OBSERVATIONS OF LATITUDE AND LONGITUDE AT ALL REMARKABLE POINTS.
No aspect of the Lewis and Clark Expedition was as significant to Thomas Jefferson and to the American republic as the need to accurately map the West. As the errors, fictions, and discrepancies in the maps of this exhibition show, geographic knowledge of the West remained incomplete and uncertain prior to the expedition. In some cases, the romantic yearnings and flights of fancy of explorers explain the differences in geographic representations. In most cases, however, persons engaged in the cartography of North America believed their maps to be true representations of the lands and seas they charted; using the tools and knowledge that they possessed, they made maps as accurately as they could.
The dramatic variations in the maps of North America, shown in chronological order in this exhibition, may be explained in large part by the limitations of technology. By the time of the Lewis and Clark Expedition, the science and traditions of mapmaking had evolved over thousands of years. The ancient Babylonians, Syrians, Egyptians, and Greeks had long studied the movements of celestial bodies in order to measure the relationship between the heavens and the earth and to chart position. Mapmakers typically represent three-dimensional position on a two-dimensional rectangular surface. Since the second century B.C., geographers have located points on the earth’s surface by rectangular coordinates known as latitude and longitude. Then, as now, the accuracy of astronomers, cartographers, and navigators depended on their application of theoretical knowledge, their ability to use navigational instruments, and the precision and sophistication of their instruments.
Without a doubt, the two most important concepts the geographer must master are latitude and longitude. The latitude of a point on the earth’s surface is the angle, in degrees, between the line from that point to the center of the earth and the equatorial plane. Latitude varies from 0 degrees at the equator to 90 degrees at either of the poles. Geographers designate either north or south latitude depending on whether the point on the surface is north or south of the equator.
Longitude depends on an arbitrary fixed point on the earth’s surface. The line on the earth’s surface formed by the intersection of a plane through this fixed point and the north and south poles is called the prime meridian. A line formed similarly through any other point on the earth’s surface is called a meridian or line of longitude. The longitude of a point on the earth’s surface is the angle, in degrees, between the plane forming the meridian of the point and the plane forming the prime meridian. Longitude begins at 0 degrees at the prime meridian and increases as one moves west, until, at 360 degrees, one reaches the prime meridian again.
The first instrument known to measure position was the gnomon, which was simply a vertical shaft. From the gnomon’s shadow, an observer could determine the exact moment of noon, the altitude of the sun, and the observer’s meridian. After the gnomon, improved navigational techniques and new instruments to measure latitude and longitude developed slowly. It was not until the fifteenth century that latitude could be accurately determined. Solutions to the more difficult problem of determining longitude remained elusive until the eighteenth century.
The instruments Lewis and Clark carried with them on their expedition across the continent and the geographic data the explorers collected may be traced to technological advancements in maritime navigation. The invention of the compass in the twelfth century allowed sailors to determine position by keeping track of their course under any weather conditions. When they used the compass in conjunction with a device that measured speed, navigators could chart how far they had traveled from a particular point. Lewis and Clark used this technique which was known as “dead-reckoning.” Like the compass, the quadrant was an invaluable navigational tool. It was used to measure altitude from which latitude could be determined. Although Columbus relied on a quadrant, in his day, the quadrant was awkward to use—it was inconveniently large and its operator had to look directly into the sun when sighting it. Around 1600 an improved version, known as the Davis quadrant, named after John Davis (1550?- 1605), allowed the operator to stand with his back to the sun and line up the edge of a shadow with the horizon. The introduction of optical elements, especially mirrors, represented an even greater advance in the quadrant. Because it used reflecting mirrors, the quadrant developed by John Hadley (1682-1744) in the 1730s read only one-half of the actual altitude of the object being observed. This allowed a scale of only forty-five degrees in width to represent ninety degrees of altitude. Hadley called his quadrant an octant since the scale occupies one-eighth of a circle.
