A sharp rebuttal to Origins of the first New Zealanders

Because overstatements of Polynesian long navigation nave obscured the issues, the ancient voyagers are not given due credit for their ingenuity and daring in establishing contact with islands several hundred miles away (1963:35).

Most people believe what they want to believe, and most people want to believe that the Polynesians sailed back and forth to their distant islands without quadrant, compass or chart (1963:53).

A sharp rebuttal to "Origins of the first New Zealanders"

Brian Hooker

1. the purpose of this article is three-fold: to denounce some of the fallacious assertions concerning Andrew Sharp and his views published in various papers in The Origins of the First New Zealanders (1994); to enlarge on the central theme of Sharp's theory, and to briefly review the mathematical and astronomical foundations of geography and navigation.

Some scholars believe that new research invalidates Sharp's theory but in reality the crux of his statement, which is concerned with fundamental navigational issues, is impossible to flaw. Geoffrey Irwin correctly sums up the views of a number of recent writers as follows:


	The tide of information and opinion has moved against many of Sharp's views, (1992:102).

It is true that a new generation of researchers has moved away from many of Sharp's beliefs but "the tide of information" is a misleading phrase. The so-called information on ancient navigation methods consists of suggestions built into old theories and put forward by modern experimenters who have no comprehension of the state of geographical and astronomical knowledge, which existed among Pacific peoples a thousand or more years ago. No firm evidence is known which supports a theory that Polynesians engaged in long-distance navigation. Sharp summarised the notion as follows:


	… I am driven to the conclusion that most people who cherish this belief do so for unconscious emotional rather than scientific reasons. These reasons are that the belief appeals to the romanticism, that it was taught to them at school, that it is flattering to the modern Polynesians, that many people have propounded it in the past, and that the modern believers have said it or written it. (Sharp 1970:19).

2. Recent promotion of unrealistic views

Authors of papers in The Origins of the First New Zealanders are not the only scholars to promote, in recent times, unrealistic views on long-distance navigation by Polynesians. Anne Salmond, in her book Two Worlds, is cautious on the subject but is obviously impressed by recent references to long-distance navigated voyages (Salmond 1991:28). Not so cautious and a firm believer in the long-distance navigation theory is Tom Davis who makes the following bold statement in his autobiography Island Boy:


	The Polynesian navigator's starting point was his reference point, which is just as valid as using a Mercator chart and expressing one's starting point in Latitude and Longitude from Greenwich. (Davis 1992: 73)

If Polynesians understood basic geographic principles and the mathematics of the problem, Davis' suggestion is sound but the discussion below under the sub-heading "Latitude and longitude," exposes Davis' statement as meaningless. His inclusion of the term "Latitude" bundled in with Longitude turns his statement into nonsense.

Ranganui Walker, in his book Struggle Without End, expresses fanciful views and credits Sharp with statements he never made. (Walker 1990:24-28)

In a book which has received a fair amount of favourable comment to date, Irwin argues that Pacific people had a position-fixing system which did not need instruments or mathematics; but Irwin's arguments become absurd when he explains the supposed ancient system in mathematical terms and suggests that early knowledge was ''esoteric and quite possibly secret." (Irwin 1989:173 and 1992:50). Thus, Sharp's words were prophetic when he wrote in his revised book:


	If and when the fallacies inherent in the prevailing views of Polynesian navigation to and from those [distant] islands become more apparent, there will no doubt be an increase in statements that we do not know the methods of prehistoric Polynesian navigators. … (Sharp, 1963:53).

Not only is there a lack of appreciation of the history of geographical exploration in many of the recent publications but also there is a reluctance to endorse certain astronomical and mathematical truths. In particular many of Irwin's statements concerning position-finding at sea are based on assumptions and are nothing more than sorties into fantasy land.

Before discussing the misleading statements it is necessary to briefly mention Sharp's qualifications.

