The captains did not calculate a longitude from any of those Lunar Distance observations they made at the junction of the Missouri and the Marias. If Lewis had made the calculations for the longitude of this junction while at Fort Clatsop, he probably would have used an assumed longitude of 111°W for his initial calculations. The longitude 111°W is suggested here because this junction is shown at that longitude on the Lewis and Clark map of 18061. A mathematician recalculating the Expedition's celestial observations to determine longitudes for the Lewis and Clark map of 18142 (Atlas map 126) and having access to Clark'smap of 18103 (Atlas map 125), would have noticed, however, that this junction was shown at 110°W on that map. A reasonable compromise would havebeen to split the difference and use 110°30'W for the initial calculations,as has been done in this evaluation. The longitudes listed below were obtained from the Expedition's Lunar Distances observations, "clearing the distance" using the method that Chevalier Jean Borda devised in 1787. The method for clearing the distance, as detailed in Robert Patterson's 1803 Astronomy Notebook that Lewis carried, yields similar results.
Longitudes from observations of Lunar Distance for longitude, mouth of Marias River in 1805 :
Using the average of 109°35' places the mouth of Marias River 54 arc minutes (a little less than 42 miles) too far east of its redetermined 1805 location. This error is too great to be acceptable. An evaluation of the longitudes calculated, however, suggests problems with Observation No. 2 for June 2 and Observation No.1 for June 9. Rejecting these observations as spurious gives an average longitude of 109°53', which is too far east by about 28 miles. An evaluation of longitudes calculated from the captains' Lunar Distance observations during the expedition shows that the moon-sun observations are the most reliable. Using just the moon-sun observations, the captains' longitude for the mouth of the Marias River (110°05Ω' west) is about 23Ω arc minutes (18 miles) east of its redetermined longitude.
Even so, the correlation between the longitude calculated from moon-sun observations and the actual longitude is somewhat below the expected accuracy for those times, but not excessively so. Even as late as the transcontinental railroad surveys in the 1850s, longitudes derived by the U.S. Army Topographical Engineers sometimes were in error by nearly half a degree.
1. Clark completed the original draft of the 1806 map at Fort Clatsop in February of that year. Nicholas King made a copy of it in 1807 (Atlas map 123), which is the only one in existence.
2. The 1814 map (Atlas map 126) was the comprehensive culmination of all Clark's geographical discoveries and measurements, "in his way."
3. The 1810 map (Atlas map 125) was Clark's first draft of the final (1814) version.
4. The captains hardly could have failed to identify this star – white and brilliant (0.8 magnitude) with no rivals nearby – yet they recorded its distance from the moon at 58+° whereas, if it was Altair, the distance should have been 68+°. Did they actually shoot the wrong star (not very likely) or did they misread the distance either on the sextant or from poorly written notes (with ditto marks for the degrees) recorded that night? The longitude for this observation was calculated for this essay using an average distance of 68°51'39", not 58°51'39".