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The Likelihood of Longitude:

Exploring the Space-Time Interface

by

Dr. Vincent H. Malmström

Emeritus Professor of Geography

Dartmouth College

© 2014

It comes as no great surprise to learn that the earliest advances in astronomy were

made in the cloudless deserts of the Middle East and the adjacent Mediterranean region

during its rainless summers. Thus, among the first practitioners of this incipient science

were the Sumerians, Egyptians, Babylonians, Persians, Greeks, and Arabs, as well as the

Chinese in the semi-arid north of their country. Fundamental to its development was the

knowledge of trigonometry – the measurement of angles, which apparently was first

utilized in Sumeria for re-surveying those agricultural areas that lay along the Tigris and

Euphrates Rivers and were inundated during the annual floods. However, it evidently

was not long before it was also employed in measuring the height of celestial bodies and

in determining the location of places in a larger, even global context. Thus, the identifi-

cation and location of both the Equator and the Tropics were accomplished well before

the beginning of the Common Era (CE), as was the realization that the Earth made one

full rotation in 23 hours and 56 minutes, instead of in 24 hours, as the Sumerians had

initially calculated.

The latter was a major advance in the measurement of time, because the early

astronomers realized that the stars rose four minutes earlier each evening. This meant

that after the passage of 30 days, they were rising a full two hours earlier than they had a

month earlier. And, after the passage of 12 months, or a year, they were rising an entire

day earlier! This must have suggested to them that the stars promised a way to measure

both time and distance, in an east-west direction, and may have been the reason for

encouraging early travelers to establish ‘meridians’ whenever they reached and explored

a new land. In any event, by the time that Eratosthenes first produced his map of the

world in the second century BCE, it contained no fewer than eleven meridians. How he

had either determined and/or acquired them, we do not know, and though they vary in

accuracy from their present-day counterparts from about four to seven degrees, they still

represent a remarkable first attempt to portray east-west distances on our globe.

Naturally, to use the stars to measure time, one has first to find a precise and

consistent method for tracking their motion across the sky. Very quickly, three such

distinct points were identified: (1) the point on the eastern horizon where the star rose,

(2) the point in the heavens where the star reached its highest point, i.e. the place in its

trajectory where it transited the meridian, against either the northern or the southern

horizon, and (3) the point on the western horizon where the star set.

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Of these, the third point – its setting position, was the easiest to determine,

because after following the star’s path throughout the night, one could see exactly where

against the western horizon it set. (Even in the Americas, where trigonometry was not

known before the Europeans arrived, the identification of the setting point of the sun was

important to such peoples as the Zoque in southern Mexico, who were responsible for

creating the Mesoamerican calendar by fixing the creation of the world at sunset on

August 13, and the Anasazi of northern New Mexico who employed the sunset on

October 4 to mark the end of their annual agricultural cycle and the onset of winter. It is

also interesting that, in their attempt to predict the occurrence of lunar eclipses, the Maya

constructed a very special pyramid at Edzná in the western Yucatan ca. 150 BCE that

marked the extreme northern setting position of the moon, a position it reached only once

in every 18.02 years. However, in the subsequent 950 years, the evidence suggests that

they were successful in predicting only one lunar eclipse in advance, but it happened to

be the longest and most spectacular lunar event of the entire 8th century!

The second easiest celestial ‘marking point’ and the most widely used by early

Eurasian astronomers was the transit, with the daily movement of the sun defining local

noon when it crossed the meridian and midnight being defined as the mid-point between

two successive noons some twelve hours later. For calibrating the movement of the stars,

however, their transit through the meridian was the only ‘marking point’ that was both

consistent and widely visible enough to be of any value. In the Americas, and

exclusively within the Tropics, the zenithal passage of the sun marked the beginning of

the New Year for both the Zoques and the Maya, for the former on August 13 and the

latter on July 26, whereas the zenithal passage of the Pleiades was a critical ritual marker

for the Aztecs, and is still associated with the “Day of the Dead”.

The most difficult of the ‘marking points’ was naturally the rising point of the

given celestial body. Of all the celestial bodies, the rising sun was the easiest to track

against the eastern horizon, for during one half of the year it gradually appeared to move

steadily northward from the Tropic of Capricorn to the Tropic of Cancer, and for the

opposite half year it appeared to steadily retreat in the reverse direction. Virtually all of

the early cultures of the world appear to have recognized the critical limits of this annual

‘migration’ -- the solstices -- with the possible exception of those closest to the Equator

that witnessed no changes other than in the apparent direction of the sun.

However, to at least one early culture, the rising point of both the sun and the

moon were deemed important enough so that they devised a technique that would enable

them to ‘foresee’ it as accurately as their technology would permit. This was the

Megalithic culture that spread ostensibly from the Mediterranean region, along the

western margin of Europe into Scandinavia.

Astronomy and the Megaliths

At Carnac, on the south coast of the peninsula of Brittany in France (latitude 47.2º

N.), they recognized that they had reached a point in their northward advance where the

moon rose and set exactly 90º apart, and so they made this site into one of their most

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important ritual centers by aligning more than 1,100 monolithic blocks into long rows

stretching into the interior, an effort that necessitated the transfer and erection of well

over 2500 tons of stone. To calculate where on the eastern horizon the moon would rise,

they merely extended a right-angle from the point where it set at its most extreme

northerly position on the western horizon to a corresponding position on the opposite

horizon – a simple but sufficiently accurate solution for their purposes.

A few degrees farther north, in the midst of the Salisbury Plain (latitude 51.2º N.),

they repeated this exercise to commemorate another astronomical relationship that was of

key importance to them – a place where a 90º angle exists between the southernmost

rising point of the moon and the southernmost setting point of the sun, but also of its

corollary – a 90º difference between the southernmost rising point of the sun and the

southernmost setting point of the moon. This place we now know as Stonehenge, and

though its construction required far less labor in transporting and erecting monumental

blocks of stone than did Carnac, its builders still went as far afield as South Wales to

procure some of their choicest and most massive lapidary artifacts.

Continuing to advance northward between the islands of Britain and Ireland, the

peoples of the Megalithic culture reached another critical latitude for them shortly before

they turned east along the northern coast of Scotland. There at Callanish (latitude 58.6º

N.), on the island of Lewis, they noticed that the reverse of the Stonehenge sun-moon

relationship existed. Here the northernmost sun rose 90º from the northernmost setting

moon, and conversely, the northernmost rising moon rose exactly 90º from the

northernmost setting sun. Here then, another ritual center, a considerably more modest

one than the earlier two, was constructed in line with the winter solstice sunset over Tirga

Mor, the second-highest peak on the island (679 m, or 2227’). The choice of Tirga Mor

for their solstitial alignment strongly suggests that the Megalithic sailors approached the

Hebrides from their outer edge, which likewise intimates that the local climate was

considerably more equable at the time of their arrival as well.

