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" . . . You will certainly take monitorings of latitude & longitude"

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


Thomas Jefferson was as interested in the methods and equipment because that "ascertaining by celestial observation the location of the country" together with any other single aspect the the Expedition. He played an important role in making certain that Lewis to buy the appropriate equipment and learned just how to use it before he left because that the West. He additionally insisted that observations be carried out with accuracy, would be redundant, would be comprehensible come others, and that sufficient duplicates of all observations would be made to guarantee versus the feasible loss of one or more sets. As faithfully as they could, the captains complied with the President"s wishes.

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Latitude


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Figure 1

Ephermeris

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Figure 2

Determining Latitude through the phibìc Star

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For Lewis and Clark, together for so numerous of their predecessors and also contemporaries, calculating latitude to be far less complicated than calculating longitude. In the northern hemisphere, latitude may be acquired by measure up the angle made in between the phibìc Star and the horizon. Crude instruments to acquire this angle have actually existed for hundreds of years and also by the time of Lewis and Clark, instruments like the sextant and also octant, just slightly less an accurate than those available to us, to be in use.

Figure 1 reflects graphically what an ephemeris mirrors in tables. The difference is that the expensive almanac gives figures for solar (sun), lunar (moon), and also astral (star) altitudes for every day of the year follow me all lines of latitude whereas the diagram suggests only solar altitude at 4 times throughout the year (equinox and solstice) and only along one line of latitude. What line of latitude? That deserve to be determined from the diagram listed below as follows: on June 21, in ~ its zenit or highest point in the sky (local noon) the sun is directly overhead (an altitude the 90°) in ~ latitude 23°30" N (the Tropic the Cancer). If the altitude that the noon sun at the suggest of observation on June 21 is 72°30" (the price " suggests a "minute," and also 60 minutes equal one degree), climate the latitude the the allude of observation is 41°N. This is acquired from individually 72-1/2 levels (altitude the the sunlight at observation point) indigenous 90 degrees (altitude of sunlight at Tropic the Cancer) and then including the result (17-1/2 degrees) come the latitude that the Tropic the Cancer (23-1/2 degrees) whereby the sun"s altitude is 90°. To usage the ephemeris, all one needs to understand is the work of the year and also the altitude that the sun, the moon, or among the crucial stars such as Betelgeuse, Aldebaran, Antares, or Vega.

Latitude may additionally be calculate by measure up the altitude that the sun, moon, or certain planets and also stars over the horizon on known days and reading latitude from tables draft for the purpose. It to be not lot more complicated for the captains to measure up these altitudes with a sextant or octant and also to calculation latitude using one of the three ephemerides or astronomical almanacs castle carried. These consisted of tables showing the day-to-day position that celestial body such together the sun, the moon, and vital stars. Calculating latitude gave Lewis and Clark couple of problems and also their readings were accurate to in ~ a fraction of a degree.

In number 2, an illustration from a 16th century portolan atlas, a seaman is determining latitude utilizing a cross-staff. This maker allowed the to measure up the "altitude" of Polaris or the north Star. Polaris is directly overhead in ~ the phibìc Pole (90° of latitude); in various other words, the angle in between Polaris and also the horizon at the north Pole is 90°. This angle is dubbed "the altitude" that Polaris. In ~ the Equator (0° of latitude), the north Star is top top the horizon, do an edge of 0°.

For any suggest between the Equator and the north Pole, latitude is acquired simply by measure up the altitude of Polaris: in ~ 30°N the star is 30° over the horizon, in ~ 63°N, it is 63° over the horizon, and so on. Before the usage of the cross-staff pictured, mariners and others who necessary to recognize latitude used level pieces of wood through holes to sight v to find Polaris and with pieces of cord fastened to measure up angles.


Figure 3

Longitude and also Time

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For lot of the at an early stage era of global exploration, longitude had actually been an overwhelming to calculate since either one elaborate collection of expensive tables and measurements were forced or an exact time-keeping maker was necessary, and also neither was available until the 18th century. As beforehand as 1610 Galileo had devised a method to recognize longitude by monitoring of the passage of the 4 moons the Jupiter.

By the beforehand 18th century, if still making use of the transit of Jupiter"s moons, navigators had learned to do approximate calculations of longitude by observing the changing angular distance in between the Moon and also a influential star such together Antares. But numerous mindful observations and extensive calculations were forced for this method to work and neither of these was yes, really feasible on board ship or in the field.

