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" . . . you will take monitorings of latitude & longitude"

—Thomas Jefferboy, Instructions to Meriwether Lewis, 20 June 1803


Thomas Jefferboy was as interested in the methods and devices for "ascertaining by celestial observation the geography of the country" as with any various other single element of the Expedition. He played a crucial role in making sure that Lewis purchased the proper equipment and learned how to use it before he left for the West. He likewise insisted that monitorings be conducted via accuracy, would certainly be redundant, would be comprehensible to others, and also that adequate duplicates of all monitorings would be made to guarantee versus the possible loss of one or even more sets. As faithcompletely as they could, the captains followed the President"s wishes.

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Latitude


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Figure 1

Ephermeris

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Figure 2

Determining Latitude by the North Star

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For Lewis and Clark, as for so many type of of their precursors and contemporaries, calculating latitude was much less complicated than calculating longitude. In the northern hemispright here, latitude might be acquired by measuring the angle made in between the North Star and also the horizon. Crude instruments to attain this angle have actually existed for countless years and also by the time of Lewis and also Clark, instruments choose the sextant and also octant, just slightly less specific than those available to us, were in use.

Figure 1 shows graphically what an ephemeris reflects in tables. The difference is that the astronomical almanac provides numbers for solar (sun), lunar (moon), and astral (star) altitudes for eincredibly day of the year alengthy all lines of latitude whereas the diagram suggests just solar altitude at 4 times throughout the year (equinox and solstice) and just alengthy one line of latitude. What line of latitude? That deserve to be figured out from the diagram listed below as follows: on June 21, at its zenith or greatest point in the sky (neighborhood noon) the sun is directly overhead (an altitude of 90°) at latitude 23°30" N (the Tropic of Cancer). If the altitude of the noon sun at the suggest of monitoring on June 21 is 72°30" (the symbol " suggests a "minute," and 60 minutes equal one degree), then the latitude of the suggest of monitoring is 41°N. This is derived from subtracting 72-1/2 levels (altitude of the sunlight at monitoring point) from 90 levels (altitude of sunlight at Tropic of Cancer) and then adding the outcome (17-1/2 degrees) to the latitude of the Tropic of Cancer (23-1/2 degrees) wbelow the sun"s altitude is 90°. To usage the ephemeris, all one demands to understand is the day of the year and also the altitude of the sun, the moon, or one of the key stars such as Betelgeusage, Aldebaran, Antares, or Vega.

Latitude may additionally be calculated by measuring the altitude of the sun, moon, or particular planets and stars over the horizon on known days and also reading latitude from tables designed for that purpose. It was not much even more tough for the captains to meacertain these altitudes via a sextant or octant and also to calculate latitude making use of one of the 3 ephemerides or astronomical almanacs they lugged. These had tables reflecting the everyday position of celestial bodies such as the sun, the moon, and essential stars. Calculating latitude offered Lewis and Clark few problems and also their readings were precise to within a portion of a degree.

In Figure 2, an illustration from a 1sixth century portolan atlas, a seaman is determining latitude making use of a cross-staff. This device allowed him to meacertain the "altitude" of Polaris or the North Star. Polaris is directly overhead at the North Pole (90° of latitude); in various other words, the angle in between Polaris and the horizon at the North Pole is 90°. This angle is called "the altitude" of Polaris. At the Equator (0° of latitude), the North Star is on the horizon, making an angle of 0°.

For any point in between the Equator and the North Pole, latitude is derived simply by measuring the altitude of Polaris: at 30°N the star is 30° above the horizon, at 63°N, it is 63° above the horizon, and also so on. Before the use of the cross-staff pictured, mariners and also others that essential to recognize latitude supplied flat pieces of wood with holes to sight with to find Polaris and also through pieces of cord attached to meacertain angles.


Figure 3

Longitude and also Time

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For a lot of the beforehand era of worldwide exploration, longitude had been hard to calculate because either a fancy set of astronomical tables and also measurements were compelled or a specific time-maintaining tool was essential, and neither was obtainable till the 18th century. As early on as 1610 Galileo had devised a method to recognize longitude by monitoring of the passage of the 4 moons of Jupiter.

By the beforehand 18th century, while still using the transit of Jupiter"s moons, navigators had actually learned to make approximate calculations of longitude by observing the changing angular distance between the Moon and also a influential star such as Antares. But many cautious monitorings and also considerable calculations were compelled for this method to job-related and also neither of these was really feasible on board ship or in the field.

Finally, in 1735, partly in response to an sell of £20,000 by the British government to anyone that can resolve the trouble of determining longitude at sea, an English clockmaker called John Harriboy devised a working spring-based chronometer that verified promise of a solution. Many sea trials and also several enhanced versions of Harrison"s original design were forced before, in 1773, Harriboy had actually a working chronometer, sturdy enough for extensive area monitoring. It was a version of this chronometer that Lewis and also Clark carried via them.