3. Andrew Sharp (1906-74)

Andrew Sharp was an outstanding New Zealander who graduated with an M.A. degree in 1927 before winning a Rhodes Scholarship in 1928. At Oxford he obtained a further degree in the social sciences. He served for a time in Upper Burma as a member of the Indian Civil Service where he became interested in the lives of primitive peoples. For a period he followed a career in the New Zealand diplomatic service and later his main interests became scholarship and sport. In 1967 he took up a three-year Senior Research Fellowship in Arts at the University of Auckland, and in 1970 had conferred on him the degree of Doctor of Literature honoris causa. He directed his attention to New Zealand and Pacific history with particular emphasis on maritime exploration. Sharp's publications total sixty-four works including fourteen monographs. [For an extended biographical note and a list of Andrew's publications go to Page MAK2, Section M in Contents.]

It is extraordinary that a number of professional scholars believe that a sailor is better qualified for studying the history of oceanic exploration than a maritime historian. The historian has been trained to consider evidence objectively and whether or not he is a practical seaman has no bearing on his ability to interpret evidence. The above remarks do not preclude the fact that some noted sailors have become eminent maritime historians. The use of the term "landlubber" in uncomplimentary terms in describing Sharp emphasises an inability on the part of some scholars to appreciate one of the basic maxims of scholarship. (See Finney 1994:53).

It is an appropriate point to mention an aspect of the argument, which is without foundation. Some scholars have made quite caustic remarks about writers with views opposite to their own. Hints that scholars who oppose the idea of Polynesian long-distance navigation are denigrating a race, or are prejudiced, surely have no place in a scholarly discussion. Any person who has studied the literature on early Pacific voyaging and vessel construction cannot help but marvel at the achievements of the Polynesians. Sharp's view, repeatedly given in his books, was that the Polynesians were outstanding voyagers and deserved their reputation as skilled and fearless seafarers. However, he summarized his views on overstatements as follows:


	The view that they were supermen is not a satisfactory basis for a theory of Polynesian navigation. The prehistoric Polynesians, ... could not extract from the facts of nature more than was in them. (Sharp 1963:53).

It is reasonable to suggest that the average person and the average scholar fail to appreciate that there are three separate subjects in a discussion of Polynesian voyaging. One is related to seamanship; the second relates to short-distance navigation and the third is long-distance position finding. The three subjects should not be rolled into one; the proof be related to for example to seamanship and the verdict given that because early Polynesians were superb seamen that they understood long-distance position finding. Or that because they were masters of the art of short-distance navigation that they could also navigate long distances.

4. Faulty quotations

From 1956 until his death, Sharp regularly crossed swords with people who misread, misunderstood, and misquoted his arguments. The situation has not changed since Sharp died. For example, Sharp opposed a drift theory. The basic meaning of drift is easily understood; "to be carried along by a current of water or by wind." (Shorter Oxford Dictionary, 3rd ed). The following detailed definition is more helpful:


	We assume that navigated voyages are not drifts and vice versa. Thus, drifts go with the wind and current, resulting in a track not influenced by consciously prescribed and enacted alternatives, which would be navigation. Navigation implies setting a course or sequence of courses and is a conscious activity directed to some goal, whether that goal is a known landfall or the search for possible homelands across a stretch of unknown ocean. In the drift situation the mariner is passive, being active only to keep the craft seaworthy, sustain himself in good heart and health, and act appropriately when landing becomes possible. (Levison, Ward, Webb 1973:11).

5. Some of Sharp's comments on drift voyages follow:

They should not be described as drift voyages as the evidence will show. (Sharp 1957:30).

It might therefore be expected that experienced voyagers who were lost at sea would sail across the wind rather than abandon themselves to the drift of the wind and the set of the current. To call the incidents 'drift voyages' is therefore an inadequate description. (Sharp 1957: 201).

No more unfortunate term than 'drift voyages' could be applied to these processes of discovery accompanied by settlement. (Sharp 1963:4).

It cannot be too strongly emphasised that 'drift voyages' is a very inadequate term for voyages arising either from storms or exile." (Sharp 1963:71).

Despite Sharp's emphatic rejection of the "drift-voyaging" theory some scholars including Finney continue to credit Sharp as a supporter of the idea as the following passages demonstrate:

At about this time [c.1965] R. Gerald Ward and his colleagues in England were starting a massive computer simulation study of Polynesian settlement that was to show the limitations of Sharp's drift-voyaging hypothesis. (Finney 1979:326). (fn. 1)

I did not take too kindly to Sharp's thesis that Polynesia had been settled accidentally by a long series of random drift and exile voyages by people. (Finney 1994:53).