However, when they reached western Sweden, they essentially duplicated the

Callanish site at a place called Ranstena (“the stones of Rane”) where 24 monstrous

boulders weighing an estimated 600 tons were lined up in the form of a ship that was also

oriented to the highest mountain in the region (Billingen, 304 m, 997’), and again marked

the winter solstice sunset. It was not until they reached southeastern Sweden that they

were first able to construct the solar counterpart of Carnac, no doubt because they had

missed this critical latitude earlier on their way northward, due to the maze of channels in

that particular section of the Scottish west coast.

Ales Stenar (”the stones of Ale”), the site they chose in southeastern Sweden, lies

atop a 100-foot moraine overlooking the Baltic Sea, and there no fewer than 58 massive

red granite boulders have been arranged in the form of a gigantic ship, some 200 feet in

length. The long axis of the “ship-setting”, as it is called in Swedish, has a ‘bow stone’,

in common with a ‘stern stone’ that are composed of a specially selected, more-angular

beige sandstone that was quarried some 20 miles farther north along the coast. The

former is pointed out to sea at precisely the azimuth of the rising sun on the Winter

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Solstice (December 22), whereas the ‘stern’ of the ship is aimed inland to the setting

point of the sun at the Summer Solstice (June 22). Once again, this massive monument is

located at the only latitude in the Northern Hemisphere where the sun rises and sets

exactly 90º apart at the solstices (55.4º N.). Although it was the last of such structures to

be built by the Megalithic culture, it was the first in which I recognized that the ‘right

angle principle’ had been incorporated, so only sometime later did I look back along the

Megalithic people’s route of movement to discover the earlier examples of the ‘right

angle principle’ having also been employed in their choices for the specific geographic

locations of their sites at Carnac, Stonehenge, and Callanish. Nevertheless, the fact that

at all five of these geographic sites the sun and /or the moon rose and set exactly 90º apart

was of no intrinsic scientific value in itself, but obviously for the Megalithic peoples was

an observation that intrigued them enough to incorporate into their religious iconography

in the form of circles divided into four equal quadrants, as witnessed in many early

Bronze Age carvings.

The northward advance of the Megalithic culture along the west coast of Europe

can be dated to the latter part of a period that the Scandinavian climatologists term the

“Climatic Optimum,” because their part of the world then enjoyed the warmest

temperatures it had experienced since the end of the Pleistocene Ice Age. This warm

period can be defined chronologically as having endured from about 6000 to 2000 BCE,

so this provides us with a general time frame for the construction of Carnac, Stonehenge,

Callinish, and Ales Stenar that extends most probably from about 2500 to 1500 BCE,

with the oldest, of course, being Carnac, and Ales Stenar the youngest.

At precisely this time in history, the Agricultural and Urban Revolutions were in

full flower in such favored places as the Tigris and Euphrates valleys of Mesopotamia,

the Nile Valley of Egypt, and the Indus Valley of Pakistan, and already their influences

were being extended into similarly endowed areas of Central Asia and the north of China.

Indeed, it is also likely that the key concepts of trigonometry were already actively in use

in Sumeria, so the Eurasian world was now rapidly nearing the dawn of the Earth’s first

scientific revolution as well.

Through their increasingly precise measurements of both space and time, the

scholars of the period were not only aware of the sphericity of the Earth, but also of the

speed of its rotation, the inclination of its axis, and even the long, slow wobble of its axis

that we term “precession”. The solstices and equinoxes had been defined, and the

position of the stars had been cataloged both with respect to their angular distance north

and south of the Equator, and even to their angular distance west and east of the Vernal

Equinox, which early astronomers had selected as the “zero point” for such

measurements. Indeed, it was in the latter exercise that they realized that space could be

equated with time, for if the circumference of the Earth measured 360º, and it took just

under 24 hours to complete one rotation, then the Earth was turning 1º in every four

minutes and 15º in every hour.

The World of Eratosthenes

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Late in the second century BCE, a Greek by the name of Eratosthenes, who had

been born in what today is the port-city of Cyrene in northeastern Libya and educated

both in Alexandria, Egypt and Athens, Greece, hit upon the idea that, by using

trigonometry, he should be able to calculate the size of the Earth. The critical clue for

such an assumption came from a traveler who had recently returned from a journey

southward along the Nile. He reported that, at the town of Syene (present-day Aswan),

there was a deep well into the bottom of which the sunlight reached on only one day in

the year, namely on the summer solstice, or June 22. To Eratosthenes, this meant that the

well must lie precisely on the Tropic of Cancer (23.5º N. latitude), and that the sun must

also be vertically overhead (i.e., at an angle 90º). Therefore, if he measured the height of

the sun at Alexandria (latitude 31º N.) at noon on the same day, he would find the angular

distance between the two places, and by dividing this value into the circumference of a

sphere (360º), he would learn how many multiples of the distance between Alexandria

and Syene would be required to determine the size of the Earth.

Naturally, a few other issues had to be resolved before he could test his theory.

One was how to equate the every-day distance measures that were currently in use with

angular degrees. From his studies in Athens, he learned that there were at least two

different lengths of a stadion in use in Greece, one in Attica, the district immediately

adjacent to Athens, and another at Olympia, where the inter-city athletic competitions

were held every four years. In modern measurements, the former had a length of 185

meters, and the latter of 176 meters. On the other hand, in Egypt, the so-called Royal

Egyptian stadion had quite a different length – namely 157 meters – and was most

frequently used for measuring the length of journeys rather than distances involved in

athletic competitions; thus, Eratosthenes’ first quandary was to decide which one of them

to use in his computations.

Eratosthenes knew that in Greece, it was also customary to measure stadia in feet,

so that if he used the Greek convention, he would assign 600 feet to a stadion. (In fact,

that is most likely how the stadion was first measured; the fact that the length of peoples’

feet varied may have responsible for the two different lengths within Greece itself.) This

suggested that a Greek foot averaged 31 or 32 centimeters in length, whereas an Egyptian

foot measured only 26 centimeters – which may, of course, have represented a biological

reality! The question was, should he be using Greek feet to measure distances in Egypt,

or Egyptian feet? (Had he actually calculated the number of Egyptian feet in a Royal

Egyptian stadion, he would have found that it too, would have come out very closely to

600 as well!)

