Maps, Wayfinding, and the Discovery of Longitude

By Mishka Vance, GIS Specialist
June 18, 2021
Stephen A. Schwarzman Building

Maps serve many purposes: archives for geographically referenced information; pictures of the spatial order of the world; tools for investigating spatial patterns, relationships, and environmental complexities; and objects of aesthetic and historical interest. Maps are also used for wayfinding, or locating oneself and navigating from place to place.

Early Navigation

The earliest navigation techniques involved observing known landmarks or celestial bodies to determine one’s position. As early as the beginning of the twelfth century BCE, the Phoenicians (from what is now Lebanon) were exploring the Mediterranean Sea. The Carthaginians (from what is now Tunisia) navigated as far as England and attempted to sail around Africa. Maps and other documents described coasts, landmarks, and moorings allowing for navigation. The development of cartography was related to the development of navigation.

Phoenician Sailors

Phoenician sailors, 1882. NYPL Digital Collections, Image ID: 1624003

Parallels and Meridians

Navigation requires knowing a location relative to other known locations. In order for maps to be useful for navigation, they need to accurately reference locations on the Earth’s surface. In the third century BCE, writer, geographer, astronomer, and poet Eratosthenes produced maps that included irregularly spaced grid lines which we would now call parallels (lines of latitude) and meridians (lines of longitude). Latitude is the distance north or south from a reference line that lies in a plane perpendicular to the Earth’s axis. Longitude is the distance east or west from a reference line that contains the plane of the Earth’s axis. Eratosthenes’ reference system laid the groundwork to define precise specifications for any location on Earth.

In the second century CE, Ptolemy, an Egyptian astronomer, mathematician, and geographer of Greek descent, built upon the work of Eratosthenes. Ptolemy created a map of the world as it was known to the Roman Empire that included curved lines of latitude to reduce the distortions inherent with representing the spherical Earth as a flat map. As a reference for latitude, Ptolemy used the Equator, the imaginary line that is equidistant from the poles. He used the Fortunate Islands off the northwest coast of Africa (now known as Madeira and the Canary Islands) as his reference for longitude. This map was a part of his seminal work, Geographia, which was highly influential in the development of geographic knowledge, astronomy, and cartography.

Map of Europe, Africa, the Mediterranean, and Asia. Personifications of the Winds. Full Gold Border

Ptolemaic world map reproduced from descriptions contained in Geographia, ca. 1460. NYPL Digital Collections, Image ID: 427011

Rhumb Lines

Dating as far back as the year 1300, medieval portolan charts were regional sailing charts compiled from written sailing directions. Portolans often lacked a consistent grid of meridians and parallels and thus a consistent way to reference locations. These charts were typically oriented to magnetic north and comprised of intersecting rhumb lines. A rhumb line, rhumb, or loxodrome is an arc that crosses all meridians of longitude at the same angle. It is a path of constant bearing relative to magnetic north. However, because of the curvature of the Earth, any oblique, constant course becomes a complex curve requiring sailors to constantly recalculate their bearing during the course. As such, portolan charts were useful for relatively short distances. As navigators dared more extensive open ocean travel, better representations of the world were needed.

America and Europe, Atlantic Ocean

Portolan chart showing the Atlantic Ocean and continents, 1552. NYPL Digital Collections, Image ID: 427089

Mercator’s Chart

Building on Ptolemy’s Geographia, Flemish cartographer Gerardus Mercator published the first sailing chart for the whole world in 1569. The map, titled "New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation," was an 18-sheet wall mosaic measuring 48 inches tall by 80 inches wide. Composed of straight lines of latitude and longitude with consistent right angles between them, his map revolutionized navigation by straightening the rhumb lines. Any straight line drawn on a Mercator chart was a line of true constant bearing that enabled a navigator to plot and follow a straight-line course.