... is the one movement for which Sharp's drift hypothesis is most appropriate ... (Finney.1994: 67 )

Andrew Sharp ... concluded; ... that the islands had actually been settled accidentally by a random series of voyages made by people drifting before wind and current, ... (Finney 1994: 71)

Referring to Finney's comments on the computer simulation project there is nothing in the published work of Ward and his colleagues that suggests they tested Sharp's precise hypothesis which includes the idea that Polynesians controlled their vessels (see Levison, Ward & Webb 1973).

Sutton claims that Sharp's view was "that New Zealand had been settled by chance, once and subsequently isolated." (Sutton 1994:6-7). In fact, Sharp wrote: "settled by chance" but not "once and subsequently isolated"; he asks the question: "Could there have been only one canoe with women aboard which arrived in the formative Period?" (Sharp 1956:124). It should be noted that he refers to the "formative period." He answers his own query in various chapters in his books by referring to "later arrivals", the "rarity of arrivals of parties including women'" and suggests:

It is possible that it was many centuries after the first party of permanent settlers established itself before another party with women came, …" (Sharp 1963:116-7).

McGlone, Anderson, and Holdaway discuss the hypothesis of settlement "by one canoe" (1994:147), and Law also misinterprets Sharp's arguments (1994:79).

6. Short navigation and long-distance navigation

David Lewis and Thomas Gladwin are two of several authors who have satisfactorily explained early navigation techniques between Pacific islands a short distance apart. (Lewis, 1972; Gladwin, 1970). And historical records show that deliberate two-way voyaging took place between islands at least 300 miles apart. In her book The Prehistory of New Zealand Janet Davidson explains that Polynesians and Micronesians were skilled navigators and regular voyaging occurred within the Fiji/Tonga/Samoa /Rotuma/Tuvalu region, with the Cook Islands, and between the Society and Tuamotu Islands (1984:26).

The evolution of long-distance navigation is the story of the application of mathematical theory to sea-going practice and the development of instruments. The nub of Sharp's accidental voyages theory is that on long-distance voyages early Polynesian sailors controlled their vessels but before the days of navigation instruments deliberate navigation to and from distant islands was beyond their ability. How long is a long distance? An example of a long distance is the gap between Rarotonga and New Zealand's East Cape - 1500 nautical miles (see Heyen 1962:9; Law 1994:82). (fn. 2)

Since the correct relationship between two points on the surface of a sphere can only be expressed in mathematical terms it is defying logic for some scholars to suggest that Polynesians solved the problem of linking (to and from) widely-separated points in the Pacific Ocean by some other method or by "a secret means."

Problems associated with set and drift, vessel construction, number of days at sea, and sailing techniques were irrelevant if the ancient mariner was unable to fix his position. Knowledge of the stars, the ability to determine direction and a dozen or more other factors encountered on a voyage, were of no use when the sailor eventually arrived at a point too remote for any of his skills and knowledge to be of use in fixing his position, and he was lost. His most important position was his departure point; and if he didn't know his starting position in relation to the shape of the earth how did he know where to return to? If he discovered a remote island, how did he relate the new position to his homeland?

The discussion below under the sub-heading "Latitude and longitude" exposes Irwin's argument that "some Pacific people had a different but equivalent system..." as fatuous. (see Irwin 1989:171). Irwin's expanded view that " ... traditional navigators had different, equivalent or alternative models, which, together, amounted to an integrated navigational system carried in the mind and did not require instruments." is also ridiculous because there is no equivalent or alternative solution to the basic scientific problem (see Irwin 1992:217).

Irwin's arguments, which are endorsed by authors of papers in The Origins of the First New Zealanders follow along the lines of earlier unrealistic views; Parsonson conjectured that "non-literate folk might easily read [complex data] in the sky and carry [complex data] in their heads." (Parsonson 1962:59). Suggs set the problem in reverse and suggested it was rather wilful assumption at best that led some theorists to hypothesize that precise methods never existed. (Suggs 1960:78). If there was any validity in statements that early Polynesians bypassed the mathematically based system of determining position and employed "alternative'" procedures then we might find examples where other ancient races had solved complex scientific riddles by non-conventional methods.

