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Brian Hooker

New Zealand


The development of navigation 


Brian Hooker

© Brian Hooker 2006. The text that follows is copyright.

The purpose of this article is to trace the advance of navigation from earliest times and briefly review a number of scientific truths. Until a number of basic geographic facts were understood, and some knowledge of mathematics was obtained and applied, long-distance navigation was impossible.

[fn.1. Navigation in this context means the finding of position; in essence the ability to relocate a remote position.]  

The foundations for successful navigation and the ability to fix a position were laid down several thousand years before the first European probes south from the Iberian peninsula midway through the 15th century.

It is sometimes claimed that ancient peoples had their own method of navigation but the reality is that the problems faced in voyaging long‑distances across the surface of the globe were the same for European, Polynesian and all ancient seafarers.

Ancient geographers, mathematicians, and the sexagesimal system

In the early period of human progress all peoples believed that the earth occupied the centre of the universe. Everyone today knows the basic truths concerning the earth and the universe but this majestic knowledge was acquired in stages over at least five thousand years.


[Aristarchus (310 - 230 BC) Although Copernicus advanced the heliocentric theory in 1543 it had been anticipated centuries earlier by the hypothesis of Aristarchus, the Alexandrian astronomer. - A sculptor's imaginary impression.]


It was  not until the end of the 16th century that the various pieces of evidence were joined together to provide a factual appreciation of the earth's form and movements and its place in the heliocentric system.    

The Greeks were the greatest geographers in the ancient world and by the sixth century BC they were engaged in intense intellectual activity. As a maritime people, the Greeks were suited by situation for the furtherance of geographical knowledge and by their temperament they brought to their task the twin attributes of philosophy and accurate observation. Greek geography, both in mathematical theory and in the art of mensuration, drew on the earlier contributions made by Babylonians, Persians, Chinese, Egyptians, and Phoenicians.

The Greeks adopted from the Babylonians an ancient tradition of grouping stars into constellations and they inherited the sexagesimal system for the division of space and time. By selecting 360 degrees for the measurement of the celestial sphere, the Greeks established a means of measuring not only the earth itself but also the relationship of the earth to the celestial bodies.

The measurement of time

The apparent diurnal revolution of the sun around the earth was used as the basis for timekeeping. That ancient geographical theory was geocentric had no bearing on the problem of designing a workable system for the measurement of time. The day had been divided into twenty-four hours each of 60 minutes with each minute subdivided into 60 seconds according to the sexagesimal system. Time  is essentially angular measurement with 24 hours corresponding to 360 degrees; thus one hour = 15 degrees, one minute of time = 15 minutes and one second of time = 15 seconds; or: 360 degrees = 24 hours, 15 degrees = one hour, one degree = four minutes, and one  minute = four seconds.

The early Babylonian astronomers knew the gnomon and observation of the sun's shadow by this means in order to determine time must have been of great antiquity. At night astronomers used the clepsydra which was devised at a very early date.

In the era of Western discovery up until at least the late-16th century, the only ship's clock available was based on another ancient invention – the sand clock, which was a half-hour glass containing enough sand to run from the upper to the lower section in exactly thirty minutes. For measuring short periods of time European navigators introduced short- and long-glasses in the 1590s; these were sand-glasses which ran out in a specified duration of time – the long-glass running out in 30 seconds and the short-glass in half this time. The ability to accurately measure time removed a large part of the guess-work from navigation by dead-reckoning.

Discovering the shape and size of the earth and the nautical mile

The Greeks are usually given the credit for first demonstrating the sphericity of the earth, but the Babylonians most likely arrived at the same conclusion several thousand years earlier. The idea was brought to general attention through the writings of Plato (c. 427 – c. 347 B.C.) Several arguments in favour of the sphericity theory were capable of being tested by straightforward observations: the curved shadow of the earth's surface on the moon during an eclipse, the passing of a vessel in any direction over the horizon, and the appearance of new groups of stars as one travels north or south. By the fourth-century B.C., Greek philosophers and scientists generally accepted the theory of the sphericity of the earth, enunciated by Pythagoras and developed by Aristotle However, there is no evidence that early Pacific peoples developed a sphericity theory and it would have been impossible to navigate three legs of a long voyage of discovery and relocation without this knowledge.

An idea that excited the attention of geographers from the fifth-century B.C. related to the measurement of the circumference of the globe. It was realized that the value of the circumference, divided by 360, would give the length of a degree.