Chart of the world on Mercator's projection

Mercator’s projection, 1798. NYPL Digital Collections, Image ID: 58102326

On a globe, the vertical lines of longitude converge at the poles. On Mercator’s map, the meridians are equally spaced and parallel to one another, meaning that the map is stretched east-west along meridians at higher latitudes. The map must then be equally stretched north-south. Mercator’s parallels are spaced farther and farther apart as their distance from the Equator increases, meaning that areas farther away from the Equator appear disproportionately large. In Mark Monmonier’s Rhumb Lines and Map Wars, Mercator concluded that “accurate bearings […] demand a locally exact representation of angles and distances, even though ‘the shapes of regions are necessarily very seriously stretched.’” Mercator’s projection maximized angles and direction at the expense of area.

Mercator’s wall map did not immediately gain popularity. First, the oversized wall map could not be easily copied or displayed. Second, Mercator did not provide the necessary mathematical equations he used for progressively spacing the lines of latitude. The later work of mathematicians Edward Wright and Henry Bond made Mercator’s chart more accurate, portable, and reproducible. In 1599, Wright published an improved version of Mercator’s map and a table to help mapmakers construct their own Mercator grid. In 1645, Bond offered a mathematical formula for constructing a Mercator grid based on Wright’s table. Navigators began to use Wright’s version of the Mercator chart in the early 1600s. Despite improvements in mapping, sea travel remained a challenge due to incomplete or inaccurate sailing charts and maps, errors in direction, and inaccuracies in determining a ship’s location at sea.

Thou Hast Here, Gentle Reader, A True Hydrographical Description of So Much of the World as Hath Beene Hetherto Discouered and Is Comne to Our Knowledge

Wright-Molyneux world map, 1599. NYPL Digital Collections, Image ID: 4056663

Sailing the Parallels

According to Dava Sobel, author of Longitude, latitude is "fixed by the laws of nature." The rotation of the Earth on its axis from west to east provides two natural points of reference, the North and South Poles. The latitude of a position can be calculated by measuring the angle of the sun or the North Star (Polaris) in the Northern Hemisphere in relation to the surface of the Earth.

Because of the relative ease with which navigators could determine latitude, "parallel sailing" in which a ship sailed along a known line of latitude east or west until they reached their destination was an often-used method of travel. In fact, Christopher Columbus sailed the parallel across the Atlantic Ocean in 1492. Although popular, parallel sailing increased a ship’s time at sea and the potential for hazards. Accurate positioning was a requisite for efficient sea travel and latitude alone was not sufficient to determine an exact location.

The Problem of Longitude

Longitude has no natural point of reference. By convention, the Prime Meridian was often placed at the Canary Islands following Ptolemy’s placement. Later mapmakers placed it at other locations including the Azores, the Cape Verde Islands, Rome, Copenhagen, Jerusalem, St. Petersburg, Pisa, Paris, Philadelphia, and later in London. Established by Sir George Airy in 1851, the Royal Observatory, Greenwich, in London, England serves as the Prime Meridian today. In 1884, representatives from twenty-six countries voted to declare the Greenwich meridian the prime meridian of the world. The French, however, continued to recognize their own Paris Observatory meridian until 1911. The placement of a Prime Meridian as a line of reference is political.

H. Kiepert's physikalische Wandkarten

Wall map showing North America using the Paris meridian as its prime meridian, 1886. NYPL Digital Collections, Image ID: 5437641

The measurement of longitude however is linked to time. The Earth rotates from west to east over its axis. A complete 360-degree rotation takes 24 hours meaning the Earth rotates 15 degrees per hour or 1 degree of longitude every four minutes. To determine longitude on a ship, one must simultaneously know what time it is aboard the ship as well as the local time of a place of known longitude. The local time at any one meridian will not be the same as the local time at another meridian as the sun cannot cross two meridians at the same time. This difference in time is proportional to the angular distance between the ship and the other location. Clocks, watches, and hourglasses, however, would slow down, speed up, or stop functioning all together during voyages.