In any case, Eratosthenes came up with a very different solution; if he divided the

length of an Egyptian foot into either the Attica stadion or the Olympic stadion, he would

get a value of about 677 feet in the first instance and almost 712 in the second, so why

not just settle on an arbitrary length of 700? In fact, he knew that there was no way that

anyone could measure the real distance from Alexandria to Syene by an overland

expedition in any case, so for a modern mathematician to postulate, as Newlyn Walkup

did in a paper in 2010, that because Eratosthenes was ‘the foremost authority on

geography at the time’, he was justified in assuming that the distance between the two

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places was 5000 stadia is patently ridiculous. No one knew better than Eratosthenes that

it would be impossible to survey a straight line between the two places, running across a

desert of shifting sand dunes the entire way, and enduring days on end of blistering sun

and mid-day temperatures in excess of 120º F. (50º +C.) to carry out such a mission.

Even so, just because Eratosthenes knew that both Alexandria and Aswan lay in the Nile

Valley did not mean they were on the same meridian; in this case, such an assumption

was warranted by Walkup, because Eratosthenes’ map shows them to be so, though

Aswan in fact lies about 3º to the east of Alexandria. Nonetheless, Eratosthenes was wise

enough to conclude that, even if the number he chose was completely arbitrary, what

really mattered was that it would provide him with a means of correlating it to precise

angular distances that he could measure trigonometrically, first on a local scale where he

could carry out the necessary observations himself, and then later apply them to his

global-scale computation. In fact, all he had to do was to take his first measurement from

the front steps of his library in Alexandria and take the second from a place such as the

corner of Tahrir Square in downtown Cairo. As long as he could accurately determine

the distance between those places in degrees and minutes, he could use the same formula

anywhere in the world, and it would always be accurate!

In none of Eratosthenes’ writings does he tell us where he made his initial

measurements, but since he lived in Alexandria and must have visited Cairo on occasion,

these would have been his most likely choices. Since it was readily apparent that Cairo is

located both east and south of Alexandria, he knew that his first task was to find out the

difference between the sun’s noontime passage of the meridian at each of the two places.

With nothing more than an hourglass or a water clock, he could accomplish this very

easily. Once he learned that the sun rose 5 minutes earlier in Cairo than it did in

Alexandria, he knew immediately that this meant they lay 1.25º apart in an east-west

direction. If he next measured the difference in sun angles from each of the two places,

for example, at noon on the equinoxes, first, let us say at Alexandria on the vernal

equinox, as the sun was crossing the Equator on its way northward, and then at Cairo on

the autumnal equinox, when the sun was again overhead at the Equator on it journey

southward, he could define the angular distance between the two cities with great

precision. Once he had completed these measurements, he learned that the two cities lay

almost exactly one degree apart in a north-south direction.

This latter discovery would have perhaps both surprised and delighted him, for

what it revealed was that Cairo lay on the parallel of 30º north latitude. This meant that

at the latitude of Egypt’s largest city, the length of one degree of longitude equals the

cosine of 30º, or .866 of the value it has at the Equator itself. Already, therefore, he had

the data for two sides of the right-angle triangle he was mentally constructing. The

adjacent (N-S side) totaled 1º or 700 of his arbitrary units, and the opposite side (E-W)

totaled 1.25º x 700, or 875 of his units, multiplied by .866 for a rounded sum of 758

units. When he measured the angle of the resulting hypotenuse, it turned out to be

47.26º, the cosine of which divided into the adjacent side, or the sine of which divided

into the opposite side equals a straight-line distance between the two cities of 1032 units.

Translated into more familiar units of distance in use today, they would equal 110.25 km

for 1º of latitude, 119.4 km for the longitudinal distance between the two cities, and 162.5

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km for the airline distance between Alexandria and Cairo – all of them virtually flawless

results!

With reference to his principal endeavor – determining the size of the Earth – his

choice of a module of 700 units for 1º of latitude was also a very felicitous one. When he

made his measurement of the noon sun angle at Alexandria on the summer solstice, he

obtained a value of 7.2º from the vertical, yielding a total of 5040 stadia between that city

and Syene. Inasmuch as 7.2º represented 1/50 of a full circle of 360º, by multiplying

5040 by 50 he obtained a total of 252,000 stadia for the size of the Earth. This, in turn,

would have equated to a circumference of 39,690 km, compared to its Metric value of

40,000 km, or, expressed in the English system, about 24,650 miles, versus its actual

circumference of 24,900 miles – again, very accurate results.

By way of a footnote, it is nevertheless interesting to observe that had he

employed a module of 600 instead, and chosen to use the Attica stadion with its length of

185 meters, he would have obtained the following values: one degree of latitude = 111

km; Cairo’s distance east of Alexandria = 120 km; and the straight-line distance between

the two cities = 163.5 km, all of which are equally good or better approximations of their

true lengths and/or distances than those he had already settled on.

Regarding his primary objective, the results he would have obtained had he

employed the latter options would have been the following: 4320 stadia for the distance

between Alexandria and Aswan, and 216,000 stadia for the size of the Earth, equating to

39,960 kilometers, or 24,815 statute miles. It is ironic, therefore, that he would have

been even more accurate in his computations had he made these choices, but probably no

one else would ever have been the wiser, unless they had made the same observations

that we have just made here and now.

An even greater irony resulted from the actions of his successor as the Head

Librarian at Alexandria some 400 years later. By now, the Hellenic era had passed and

the Roman era was in full flower. One Claudius Ptolemaeus, often referred to simply as

Ptolemy, took it upon himself to recalculate the size of the Earth, most likely by reducing

the number of stadia in a degree from 700 to 500, or by employing some fraction of the

Roman mile instead. In any event, his revised circumference was about one-sixth too

small, but, for the Europeans who lacked any knowledge of Eratosthenes’ work, it was

eagerly adopted when they first discovered it in the 1400’s. (Ptolemy’s

miscalculation of the length of the Mediterranean Sea we shall discuss somewhat later.)

This may not have been the first time that a later ‘revision’ of an earlier finding proved to

be less accurate than the original, but it certainly was not the last. A notable example is

John Eric Sydney Thompson’s abandonment of his original correlation from 1927

between the Mesoamerican calendar and our own (which was correct to the day!), and his

replacement of it by his ‘revision’ of 1935 (which is two days in error!), leaving several

generations of archaeologists hopelessly confounded ever since.

