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De Zeventiende Eeuw. Jaargang 12 (1996)

De Zeventiende Eeuw. Jaargang 12

(1996)– [tijdschrift] Zeventiende Eeuw, De–rechtenstatus Auteursrechtelijk beschermd

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Finding longitude at sea: early attempts in Dutch navigation
A.R.T. Jonkers

If one were to ask a maritime historian to name the most enduring problem in ocean navigation during the early modern period, chances are that he would mention the difficulty of finding longitude, the establishment a ship's position relative to a prime meridian, far from known landmarks, in an age without atom clocks and satellite navigation. In trying to solve this problem, nautical experts, astronomers, mathematicians, pilots and laymen alike proposed a number of very different solutions. In retrospect, it is easy to determine who was wrong and who was right. History sometimes seems to focus attention primarily on those who contributed to the correct solution, while proponents of other ideas, which at the time itself may have received equal or even more attention, are now reduced to footnotes. This is not to detract from the genius of a Huygens, but merely to show that technological development is seldom a linear process, but rather a journey through a maze with many dead ends and alternative routes. The early decades of Dutch maritime expansion provide historians with a good example of this quest.

This process of expansion really took off from the second half of the sixteenth century, when the merchant marine more than doubled and the scope of the Dutch mariner was widely expanded to include most of the European coastline, from Kola in Russia to the eastern Mediterranean.1. Attempts in the 1590s to reach the profitable Spice Islands in the East Indies through a northwest-passage led to the discovery of Spitsbergen and the establishment of Dutch whaling companies.2. In 1597 the Indies were reached via the traditional Portuguese route around Africa, resulting five years later in the founding of the Dutch East India Company, the V.O.C.3. To the west, the salt and slave trade were developed through treaties and brute force. During the first decades of the seventeenth century, Dutch strongholds and tradeposts arose on the shores of West-Africa, Angola, Brazil, Guyana, the Caribbean and North-America.4. Around the middle of the century, this inflationary phase was completed; the only region not busily traversed by Dutch vessels remained the Pacific Ocean.

At the outset Dutch navigators relied heavily upon Portuguese experience laid down in sailing directions, to become acquainted with hitherto uncharted waters. Within a few years, however, inefficient coastal navigation through doldrums and counter-currents was abandoned in favour of more direct routes across the open oceans. This implied navigating a ship off the continental shelves within narrowly defined course-corridors, without the benefit of landmarks and soundings to establish position. Although latitude could be determined accurately to within a couple of minutes using astrolabe or quadrant, establishing the vessel's longitude remained an insoluble problem. Already in the sixteenth century three different solutions had been formulated.

The first one was to use predictable astronomical events - such as eclipses - as a universal clock. Already on his second voyage to the Americas in 1494, the Genoese explorer Christopher Columbus tried to establish his ship's longitude by observing a lunar eclipse.5. Although feasible in theory, astronomy and technology were still insufficient for accurate prediction and measurement of those phenomena, which happened frequently enough to serve as a time-piece. Only in the 1770s did a comparable technique involving lunar distances to fixed stars become of practical use to Dutch navigators. The moon's heavenly trajectory was then laid down in extensive tables, which were made available to seafarers through nautical almanacs.6. In addition, improved instruments were introduced such as the sextant, allowing observance of angles up to 120 degrees.7.

The second solution to finding longitude at sea involved accurate time measurement; a mariner could take with him a chronometer set to the time on a prime meridian, to compare with local time. Four minutes difference would equal one degree of longitude. This idea was already formulated by the Dutch astronomer Gemma Frisius in 1530, and it was the one pursued by Christiaan Huygens.8.

In 1663 and '64 his first marine pendulum clock was tested at sea by captain Robert Holmes, with encouraging results. A French test voyage to Cayenne six years later, sponsored by the Académie des Sciences, was less successful; possibly due to the negligence of custodian Jean Richer, both clocks taken on the journey had stopped.9.