The critics of Sharp and others are on unsafe ground when they refer to "landlubbers" in unflattering terms. The long line of scientists who made major contributions to the art of long-distance oceanic navigation were all landlubbers; men like Aristotle, Eratosthenes, Marinus, Pythagorus, Euclid, Copernicus, Claudius Ptolemy, Galileo, Mercator, Edward Wright, Tycho Brahe, Cassini, Gilbert, Halley, Huygens, Isaac Newton, and John Harrison. Some of these men are mentioned in the brief review of the mathematical and astronomical foundations of geography and navigation that follows.

7. Ancient geographers, mathematicians, and the sexagesimal system

of geography and navigation that follows.

7. 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 and there is no reason to think that Polynesians held a different view. 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. It was not until the end of the sixteenth century that the various pieces of evidence were pieced 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 B.C. they were engaged in intense intellectual activity. Greek geography, both in mathematical theory and in the art of mensuration, drew on the earlier contributions made by Babylonians, Persians, Chinese, Ancient Egyptians, and Phoenicians. 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 theory and accurate observation.

The Greeks adopted from the Babylonians the sexagesimal system and an ancient tradition of grouping stars into constellations, which the Babylonians had inherited from earlier peoples who lived near the eastern end of the Mediterranean. The sexagesimal system emerged about five thousand years ago probably from two earlier systems, one a decimal system and the other a duodecimal method. The sexagesimal technique for the division of space and time must be the earliest invention still in everyday use. By the adoption of 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.

8. The measurement of time

That ancient geographical theory was geocentric made no difference to the

measurement of time. The apparent diurnal revolution of the sun around the earth was used as the basis for timekeeping and of course for general purposes it is the sun that has always regulated the lives of human beings. 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 1 hour = 15 degrees, one minute of time = 15' and 1 second of time = 15º; or: 360 degrees = 24 hours, 15 degrees = 1 hour, 1 degree = 4 minutes, and 1' = 4 seconds.

The early Babylonian astronomers knew the gnomon and the observation of the sun's shadow by this means in order to determine time must be of great antiquity. At night, astronomers used the clepsydra or water clock, which was invented at a very early date probably in Egypt.

In the era of Western discovery up until at least the late sixteenth 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. The only way the navigator could mark correct sun time during this period, was to erect a pin on the centre of the compass card, and watch for the exact moment of noon when the sun's shadow touched the fleur-de-lis that marked north (or, if in the Southern Hemisphere, south), and then turn the glass. But the method could not be counted on to give true noon nearer than about 15 or 20 minutes.

For measuring short periods of time European navigators introduced, in the 1590s, short and long 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 guesswork from navigation by dead reckoning.

Although Irwin, Finney, Lewis and others claim that Polynesians were capable of navigating by dead-reckoning they provide few details of the methods that might have been used to obtain a reasonable degree of accuracy in measuring time and speed.

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

Aristotle (384-322 B.C.) is usually given the credit for first demonstrating the sphericity of the earth and the suggestion that the East could be reached by sailing west. However, it is likely that the Babylonians arrived at the same conclusion several thousand years before the time of Aristotle. The idea was first brought to general attention through the writings of Plato (c.427-c.347 B.C.). And undoubtedly early Polynesians also knew the earth was a sphere.

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.

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. With the aid of mathematics, and of accurate mensuration learned from the ancient Egyptians, the Greeks evolved a method of measuring the circumference.

The earliest reliable account of how the earth was measured relates to Eratosthenes (c. 276-194 B.C.), who measured the meridian arc between Alexandria and Syene in Upper Egypt (modern Aswan). Eratosthenes, who was head of the Alexandrian Library, found the distance between the base points as 1/50th of the meridian, or the angle of subtension of the sun south of the zenith as 7 degrees 12 minutes (l/50th of 360 degrees). Although Eratostnenes' values for the circumference and the degree were faulty, and some later measurements were less accurate, the importance of the relationship between the circumference and the length of the degree was firmly established.