Probably not long after Eratosthenes had calculated the size of the Earth, he also

produced his famous map of the ‘world’ as he knew it. From the detail it contained, it

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represented about a quarter of the globe, stretching from the Atlantic margins of Europe

to just beyond the eastern limits of India. At least seven of the eleven meridians he shows

can be correlated with the places through which they pass, including the Scilly Islands off

the western tip of Cornwall; the headland of Sagres, Portugal, later selected as the site of

Prince Henry the Navigator’s maritime school; the Pillars of Hercules, or the Rock of

Gibraltar; the meridian of Carthage in the central Mediterranean; the meridian of

Alexandria in the eastern Mediterranean; what appears to be the meridian of Babylon in

Mesopotamia; and finally, the meridian of Hormuz, marking the narrow strait that

connects the Persian Gulf with the Arabian Sea. Up to this point, the coastal configura-

tions on his map are at least recognizable, but continuing eastward, directions and shapes

become increasingly distorted. For example, what appears to be a meridian marking the

mouth of the Indus River debouches on a long stretch of coast running west - east that

terminates in the southern tip of India; another meridian that appears to mark the mouth

of the Ganges, reaches a coast that is oriented strictly north - south, but also ends at the

southern tip of India. At least, Eratosthenes seems to have been aware that India’s two

major rivers lay on opposite sides of the country, whereas Waldseemüller’s map from

1507 shows both of them reaching the sea on the same side of the country – a clear

example of a map that was produced 1700-years later, but that was far less accurate than

its 200 BCE predecessor!

Eratosthenes’ world map was probably the first that attempted to display the

landmasses of the Earth against a grid-system of latitude and longitude, but, as mentioned

above, how the latter was derived is not known. The fact that it does not display the first

known meridian in India is also something of a mystery. We know that it was already in

existence as early as the 5th century CE, for the Indian mathematician and astronomer

Aryabhata cites its presence as making it unnecessary for him to survey a new meridian

of his own. Instead, he extended it northward from the southwestern coastal town of

Kozhikode (later known as Cochin) into the interior as far as Ujjain, which he recognized

as lying on the Tropic of Cancer and which prompted him to erect India’s first

astronomical observatory there, probably ca. 516 CE. We are not certain which foreign

people had initially landed on this shore, already armed with a knowledge of

trigonometry, but the fact that they established this meridian on their arrival, obviously

meant that they intended it to measure how far they had come from their original

homeland. Therefore, the most likely candidates to have established the meridian were

the Sumerians, the Egyptians, the Babylonians, or the Persians, so any knowledge of it

may simply not yet have reached scholars in the Hellenic world, such as Eratosthenes. If

so, this would limit the choices of the homeports from which they came to such places as

Ur at the head of the Persian Gulf or Myos Hormos on the northwestern shore of the Red

Sea. This meant that either route to India was convoluted in its initial section, obliging

the Sumerians or the Egyptians to sail through lengthy, restricted channels, such as the

Persian Gulf or the Red Sea, on their way into the more open Arabian Sea. Thus, the

course that either of these early peoples could have sailed to reach the subcontinent of

India was anything but a simple rhumb-line between origin and destination, and would

more likely have approximated sailing first along the adjacent side of a triangle and then

along its opposite side, rather that following its hypotenuse. Yet, with their knowledge of

trigonometry, all three of the triangle’s sides could easily have been calculated – just as

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Eratosthenes most likely had done between Alexandria and Cairo, even though his real

objective was much more ambitious. The adjacent side would represent the north-south

distance between their home port and India, the opposite side would measure the east-

west distance between origin and destination, and the hypotenuse would reveal the

shortest, most direct line between the two places. Although in this instance the latter line

could not have been sailed, it did serve as an indicator of the minimum distance that

separated the two places in question, and in lieu of the concept of ‘universal time’, may

have been useful in reinforcing the number of hours of sun-time that existed between the

origin and destination as well.

In testing the present author’s theory that early navigators used the stars to

measure time, he postulated that no astronomical event served that purpose more

dependably and regularly than did the transit of some easily recognized star. Each

evening, the star would rise 4 minutes earlier, and if the length of a given voyage was

known to the day, then the calculation of the distance covered between any two places

should be possible to determine within the accuracy of one degree. Although the author

was able to test this hypothesis by making some computer simulations of voyages in the

Mediterranean Sea and the Indian Ocean, he did not have the satisfaction of confirming

just how long such voyages would actually take. It quickly became apparent that, with the

‘celestial clock’ continuously running, any and every superfluous day would add one

more degree to the supposed distance between the places being studied, so it was

essential that the length of the journey be known as precisely as possible. (Indeed, this

may be the reason that several of Eratosthenes’ meridians were off by 4-5 degrees; the

true length of the journey has not been accurately known.) It was at this juncture that the

author hit upon the idea of using Columbus’ first voyage to America as ‘a controlled

medieval experiment’ -- one that had been carefully documented, day-for-day, by none

other than the navigator himself.

The First Voyage of Columbus to America

Having received funding from King Ferdinand and Queen Isabella of Spain,

Columbus had proceeded to the port of Palos in the south of the country to hire a crew,

lay in supplies, and outfit his little fleet of three vessels. He was to serve as the Admiral

of the fleet, in command of its largest vessel, the Santa Maria, whereas the smaller

vessels, the Niña and the Pinta, were to be under the command of the Pinzon brothers,

Vincent Yanez of the former and Martin Alonzo of the latter.

Although Columbus began the preparations for his voyage of discovery in early

May 1492, he was not ready to depart until August 6th of that year. Rather than heading

directly west out to sea in the direction of the Portuguese-owned Azores Islands, he opted

to head southwest toward the Spanish island group of the Canaries instead, using the

strong flow of the Canaries Current to help push him along. However, on the first leg of

their voyage, the rudder of the Pinta came loose, a situation for which Columbus charged

two crew members with sabotage. (Indeed, during the entire voyage, Columbus was

obliged to cajole the crew almost continuously with “positive thinking”, going so far as to

keep one log with abbreviated sailing distances to show them, and another with the actual

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distances that he kept for himself.) The fleet reached Gomera, the westernmost of the

Canary Islands on August 9th, where Columbus was obliged to put in for repairs.

Apparently refitting the rudder of the Pinta turned into a bigger job than he had expected,

because he was delayed there until early September.

The only map of the Atlantic Ocean that Columbus had ever seen was by a fellow

Italian countryman of his named Paolo dal Pozzo Toscanelli and had been drafted in the

year 1474. Actually, the map had little to recommend it, for Toscanelli had never been

outside of his native country and knew nothing of the more recent writings of the Roman

geographer, Strabo. Not only was the Atlantic shown to be dotted with numerous islands,

among them several with the name of “Java”, but it also was drawn in such a way that

there seemed to be a sharp edge running along the Equator, which certainly would have

made any contemporary sailor who happened to see it exceedingly apprehensive. On the

other hand, for Columbus, one of the map’s most redeeming features was that the island

of Zipango (Japan) was shown to lie about 2200 miles to the west of Spain, rather than at

its real distance, 12,000 miles away! Evidently while Columbus was in the Canaries, he

also seems to have spoken to some Basque sailors who assured him that there was

definitely land to the west, because they had fished for cod and hunted whales off of its

coast for centuries.