After a long interlude Huygens received formal encouragement from the Directors of the Dutch East India Company in 1682. Four years later, he was allowed to send his chronometers with detailed instructions for mounting, regulating and maintenance on a new testvoyage to the Cape of Good Hope. Upon return, the logbooks showed that the clocks had performed badly during heavy seas, and according to their longitudes the ship had sailed right through Scotland and Ireland. This error was due to an effect, that Huygens had hitherto neglected, namely the Earth's centrifugal force diminishing the weight of bodies by a factor proportional to their colatitude. This meant that a pendulum would be about a third of a percent lighter on the equator than on the poles, lagging behind approximately 2½ minutes per day. New trials in the early nineties did not yield a breakthrough. Sadly, constructing a sea-worthy clock, which would not be perturbed by the ship's movements and changes in temperature and humidity was beyond the reach of seventeenth-century technology.10.

The third option to determine longitude at sea followed a very different line of reasoning, based on the hypothetical existence of a relationship between longitude and magnetic declination, that is, the difference between geographic and magnetic North. This brings up the complexity of the Earth's magnetic field, which even today lacks a complete scientific theory, and thus warrants a short description at this point.

The Earth consists of a thin, light crust, a heavier mantle, and an iron core. Because of the intense heat inside, the outer core is in a liquid state, whereas the gigantic pressures keep the inner core in a solid, crystallised form.11. Propelled by the Earth's heat and rotation, the molten iron of the outer core churns around the solid inner core, acting as a dynamo that generates the Earth's magnetic field. The simplest form of such a field has two poles where the strength is greatest and hence

is known as a dipole field. Maps of the magnetic field at the core-mantle boundary show a more complex picture, consisting of anomalies in different shapes and sizes, which grow, drift westward and decay over periods from decades to tens of thousands of years. These non-dipole elements of the field have been named the field's secular variation. This variation is probably caused by the fluid flow in the upper outer core, influenced by physical undulations at the core-mantle boundary and heat convection through the mantle.12. These complex processes create rather irregular, slowly moving patterns of magnetic field lines at the surface. A compass will align itself with the local magnetic flux, so the needle will only rarely and accidentally point to geographic north. This angle difference is called magnetic declination. Lines of equal declination are known as isogonic lines; a line of zero declination, on which a compass would point to true north, is named an agonic line.

Although the field's gradual change over time was not generally known until 1635,13. the existence of compass variation, as it was termed by mariners, had been known since the first half of the fifteenth century. Evidence of this can be found on small, portable sun dials made in Neurenberg and Augsburg. For correct alignment relative to the sun's path across the heavens these instruments had tiny compasses built into the frame; the term compassus was originally even meant to denote the whole sun dial. Comparison of the sun's meridian with the compass soon brought the needle's deviation from true north to light. This was corrected by the makers from circa 1450 onwards, by putting a mark next to the compass to indicate the contemporary northeasting.14. Although initially dismissed as being solely due to material or construction defects, magnetic declination was recognized as a phenomenon no later than the mid-fifteenth century. Persistent claims as to the discovery being made first by Columbus on his Atlantic traverses in the 1490s have thus to be rejected. During his westward voyages he did however become one of the first to witness the change in declination sign, from northeasting to northwesting.15.

Measuring the difference between the magnetised needle and the local meridian was a relatively simple procedure, even at sea. The direction and amount could easily be established by comparing the needle's orientation to the middle of two compass bearings of any celestial body at equal time before and after noon, for instance by observing the sun on the horizon at sunrise and sunset. Measuring local declination on board ship was necessary for steering a correct compass course and subsequent dead-reckoning calculations. In addition, when exploring new coastlines, true compass bearings of landmarks had to be taken to construct correct charts. It will come as no great surprise, then, that from the early days of Portuguese exploration until the advent of chronometer and gyro-compass, local variation was diligently measured, corrected for and noted down in navigational logbooks. Thus was made a descriptive study of the local magnetic declination, which through experience, sailing directions, isogonic charts and journals became part of local knowledge, aiding the navigator in the determination of position. It was known that in year X near to Cape A or west of island B the compass needle pointed so many degrees west or east of true north. Thus, in the absence of reliable coordinates of longitude, a virtual magnetic coordinate was sometimes used to designate a geographic position, keeping in mind that unlike degrees of longitude, degrees of declination tended to change in a non-linear fashion during a voyage, depending on the density and direction of the local isogonics.