All this seems rather simple. Why, then, were the captain"s longitudinal monitorings so at risk to error? The answer is additionally simple: they did not have, as we perform, trustworthy battery-powered watches through quartz activities. When their chronometer ran dvery own, it had to be re-calibrated on neighborhood time, which forced them to make observations to determine the sun"s zenith or regional "noon" and then setting the chronometer by estimating the Expedition"s current longitudinal place. Over the course of their journey, the tiny increpsychological errors developed by this procedure came to be bigger ones.

There were other approaches of calculating longitude available to them, using expensive observation. But many kind of expensive readings had to be acquired over the course of a night in order to acquire sufficiently precise information to determine longitude. It was asking a lot for guys exhausted by the rigors of their daily trek, to spfinish three or 4 hours in the cold and damp of a hill night taking sightings of the moon and stars, recording observations, and also making calculations by firelight. It was only herbal that errors would exist in information derived in this manner. Even the a lot of experienced astronomer or surveyor would have been hard pressed to make highly specific monitorings under such scenarios.


Longitude deserve to be calculated making use of either time or astronomical observation. Calculating longitude by chronometer is based on the truth that any type of point on the earth"s surface moves with a finish circle of 360 levels as soon as in a 24-hour period; during 1 hour, any type of suggest on the earth"s surchallenge moves via an east-to-west 15° arc of a complete circle. If time can be solved alengthy any meridian of longitude, then longitudinal distance have the right to be identified by comparing time at that meridian with regional time, typically based on the allude at which the sunlight reaches its zenith.

From Figure 3 it can be checked out that if it is noon alengthy the prime or Greenwich meridian of longitude, it will be 1:00 pm 15° to the eastern and 11:00 am 15° to the west. These times are described respectively as being "ahead" or "behind" Greenwich Mean Time (GMT), or time along the prime meridian. Using this principle, it is basic to recognize longitude. For instance, if a chronometer set on Greenwich Median Time reads 6:00 pm or 1800 GMT at the moment when the sunlight reaches its highest possible suggest in the sky (local noon) from the vantage point of the observer, then the sun reached its zenith over the prime meridian 6 hrs earlier. The observer is, therefore, 90° west of prime meridian (6 hrs x 15° = 90° of longitude). Since regional sun time is various all over from GMT, trying to store track of train schedules on east-west paths came to be difficult by the mid-1nine century and so, by worldwide convention in 1877, typical time areas of approximately 15° of longitudinal width were established, focused on 0°, 15°E and W, 30°E and W, and so on. Within each time zone, time is the exact same almost everywhere, quite than being retained locally.


The errors that Lewis and also Clark made in latitude and longitude calculations were less the outcome of their tools, their mathematics, or field problems than by little errors of three types that influence all astronomical observations:

(1) miscalculating refraction or the bending of light in the environment, which causes altitudes to appear slightly better than they actually are;

(2) estimating semidiameter of either the sun or moon, the discs of which are too huge to be used entire once making a sighting. Thus it is vital to sight the "sun"s upper limb" or top fifty percent or the "moon"s lower limb" or bottom fifty percent and also then correct by calculation to attain a reading at the center of the disc; and

(3) correcting for "parallax," the reality that while navigational tables are based on distances and angles calculated from the earth"s center, monitorings are made from the earth"s surconfront.


" . . . that they may via certainty be recognised hereafter."

—Thomas Jefferson, Instructions to Meriwether Lewis, 20 June 1803


After the Expedition Jefferson provided that "it is just to latitudes that map might be taken into consideration as tolerably correct, not regarding its longitudes." This was overly critical: definitely the captains" longitude monitorings were much less than perfect. Yet William Clark"s ultimate map of the western percentage of The United States and Canada, based in component on those monitorings, nevertheless showed fairly exact in its longitudinal reckoning. In the last analysis, in spite of the extant errors, their longitudinal observations were better than can or should have been supposed. The ultimate results of their "observations of latitude & longitude" bore that out.

Clark"s final map was the finishing item of geographical indevelopment arising from the Expedition and resulting straight from Jefferson"s injunction to keep expertise for the future. Completed in manumanuscript create by 1811, engraved and also published with the Biddle History of the Expedition . . . in 1814, it shown with artistry, ability, and accuracy the area through which the Expedition had actually passed. Course and also distance indevelopment is evident on that map and coordinate positions are precise to within 5%, an accuracy level that would not be matched by many kind of cartographers till the introduction of mapping aided by aerial photography in the beforehand 20th century.

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Clark"s map stood for the ultimate triumph of the vertical perspective, the capability to synthesize psychological and actual maps and also to portray geographical functions with precision in the conmessage of the geographical coordinate system within which he operated.