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Latitude & Longitude

The Lewis and Clark Expedition in 1803-1806 was not the first nor is it the most recent of mankind's great scientific explorations, although it certainly ranks amongst the top. Following the design and nurture of its grand architect, President Thomas Jefferson, it was, at least until modern times, probably the most rigorously and best documented of all.

NASA's manned flight to, and landing on, the surface of Earth's moon in the 20th century is a recent great exploration that some people living today can actually remember. It too is well documented, in conventional print and electronically (www.hq.nasa.gov/office/pao/History/ap11ann/introduction.htm). The exceptional accomplishment itself was possible because of the wonders of electronic communication, and, for that same reason, people alive in 1969, when the historic landing occurred, were able to watch the event in real time. That was a first among other firsts, and quite unlike the months and often years required to learn about earlier great events.

Ongoing probes of Mars represent another great exploration in our time. This is a case for which travel through space is dependent entirely on electronic communication and images being transmitted back to earth. We can keep up with events concerning expeditions to Mars by connecting to the NASA Web site at http://mars.jpl.nasa.gov/ .

Technology of Western Civilization was obviously in a much more formative state in the 15th century when Christopher Columbus landed in the new world. Nevertheless, for its time, the technology at hand was important to the whole fabric of discovery. Moreover, there was even then a technology center comparable to NASA. This center sponsored seagoing voyages in lateen-rigged caravels, fast wooden sailing vessels of the day (1,2). This early "NASA" also developed capabilities in cartography, mathematics and astronomy, and fostered navigation with instruments for celestial sightings (1,2). Navigation on the open sea, without landmarks on the horizon, was indeed a difficult problem, but one worth solving, because the sea promised new trade routes. Competition by nations on matters of trade has often been an incentive for great explorations; it was for the Lewis and Clark Expedition. With trade as a goal, the early center for exploration by sea was founded by Prince Henry the Navigator in approximately 1420, at Sagres on Cape St. Vincent in southwestern Portugal (1,2). Portugal was the western world's leader in navigation for some time thereafter, and Columbus, though he sailed to the new world under Spanish flag, most surely benefited from opportunities to learn its ways (1,2).

The compass for locating magnetic north was already known since the late 12th century (2). Columbus did employ this instrument for his remarkably skillful navigations at sea, along with the practice of dead-reckoning, but he was apparently not able to make good use of either the astrolabe or quadrant of his time for celestial navigation (1). Dead-reckoning is an application of the formula distance = rate x time. Rate was reckoned on the open sea by playing out a rope with knots in it over a measured period of time, hence the use of the term knots even today (1). Over a full day, the straight-ahead distance traveled could then be calculated after factoring in the actual compass directions of sailing. Lewis and Clark used a similar technique of dead-reckoning with a "log line reel" (www.edgate.com/lewisandclark/ ).

The astrolabe and quadrant are hand-held and difficult to steady for celestial sightings of angle to the horizontal aboard a pitching and rolling ship. They were better used on shore for the desired determination of latitude by sighting the sun or Polaris. This is how such instruments were used by the highly trained Portuguese explorers plying the African coast. Neither they nor Columbus depended on celestial navigation on the open sea (1).

The sextant is a more modern and sophisticated instrument than the astrolabe or quadrant for determining latitude. It was invented in 1731 in England and America independently (3). The Smithsonian National Museum of Natural History Web site www.edgate.com/lewisandclark/ gives a very nice photograph of a sextant; two were obtained by Meriwether Lewis in Philadelphia in 1803 during his visit there to extend his scientific learning and buy articles for the Expedition (4,5). After viewing the Smithsonian Web site image, the text in the next paragraph will make sense to the reader. This Web site also shows a picture of a compass carried by William Clark.

The sextant is an optical device that lines up the reflected image of the sun with a view of the horizon, such that the arc of the sun's altitude is obtained by the intersection of an index arm with a graduated arc (3). "Its construction is based on the principle that a reflected ray of light leaves a plane surface at the same angle at which the direct ray strikes the surface. The sextant consists basically of a triangular frame, the bottom of which is a graduated arc of 60°; a telescope is attached horizontally to the plane of the frame. A small index mirror is mounted perpendicular to the frame at the top of a movable index arm or bar, which swings along the arc. In front of the telescope is the horizon glass, half transparent and half mirror. The image of the sun or other body is reflected from the index mirror to the mirror half of the horizon glass, and then into the telescope. If the index (or image) arm is then adjusted so that the horizon is seen through the transparent half of the horizon glass, with the reflected image of the sun lined up with it, the sun's altitude can be read from the position of the index arm on the arc. By reference to navigational tables, the geographical position can then be determined" (3). The sextant is an improvement on the marine quadrant. With it, Lewis and Clark determined latitude at well defined landmarks, as Lewis was instructed to do by Mr. Jefferson.

Inquiry project: Build your own sextant based on the information given above and use it to measure "latitude" by sighting on a distant incandescent light source, BUT DO NOT SIGHT ON THE SUN. It is very injurious to the eyes to do so, which Lewis and Clark probably did not know in their day. The ultraviolet rays of the sun are extremely damaging and are today believed to cause such permanently blinding retinal diseases as macular degeneration. Ultraviolet rays are energetic enough to break carbon-carbon and carbon-hydrogen bonds, vital molecular bonds of all living matter.

