Pursuant to President Jefferson's orders, Lewis and Clark made celestial observations at "all remarkeable points on the river, & especially at the mouths of rivers." The purpose of the observations was to obtain data to calculate the latitude and longitude of these points and to correct the expedition's river survey – based on magnetic north – to true north. By fitting their river survey between points of known latitude and longitude, the Expedition's estimated distances also could be corrected. The captains made a total of 278 sets of observations at 111 different locations between the mouth of the Missouri and the mouth of the Columbia.^{1}

The calculating of longitude from a celestial observation required the use of complex mathematical procedures based on spherical trigonometry.^{2} Those calculations were to have been completed by a qualified mathematician after the expedition's return. Some of Lewis's data were given to Ferdinand Hassler, of West Point, for him to work with, but he never finished the job. In December of 1810 Clark sent "a large Connected Map" to his editor, Nicholas Biddle, which was to be included in Biddle's paraphrase of the captains' journals. "The Map will not be Corrected by Celestial observations," Clark wrote, "but I think verry correct."^{3}

Jefferson was not satisfied. In 1816 – he was then seventy-three years old – he lamented in a letter to a friend that "the most important justification of [the Lewis and Clark expedition], still due to the public depends on these astronomical observations, as from them alone can be obtained the correct geography of the country, which was the main object of the expedition."^{4} Inexplicably, he never succeeded in finding anyone to help him pay his debt to the people.

Since the mid-1980s other students have made important contributions to understanding the equipment and observational techniques that Lewis and Clark used. Several more have written articles on the results and accuracy of some of the captains' celestial observations. The following calculations – made especially for *Discovering Lewis and Clark®* – from the expedition's celestial observations make use of all the valid data obtained at nine of the expedition's geographically most significant campsites. These data then were converted into geographic data using procedures that were common at the time of the expedition.^{5}

In the first essay that follows, I review the Astronomy Notebook, an instruction manual that Robert Patterson prepared for Meriwether Lewis's reference. In the remaining essays I examine the celestial observations taken at nine of those 111 "remarkeable points," and solve the problems they pose. Those points are: The mouth of the Kansas River, Fort Mandan, the mouth of the Marias River, the Headwaters of the Missouri, Fortunate Camp, Clearwater Canoe Camp, the mouth of the Snake River, Station Camp on the Columbia, and Camp Chopunnish.

How much work would it have been for Lewis to complete the entire process of converting his celestial observations into latitudes and longitudes for each one of the locations for which he had taken observations – *if* he had had the time and the mathematical skill, and *if* he had completed his observations accurately to begin with? I have provided one example of the entire process as it would have been done during Lewis's generation,^{6} in "Calculations for the Celestial Observations that Meriwether Lewis made at the Three Forks of the Missouri". In this instance, the process fills thirty-two consecutive pages with mathematical expressions. It is no wonder that Jefferson excused Lewis from this responsibility.

Obviously, I have not paid Jefferson's debt in full, nor would there really have been a reason to do so, even back in his day. My choice of sites to complete was based mainly on 1) the quality of the chronometer data, and 2) the site's location with respect to major changes in the direction of the expedition's route. A few other sites have fair-to-middling chronometer data and could have been included, but that would have made little difference in a map the scale of the one published in 1814. If Jefferson had wanted a series of more detailed maps, calculations for longitude for other places such as White Catfish Camp and Council Bluff could have been included. But it would have been far more practical to calculate *all the latitudes* – a comparatively simple exercise – but *only the longitudes where the better data existed*. Having done that, the compass survey could have been made to fit between as few as these nine control points plus the Missouri's confluence with the Mississippi. Such a map probably could not have been bettered, at least along the expedition's route, until the era of the transcontinental railroad surveys.

1. The captains reported at least 36 observations attempted between November 12, 1803 and May 14, 1804. From May 14, 1804 until August 25, 1806 I count 278 distinct observations. Equal altitudes (AM and PM) count as only one observation, The same is true for observations for magnetic declination even if taken 10 or so minutes apart, although if AM and PM they are counted as separate observations. Lunar distances are counted by the object observed with the moon even if several sets of 6 to 12 measurements were taken.

2. Navigators themselves rarely use spherical trigonometry any more to find their location, but GPS still uses spherical trig in conjunction with time signals to determine a position. Although almost all the calculations navigators made before 1993 (except for Latitude from Meridian Altitude) were based on spherical trig, the methods they used were "cook book" applications like Robert Patterson's, where the navigator or mathematician followed the procedures outlined in the examples given for each type of observation. My efforts are based on the same procedures. The biggest problem I had was in interpreting them (that is, deciphering the mathematical logic in them) and restructuring them to be used to provide the geographic data needed.

3. Donald Jackson, ed.,

Letters of the Lewis and Clark Expedition With Related Documents 1783-1854,2 vols. (Urbana: University of Illinois Press, 1987), 2:562-63.4. Jefferson to José CorrËa da Serra, July 20, 1816. Ibid., 2:618. da Serra, the Minister from Portugal, who called Washington the "city of magnificent distances," was a noted botanist, as well as a famous wit. Margaret Bayard Smith,

The First Forty Years of Washington Society(1906, reprint, New York: F. Ungar, 1965), 135.5. I have recalculated all the latitudes and all the chronometer errors on Local Time, but longitudes have been calculated for only about 11 sites, and magnetic declination for about 15.

6. Not included in that mass of calculations is Latitude from the Double Altitude of the Sun, because Lewis didn't make that observation at the Three Forks.

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