Until the beginning of the sixteenth century, navigators had scant need to fix their precise position by latitude and longitude. Voyages were short and principally followed the coast; ships were rarely out of sight of land for more than a few hours' time. As voyaging increased into the uncharted regions of the open ocean, the navigator had to know his exact position at sea, and, its corollary, be able to return whence he started in order to bring back information about his discoveries. The most basic method used by the navigator to plot the course on a chart is called "deduced" (or "dead") reckoning. Continuous records were made of the direction traveled, provided by the magnetic compass, and distance as the result of time elapsed the time elapsed (measured by a sand-glass) multiplied by speed. The course was calculated hourly. When conditions were right for taking celestial sightings, the dead reckoning course was updated and corrected. Another method is known as "latitude sailing" or "running down your easting (or westing)." Once the navigator reached a desired latitude, which he determined by sightings of a celestial body (Sun or the Pole Star), he maintained his course on that latitude by sailing due east or west. This method required no elaborate tables of declination or complex mathematical calculations; all that was needed was to keep that celestial body at the same declination, its angular height above the horizon. Latitude sailing enabled the mariner to reach his objective without having to know the longitude--it was only necessary to keep sailing at the same latitude until the destination was reached. Christopher Columbus practiced latitude sailing on his 1492-1493 voyage, as did Vasco da Gama when he rounded Cape of Good Hope and reached Calicut, India in 1498. Celestial navigation--determining one's position from observations of the sun or stars--provided greater flexibility. To the end of the fifteenth century, the celestial body most often used was Polaris, the North Star, for this was the easiest to use and required no tables of declination. At first, only the meridian altitude of Polaris was used--that point when it reached its zenith in the sky. Later, navigators were able to use Polaris at any time of the night without having to wait for it to reach its zenith. By the end of the fifteenth century, mariners could determine their latitude position from the sun as well as from the stars. And finally, with the development of the marine chronometer in 1761, navigators could also determine longitude. With a grid pattern to mark their position on the surface of the earth, and the means to plot a course, mariners confidently moved across the trackless, open ocean.


By the fourteenth century, the eight primary points of the compass were sub-divided into sixteen and then thirty-two points; each point equally spaced at 11°15'. By the end of the sixteenth century, compass cards carried a dual system of points and degrees. Any good sailor could "box the compass," giving the name of each point in turn: north, north by east, north northeast, northeast by north, etc., until all thirty-two points were covered. This arrangement of compass points remained until the first half of the twentieth century when it was replaced with the degrees of a circle.

Willem Janszoon Blaeu
Dutch, 1571-1638
From: Le Flambeav de la Navigation (Amsterdam, 1619)

White Star Line Gimbaled Boxed Compass

Stanley London Brass Compass
White Star Line Gimbaled Boxed Compass
Brass and Wood, 16 cm
Modern Replica

Sand Glass

In navigating long distances across the open ocean, the sand-glass for making time was as important an instrument as the compass for showing direction. Filed with the amount of sand to measure a half hour of time, each emptying of the sand was called a "glass", and eight glasses (four hours) made up one "watch." The compass and sand-glass, along with a chip-log to measure speed, enabled the navigator to plot his ship's position on a chart. Speed times time gave the distance, and the compass showed the direction of the course sailed. This simple method of navigation is called dead-reckoning, short for deduced reckoning.

Authentic Models, Inc.
French Admiralty Glass, ca. 1800
Brass and Glass
Modern replica


In the Middle Ages, the instrument used for measuring the angular height of a celestial body above the horizon was the planispheric astrolabe. This instrument adapted to one more suitable for "taking the height" while at sea--the nautical astrolabe. Consisting of a perforated disc made of bronze or brass, which gave it weight, the astrolabe was suspended from a ring at the top. Affixed to the center of the disc was a sighting bar called the alidade, which could be turned in a complete circle. The navigator aimed the alidade at the heavenly body, either the sun during the day or the pole star at night, aligning it by sighting through holes or notches in plates at each end. He read the altitude in degrees directly off a scale inscribed around the circumference of the disc. In the illustration here, from The Light of Navigation (1612) by Willem Jansz Blaeu, line P-G is the angle of the axis of the earth at the time the celestial observation is made; this angle taken from astronomical tables. Z equals zenith, and D is the observed altitude of the sun. To obtain a noon position fix from the sun at its meridian passage, the observed altitude of the sun is subtracted from 90° and the declination of the sun is added algebraically to the result.

Modern replica


The cross-staff, originating sometime in the thirteenth or early part of the fourteenth century, was a better instrument for taking readings of the altitude of a celestial body than the quadrant or the astrolabe. The ultimate in simplicity, it was but a long stick with a movable cross-bar called the transversary. The navigator aimed the lower point of the cross-bar at the horizon and moved the cross-bar until its upper tip touched the celestial body; then he read the altitude on the scale inscribed along the length of the staff. To prevent painful damage to the eyes by having to look directly at the sun, a small shield blocked the sun (except its uppermost edge), and the navigator made a correction value to find the true reading. Alternatively, a small piece of smoked glass was used. In spite of the knowledge of how to determine latitude by means of celestial observations, and the existence of nautical instruments to take these measurements, there was a vast difference between theory and practice. The instruments themselves caused a certain amount of error; with the astrolabe, this could be as great as one whole degree of arc, equal to an error of sixty nautical miles. It was no small feat for the navigator to keep the cross-staff aimed at the horizon, while at the same time moving the cross-bar so as to have its upper tip touch the celestial body, all the while trying to brace himself on the pitching and rolling deck of a ship. Under these conditions it was no easier to maintain a star or the sun in the sighting holes of the alidade of an astrolabe.