The reason that an Italian was trying to reach the Orient by way of the Atlantic

may have seemed strange to anyone living on the western edge of Europe, but ever since

the Turks cut off access to the Black Sea with the capture of Constantinople in 1453, such

a concern had become a matter of prime importance to them. The maritime economies of

Venice, Genoa, and Pisa were now severely depressed, and unemployment was rampant

among Italian seamen, including Columbus, who was looking for a new career himself.

Strangely enough, when the repairs were completed on the Pinta and Columbus

was ready to resume his voyage, he makes no mention of having made any observations

that might have helped him to chart the progress of his expedition. His only mention of

attempting to determine his location at any time during the voyage involved an eclipse he

had heard mention of, remarking that he hoped “it would be a lunar eclipse because then

it would be visible over half the world.” The implication, of course, was that, by

comparing the time the eclipse was reported in the Canaries with that when he observed it

in the western ocean, would allow him to calculate how far he had actually sailed.

Yet, had he but made one observation on the evening before his departure, he

could have laid the groundwork for determining the extent of his voyage with a very high

degree of precision. (The modern sky-watcher can replicate Columbus’ observations by

employing a computer program such as “Voyager”, a product of Carina Software, San

Leandro, California) to witness these events for him or herself by setting it to the times

and places outlined below.) For example, had he timed the transit of one easily

identifiable star on that evening – say, Rigel at 4:48 AM at Gomera – and then repeated

the observation upon his arrival at San Salvador some 34 days later, he would have found

that it transited the latter meridian at 3:13 AM, a difference of 1 hour and 35 minutes in

timing. During that 34 day interval, all the stars had advanced their transits by 2 hours

11

and 16 minutes, so when that value was added to the observed differences in transit

times, that meant that Gomera and San Salvador were not only exactly 3 hours and 51

minutes apart in time, but also by 57.35º in longitude.

Figure 1. Print out from “Trig Test” Program Displaying Results of

Columbus’ First Voyage to America.

LONGITUDE MAY BE DETERMINED BY OBSERVATIONS CARRIED

OUT ON THE SAME EVENING (1), OR AT THE CONCLUSION OF A

JOURNEY, OR AN INTERVAL OF A SPECIFIED NUMBER OF NIGHTS (2).

THIS PROGRAM CALCULATES THE SECOND OPTION!

TIME FRAME OF YOUR STUDY: 1 = PRESENT, 2 = MEDIEVAL, 3 =

ANCIENT? 2

VERNAL EQUINOX – MARCH 11 (03/11)

TRANSIT OF WHICH STAR, TIME OF TRANSIT AT ORIGIN (H, M): ?

RIGEL, 4, 48

DATE JOURNEY BEGINS: MONTH, DAY: ---. ---

? 9, 6

230 DAYS -- 920 MINUTES – 15 HOURS, 20 MINUTES

DATE JOURNEY ENDS: MONTH, DAY: ---, ---

? 10, 10

264 DAYS – 1056 MINUTES – 17 HOURS, 36 MINUTES

ADVANCE IN STAR TIME DURING JOURNEY: 2 HOURS, 16 MINUTES

TRANSIT OF RIGEL AT DESTINATION: (H, M): ? 3,13

DIFFERENCE IN TRANSIT TIMES AT ORIGIN AND DESTINATION:

1 HOUR (S): 35 MINUTES

TOTAL DIFFERENCE IN TIME BETWEEN ORIGIN AND DESTINTION:

3 HOUR (S): 51 MINUTES

EQUIVALENT TO 57.75 DEGREES OF LONGITUDE

However, as far as the eclipse was concerned, the Voyager program proved that it

did not take place until ten days after Columbus had reached San Salvador, and, because

it was a solar eclipse, it turned out that it was not visible in the far western reaches of the

Atlantic where he then found himself. This meant that at the end of his voyage,

Columbus still didn’t know where he was, but, having assumed that he must be off the

coast of India, he felt safe in calling the people that he encountered “Indians”.

12

With respect to the usefulness of Columbus’ log, we learn that the very first day

after leaving Gomera had to be written off as a ‘wasted day’, because, as Columbus

described it, “the crew was steering badly” – so badly, in fact, that for that entire day their

course had been northeasterly, back toward the Canaries! Similarly, when the pilot of the

Pinta reported seeing land off to the southwest on October 7th, and argued that the fleet

should continue in that direction for another whole day -- only to find that what he had

seen was a cloudbank -- a second entire day had likewise to be written off as ‘wasted’.

Thus, Columbus’ log proves that although the fleet was underway for 36 days, the two

days of sailing aberrant courses had to be deducted, because the constantly running

“celestial clock” had added two extra degrees to the distance measured between Gomera

and San Salvador. However, once the day-count was reduced from 36 to 34 days, a very

accurate sailing distance between the two islands was obtained. Moreover, by holding to

a course of 4º to the south of west, as a Mercator map of its direction confirmed, the fleet

had benefited from both the Canaries Current and the North Equatorial Current almost

the entire way, logging an average speed of 116.5 statute miles per day. Compared to the

41 miles per day that the Kon-Tiki raft averaged during its 101-day drift across the

Pacific in 1947, this was a most impressive achievement indeed.

The Accumulation of Travel Experience and Astronomical Data

Despite the almost casual attitude Columbus seems to have had regarding his

whereabouts on his first voyage of discovery, most early travelers appear to have taken

advantage of whatever clues they could from the changing skies above them. Of course,

for most of them, their missions were of quite a different nature, because apart from the

Phoenicians on their circumnavigation of Africa about 600 BCE or the Megalithic sailors

pushing their way northward along the coast of Europe some two millennia earlier, their

peregrinations were chiefly of a commercial nature between well known ports. Armed

with a basic knowledge of trigonometry, they were in essence measuring the world in a

systematic way for the first time. And, for many of them, this was a cooperative venture,

because what new observations they were making only had meaning and importance

when they could be compared to what was already known. For example, the voyage of a

Phoenician who was venturing west from Sidon or Tyre to Carthage or Gades for the first

time would take on an even greater significance if it returned with a harvest of new

sailing instructions or reports on weather, currents, or information on contemporary

economic or political conditions in the regions it touched upon. But it was only when the

navigator’s observations included data on the timing of celestial events in the new area

that they then could be compared with those of his homeport and the true geographic

distance between places could be determined and recorded. It was this kind of

information that was being preserved by the Persians as early as the 8th century CE.