This last characteristic only gradually became apparent to mariners, as more information on local declination was collected over the ages. In the sixteenth and early seventeenth century information was still so scarce that a few, widely distant, local values gave rise to a number of hypotheses of some regular, longitude-dependent structure of the magnetic field lines, relative to a prime meridian on which the needle would point to true north. In such a system the magnetic coordinate effectively replaced the more elusive coordinate of longitude. The Portuguese were the first to postulate these simple, dipole-like field models for navigational purposes. They are characterised by regularly spaced isogonics, running straight from pole to pole just like meridians. Moving due east from a prime meridian, the declination was deemed to rise steadily from zero to a maximum of northeasting, then decline to zero, continue to fall to reach a maximum of northwesting, and finally return to zero again.

The first clear description of a ‘magnetic model’, in the sense of an inferred spatial distribution of field lines (without implied causal concepts), can be found in a 1514 manuscript by the Portuguese pilot Joao de Lisboa, entitled Tratado da agulha de marear ho ano de 1514.16. After a description of several types of compasses and techniques to establish true north and south (using the Pole star and the constellation Southern Cross respectively), the writer presented his magnetic model relative to a prime meridian, situated near the Azores (the islands Santa Maria and Sao Miguel) and the Cape Verdes (Sao Vicente).17. De Lisboa imagined the eastern hemisphere to be subject to easterly declination and the western hemisphere to northwesting, rising and falling steadily as a function of longitude. Separating these two regions was an agonic great circle, where a compass would not deviate from true north, passing through 0o and 180o; declination was deemed to peak at a maximum of 45o east and west of true north halfway in between, at longitudes 90oE and 270oE.18.

Although de Lisboa was considered an able navigator, he did not circumvent the whole globe on his travels. So how did he come up with a planet-spanning model? A possible indication is his remark on the quantified growth of the declination with longitude, stated as being one point (or 11o15′) per 250 legoas at latitudes between 30o and 45o. In the northern hemisphere this latitude interval covers the then already busy sea routes between Portugal, Madeira and the Canaries. Observation of compass variation would show decreasing northeasting while going west (towards the Azores, for instance). Presumably de Lisboa could have used these measurements to extrapolate a regular progression the world around.

Similar views were expressed by the Italian Antonio Pigafetta, who participated in Magellan's circumnavigation (1519-1522) and who claimed that determining longitude from compass variation had already been proved by experience.19. De Lisboa's view was also supported by the Portuguese Francisco Faleiro; in his navigational tract Tratado del sphera del mundo y del arte de navigar20. he reiterated the Lisboa model, now relative to a prime meridian over Corvo (one of the other islands in the Azores).21.

A slightly different picture was presented in 1542 by Alonso de Santa Cruz in his ‘Libro de Longitudines’; he surmised a change of only a half point declination per fifteen degrees longitude, resulting in a maximum of 33o45′ at 90o and 270o.22.

JOAO DE LISBOA (1514) & ALONSO DE SANTA CRUZ (1642)
LONGITUDE DIRECTION DE LISBOA DE SANTA CRUZ
0o   meridional agonic line 0o   0o  
0o-90o E waxing northeasting 0o-45o NE 0o-33o45′ NE
90o E maximal northeasting 45o NE 33o45′ NE
90o-180o E waning northeasting 45o-0o NE 33o45′-0o NE
180o E meridional agonic line 0o   0o  
180o-270o E waxing northwesting 0o-45o NW 0o-33o45′ NW
270o E maximal northwesting 45o NW 33o45′ NW
270o-360o E waning northwesting 45o-0o NW 33o45′-0o NW

Why go into such detail on sixteenth century Iberian developments? Because the development of Dutch ocean navigation is directly linked to that of our south-European counterparts, mostly through translations of their nautical publications. A few examples will suffice to illustrate the diffusion of navigational knowledge to the mariners of more northern latitudes. Within eight years of publication, Pedro de Medina's opus Arte de navigar, en que se contienen todas las replas (...) que a la buena navegacion son necessarios... (1545) had been translated into Italian and French, the French version serving in turn as the basis for a German and an English edition. To a Dutch translation in 1580 was added a clear, practical commentary by the Antwerp navigation and mathematics teacher Michiel Coignet.23. In the twenty years until the turn of the century three new editions were printed in Amsterdam. Although Medina himself did not mention magnetic variation, Coignet echoed Portuguese notions of the standard dipole field with one agonic great circle and maximums halfway in between, but added the notion of increased declination at higher latitudes.24. Rodrigo Zamorano's Compendium del arte de navigar (1581) appeared in a Dutch translation a mere seven years later.25. Besides these printed sources Dutch navigators also had access to Portuguese manuscripts on ocean navigation and the route to the Indies, such as the loose roteiros, gathered in Portugal from 1592-94 by the brothers Cornelis and Frederick de Houtman, to be used in the preparation for Dutch voyages to the Indies.26.