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 modern 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 centre, contains sixty nautical miles. That Polynesians used a single-dimensional measuring system and present-day sailors automatically think in terms of nautical miles and degrees is one of several reasons why replica voyages are of little scientific value.

Courtesy Library of Congress.

World Map after Claudius Ptolemy usually known as the Ulm edition published

in 1482.Ptolemy's thirty-sixth parallel is 30º 12' too far north at Sardinia,

Carthage is placed10º 20' south of the parallel at Rhodes when it should be

10º north of it Byzantium is placed more than 20º above its true position. In

a present-day map the thirty-sixth parallel passes over the Strait of Gibraltar,

touches the northern tip of Malta, passes over the southern part of Rhodes

and then continues over the southernmost part of Turkey.

The figure for a one-degree arc of the earth's surface adopted by Claudius Ptolemy the last of the great astronomers of antiquity, and who flourished at Alexandria in the second century of the Christian era, was 30,000. This gave 5,000 feet per minute of arc and equalled sixty-nine land miles per degree of arc of the earth's surface.

10. Latitude and longitude

Irwin's statement that latitude and longitude are "arbitrary Western scales" does not square with the fact that an established reference datum is provided by the axis of the earth. (see Irwin 1989).

Everyone familiar with basic geographic principles knows that the great circle on the earth's surface, lying in the plane of the earth's spin, serves as the datum parallel of zero latitude; this circle called the equator, divides the earth into northern and southern hemispheres. Parallels of latitude are small circles that are parallel to the equator.

In ancient times in the Middle East, 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 sundial.

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.

The concept of longitude derived from understanding the idea of latitude and through celestial observations. The north and south poles of the earth lie at the extremities of the axis of rotation and the earth makes one revolution in a day, more or less. That the ancient philosophers believed in the geocentric system and were unaware that the earth spins on its axis made no difference to the idea of longitude. It was early recognised that simultaneous observations of a celestial phenomenon such as a lunar eclipse would, through the difference in local times at the moment of observation, give a value for the difference of longitude (as noted above - for example - 1 hour = 15 degrees of longitude).

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 by international agreement. 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 (Hewson 1951:223).

Irwin and others base many of their arguments on an assumption that Polynesians understood the concept of latitude and longitude or of latitude alone and if in fact they did not then entire theories disintegrate. It is worth noticing that it is difficult to define the terms in nonmathematical language.

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 Dicaearcnus 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 Eratosthens, Hipparchus (fl. 160-125 B.C.), developed a method of measurement based on the sexagesimal system whereby east and west of the prime meridian the two sections of the sphere were divided into 180 meridians, and similarly 180 parallels of latitude stretched from the equator to the north pole with another 180 parallels reaching 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. Through his two great studies, Almagest,and Geographia, Ptolemy maintained an influence over geography and astronomy that lasted for almost fifteen hundred years.

Since a great deal of the current argument concerning Polynesian navigation focuses on the reckoning of latitude it is necessary to dwell for a few moments on the latitude errors in Ptolemy's world map.

Although the foundations for position finding had been well established by the time of Ptolemy, errors were still of major proportions. Ptolemy's best known parallel, 36 degrees North, is not a parallel at all as drawn on his map and if in Polynesians understood the idea of latitude they must have also incorporated enormous errors in any mental concept they employed. In a present-day map the thirty-sixth parallel passes over the Strait of Gibraltar, touches the northern tip of Malta, passes over the southern part of Rhodes and then continues over the most southern part of 'Turkey. Ptolemy's parallel is 3 degrees 12 minutes too far north at Sardinia, Carthage is placed 1 degree 20 minutes south of the parallel at Rhodes when it should be 1 degree north of it. Byzantium is placed more than 2 degrees above its true position.

It is unrealistic to believe that pre-literate people could have collated star-data obtained from a number of widely separated places and then converted it into a mental concept of parallels of latitude. Likewise it is absurd for anyone to think that without maps and instruments, and lacking in mathematical ability, early Polynesians were in advance of the Greeks in scientific endeavour. Yet, lrwin, McClone, Anderson & Holdaway, and others, including Davis support the idea that early Polynesians developed a system of '"altitude sailing". This procedure, developed by Europeans in the fifteenth century involved steering as directly as possible for a destination whose latitude was known, making of course the best use of the wind, and then altering course east or west until land was made.