Apparently organizing astronomical data into tables that consisted of rows and

columns was such a new experience for the Persians that they could only liken it to what

was required in weaving -- matching up colors and patterns in an orderly manner -- for

they called their resultant products zijes, meaning “cords” or “threads”. Altogether over

200 zijes were written and preserved in this form. Naturally, other scholars soon began

to follow suit, and catalogs of astronomical data called ephemerides gradually developed

13

into some of the most prized repositories of this growing volume of written information,

among them the Toledano Tables in Spain about 1080 CE, and in the Alfonsine Tables

that succeeded them during the 1270’s.

One of the principal authors of the Toledano Tables was a resident of Toledo,

which had long served as the Visigothic capital of Spain, but had been conquered by the

Moors in the early 8th century. Although a Visigoth himself, he found it in his interest to

become a Moslem if he were to be able to pursue his interests in astronomy and

mathematics, so we know him best by his Arabic name, Al Zarqali. Not only did he

construct metal models of the known solar system but he also compiled detailed statistics

on the movements of the heavenly bodies. Perhaps the most important single

contribution that he made to medieval astronomy was his correction of the length of the

Mediterranean Sea. Although Ptolemy’s map had shown it to be 62º in length from east

to west, Al Zarqali corrected it to 42º, which is almost exactly its true length.

The fact that Ptolemy’s measurement was almost one-third too long raises an

interesting question: what could have possibly caused him to be so far off in his

calculation? Could it have been that in his day – the second century BCE – it took about

twenty days longer to sail the length of the sea than in did in Al Zarqali’s days, twelve

centuries later? Or was it simply a matter of Ptolemy’s not knowing the actual number of

days that such a voyage required? As we have already learned, for every ‘wasted day’ at

sea, the error in a navigator’s longitude calculation would be increased by at least one full

degree! Had Ptolemy based his calculation on sailing against the wind the whole way to

the west during the winter months, whereas Al Zarqali had measured the length of the

voyage during the summer months, when there were no such headwinds to battle? Or

had the improvements in ships and sails been so great in the intervening centuries, that

such innovations had themselves speeded up the length of the voyage?

Fortunately, evidence is available from other regions where contrary weather

conditions seriously impeded sailing in earlier times. A case in point is the Black Sea

and its shallow northeastern extremity, the Sea of Azov. The persistence of northeasterly

winds is so pronounced in this region that no fewer than six lengthy spits of sand project

from the Azov’s northern shore as geomorphic testaments to its dominance (see Figure

2), whereas in westernmost Turkey, the trees themselves have been so severely sheared

by the constant winds that they all lean markedly to the southwest. (See Figure 3.)

As a result, early Greek depictions of the Black and Azov Seas show the latter to

be almost the same size as the former, for struggling against the wind coming off the

Russian steppes may well have taken as much or more time than crossing the Black Sea

between Istanbul and the Kerch Peninsula.

14

Figure 2. The Sea of Azov is nowhere deeper than 14 m, or 46 feet, and in

this satellite photo the water is shown in green. The sand spits along the north shore

are numbered from 2 to 7.)

.

15

Figure 3. A roadside park in European Turkey developed as a shady rest

stop for motorists. The age and size of the trees reveal the constancy of the

northeasterly winds in this part of the eastern Mediterranean.

By the time these same winds reach Egypt, they are blowing almost continuously

from the north, a fact which made it easily possible for the ancient Egyptians to ascend

the Nile with the help of the wind when they were going south, versus drifting with the

current when going north. (Indeed, this fortuitous combination may in itself have

accounted for the early beginnings of sailing in this part of the world.) Through the

entire length of the Red Sea, the prevailing wind is northerly as well, so voyages headed

to India or beyond had a favorable start, but a difficult return. Unfortunately, the

prevailing westerly winds of the Mediterranean in the winter season are sometimes so

strong and continuous that their effect is felt farther east in the Persian Gulf region as

well – resulting in what Middle Eastern and Indian meteorologists call a “Western

Disturbance”. (The bitter winter that afflicted the thousands of refugees from Syria in

2013 was a more tragic illustration of just such a situation.)

Returning from our digression on how wind and weather may have left their mark

on the accuracy of calculating longitude in earlier times, the same can be said for the

absence of such a luxury as Universal Time, which did not become available until the

adoption of the Greenwich meridian in 1884. As a result, early travelers were always in

some doubt as to the number of hours that had elapsed on their journeys, because they

had no fixed “standard” against which to compare their own observations made in the

field. Following the invention of the maritime chronometer by John Harrison in the

1760’s, most ships have carried one chronometer that was set to the current time in

London and another to the local time where the ship was; the difference between the two

represented the ship’s longitude, with every hour’s difference, of course, corresponding

to 15º. However, had the early navigators taken the time and the trouble to work out the

hypotenuse of the triangle that their measurements of the adjacent and opposite sides had

produced -- as Eratosthenes had done -- then calculating the angle between the origin

and the destination would likewise have helped them to close this gap in their knowledge

as well. Once more we will turn to Columbus’s first voyage to demonstrate how this

might have been done.

Had Columbus measured the respective latitudes of Gomera and San Salvador he

would have found that the first was located at 28.1º North, while the second was situated

at 24.13º N. Thus, his adjacent angle measured no more than 3.97º in length. On the

other hand, had he made observations of the transit of Rigel at both places, he would have

found that the difference in longitude between his origin and his destination amounted to

57.35º, and by dividing this value by 15º, he would have discovered that this represented

a difference in sun time between them of 3 hours and 51 minutes. As was noted earlier,

the resultant angle he sailed was 86.04º, or just under 4º south of west, and yielded a

hypotenuse that was 6381 kilometers, or 3962 statute miles in length. It was the latter

distance that provided a clue to the shortest course they might have sailed, if a great circle

or rhumb line had been possible.

16

However, unlike Columbus’ first voyage to America, most of the voyages carried

out by early navigators in the Middle Eastern and European arenas were between known

ports, primarily for reasons of commerce. Initially, what wasn’t known was the distance

that separated these places, but once such a voyage had been successfully completed, a

description of the journey was often prepared for the benefit of later travelers who might

wish to carry out a similar mission. Indeed, it was just such a motive that led to the

writing of the “Periplus of the Erythraean Sea”, a journal by a Greek navigator named

Hippalus that dated from the 1st century BCE and described the coastal areas that lay

between the Red Sea ports of Egypt and those of western India, as well as the goods that

they produced. Though the “Periplus” does not contain astronomical data relating to the

distances between ports, such information was most likely already being collected and

recorded, at least on a limited scale, by the Sumerians and Egyptians well before either

the Greeks or the Persians.

Figure 4. Print out of “Voyage Direction” Program Displaying Results of a

Hypothetical Voyage between Myos Hormos, Egypt and Calicut, India.