Hadley’s octant was much more compact than previous instruments but still crude. For example, the scale on the instrument was unreliable and difficult to read. Mathematicians, however, had independently sought ways to refine the scale and permit more precise measurements. By the mid-1500s an auxiliary device called the nonius calculated scale measurements to fractions of a degree. The nonius was replaced by the much simpler and more finely calibrated vernier or vernier scale, named for the French mathematician Pierre Vernier (1580-1637). The addition of a tangent screw permitted finer adjustments on the vernier scale. By 1750 most octants were equipped with a vernier scale.
The precision of the octant improved still further with other advances in technology. The addition of a magnifying glass proved a valuable aid in reading the scale. Improvements in glass mirrors in the latter part of the eighteenth century reduced the problem of distortion in the reflection. A more vexing problem concerned the frame of the octant. Because the size of the scale on the octant was so large, the instrument’s frame was usually made of wood rather than metal, which would have been too heavy. Even a slight warpage or loosening of the frame caused significant inaccuracies. When Jesse Ramsden’s (1735-1800) invention of a dividing engine produced scales of much higher precision and reduced the radius of the octant, brass became a practical material for the frame and the inaccuracies brought on by warpage were eliminated.
All of the above innovations were combined in the design of the sextant which was improved by John Campbell (1720-1780). Campbell, who had conducted the first sea trials of Hadley’s octant, saw that by expanding the arc of the octant he could measure an object’s altitude with greater precision. The sextant enlarged the arc to one-sixth of a circle, which allowed the scale to be extended to 120 degrees. On many sextants a small telescope served as the eyepiece. The greater precision of the sextant compared to the octant made the use of lunar distances—the distances between the moon and certain stars—a practical approach to finding longitude. Lewis and Clark used the octant and the sextant to determine lunar distances on the expedition.
Several methods of determining latitude and longitude required positional information on the moon, the sun, and the stars. Lewis and Clark, for the most part, used lunar distances to collect data for calculating longitude. Although astronomers and geographers since the ancient Greeks had devised tables which predicted the positions of celestial bodies, significant improvements in these tables awaited a fuller understanding of orbital motion. Sir Isaac Newton’s discovery of the laws of gravitational motion helped provide that understanding by the late 1600s. A German, Tobias Mayer (1723-1762), with the help of orbital formulas from the great Swiss mathematician Leonhard Euler (1707-1783), suggested a way to predict lunar distances to determine longitude and prepared tables of lunar positions. The astronomer Nevil Maskelyne (1732-1811) refined Mayer’s method for his own table of lunar positions, which he included in the Nautical Almanac and Nautical Ephemeris, first published in 1765. Lewis and Clark carried copies of the Nautical Almanac with them on the expedition.
Since measures of longitude required precise measurements of time, the accuracy of longitudinal readings depended on the accuracy of clocks. Christiaan Huygens (1629- 1695) invented his pendulum clock in 1656, but this clock was not suitable for shipboard use or rugged land travel. John Harrison (1693-1776) perfected a marine chronometer for long sea voyages but its bulky five-inch size and the necessity of it being maintained in a horizontal position made it impractical for use on overland expeditions. Finally, in the 1770s John Arnold (1736-1799) invented the pocket chronometer. For the journey to the Pacific, Meriwether Lewis purchased a gold pocket chronometer.
Another of the navigational aids used by Lewis and Clark was the artificial horizon. Whereas sea voyages always offered mariners a natural horizon from which to measure the altitude of an object, land expeditions rarely presented explorers with a clear horizon; thus, explorers employed an artificial horizon, which was a reflective horizontal surface, to measure altitudes. Lewis and Clark used three different types of artificial horizons. The simplest and most preferred was a small tray of water which was protected from the wind by a glass plate. The efficacy of this type of artificial horizon, a favorite of Meriwether Lewis’s geographic advisor Andrew Ellicott, depended on the brightness of the object. The second type of artificial horizon, suggested by Patterson, was made of a piece of “parallel” glass plate which could be adjusted on a mount to a horizontal position by a spirit level. It was used with stars or the moon. The third artificial horizon used by Lewis and Clark consisted of an index mirror taken from a sextant and mounted in the same fashion as the glass plate. It was used for observing stars.