It is interesting to compare Irwin's statement that Polynesians could have determined approximate latitude, with the view of a number of eminent scholars including J. H. Parry a noted maritime historian (see Irwin 1989:174). Parry explains that by the late sixteenth century western navigators arrived at the stage, whereby in good weather, with open-sight instruments, they could observe altitudes to within half a degree, and could hope to sight land within thirty miles north or south of their destination (Parry 1963:99). Yet, Irwin claims Polynesians could have obtained the identical degree of accuracy without instruments! (1989:174)

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 sixteenth 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.

That it is possible for an astute and experienced sailor today to find his approximate latitude at sea without scientific equipment is not surprising, since every modern mariner knows the basic geographical, astronomical, and mathematical principles and is aware of the precise latitude of his departure point. He also knows the principles for making a basic angle-measuring device. Every proficient sailor has studied charts and navigation theory and is most likely familiar with the night sky in both the northern and southern hemispheres. He is aware of the apparent diurnal movement of the heavenly bodies caused by the earth rotating slowly and uniformly about its polar axis. Wherever he is, he has a rough idea of the answers to many of the questions relating to position finding.

Hilder ridicules the idea of early Polynesians developing an "atitude sailing system" (1962:93-95); and Akerblom points out 'it is unlikely that the navigational method us latitude sailing' (1968:47).

It would take too long to rehearse the history of the long struggle which finally overcame the difficult problems associated with measuring longitude at sea but it is worth mentioning that the perplexities of longitude were beyond the comprehension of most western sailors up till at least the end of the sixteenth century.

Taking into account the above explanations the following statements by recent writers make no sense:

The essential point about longitude and Pacific voyaging is that since navigators could not control longitude they must have developed a system free of its control (Irwin 1992:49).

Navigational skills permitted accurate calculation of latitude; with increasing geographical information longitude could also be roughly determine (McFagden, Anderson, & Holdaway 1994:141).

Upon return to the source island group, the essential information was transmitted about the new land to the south. Potential migrants would therefore have instructions on how to get to New Zealand. (1994:147).

11. 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 current and leeway, and without reference to astronomical observations (see Hewson 1951:176).

Irwin correctly interprets the definition but adds the following comment in a futile attempt to by-pass the mathematics of the problem:

Dead-reckoning does not mean fixing one's position in any absolute sense, such as by latitude estimations, although this can be done, but simply knowing where one is in relation to some other known point, such as an origin or destination or some intermediate reference island along the way, or all of these things (1992:46).

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.

According to Lewis and Finney errors due to fluctuation in current set and in navigation by dead reckoning in general tend to cancel out (see Lewis 1972:104-05; Finney 1979:334). However, arguments about ancient dead-reckoning techniques lose credibility when theorists discuss methods in mod terms including nautical miles and knots.

After western navigators first ventured south from ports on the Iberian Peninsula in the early part of the fifteenth century, navigation out of sight of land was a matter of dead-reckoning checked and supplemented by observed latitude. Martin Cortes who published his famous sailing manual, at Seville, in 1551, is explicit on this aspect (see Parry 1963:98). Parry emphasises the point that 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 (Parry 1963:98).

The common log used for measuring a ship's speed through the water did not come into general use until the middle of the seventeenth century. 'The associated equipment consisted of a log-ship. -reel, -line and ~glass. We noticed above that the figure of sixty-nine land miles per degree of arc of the earth's surface was the figure 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 as a basis for marking their log lines when navigating by dead-reckoning.

Lewis has proved it is possible for a perceptive sailor to navigate long distances by dead-reckoning with the aid of astronomical observations but without instruments (see Lewis 1972). However, this doesn't prove that early Polynesian sailors either navigate- long distances by dead reckoning with or without observed latitude.