Principal Direction of Voyage: 1 = West, 2 = East: ? 2

Name of Westernmost Station: Myos Hormos

Name of Easternmost Station: Calicut

Longitude Between Stations: 41.57º (unknown to program user)

Time of Departure Eastbound: Month, Day, Hour, Minute: 3, 20, 2, 7

(Note: Records local transit of Arcturus on this day)

Anticipated Length of Voyage in Days: 41

Departure Time in Minutes: 847

Time of Arrival at Destination: Month, Day, Hour, Minute: 4, 30, 11, 38

(Note: Records local transit on Arcturus on this day)

Arrival Time in Minutes: 698

Star Advance Underway: 149 Minutes ( 2 Hours, 29 Minutes )

Voyage (Days) Star Transit Longitude (º)

44 11:50 38,25

43 11:46 39,25

42 11:42 40.25

41 11:38 41.25

40 11:34 42.25

39 11:30 43.25

38 11:26 44.25

17

In the Periplus we learn that some 120 vessels a year were employed in the sea

trade between Myos Hormos and India, which, although governed in large part by the

prevailing winds of the Indian Monsoon, reveals that the volume of traffic averaged one

departure or arrival every three days as early as the first century CE. Because the bulk of

this trade involved exotic spices from the Indian west coast, their western destination was

in no way limited to Egypt, which served instead as an entrepot for much of Europe, with

Roman vessels carrying the precious commodities further across the Mediterranean.

There is, of course, every reason to believe that in the first century CE what the Egyptians

and Romans were engaged in was simply a continuation of an exchange that had begun

many centuries earlier by the Sumerians and the Persians, so in Figure 5 we present the

results of a hypothetical voyage between Ur and Calicut that could have taken place

through the Persian Gulf. Such a route would have involved a voyage averaging about 29

days, compared to that between Egypt and India that normally would have taken an

average of 41 days.

Figure 5. Print out of “Voyage Direction” Program Displaying Results of

Hypothetical Voyage between Ur, Mesopotamia and Calicut, India.

Principal Direction of Voyage: 1 = West, 2 = East: ? 2

Name of Westernmost Station: Ur

Name of Easternmost Station: Calicut

Longitude Between Stations: 29.62º (unknown to program user)

Time of Departure Eastbound: Month, Day, Hour, Minute: 3, 20, 2, 21

(Note: Records local transit of Arcturus on this day)

Anticipated Length of Voyage in Days: 29

Departure Time in Minutes: 861

Time of Arrival at Destination: Month, Day, Hour, Minute: 4, 18, 12, 38

(Note: Records local transit on Arcturus on this day)

Arrival Time in Minutes: 758

Star Advance Underway: 103 Minutes ( 1 Hour, 43 Minutes )

Voyage (Days) Star Transit Longitude (º)

32 12:50 26.75

31 12:46 27.75

30 12:42 28.75

29 12:38 29.75

28 12:34 30.75

27 12:30 31.75

26 12:26 32.75

18

It wasn’t necessary to undertake a voyage to a new or unknown part of the world

to find out how distant it was, however. As long as any two sky-watchers could be in

contact with each other, even if it involved a lead-time of several months to arrange for

the observation of some celestial event of mutual interest to them, the subsequent

comparison of their results would no doubt prove to be just the kind of data that were

needed. At first this may have been limited to observers of the same culture or language

group, such as a Phoenician in Sidon or Tyre contacting another in Carthage, or Gades,

but that it also came to involve sky-watchers of disparate cultural backgrounds is obvious

from very early times. For example, once the Chinese had learned that the Hindu

mathematician and astronomer, Aryabhata, had found an accurate measure of pi, they

dispatched a delegation to India to translate all of his writings in Sanskrit into Chinese.

The Chinese had long wrestled with what was a usable version of pi themselves,

beginning with a truncated version that consisted only of the integer “3” that obviously

didn’t produce very accurate results. Even when they had expanded it to two decimal

places, it was hardly any more helpful, so they were extremely delighted to get the

formula that Aryabhata had developed to define it more precisely.

Of course, Aryabhata was also no doubt very flattered by the fact that scholars

had come all the way from Beijing to get the answer from him, and one can imagine that

he introduced his explanation by pointing out that pi was an irrational number --

something that the Chinese may or may not have already decided for themselves. In any

case, because it was irrational, he next would probably have advised them that what he

was about to tell them would not seem to make much sense either. However, he could

assure them that as long as they carefully followed his instructions without question, they

would find that it worked very well, and he then proceeded to divulge his formula. “First,

you add the number 4 to 100. Second, you multiply this value by 8. Third, to this value,

i.e., 832, you now add 62,000. Fourth, you then divide this value, i.e., 62,832, by 20,000,

resulting in a value of pi that is correct to four decimal places, namely 3.1416.”

There is no question but that when the Chinese returned home, it was with a gold

mine of information from their Hindu consultant, initiating one of the earliest exchanges

of scientific data that the world had ever witnessed. (The astronomical table of sines

authored by Aryabhata provided exquisite proof to the Chinese of the validity and use of

his value for pi.) By the time that such continued exchanges culminated in the Middle

Ages, they had been steadily expanded into an amicable pattern of sharing astronomical

information throughout the ancient Eurasian heartland, embracing not only the earliest

cultures of the region -- the Sumerians, Egyptians, and Persians -- but also the

Phoenicians and Greeks, the Indians, Chinese, Arabs, and finally, even the Mongols.

Although Chinese astronomical studies began with the founding of East Asia’s oldest

observatory at Taosi, probably already about 2300 BCE, it was enhanced by Buddhist

influences in the early centuries CE and later by Hindu scholars like Aryabhata and the

founding of other observatories at Gaocheng and Deng Feng. The subsequent advance of

Islam through Central Asia introduced both Arab and Persian influences to the Mongols,

and when Genghis Khan first visited Persia, he brought a Chinese scholar with him to

19

study the calendar that was in use there. In return, his son, Kublai Khan, brought a

Persian scholar back to Beijing to construct an observatory there, and a couple of his

grandsons were responsible for building observatories at both Samarkand and Maragheh,

whose influences were later to spread west to Istanbul as well as south into Mogul India.

In the process, new meridians were also established in such places as Baghdad,

Damascus, and Cordoba Spain, as well as in Novara Italy. Indeed, the 8th through the

15th centuries marked the Golden Age of astronomy in the Islamic world, with some of

the most notable compilations of data coming from Khwarezmia, a Moslem kingdom on

the shore of the Aral Sea in the heart of Central Asia.

Apart from the advances in astronomy that were made in Europe during the

sixteenth and seventeenth centuries by men such as Gallileo, Brahe, Kepler, and

Copernicus, by the 18th century some of the most interesting work on expanding the

scope of longitude studies was taking place in India. A Hindu nobleman by the name of

Jai Singh II, a local rajah in the state of Rajastan, was commissioned by the Mughal (i.e.

