis's three observations (as he calculated them while at the mouth of the Marias) would put the mouth of the river about 30Ω arc minutes (about 35 miles) south of its actual location4. The average these same observations, correctly calculated, however, puts the 1805 mouth of Marias River only about 1 mile south of its redetermined location. Considering the difficulties in making the observations by the back method, Lewis's observations were excellent, sometimes reaching the accuracy of good sextant observations.
The latitude of the mouth of Marias River is shown at 47°19' on the Lewis and Clark map of 1806, at 47°27' on Clark's map of 1810 and at 47°22' on the Lewis and Clark map of 1814.
1. For the latitude at the mouth of Marias River in 1892 see Elliott Coues, History of the Expedition, 3 vols. (1892; New York: Dover 1965), 2:357n: "The mouth of Maria's river is nearly up to 48° N. lat."
Stephen Ambrose quoted Arlen Large from a personal communication regarding Lewis's meridian observation of the sun at Camp Disappointment, 23 July 1806:Lewis measured the sun's noon altitude...getting a raw octant reading of 62 degrees, 00' 00"". He didn't record any conversion of that suspiciously rounded number into a latitude. Using an 1806 Nautical Almanac and Lewis's usual method of computation, that octant reading would have produced a latitude of 48 degrees, 10', or some 30' too far south.Stephen Ambrose, Undaunted Courage: Meriwether Lewis, Thomas Jefferson and the Opening of the American West (New York: Simon and Schuster, 1996) 376. Lewis's meridian observation at Camp Disappointment, correctly calculated, produces a latitude for that camp of about 1Ω miles too far north of the latitude compared to its redetermined location. The "suspiciously rounded number" was not rounded; Lewis could read the octant only to the nearest 30"".
2. Actually, its half-error. Lewis divided the observed angle by two before correcting for the index error. See Lewis's description of his octant on 22 July 1804, in Moulton, Journals, 2:411.
3. See Lewis, 12 April 1805, in Moulton, Journals, 4:25.
4. Location determined from the Expedition's surveys and descriptions, and comparison of that information with the oldest detailed maps and with modern maps and aerial photos.5. Moulton, Journals, 6:496.6. Using 110°30'W for longitude, to adjust the sun's declination and a half index error of 2°11'40.3"".
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