Finally, in 1735, partly in an answer to an market of £20,000 by the British government to anyone who might solve the problem of identify longitude in ~ sea, an English clockmaker named John Harrison devised a functioning spring-based chronometer that verified promise that a solution. Numerous sea trials and several boosted versions the Harrison"s original version were required before, in 1773, Harrison had actually a functioning chronometer, resilient enough for extensive field observation. It to be a version of this chronometer that Lewis and also Clark brought with them.

All this seems fairly simple. Why, then, to be the captain"s longitudinal observations so at risk to error? The prize is likewise simple: castle did no have, together we do, trusted battery-powered watches v quartz movements. As soon as their chronometer ran down, it had to be re-calibrated on neighborhood time, which required them come make observations to identify the sun"s janice or regional "noon" and then setting the chronometer by estimating the Expedition"s present longitudinal position. End the food of your journey, the little incremental errors created by this procedure became larger ones.

There were other approaches of calculating longitude available to them, using huge observation. Yet many huge readings had actually to be acquired over the food of a night in stimulate to achieve sufficiently precise data to recognize longitude. The was questioning a lot because that men worn down by the rigors that their everyday trek, to spend three or 4 hours in the cold and also damp the a hill night acquisition sightings the the moon and stars, recording observations, and making calculations through firelight. It was only organic that errors would certainly exist in data acquired in this manner. Also the most skilled astronomer or surveyor would have actually been hard pressed to make extremely accurate observations under together circumstances.


Longitude can be calculated making use of either time or huge observation. Calculating longitude by chronometer is based upon the fact that any suggest on the earth"s surface moves through a complete circle that 360 degrees once in a 24-hour period; during 1 hour, any point on the earth"s surface ar moves through an east-to-west 15° arc of a complete circle. If time deserve to be resolved along any meridian that longitude, climate longitudinal distance have the right to be figured out by to compare time at the meridian with local time, usually based upon the suggest at which the sun reaches its zenith.

From number 3 it can be viewed that if the is noon along the element or Greenwich meridian that longitude, it will certainly be 1:00 pm 15° come the east and 11:00 to be 15° to the west. These times are described respectively as being "ahead" or "behind" Greenwich average Time (GMT), or time follow me the prime meridian. Using this principle, that is simple to recognize longitude. Because that example, if a chronometer set on Greenwich average Time reads 6:00 pm or 1800 GMT at the time as soon as the sunlight reaches the highest suggest in the sky (local noon) from the vantage suggest of the observer, climate the sun reached its zenith over the element meridian 6 hrs earlier. The observer is, therefore, 90° west of element meridian (6 hrs x 15° = 90° of longitude). Since local sun time is various everywhere native GMT, trying to save track that train schedule on east-west routes came to be impossible by the mid-19th century and also so, by international convention in 1877, traditional time zones of roughly 15° that longitudinal broad were established, focused on 0°, 15°E and also W, 30°E and W, and also so on. Within each time zone, time is the exact same everywhere, rather than being retained locally.


The errors the Lewis and also Clark do in latitude and also longitude calculations were much less the result of your instruments, their mathematics, or field conditions than by little errors that three species that influence all expensive observations:

(1) miscalculating refraction or the bending of irradiate in the atmosphere, which reasons altitudes to appear slightly higher than they actually are;

(2) estimating semidiameter of either the sun or moon, the discs the which room too large to it is in used whole when making a sighting. As such it is necessary to sight the "sun"s top limb" or top half or the "moon"s reduced limb" or bottom fifty percent and climate correct by calculate to achieve a reading at the center of the disc; and

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


" . . . The they might with certainty it is in recognised hereafter."

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


After the expedition Jefferson listed that "it is only to latitudes that map might be considered as tolerably correct, not as to its longitudes." This was overly critical: certainly the captains" longitude observations were much less than perfect. Yet william Clark"s can be fried map of the western part of phibìc America, based in component on those observations, nonetheless proved quite accurate in the longitudinal reckoning. In the final analysis, regardless of the extant errors, their longitudinal monitorings were better than might or should have been expected. The ultimate results of their "observations the latitude & longitude" bore that out.

Clark"s last map to be the culminating piece of geographical information arising from the Expedition and resulting directly from Jefferson"s injunction to preserve understanding for the future. Perfect in manuscript kind by 1811, engraved and published v the Biddle History of the expedition . . . in 1814, it shown with artistry, skill, and also accuracy the area through which the exploration had passed. Course and also distance details is noticeable on the map and coordinate location are precise to within 5%, an accuracy level that would not be suitable by numerous cartographers till the arrival of mapping aided by aerial photography in the early on 20th century.

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Clark"s map represented the can be fried triumph that the vertical perspective, the capacity to synthesize mental and also actual maps and also to portray geographical attributes with precision in the context of the geographical coordinate system within which he operated.