While maritime instruments were known well before the early 19th century for determining latitude, with difficulty, there was even less of practical success for the more challenging problem of determining longitude. The modern earth is divided up into imaginary grids of latitude, which run parallel to the Equator, and longitude, which run pole to pole. The determination of longitude requires knowledge of local time, which can be determined from a sighting of the sun, relative to that of a reference. Knowing the reference time without an accurate clock at hand and running on that time was the problem. Officially, the reference has been the prime meridian at the Royal Observatory in Greenwich since 1884; it is the 0° longitude.

"The only known method of ascertaining longitude in Columbus's day was by timing an eclipse" (1). Columbus had only two chances during his four voyages to fix his time against predicted total eclipses, one at Nuremburg and one at Salamanca, and "muffed" them both (1). Galileo, in the early 17th century, presented another celestial means of fixing time, when he observed the four major, or Galilean, moons of Jupiter in revolution about the planet (6) (www.seds.org/nineplanets/nineplanets/jupiter.html). He developed fairly accurate tables of positions and eclipses for Jupiter's satellites, but, as with the astrolabe and quadrant, the task aboard a ship was realized to be a deterrent to practical use at sea (6).

In the 18th century, a Board of Longitude in England offered a prize for inventing a sufficiently accurate ship's chronometer for keeping the reference time (7). Sufficient accuracy was defined as measuring longitude within 30 seconds of arc. In a complicated story of technical accomplishment, and frustration with the Board (http://www.nmm.ac.uk/server.php?navId=005001004001), the talented and persistent John Harrison succeeded as he built a succession of four different mechanical clocks. These are known as the H1 to H4 designs, and they are beautifully shown in the Web citation above. A chronometer of his design, based on H4, was even tested successfully on the second voyage of Captain James Cook (8). The sad thing for John Harrison was that it was a struggle for him to realize the prize money before he died at age 83.

When Meriwether Lewis visited Lancaster in 1803, less than a century later, before going on to Philadelphia, he was continuing his scientific preparations beyond those he had already received under Jefferson. He received additional training (4,5) on the use of the chronometer and sextant from Andrew Ellicott, America's leading astronomer of the day. He then continued on to Philadelphia, where Robert Patterson, a distinguished mathematician, furthered the instruction and helped Lewis buy a chronometer for the Expedition. Lewis purchased one for $250, the largest of his expenditures for a single item, and then had Ellicott regulate the clock in Lancaster (4,5). Thereafter, it required winding every day, done at noon according to Lewis (4,9). It was, of course, difficult to maintain Greenwich time consistently on such a journey (9), so other astronomical means of the day, although also difficult, had to be used. Ultimately, mapmaking was accomplished with accumulated data from various measurements, but not any were obtained with a theodolite. Both Ellicott and Patterson counseled against the use of a theodolite, in favor of the sextant. The theodolite is an instrument similar in function to a surveyor's transit, with which Jefferson was familiar. It was deemed to be too fragile for the voyage by these experts (4).

Inquiry project: Compare the sextant and theodolite for function and problems. When is the latter better to use?

With the end of Lewis's Philadelphia training, the chronometer, the sextants and much more were shipped by wagon to Pittsburgh (4,5), the place of staging for the trip by keelboat down the Ohio River to the Missouri, eventually to really reach the Pacific Ocean itself. These instruments were amongst the most "high-tech" items on the voyage, and they had to withstand difficult portages and overland hikes. Because of Jefferson's concentration and emphasis on mapping the new lands, their use was a significant part of Lewis's training. With difficulty, they contributed to the scientific efforts of the Expedition, and data may not have always been accurate (9).

As with many other aspects of the Expedition, Jefferson's extensive reading, scientific knowledge and association with the learned scientists of America made the Expedition the lasting scientific event that it is. He shaped Meriwether Lewis, and William Clark by extension. He gave new meaning to the use of compass, sextant and chronometer, all of which have been highlighted in this Pennsylvania link to the Lewis and Clark Expedition.

Inquiry project: Compare the mechanisms of H1 and H4 and see if you can chart John Harrison's thinking process.

Latitude and Longitude References

1. Morison, Samuel Eliot, Admiral of the Ocean Sea, Boston: Little, Brown and Company (1942), pp.     27- 42, 183-196.

2. Morison, Samuel Eliot, The European Discovery of America: The Northern Voyages, New York:     Oxford University Press (1971), pp. 34, 94-111.

3. Harris, William H. and Levey, Judith S., eds., The New Columbia Encyclopedia, New York:
    Columbia University Press (1975).

4. Cutright, Paul Russell, Lewis & Clark: Pioneering Naturalists, Lincoln, NB: University of
    Nebraska Press (1989), pp. 19-29, 54.

5. Ambrose, Stephen E., Undaunted Courage, New York: Simon & Schuster (1996), pp. 80-92.

6. Drake, Stillman, Galileo at Work: His Scientific Biography, New York: Dover Publications (1978),
     p. 193.

7. Sobel, Dava, Longitude: The Story of a Lone Genius Who Solved the Greatest Scientific Problem     of His Time, New York: Walker (1995).

8. Price, Grenfell, ed., The Explorations of Captain James Cook in the Pacific As Told by Selections
    of His Own Journals
, New York: Dover (1971), pp. 98-99, 192-193.

9. Moulton, Gary E., ed., The Journals of the Lewis & Clark Expedition, Vol. 2 of Vols. 1-13,
    Lincoln, NB: University of Nebraska Press (2001), pp. 87 381-382, 412-413.

 

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