A wealth of manuscript sailing directions, hydrographic tracts and other descriptions collected by the Dutchman Jan Huyghen van Linschoten during his thirteen years in Portuguese service in Asia and the Azores, were compiled and published in Amsterdam as the Itinerario. The first volume to appear (actually to be the last in the series), the Reys-geschrift van de navigatien der Portugaloyers, was printed in 1595, just in time to accompany the first Dutch venture to the East Indies (1595-1597).27. In 1598 Van Linschoten also published a treatise by the Spanish Jesuit missionary José de Acosta, in which a new magnetic model was presented with declination dependent on latitude and four meridional agonic lines, based on hearsay from an ‘experienced Portuguese pilot’.28. With the exception of the agonic prime meridian over Corvo, de Acosta did not specify the exact whereabouts of these meridians, but a slightly later text does: Manoel de Figueiredo, royal cosmographer at the Portuguese court, in his Hidrographia Exame de Pilotos (printed in 1625) determined the places these lines pass through as being the Azores, Cape Agulhas (South Africa), Canton (China) and near Acapulco (Mexico).29. Relative to Corvo the longitudes of these locations are 0o, 60o, 160o and 260oE. Like his

predecessors de Figueiredo once more envisaged maximums halfway between these meridional agonics, peaking at 2 quartas, or 22½ degrees (see the following table). He also stated that magnetic variation would increase towards the equator.30.



illustratie
1. Modelled isogonics of the Plancius concept.


A very similar model was postulated in Van de graden der lancte ende het affmeten der selver door het noordoosteren ende noordwesteren der naelde (1598) by Petrus Plancius, a calvinist minister from the southern Netherlands, who settled in Amsterdam around 1585. There he became a distinguished geographer, and a driving force behind the founding of the first Dutch overseas trade companies. He drew charts, taught and wrote on nautical science, and developed an instrument to transform his geomagnetic vision into a practical tool to determine longitude at sea.31. At the heart of his concept lay the conviction that the magnetic meridian of any place on Earth and the nearest agonic line would intersect on the Arctic Circle. This implied that the predicted magnetic variation was not only dependent on longitude but also on latitude. Nevertheless, his model kept a number of dipole-field characteristics strongly reminiscent of the Portuguese postulates he was acquainted with, and which may at the least have served as an inspiration. Whether or not he was aware of the exact characteristics of the Acosta/Figueiredo model at the time of his own concept's inception remains an open question, though the resemblance is striking. This similarity has not previously been explored at length. Plancius divided the world in four unequal parts with four meridional agonic lines: over the Azores, and from there at 60, 160, and 260 degrees east. In the first and third quarter the compass northeasted; in the other two parts it northwested. Latitudewise the field lines were mirrored around the parallel of 20 degrees North.32.

As the involved spherical trigonometry was beyond the calculating capacity of the mariners, who had to use his system at sea, Plancius developed the longitudefinder, a small flat copper plate with arced sides, engraved with curved meridians converging into a pole. This instrument could be fitted onto an astrolabium catholicum, a flat circular disk on which a network of meridians and parallels was drawn in equatorio-stereographic projection. Using colatitude of the ship and magnetic declination, the distance to the nearest agonic line could then simply be read off.33.

PETRUS PLANCIUS (1598) & MANOEL DE FIGUEIREDO (1625)
LONGITUDE DIRECTION Plancius at 85oN Plancius at 20oN Figueiredo
0o   meridional agonic line 0o   0o   0o  
0-30o E waxing northeasting 0-25o NE 0o-12o NE 0o-22o30′ NE
30o E maximal northeasting 25o NE 12o NE 22o30′ NE
30-60o E waning northeasting 25o-0o NE 12o-0o NE 22o30′-0o NE
60o E meridional agonic line 0o   0o   0o  
60-110o E waxing northwesting 0o-42o NW 0o-18o NW 0-22o30′ NW
110o E maximal northwesting 42o NW 18o NW 22o30′ NW
110-160o E waning northwesting 42o-0o NW 18o-0o NW 22o30′-0o NW
160o E meridional agonic line 0o   0o   0o  
160-210o E waxing northeasting 0o-42o NE 0o-18o NE 0-22o30′ NE
210o E maximal northeasting 42o NE 18o NE 22o30′ NE
210-260o E waning northeasting 42o-0o NE 18o-0o NE 22o30′-0o NE
260o E meridional agonic line 0o   0o   0o  
260-310o E waxing northwesting 0o-42o NW 0-18o NW 0-22o30′ NW
310o E maximal northwesting 42o NW 18o NW 22o30′ NW
310-360o E waning northwesting 42o-0o NW 18o-0o NW 22o30′-0o NW