Harriet Wynter Ltd
English, 20th Century
Cross Staff
Rosewood and Cherry
Modern replica


Essentially, the Back-staff was a modification of the cross-staff, having a sliding half-transom in the form of an arc, and a horizon vane at its proximal end. Instead of looking directly at the sun, the observer turned his back toward the sun (hence the name back-staff) and moved a cross-piece along the arc. When the shadow cast by the sun was aligned with the horizon on the horizon vane, a reading was taken off a scale. This eliminated the problem caused by the cross-staff of having to look in two directions at the same time, as well as distortion and errors caused by irregularities in the glass. It also prevented temporary blindness by having to look directly at the sun.

William Hart
American, 1734-1812
Backstaff (Davis Quadrant)
Rosewood, Walnut and Mahogany
Portsmouth, NH, 1767

The Octant

Obtaining measurements of the angular height of a celestial body above the horizon is not difficult, as attested to by the early development of the cross-staff, back-staff, and marine astrolabe. The real problem lies in being able to achieve this with great accuracy, and under the difficult conditions of being at sea on a small boat. With the rise of exploration during the seventeenth century, maritime nations of the world encouraged the development of better navigational instruments. Voyages of increased distance and duration required being able to more correctly plot position at sea, and to locate newly discovered lands that they be accurately shown on maps. In 1731, John Hadley, an English astronomer, mathematician, and physicist invented the octant. He added to the simple quadrant, optics, and a reflecting mirror to bring a body in the heavens into coincidence with the horizon, thereby turning the quadrant into a reflecting telescope. At nearly the same time, in Philadelphia, Thomas Godfrey arrived at the same solution. This instrument, the octant, is the predecessor of out present-day sextant.

Octant (Hadley's Quadrant)
Rosewood with ivory scales and brass fittings
46.4 cm
English, ca. 1780

The Use of a Mathematical Instrument Called a Quadrant

Joseph Moxon
English, 1627-1691
The Use of a Mathematical Instrument Called a Quadrant
15.2cm x 9.9cm
London, James Moxon or Heirs, 1708

Astronomical Tables

Abraham ben Samuel Zacuto was personally consulted by Vasco da Gama before he undertook his voyage around the Cape of Good Hope to Calicut, India. In this mural painting by Amshewitz, Zacuto is shown presenting his astronomical tables to Da Gama before his departure from Lisbon in 1497.

John Henry Amshewitz, RBA
British/South African, 1882-1942
Vasco da Gama Leaving Portugal
Photograph by courtesy of the Archives of the University of the Witwatersrand, Johannesburg

[tables of declination of the Sun]

As early as the eighth century the Arabian geographer Msha'allah described how to determine latitude from the meridian altitude and declination of the sun. By the late fifteenth century, the daily declination of the sun had been recorded on simplified solar tables derived from these early works. The noted Jewish astronomer and historian, Abraham ben Samuel Zacuto, produced tables of declination of the sun in his major astronomical work, Ha-Hibbur ha-Gadol (Rules of the Astrolabe). Zacuto's works on astronomy were used throughout the Christian and Islamic world, and were the basis for the Regimento do Astrolabio do Quadrante (Regiment for the Astrolabe and Quadrant) prepared for Portuguese mariners under Prince Henry the Navigator. The photograph displayed here is of a page from Zacuto's tables of declination of the sun, produced in 1473-1478. In addition, Zacuto wrote a book on the influence of the stars which included a treatise on solar and lunar eclipses. Originally written in Hebrew, it was translated into Spanish as Tratado breve en las influencias del cielo. Christopher Columbus used these tables, and the solar declination tables, on his voyages.

Abraham Ben Samel Zacuto
Sephardic Jew, ca.1452-1515
[tables of declination of the Sun]
From: Ha- Hibbur ha-Gadol, (Salamanca, 1491)
Photo courtesy of the Jewish Theological Seminary of America, New York City, New York.

Information useful for navigation

To determine latitude by celestial observation, very little is needed in the way of instruments. All that is required is a means of measuring the altitude of a celestial body above the horizon at its point of meridian passage, that is, when it reaches its highest point (zenith) in the sky. This altitude is compared with tables of declination, the vertical angle of a celestial body above the horizon, on that particular day. Since the celestial equator corresponds with the earth's equator, declination coincides with latitude on the earth's surface. For example, if the altitude of the sun (its vertical angle above the horizon) is observed at 40°26'34", it is subtracted from 89°59'60" (90°), with the resultant difference of 49°33'26". From almanac tables of the sun's declination on that day, that figure is added to 49°33'26" to give the latitude. If the sun's declination in this example was 3°41'34", the total would be 53°15'00" -- the latitude of Galway Bay, Ireland.

Samuel Lambert
American, fl. 1820
Information useful for navigation
31.7cm x 22cm
Salem MA: T. C. Cushing, 1820


Plan, or bird's-eye, views of land on nautical charts in pilot books were often accompanied by horizon profiles of the coast. These small scenes depicted the land as a mariner would see it when approaching from seaward, and aided him in identification to assure a proper landfall. In the centuries following their introduction they were sometimes elevated to exquisitely detailed landscape engravings or watercolor drawings, far surpassing in aesthetic appeal their original intended function.

Mount Desart Hills
Wood cut, 1.5cm x 20.0cm
From: The English Pilot. Fourth Book (London: W. and J. Mount, T. Page, and Son, 1760)

[untitled view of Wolves Islands, Passamaqouddy Bay]

Joseph F. W. DesBarres
Swiss/English, ca.1729-1827
[untitled view of Wolves Islands, Passamaqouddy Bay]
Copper engraving, hand-colored, 9.2cm x 71.3cm
From: The Atlantic Neptune (London, 1781)