As the two primary planners of the Lewis and Clark Expedition, Thomas Jefferson and Meriwether Lewis tried to secure the most up-to-date navigational equipment for the journey. Jefferson, an accomplished surveyor and cartographer himself, realized that the resources and instruments available on the expedition, as well as the accuracy of the instruments and the expertise of the men who used them, were vitally important to the mapping of the West. Not surprisingly, Jefferson sought the advice of various experts in geography before he sent the expeditionary team off to the West. Jefferson arranged for Lewis to receive instruction in geography and cartography under two men: the early republic’s most highly regarded surveyor, Andrew Ellicott, and Robert Patterson, a respected mathematician living in Philadelphia. Lewis accepted Ellicott’s recommendations on the equipment needs of the expedition and Patterson’s suggestion that the sextant be set up for back observations, which allowed altitude measurements above eighty degrees. Ellicott regulated Lewis’s chronometer and instructed him in the use of the octant and sextant. Patterson prepared tabular forms for the entry of astronomical data, precluding the need to perform complicated calculations for determining longitude until after the expedition returned.
The instruments and resources that Lewis and Clark brought along on the expedition to the West gave rise to the data they collected and the maps and charts they produced. The concluding section of this exhibition explicates the four primary positional measurements that Lewis and Clark recorded on the expedition and displays the navigational instruments that the explorers used to make those measurements. The accompanying diagrams, prepared especially for this exhibition, give examples of each of the positional measurements Lewis and Clark took on July 29, 1805 at the Three Forks of the Missouri River.
Explorers such as Lewis and Clark could determine latitude if they knew the position of the sun in the noon-day sky. The first step in determining latitude in degrees from the equator is to measure the angular distance of the noon sun from the horizon. North of the equator, the sun appears higher and higher in the sky as a traveler moves south, and lower as he goes north. To track these changes Lewis and Clark used either a sextant or an octant. They made their measurements with a sextant during the winter when the sun was seasonally low at noon; in the summer, when the sun was high, they employed an octant. Lewis and Clark used artificial horizons with both instruments.
In order to achieve an accurate determination of latitude from the angle between the noon sun and the southern horizon, explorers had to make allowance for the sun’s movement with the seasons. The sun rises higher in the sky as the seasons change from winter to summer. Like other explorers of their day, Lewis and Clark consulted latitude-neutral tables in the Nautical Almanac that showed the sun’s seasonal height, or declination, for every day of the year. Declination is the angular distance from the celestial equator—the projection of the earth’s equator upon the sky. It varies from 23½ degrees above the equator in summer to 23½ degrees below the equator in winter. Any measured difference from this seasonal position of the sun would be due to the traveler’s latitude.
When Lewis and Clark took their latitude readings from the Nautical Almanac, they also had to make allowances for such variables as the refraction of the sun’s image by the atmosphere and the apparent size of the sun’s disk. Another reference book, Tables Requisite to be used with the Nautical Ephemeris by Nevil Maskelyne, supplied the mathematical factors for calculating these adjustments.
For Lewis and Clark, determining longitude was a matter of comparing local time with Greenwich time. To find local time in the late eighteenth and early nineteenth centuries an observer used a sextant to measure equal altitudes of the morning and afternoon sun. Andrew Ellicott advised that these observations ”be taken at least two hours before, and after noon.“ In explaining the technique to Thomas Jefferson, he wrote: ”After the forenoon equal altitudes have been taken, the sextant should be carefully laid away, and the index not moved, till the afternoon ones are taken.“ The recorded times of these observations were then averaged to determine the precise moment of noon at the observer’s location. Having determined local time, the observer would then calibrate his chronometer to that time.