The earliest reliable account of how the circumference of the earth was determined relates to the Greek mathematician and geographer, Eratosthenes of Cyrene, who died about 194 B.C. 

[An 18th-century engraver's representation of Eratosthenes - left.]

Eratosthenes learned that on the day of the summer solstice, the rays of the midday sun were reflected from the water in a deep well at Syenê (present-day Aswan) and that a gnomon cast no shadow.  At Alexandria, however, on that day, the sun was not overhead at midday, and a gnomon cast a shadow equal to 1/50th part of a circle. Eratosthenes reckoned therefore that the angular distance between the two sites (which are roughly on the same meridian) was equal to 1/50th of the circumference of the globe, or 7 1/5 degrees.  The basis for his circumference calculation was the linear distance between Syenê and Alexandria; this figure multiplied by fifty would provide the linear distance around the globe.

The circumference result arrived at by Eratosthenes was 252,000 stadia. G.R. Crone, in his book Maps and their makers, (4th ed., London, 1968), provides a modern figure of 24,662 miles, assuming Eratosthenes employed the short stadium; this result, according to Crone, is only 50 miles short of reality and gives a figure for one degree equal to 68.5 miles.

Unfortunately, Eratosthenes' quite accurate circumference reckoning was not accepted by his successors.

[Claudius Ptolemy, died about 165 in Alexandria. He was an astronomer, mathematician and geographer. He believed the planets and sun to orbit the Earth in the order Mercury, Venus, Sun, Mars, Jupiter, Saturn . This system became known as the Ptolemaic system. It predicts the positions of the planets accurately enough for naked-eye observations - an artist's imaginary portrait.]  

One of the greatest mistakes made and carried forward as exploration developed was when the Greek geographer of Alexandria, Claudius Ptolemy, adopted a value for the length of a degree equivalent to 56½ miles. Thus, when he transformed distances into degrees he obtained greatly exaggerated figures.  In a world map, published in the 15th century, and based on texts written by Ptolemy, he purports to portray rather more than a quadrant of the sphere, extending in latitude from approximately the Tropic of Capricorn to the Arctic Circle. 

[World map drawn in the 15th century from Claudius Ptolemy's data. The map extends through 180 degrees of longitude eastwards from the prime meridian in the Canary Islands to eastern Asia, but not including the coastline of China. The effect of this is to exaggerate the breadth of Eurasia considerably, and reduce the apparent gap eastward, from the eastern shores of Asia to western Europe, by about 50 degrees. This was to cause major problems for Pacific navigators from around the beginning of the 16th century, until late in the 18th century.]

The map extends through 180 degrees  of longitude eastwards from the prime meridian in  he Canary Islands to eastern Asia, but not including the coastline of China. The effect of this is to exaggerate the breadth of Eurasia considerably, and reduce the apparent gap eastward, from the eastern shores of Asia to western Europe, by about 50 degrees.  This was to cause major problems for Pacific navigators from around the beginning of the 16th century, until late in the 18th century.

Early units of distance – for example the Roman mile – were arbitrary measurements but the nautical mile is a unit of distance related intimately to the size of the earth. Every sailor knows that, if the earth is treated as a sphere, the nautical mile is equivalent to the length of a minute of arc of a meridian; that is to say, an arc of the earth's surface subtended by an angle of one degree at the earth's centre, contains sixty nautical miles.


Since oceanic navigation is the art of finding the way at sea, the successful navigator must know where he is, where he wishes to sail to, and how to get from one to the other. Position at sea can sometimes be related to fixed points; otherwise, it must be determined with relation to arbitrary datum lines. The lines used are the equator and a line at right angles to it, known as the prime meridian.

The great circle of the earth's surface, lying in the plane of the earth's spin, serves as the datum parallel of zero latitude; this great circle called the equator, divides the earth into northern and southern hemispheres. Parallels of latitude are small circles.

Latitude is so patently correlated with the appearance of the heavens that the relationship was noted at a very early date in the Middle East. Whether early Pacific peoples understood the concept is an open question. The idea of an equator developed from studies of the sun's shadow. When the spherical character of the earth was recognised, and later the obliquity of the ecliptic, astronomers were able to deduce latitudes from the proportions between the lengths of the shadow and the pointer of the sun dial.

