Early in the afternoon of January 30, 1805, Larocque went to the captains' quarters to see about having his broken compass repaired. While Lewis worked on it the rest of the day, they talked. "The captains are busy making charts of the country through which they had passed, and delineating the Head of the Missouri according to the information they had from the Indians, who described a river as being four days march west of the last navigable part of the Missouri, which river, they say, is very large." The old legend of a day's portage across a "height of land" between the two great rivers had begun to crumble.
...I Remain'd here a Couple of days, being pressed so to by the Captains. They took observations for the Longitude & Latitude of the place while, I was with them, & often since their arrival here. They differ much from Mr. [David] Thompson, in the Longitude of this place, & say that Mr. Thompson has placed these villages, & this part of the river, a great deal too westerly, which they think is the Case, with all his observations for the Longitude; they observed some time ago an Eclipse of the moon which they say is an Infallible rule for finding the Exact Longitude of a place. But they do not differ from him in the Latitude.1
Thompson, who had been at the Mandan villages in 1798, calculated their longitude at 101° 14' 24" West, which is roughly 11 miles east of their actual position at 101° 27' West, whereas Lewis's calculation placed them at 99° 26' 45" West, or about 122 miles too far east. But Lewis, realizing that his chronometer was running slow, later had second thoughts about the accuracy of his own calculations.
Lewis further mentioned to Larocque that the boundary of Louisiana Territory might extend as far north as the mouth of the Qu' Appelle River at the Assiniboine River. In fact, Clark's first composite map, compiled during the Fort Mandan winter, showed the Souris and Missouri River drainages coming within but a few miles of one another in the vicinity of the Knife River villages--actually it's about 30 miles (48 km)--which meant that the boundary there was the Coteau du Missouri, well south of the 50th parallel.
Furthermore, Clark showed the White Earth River beginning about two degrees (140 miles) north of the Qu' Appelle's source, when in fact it rises just below 48° 39' North. It joins the Assiniboine in western Manitoba at approximately 50° 27' North. It is the Milk River, whose northernmost tributaries begin at around 49° 15' North, that actually defined the northernmost boundary of Louisiana Territory at that time. The whole question became moot in 1818, when the 49th parallel was officially established as the boundary between the United States and Canada from the Great Lakes to the Rockies.
1. See Arlen Large, "Fort Mandan's Dancing Longitude," We Proceeded On, Vol. 13, No. 1 (February 1987), and "Lewis and Clark: Part Time Astronomers," We Proceeded On, Vol. 5, No. 1 (February 1979). Also "Shooting the Moon (and the Sun and Stars): Lewis and Clark as Celestial Navigators," We Proceeded On, Vol. 27, No. 4 (November 2001), featuring articles by James Merritt, Eileen Star, Robert N. Bergantino, Lawrence A. Rudner and Hans A. Heynau.