Accurate Longitude Observations

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Despite the advancements in chronometer technology since John Harrison constructed a time piece in the mid-1700s that met the specifications of Great Britain's Commissioners of Longitude, finding a longitude on sea or on land was still a difficult process in 1805. The usual limits of accuracy often were as great as ± 15 minutes; at 45° north latitude, an error of 15' of longitude means an error of ± 12 miles.

Lewis took a series of observations on August 19, and another series on the twentieth, to obtain the data necessary to calculate a longitude for Fortunate Camp. However, he did not make any calculations from them.12 How good were his observations?

Long-time practical navigator Bruce Stark of Eugene, Oregon, suggests that Lewis missed the longitude for Fortunate Camp by a mere three miles.13 Such an observation was far better than what most trained navigators could do at that time and as good as, and even better than, the average longitude values determined by the great Canadian trapper-surveyor David Thompson. My method of checking Lewis's observations for longitude is somewhat different from that used by Mr. Stark. From a software program I determine the apparent positions of the celestial objects, then back-calculate to the angle Lewis should have observed for the time and his location. From these calculations I conclude that the angular error of Lewis's observation on the nineteenth was 13 arc seconds too small and on the twentieth it was 38 arc seconds too large. Given the rate at which the sun and moon were approaching each other at the time those observations were made, my findings are in complete agreement with those calculated in the standard method by Mr. Stark.

The Dimensions of Navigation

The foregoing discussion summarizes the mathematical dimension of celestial navigation on land; an orderly sequence of measurements, addition, subtraction, multiplication, division. The second dimension of the process is physical. The technique of making a meridian observation of the sun with an octant by the back sight method, on land, using an artificial horizon is a difficult operation. The observer does not stand bold upright looking toward the horizon as the common image of the marine navigator depicts, but must hold the handle-less instrument in the left hand, usually while kneeling down or sitting cross-legged, looking down at a very steep angle into the artificial horizon while trying to adjust the index arm with the right hand until the image from the index mirror and that reflected from the artificial horizon (there was no telescope on Lewis's octant) were matched. It was not much easier using the sextant and artificial horizon except that you could hold the instrument in your right hand. And then there were the observations taken at night by torchlight with mosquitoes, flies, gnats and fatigue that could strain the last fiber of an explorer's soul. Despite these ordeals, the captains made these observations at nearly every significant point along the route.

The third dimension might be called the contextual setting. The moments devoted to celestial observations were islands of intense concentration and mental exertion injected into the dense daily array of routines, opportunities, anxieties, and unforeseen occurrences. In that context, especially during the busy fortnight at Fortunate Camp, it is remarkable that their observations provided coordinates that were as close to correct as they were. Bearing this in mind, it is easy to forgive the captains the few errors they committed.

For the Corps of Discovery there was yet one more dimension to the carrying out of celestial observations. Consider the baffled Indian onlookers, wondering what occult rituals the white chief and his acolytes were practicing. Was sign-talker George Drouillard equal to this challenge? Could his eloquent hands, which so often had bridged cultural chasms to shape mutual understandings, reduce this arcane tale to concepts that could be grasped? How could he possibly have explained the sextant and octant, when the magic of the compass needle was simply "medicine" to Indian people? How could he have expressed their uses and purposes to people without words of their own for hour, minute, degree, arc, second, angle, decimal point, or statute mile? Never mind all that, and the murky labyrinths of trigonometry and spherical geometry through which even the captains took wrong turns. How might Drouillard have broached the bold preposterous concept of Earth as a globe to people with their own holy mysteries of sun, moon, stars, land, and sky, who already had orderly, practical understandings of time, space, pace and place? Or would a mere nod, a smile, and a shrug have satisfied their inquisitive eyes?

12. Jefferson directed Lewis to take the necessary observations for the determination of longitude, but did not expect him to make the complicated calculations. These were to be made by mathematicians in the War Department. The expedition's data ultimately were delivered to Ferdinand Hassler, a Swiss mathematician of the faculty of the newly founded (1802) U.S. Military Academy at West Point, but for various reasons the task never was completed. Moulton, Journals 2:533-34. Richard S. Preston, "The Accuracy of the Astronomical Observations of Lewis and Clark," Proceedings of the American Philosophical Society, vol. 144, no. 2 (June 2000), 169–91.

13. Letter to the Editor, We Proceeded On, Vol. 28, No. 3 (August 2002), 3-4.

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