12. Astronomical facts and the firmament

Irwin's claim that Pacific peoples 'knowledge of the sky astronomical' is not disputed (see Irwin 1.992:45). In his book Astronomy and Navigation in Polynesia and Micronesia Kjell Akerblom provides an immense amount of information on Polynesian knowledge of the heavens. The Polynesians, the Phoenicians, the Babylonians, the Greeks, the Chinese, the Arabs, and many other ancient races studied the firmament intently but before the important basic principles mentioned in earlier sections were understood, scrutiny of the sky was little more than observations. Undoubtedly, Polynesian seafarers used the stars for setting a course and steering at sea but techniques used in direction finding were of limited assistance in fixing a position.

One further assumption worth mentioning is Irwin's remark concerning the north/south axis from the Pole Star (x Ursa Minoris) to the upright Southern Cross (1992:217). There are parts of the central Pacific Ocean where both the Southern Cross and the Pole Star are at times visible simultaneously but without knowledge of latitude and lacking the compass it would have been beyond the ability of Polynesians to appreciate the facts, which are useful and obvious today. In any case the exact relationship across the hemispheres is not straightforward (see Dekker 1990:545).

The earliest known reference to the interesting fact of the north/south axis from the Pole Star to the Southern Cross is recorded in the Tratado da ulha de ma rear de Joao de Lisboa of 1514:


	I have considered to make a statement about the Southern Cross which is the most striking sign [constellation] for the navigators; and many times Pêro Anes ... and we have compared this sign with that of the North, and we have found when we were at a place from which one could see both signs well, that they are on the same line over the poles of the world [meridian]; and this was done at Cochin with the aid of a [compass] needle (de Albuquerque)

13. Conclusion

The facts reviewed in this paper confirm that the Western development of long-distance navigation engaged the best minds of the Eastern and Western world for more than five thousand years. Success with position-finding techniques at sea resulted from the application of mathematical theory to ocean-going practice and the development of instruments.

Authors of papers in "The Origins of the First New Zealanders," Finney, Irwin and others, base many of their arguments on assumptions not only that Polynesians understood a number of facts relating to natural phenomena, but also that they had the ability to collate data gained through observations and reach scientific conclusions. There is no evidence to support a view that they comprehended the concepts of latitude and longitude or that they had an elementary understanding of the mathematical rules needed for calculating with the circle or the sphere. It is easy today to assume that ancient people knew about some or many of the seemingly straightforward facts of geography and astronomy but these truths were only discovered as the result of intense and prolonged human endeavour.

The idea that Polynesians navigated long distances by dead reckoning assumes that they were capable of making precise measurements. Whether or not errors tended to cancel out it would have been necessary to make calculations and keep accurate records. When it is considered that early Western explorers often introduced errors of hundreds of miles it is unrealistic to believe that a pre-literate people without instruments could have achieved results in advance of the scientific endeavours of European navigators.

Some writers believe that the discovery of New Zealand-type obsidian flakes in the Kermadec Islands proves that long-distance navigated voyages took place to and from New Zealand. There are a number of riddles throughout the Pacific in regard to ancient objects found in unlikely places and obsidian flakes found remote from their place of origin is a puzzle but nothing more (see Anderson & McFagden, 1990:37). If the obsidian flakes originated from Mayor Island then a straightforward explanation would be that they reached the Kermadecs on a vessel following an un-navigated voyage.

There is no evidence, which confirms that Polynesians discovered a remote island, returned to their homeland and then relocated their original discovery. That descendants of ancient Polynesians were found living in remote islands including New Zealand at the time of first European contact proves that their ancestors were fearless and skilled seafarers who survived long-distance voyages to arrive at distant lands.

It is appropriate to conclude with Sharp's words:

Notes and references

1 There is nothing in the published work of Ward and his colleagues that suggests they tested Sharp's precise hypothesis which includes the idea that Polynesians controlled their vessels - see Levison, M., Ward, R. G. & Webb, J. W. (1973). The settlement of Polynesia - A Computer Simulation. Minneapolis: University Press.

2 See Heyen, G.H. (1962). Polynesia: Distance Tables (in) Golson, J., ed., (1962)

3 Polynesian Navigation: A Symposium, p.9.

4 See Dekker, E. The Light and the Dark: A Reassessment of the Discovery of the Coalsack Nebula, the Magellanic Clouds and the Southern Cross (in) Annals of Science, 47, p. 545.