Ignorance of longitude was the cause of hundreds of shipwrecks and innumerable deaths from scurvy, starvation, and drowning in the fifteenth, sixteenth, and seventeenth centuries. It was also economically devastating as nations were dependent on sea travel for trade and the shipment of goods. Yet, determining longitude at sea stumped the greatest minds in the world for the better part of human history. Galileo proposed a method to find longitude based on the moons of Jupiter. Another lunar method was based on the motion of the Earth’s moon relative to the positions of other celestial bodies. The variation of the terrestrial magnetic field was another avenue of investigation. The governments of Spain and Holland offered monetary prizes for a solution in 1567 and 1636, respectively. The French government established the Academie Royale des Sciences in 1666 to tackle the issue.


Map of compass variations and general winds, 1765. Map by Jacques Nicolas Bellin, “Carte des variations de la boussole et des vents generaux. NYPL Digital Collections, Image ID: 478197

Death by Dead Reckoning

In 1707, Admiral Sir Clowdisley Shovell and his fleet of English ships travelled north through the Atlantic Ocean from Gibraltar toward the English Channel. Visibility was difficult due to bad weather, so the crew calculated their position by dead reckoning. Dead reckoning was the practice of using a past position to estimate a current position based on speed, direction of travel determined by the stars or a compass, and the length of time on a particular course, determined with a watch or clock. Dead reckoning was not very reliable as errors accumulated over the course of the journey.

Sir Cloudisley Shovell

Portrait of Admiral Sir Clowdisley Shovell. NYPL Digital Collections, Image ID: 3979767

Shovell’s crew incorrectly estimated their position near the Scilly Isles (an error of about 50 miles). Four of the five ships crashed onto the rocks and sank, resulting in the deaths of two thousand troops and the murder of Admiral Shovell by a local woman after he washed ashore. The Shovell incident, one of the worst shipwrecks in British history, precipitated the passage of the Longitude Act of 1714 in which the British government offered the largest monetary prize yet for a solution to the problem of longitude.

The Discovery of Longitude

The relationship between time and longitude was well understood, yet no device could maintain accurate time while in motion at sea. Wind, water, changes in temperature and orientation as the ship moved would affect the ability of the clock to keep precise time. This is because time is relative. Published as a series of papers later in 1905, Albert Einstein’s theory of special relativity would conclude that the relative speed of an object affects how it experiences time. In this case, a clock aboard a ship in motion is moving faster relative to a clock on land and therefore experiences time differently. The faster the speed, the greater the effect on time.

A carpenter from Yorkshire in northern England, John Harrison’s work in the eighteenth century with timekeeping devices called chronometers at long last provided an accurate way to keep the time necessary to calculate longitude. Harrison built a series of chronometers, later named H-1 through H-4, that used innovative concepts like suspended mechanisms whose motion was not influenced by gravity or the motion of a ship.

John Harrison

Portrait of John Harrison, 1768. NYPL Digital Collections, Image ID: 1250720

One of the most famous demonstrations of the efficiency of Harrison’s chronometers was during Captain James Cook’s 1772 Antarctic voyage. After 171 days and more than 40,000 nautical miles, Harrison’s H-4 lost fewer than eight seconds during the entire trip, proving that precise timekeeping was possible for the measurement of longitude. Harrison and his son, William, received the first half of the longitude prize money in 1765, and was awarded the other half by an act of the British Parliament in 1773.

Chart of the N.W. coast of America and the N.E. coast of Asia, explored in the years 1778 and 1779

The paths of Captain James Cook’s voyages in 1778 (pink) and 1779 (green). Map by William Faden, “Chart of the N.W. coast of America and the N.E. coast of Asia, explored in the years 1778 and 1779. NYPL Digital Collections, Image ID: 1952935

The discovery of an accurate and reliable method of determining longitude took four centuries of study. Harrison’s chronometers were part of the puzzle that enabled sailors to locate themselves and navigate safely and efficiently to their destination. Without this and other innovations in pre-modern navigation, we’d be lost.


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