from “The Homeward Bound Journey”

On October 4, 2010, George Huxtable, who lives in the United Kingdom, sent an e-mail to the Missouri State Archives in Jefferson City, Missouri, inquiring about specialized and arcane information concerning latitude and longitude in 1803–1804, the time period of the Lewis and Clark Expedition. He wrote:

In the course of some research into Lewis and Clark's wintering at Fort Dubois, 1803–4. I'm interested in the following question—

At or about the time of the handover to the US, in March 1804, was there any knowledge, in St. Louis, of the town's geographical position, latitude and longitude, particularly longitude?

It might possibly have been established by a military surveyor attached to the expeditionary force when St. Louis was founded 30 years earlier. After all, the French were the world experts, at that time, in such land-survey, with longitude based primarily on timed observations of satellites of Jupiter.

I wonder if there might have been, in the town prior to 1804, a resident savant, amateur astronomer, surveyor, geographer, clockmaker, schoolteacher, who might have taken an interest in such observations (French or Spanish). Or whether the US sent an official who was capable of delineating the position of the new Gateway, as part of the junketings associated with Three Flags Day.

And if the answer isn't known, what's the earliest date for the position of St. Louis to be recorded? I am aware that Lewis and Clark themselves noted coordinates for Fort Dubois, but I am trying to discover whether they might have been assisted in this by the prior knowledge of the St. Louis citizenry.

A few days later, Huxtable's e-mail was forwarded to me, and during our correspondence over the next few months, I gave him the information he sought. To return the favor, he provided the “back office” information on Lewis's trip to the Cumberland Gap explained in chapter 5 of this book.

Lewis had used several instruments at the Cumberland Gap that were utterly foreign to me, but when I mentioned them to Huxtable, he easily expounded on what they were. This led to a larger discussion, which is detailed below. As an expert on early survey techniques, Huxtable observed that

throughout the expedition, Lewis & Clark made a consistent mistake in correcting for the index error of their sextant or octant when measuring reflected altitudes in an artificial horizon. Instead of correcting the sextant reading for index error, and then halving to allow for the doubled angle due to reflection, as they should have, they would halve the reading and then correct it for index error. The result was that measured altitudes were always in error by half of the index error of the instrument. When the sextant was used, for which the measured correction was normally 8’ 45” (to be subtracted), the erroneous procedure caused the deduced altitude to be too low by 4’ 22''.

When used to obtain a latitude from a meridian altitude, that latitude would always be too high by a corresponding amount, 4’ 22''. The effects of this problem became much more serious when the sun's altitude exceeded 60°, as it did at summer noons. In that case their octant, in back-observation mode, had to be used, and in this mode the index correction was as great as 2° 11’ 40” (to be added). As a result, altitudes calculated in this erroneous way from an observation would be too high by 1° 05’ 50'', and latitudes derived from such a meridian altitude would be too low by nearly that same amount.

Huxtable also provided much information about reading a sextant, which he said

is capable of looking in two directions at once, and precisely measuring the angle between the two views. For measuring latitudes at sea, the sun appears in view in one mirror, and the sea-horizon in the other. The sextant itself does not need to be precisely aligned with anything though its frame needs to be kept in a vertical plane. The altitude, the angle by which the sun is above the horizon, reaches a maximum near noon, and that maximum value is noted, before the sun starts to fall again. All that's needed is for both the sun and the horizon to be seen, clearly and sharply, for a few minutes around noon. No timepiece is required.

The land-navigator has no sea-horizon to measure up from, so his procedure has to be different. Instead, he measures the angle between the sun up in the sky, and the sun's reflection seen looking down into the horizontal surface of a bowl of liquid; which was often simply water, but which could be mercury. The angle between those two views of the sun is exactly twice the sun's altitude, so the angle, as measured, has to be halved. This works well, as long as the surface can be shielded from being ruffled by wind. However, the standard mariner's sextant could measure only up to an angle of 120°, which meant that it could not tackle noon sun altitudes greater than 60°; which they were, over the months of high summer, throughout the United States. In that case, a different instrument, or another technique, was called for.