Muslim) emperor to further the study of astronomy by erecting no fewer than three

observatories in the area within the latter’s domain. That in Jaipur, Singh’s new capital

founded in 1727, was not only positioned on the same meridian as that first demarcated

on the coast of India at Kozhikode and later extended to Ujjain by Aryabhata, but was

also selected to assemble the data for the final zij that was published in the traditional

medieval manner. That an observatory was also built in Delhi was clearly predicated on

the fact that the Mughal emperor Shah Jahan had chosen the latter city as his imperial

capital in 1639, though it is less clear why one also was founded at Mathura, scarcely 150

km (90 miles) away to the southeast. As a Hindu, Jai Singh knew full well that Mathura

was the supposed birthplace of the goddess Indira, but it is quite unlikely that the emperor

would have approved its construction if he had understood the motive behind Singh’s

choice of location. The same would most likely have been true if the emperor had been

aware that Singh had also erected a fourth observatory far to the east, and that the site he

had chosen was Varanasi, the holiest of Hindu cities. (Much as the Muslim emperor

valued the intellect of his Hindu subordinate, he only accorded him a grudging rank

equivalent to ‘one and a quarter persons.’) If Jai Singh II had not already calculated the

size of the Earth by using his measurements between Calicut, Ujjain, and Jaipur, once his

observatory in Varanasi was operational he could easily confirm not only the globe’s

circumference but also the speed of its rotation. The Jantar Mantar observatory in

Varanasi, opened in 1737, is described as being “less well equipped that either of those

at Jaipur or Delhi”, but having “a unique equatorial sundial that could allow

measurements to be monitored and recorded by one person”, certainly an advantage if it

was intended to be used for clandestine observations.

In November 1707, the fleet of British Admiral Sir Clowdisley Shovell, returning

from an engagement in the Mediterranean during the War of the Spanish Succession, was

plagued by such atrocious weather that the navigators had been unable to keep track of

their position. Thinking themselves to be off the coast of Brittany in France, they ran

onto the reefs to the west of the Scilly Islands instead, losing at least four of their larger

ships and over 2000 men, including Admiral Shovell. Although their mishap resulted

from being about two degrees farther north in latitude than expected, and about one

20

degree off course in longitude, it was the latter that was considered to have been the

primary cause of the tragedy, for it led to the passage in Parliament in July 1714 of the

so-called “Longitude Act”. This, in turn, resulted in the establishment of “a Board of

Longitude to examine the problem” and “to set up a prize of 20,000 pounds for the

person who could invent a means of finding longitude to an accuracy within 30 miles

(one half of a degree) after a six-week voyage to the West Indies”.

The Astronomer Royal, Nevil Maskelyne, absolutely rejected the notion that any

mechanical device would solve the longitude problem, arguing instead that only tables of

lunar and star positions, i.e., zijes, or ephemerides, would accomplish the task. There-

fore, when John Harrison, a Yorkshire carpenter, came forward in 1735 with the first of

his series of clocks that weighed 72 pounds, it was tested on a round trip voyage to

Lisbon and awarded a prize of 500 pounds for being “a minor discovery” but was

rejected for being too cumbersome. For Harrison the creation of an acceptable

chronometer had now become an all-consuming goal, and in 1739 he produced a much

less cumbersome second model, only to have it rejected as well. However, after ten more

years of work he produced his third timepiece, which received the Copley Medal from

the Royal Society, but again it didn’t satisfy Maskelyne.

Another ten years of labor followed for Harrison, after which he presented his

fourth time piece, that he now had ‘miniaturized’ to the size of a pocket watch. It was

this model that Harrison felt would surely win the prize, and in order to be tested, it was

put aboard a voyage scheduled from Portsmouth to Jamaica on which Harrison’s son

William was sent along to make sure it was properly wound each day. The journey was

completed between November 1761 and March 1762, and on arrival in Jamaica,

Harrison’s timepiece was found to be only 1 minute and 54 seconds off in time and only

18 geographic miles off in longitude. Once he received word of his success, having

finally met the critical standards set by Parliament for the grand prize, Harrison felt

entitled to claim the prize.

This time Maskelyne had no recourse but to “pull rank”. Being a ‘more educated

man’ than Harrison, Maskelyne was able to persuade the Board not to award the prize,

forcing Harrison to petition Parliament for his due. After some debate, Parliament voted

him a special prize of 5000 pounds, but Harrison objected, saying that was not how the

original terms of the award had been announced. In the meantime, another voyage with

his timepiece had been made to Barbados, and this time it proved its accuracy to within

10 geographic miles – almost twice as good as on the first voyage. Even so, the Board

refused to award the full prize, though it did admit that ‘the clock was effective’. Once

more Parliament felt obliged to intervene, this time specifying to Harrison that they

would award him another 10,000 pounds if he explained the principles of the

chronometer in full, and how it might be replicated so that it would work effectively for

other craftsmen as well. Then he would be given the balance of the prize. Although

Harrison was angered at the way he was being given the run–around and being forced to

share the details of his instruments that he had worked over 30 years to perfect, he had no

other recourse but to agree. An exact copy of his fourth timepiece was made by another

craftsman known as Larcum Kendal, and was used by Captain Cook -- with great

21

satisfaction and high praise -- on his second voyage to the Pacific in 1772-1774. Because

the earliest chronometers had an “astronomical price” of 400 or more pounds -- roughly

30% of the value of the ship itself, it is small wonder that Kendal’s copy was enthusiast-

ically described by the Master of Cook’s ship “Resolution” as ”the greatest piece of

mechanism the world has ever seen”.

Despite the fact that it had taken Harrison over half a lifetime to win the

equivalent of the award that the Admiralty had originally offered, the prize itself was

never awarded, no doubt thanks to the continuing opposition of ‘more educated’ persons

like Maskelyne. Yet, the tests his chronometer had been put through confirmed that the

age-old problem of determining one’s longitude had literally become ‘child’s play’, for

by comparing one such device set to local time and another to London time, there was no

longer any question as to the difference in distance between any two places. Though the

concepts of both standard and universal time took a couple of additional centuries for the

international community to agree upon, including assigning the zero meridian to

Greenwich, England, today anyone with a GPS receiver can determine his or her location

merely by pressing a button – and, by using a modern maritime instrument (such as that

cited below), with a precision up to ten decimal places!

Figure 6. View from the bridge of the Norwegian ship “M/S Sjøkurs” as it enters the

waters of Norway’s northernmost province (Finnmark) in July 2013. It has just passed

latitude 70º North and longitude 21º East and is on a course of just under 20º west of

North with a speed of 13 knots, beginning to cross an arm of the Arctic Ocean known as

Kvaenangen.