Changes in latitude were also measured with the sand glass and clepsydra and expressed in terms of the longest day of the year. Astronomers were familiar with the fact that the number of hours of daylight on the day of the summer solstice was a gauge of latitude; in fact it was just another way of recording the angular height of the sun, because the length of the longest day, in hours and minutes, is directly proportional to the angular height of the sun.

For the determination of latitude at sea, an instrument was required for measuring the altitude of the sun or a star. The idea came only after the establishment of the principles by the ancient schoolmen and the development of the mariner's astrolabe and later the seaman's quadrant.  By the middle of the 16th century there were two established methods of finding latitude at sea in the northern hemisphere. The first was to establish the height of the sun above the horizon at the place of observation; the second was to determine the height of the Pole Star. For navigation near the equator or in the southern hemisphere a rule had been formulated for using the Southern Cross in determining latitude. Angle-measuring instruments were required in all cases and the navigator, having determined the observed height of the celestial bodies, had to make certain corrections aided by mathematical tables. Of the two co-ordinates of an observed position, the measurement of latitude was mastered first with relatively simple instruments and fairly straightforward calculations.


Semicircles, which extend from any place on the earth's surface to the North and South Poles and cross the equator at an angle of 90 degrees, are called meridians. Since no natural division relates to longitude, the first meridian is an arbitrary semicircle, and over the course of two thousand years it has moved from place to place until, in 1884, it settled on Greenwich. The longitude of a place is the arc of the equator or the angle at the pole between the prime meridian, which is zero, and the meridian of that place.

The concept of longitude derived from understanding the idea of latitude and through celestial observations. Reckoning longitude was a much more troublesome problem than finding latitude and most  of the different approaches met with little or no success. Early sages, realizing that the earth is a sphere revolving once in twenty-four hours more or less, reckoned that simultaneous observations of a celestial phenomenon, such as a lunar eclipse, would form the basis of a solution to the longitude-measuring problem. The difference in local times at the moment of observation would provide a value for the difference of longitude (e.g. 1 hour or 1/24th of a day [360 degrees  ÷ 24] = 15 degrees). However, it was necessary to apply the values arrived at to the circumference of the globe.

Over the centuries a number of solutions were suggested for the longitude-measuring problem. By the early part of the 16th century, five different methods were used or suggested; the hourglass, eclipses, lunar distances, portable timepieces, and magnetic variation. The latter method, which was concerned with variation of the compass from true north, was based on inadequate knowledge of the complexities of terrestrial magnetism. The two astronomical methods were practised from a very early date although the technique of obtaining longitude by means of lunar distances is often credited to Johan Werner, in 1511. The lack of sufficiently accurate tables produced enormous errors with both astronomical methods until the late 1760s.

The publication, in 1767, of Nevil Maskelyne's Nautical Almanac, with tables based on the meridian of the Royal Observatory, at Greenwich, offered the seaman, for the first time, a method for finding his approximate longitude by means of lunar distances observations.  The moon's angular distance from the sun or a suitable star was observed. Greenwich time at the moment of observation was obtained from tables predicting the moon's motion and position in relation to other heavenly bodies, and comparison with the local time gave the observer his longitude.

It was realized at a very early date that an accurate system of measuring time would provide an ideal answer to the problem of measuring longitude.

[Gemma Frisius (1508-1555), was a Dutch mathematician who applied his mathematical expertise to geography, astronomy and map making. He became the leading theoretical mathematician in the Low Countries.]

The great 16th-century mathematician, Gemma Frisius, published in 1530, details of a practical method for determining longitude using portable clocks. Galileo made his first important contribution, in 1583, by his studies of the value of the pendulum for the exact measurement of time. A Dutch physicist, Christian Huygens, followed up a suggestion by Galileo and made a pendulum clock in 1657. In 1660, Huygens designed a timekeeper using an escapement controlled by a pendulum, but it proved useless on ships except in a flat calm. Another 80 years would elapse before the engineering difficulties in making accurate clocks for use at sea were overcome.

Early in the seventeenth century, Galileo made his second major contribution when he discovered the satellites of Jupiter during pioneer use of the telescope in astronomy. He argued that the satellites could serve as a celestial timekeeper and Giovanni Cassini later developed this idea.

Substantial rewards were offered in several European countries to the inventor of a reliable method of finding longitude at sea. Ultimately, the best solution was found with the perfection of John Harrison's chronometer, near the end of the third quarter of the eighteenth century.

[Left - John Harrison (1693-1776.]