Measurements of longitude varied between sea voyages and landed expeditions. At sea, navigators compared local time with Greenwich time by using a chronometer; the navigator kept his chronometer on Greenwich time. On a landed expedition, however, the precision of the chronometer was not nearly so important as the combined reliability, portability, and durability of the timepiece. The great Canadian explorer David Thompson, for example, never carried a chronometer. Lewis and Clark decided to use lunar distances to determine Greenwich time which meant that they needed only an accurate or consistent pocket watch. Nevertheless, Andrew Ellicott recommended that Meriwether Lewis acquire an Arnold’s chronometer for the expedition to the West.
The second part of determining longitude entailed determining Greenwich time. Lewis and Clark used lunar distances to obtain Greenwich time. Their Nautical Almanac contained tables of predictions by the Royal Greenwich Observatory of the moon’s position relative to nine conspicuous stars and the sun. The tables showed the moving moon’s angular distance from these targets at intervals of three hours, Greenwich time, throughout the year. Using a sextant to measure the moon-star angle seen in their own sky, Lewis and Clark could then match the angle against the appropriate Nautical Almanac table to determine Greenwich time.
The comparison of these angles, however, required a series of fine mathematical adjustments that could vex even the most careful geographer. For example, the angles in the tables from the Nautical Almanac assumed that the observer was standing at the center of the earth rather than on the earth’s surface. Rather than making the necessary mathematical adjustments to perform the longitudinal computations in the field, Lewis and Clark merely recorded the raw moon-star angles. Lewis’s writings reveal that he only completed one entire computation of longitude on the expedition and that computation was performed early in the expedition before the journey up the Missouri River. Clearly, Lewis and Clark decided to gather the necessary data and leave the complex calculations to experts back East. These calculations later proved to be a difficult task even for mathematicians. Four years after the expedition, F. R. Hassler, a mathematics instructor at West Point, tried unsuccessfully to complete the longitude calculations.
One of the tasks explorers continually face is the need to align their maps properly. Although maps are typically aligned with the geographic north pole, an explorer’s compass points to the magnetic north pole high in the Canadian arctic. The difference between geographic north and magnetic north is called compass variation. The amount of variation will change as the traveler moves east or west. The explorers of the American West had to perform frequent measurements of the local compass variation from true north to guarantee the proper alignment of the maps they consulted.
A relatively easy way to measure compass variation is to aim the “north” arrow of the compass card at the North Star—Polaris—and determine how far the magnetic needle points away from that line. Probably using this technique, Lewis and Clark recorded five such measurements of the North Star’s magnetic azimuth, or variation, with their boxed surveyor’s compass, or circumferentor, as it was referred to in the journals of the expedition. They observed a compass variation of 15½ degrees east at the junction of the Marias and the Missouri rivers. However, because Polaris does not mark exactly the celestial pole, this method of measuring compass variation is imprecise.
A second method of determining compass variation promised more accuracy but required the explorer to use spherical trigonometry. After the sun had risen to a convenient height in the morning, an observer would use his sextant to measure its altitude above the horizon and note the time. Simultaneously, he would also record the sun’s magnetic azimuth. The trigonometric solution would give the sun’s azimuth from true north, against which the above magnetic azimuth could be compared to ascertain the compass variation at that location. Lewis and Clark made twenty-four such observations during their expedition. Lewis and Clark carried a standard text on spherical geometry—A Practical Introduction to Spherics and Nautical Astronomy by Patrick Kelly—on the expedition, they apparently never, however, attempted the mathematical calculations needed to produce a solution for any of their observations. As with their lunar-distance longitudes, they evidently left the computations to the experts in Washington upon their return.
Gilbert & Coy. London. c. 1800.
35. ARNOLD'S CHRONOMETER
Joshua Romer. London. 1807.
W & S Jones. London. c. 1800-1815.
37. WILLIAM CLARK'S SURVEYOR'S COMPASS
Joshua Romer. London. 1807.
38. PATRICK KELLY
A Practical Introduction to Spherics and Nautical Astronomy. London. 1805.