In either case, there are important corrections to be made to the sun's measured altitude, and it was these corrections that Lewis and Clark tended to get wrong, rather than the basic measurement of angle. The largest correction allowed for the sun's slowly changing declination as it moved north of the equator in northern summer and south in northern winter, which was readily available from an almanac.

After those corrections had all been made, an experienced observer, with a good instrument, could reliably determine land-latitudes within rather better than a minute of arc, or within about one land-mile of the true position.

The sextant was the instrument favoured by travelers as, being hand-held, it needed no elaborate setting-up, so latitude could be determined at a short pause in a journey, around noon. Surveyors, on the other hand, were under less time pressure and sought greater accuracy, so in preference to a sextant they would employ a theodolite, or a zenith sector, and might well use observations of stars rather than the sun. But these instruments would call for a firm base, such as the stump of a felled tree, and needed precise orientation and levelling beforehand.

Huxtable gave a detailed explanation for Lewis's readings using what Lewis called Ellicott's “much approved Zenith Sector.” Lewis had to take a crash course in surveying and taking latitude and longitude measurements using celestial bodies in order to prepare for the expedition in 1803. Huxtable explained that Lewis's instruction “was aimed at sea-navigation, not the special aspects of navigating on land. But nobody should be sent off with only a few weeks of instruction under his belt, without some expert on hand to turn to.” Huxtable continued:

I understand that Ellicott had two zenith sectors made for him by David Rittenhouse, the larger of which could be transported only by water. A zenith sector, which measures the altitudes of stars that lie nearly overhead, is indeed a very precise instrument for determining latitude. Ellicott's observation of the position of the Ohio-Mississippi junction may have taken place on December 18, 1796, on his way to establish the border between Spanish and U.S. America. Lewis doesn't quote Ellicott's results, but the modern reckoning of that point, south of modern Cairo, between the two rivers, puts it at 37° 00’ N. Nor has Lewis's deduced latitude for that point survived, in his journal for November 14–20, 1803, though we can make deductions from his equal-altitude observations (that were beyond him), and obtain good agreement with the modern latitude. However, any meridian altitude observation made by Lewis would always have produced a deduced latitude that was too high by more than 4’ (nearly 5 land-miles too far north), because of his incorrect procedure in subtracting his sextant's index error after (rather than before) halving the altitude. I am, then, surprised that he found such agreement with Ellicott's observations at that same spot. As he provides no numbers, neither his nor Ellicott's, we are not in a position to assess for ourselves whether (and to what extent) he did.

Huxtable also talked about the zenith sectors, which “have little relevance to a study of Lewis and Clark, as they never used such an instrument, as far as I know. The only way they enter into the discussion is Lewis's claim, a doubtful one to me, that at the same spot as modern Cairo, Lewis obtained the same latitude with his sextant as Ellicott had previously measured with his zenith sector.”

Huxtable also provided information on Ellicott's instruments, which can be found at the Smithsonian Institution's Website. “Both Ellicott's instruments, made by David Rittenhouse…seem to be beautifully made, in two very different sizes. The smaller one, much more portable, was probably the one used by Ellicott in 1796.” To view these instruments, consult the following Web addresses.

Zenith telescope (19 inches long):
http://americanhistory.si.edu/collections/surveying/object.cfm?recordnumber=758696

Zenith telescope (5.5 feet long):
http://americanhistory.si.edu/collections/surveying/object.cfm?recordnumber=758697

Huxtable's Website, “Lewis and Clark on the Mississippi: Commentary on Their Celestial Navigation,” provides much information on what he calls the “Index mixup,” section 1.11.2. http://www.hux.me.uk/lewis02.htm. For Huxtable's own work, see George Huxtable and Ian Jackson, “Journey to Work: James Cook's Transatlantic Voyages in the Grenville 1764–1767,” Journal of Navigation 63 (2010). Huxtable also recommended Lawrence A. Rudner and Hans A. Heynau, “Revisiting Fort Mandan's Longitude,” We Proceeded On 27, no. 4 (November 2001): 27–30. This article also describes other aspects of sextant calculations on the Lewis and Clark Expedition.