 James Cook was without the chronometer on his first Pacific voyage but on his second voyage   he carried a copy of Harrison's chronometer made by an expert watchmaker, Larcum Kendall.

Development of the graticule

Eratosthenes was the first to devise a grid of latitude and longitude lines through known localities both in and outside the Mediterranean area. He laid down a map with a line roughly parallel to the equator through places he supposed were in the same latitude. A hundred years or more previously Dicaearchus of Messana (died c. B.C. 285), first laid down the base parallel of latitude from the Pillars of Hercules (the Peaks of Gibraltar and Ceuta to the Himalayas).

Following on from Eratosthenes, Hipparchus (fl. 160-125 B.C.), developed a method of measurement based on the sexagesimal system. East and west of the prime meridian the two sections of the sphere were divided into 180 meridians, and parallels of latitude were drawn to circle the earth north and south from the equator; 90 parallels from the equator to the north pole and 90 parallels from the equator to the south pole. Plotting the positions of places on a map with reference to an agreed meridian of longitude and the equator enabled localities to be truly related to one another. Hipparchus, the inventor of trigonometry, drew parallels additional to Eratosthenes’ main parallel, computed from the length in different places between the equator and the pole of the longest day on the date of the summer solstice. Marinus of Tyre (c. A.D. 100), one of the founders of mathematical geography, was the first to provide practical expression to the discovery of Hipparchus that a place could be fixed on a map by the intersection of its co-ordinates.

Claudius Ptolemy introduced the plan of designating the position of places by stating the numbers which represent the latitudes and longitudes of each. He also attacked the problem of projecting the  earth’s surface on to a plane in order to arrive at an orderly graticule.

Dead reckoning

From the time the term was invented, dead reckoning has meant the estimation of a ship's position solely from the distance run by the log, and the courses steered by compass, corrected for variation of current and leeway, and without reference to astronomical observations.

In theory it is possible by dead reckoning alone to establish a remote position in relation to a departure point or another position with great precision. The concept is straightforward but the practical difficulties in keeping track of direction and distance travelled, and allowing for set and drift, without sophisticated equipment, are enormous. The inertial navigation system developed after World War II, which enables submarines to cruise underwater over very long distances and determine their precise position, is an advanced type of dead reckoning.

After Western navigators first ventured south from ports on the Iberian Peninsula in the early part of the 15th century, navigation out of sight of land was a matter of dead-reckoning, checked and supplemented by observed latitude. The navigator kept a careful ‘account’ but on long voyages the errors of dead-reckoning were cumulative; therefore he checked his account by daily observations of latitude.

The common log used for measuring a ship's speed through the water did not come into general use until the middle of the 17th century. The associated equipment consisted of a log-ship, -reel, -line, and –glass. The figure mentioned above of 69 land miles per degree of arc of the earth’s surface was the standard adopted by European seamen as a basis for marking their log-lines when navigating by dead reckoning.  Using a 30-second glass, the distance between the knotted cords on the log-line was reckoned to be 41 2/3 feet; this distance in 30 seconds being equivalent to 5,000 feet per hour.


This list provides a guide to the principal printed works consulted during the preparation of this article. 

Admiralty manual of navigation 3 vols. London: Her Majesty's Stationery Office, 1959 – 1973.

Brown, L.A.  The story of maps.  New York, N.Y., Dover, 1979.

Crone, G. R.  Maps and their makers,  London, Hutchinson. 

(4th ed.), 1968.

Day, A.  The Admiralty Hydrographic Service 1795 – 1919.  London:  Her Majesty's Stationery Office, 1967. 

Morison, S.E. The European discovery of America – The southern voyages 1492 – 1616.  New York, OUP, 1974. (6,  12)

Wroth, L.C.  The early cartography of the Pacific.  The Papers of the Bibliographical Society of America, vol. 38, no. 2, New York, N.Y., 1944.  (4, 7, App B)

Boxer, C.R.  The Dutch seaborne empire  1600 – 1800 London: Hutchinson, 1965.

Friis, Herman R. (ed)   The Pacific Basin – A history of its geographical exploration.  New York:  American Geographical Society – special publication no. 38, 1967.

Parry, J.H. The age of reconnaissance.  London: Weidenfeld & Nicolson, 1966. 

Penrose, Boies, Travel & discovery in the renaissance 1420 – 1620. New York: Athenium, 1975. 

Spate, O. H. K. The Pacific since Magellan 1 The Spanish Lake. Canberra: Australian National University Press, 1979.