The whole concept was based on a rather weak foundation of less than a hundred collected magnetic measurements, with none in the region between the meridians over China and Mexico, in other words, almost the whole of the Pacific Ocean. This large gap led the Dutch mathematician Simon Stevin to postulate a somewhat different model. In 1599 he published The Haven-finding, wherein he suggests, that the first three meridional agonics in the Plancius model may in fact be great circles, continuing over the Earth's ‘backside’. This would divide the planet in six parts of different magnetic direction. But unlike Plancius, who preached his vision as if it was the gospel, Stevin was much more careful in stressing the preliminary nature of the hypothesis, and the need for more research.34.

During the first decades of the Dutch maritime expansion the method devised by Plancius was actually used on board ship, as is attested by references in extant ship's logs from the period. The explorer William Barentsz and his crew, who had to winter at Nova Zembla during their expedition in 1596 to find a northeast-passage to China, even left a longitude-finder on the island.35. Plenty of written examples also exist of vigorous debate between the nautical experts of the time as to the merits and flaws of the system. Some navigators en route to the Indies seem to have been favourably impressed;36. others less so, as was attested by captain Jan Cornelisz May, who tested the Plancius-method in 1611 and reported afterwards that: ‘the method is imperfect and complete folly’.37.

References to the Plancius concept kept appearing in Dutch logbooks until circa 1635. This is confirmed by a sample of 25 ship's logs, taken at the Dutch National Archives (The Hague): of seven logbooks spanning the period 1608-1636 all except one contain references to the Plancius concept, whereas of the eighteen consulted for the period 1637-1700 only one journal can lay claim to a similar feat.38. This clear demarcation about halfway through the fourth decade of the seventeenth century is correlated with the publication in 1635 by the English astronomer Henry Gellibrand of his findings, that the Earth's magnetic field changed over time.39. Dif-

ferences of local declination with earlier figures that hitherto had been ascribed to inaccuracies in compass and measurement, could then corroborate this new insight, which completely refuted all static magnetic models, both Portuguese, Spanish and Dutch.

Although this discovery was quickly and generally accepted, it did not prevent various individuals to reinvent the crooked wheel time and again. In 1647 Gabriel Grisly van Offenburg sought a reward from the Dutch East India Company for solving the longitude-problem with a completely steady, somewhat tilted magnetic dipole model with four agonics.40. Even more striking, in 1738 the well-known cartographer, meteorologist, and mathematician Nicolaas Cruquius proposed another time-independent magnetic field model, and suggested it be used for navigating purposes.41.



illustratie
2. Modelled isogonics of the Cruquius concept.


As can readily be discerned from the isogonics in the diagram, once more a simple dipole with two agonic meridians, in all probability generated with a mathematical equation, and of course, fully static.42. Less gifted amateurs continued to launch similar views to Boards of Longitude in several European countries throughout the eighteenth century.

The refutation of static dipole models to explain the Earth's magnetic field did not, however, lead to the abandonment of measuring magnetic declination on board ship. On the contrary. Since it was known that the field changed over time, the need to keep track of the local change in declination was felt even more strongly. In the eighteenth century V.O.C. regulations expressly stipulated that navigators should take magnetic measurements as often as possible, and the values mentioned in sailing directions were checked and corrected every few years or so. Declination thus remained part of local knowledge, and an important indication of position in the open seas.43.

 

The descriptive study of the field and its secular variation, laid down in logbooks and used in navigation during the sixteenth, seventeenth, and eighteenth century had been all but forgotten, gathering dust in the archives of admiralties and East India Companies. However, the recent developments in mathematical modelling of the convection processes at the Earth's core-mantle boundary have engendered a fresh interest in this potentially rich source of long-term magnetic declination

data.44. Currently an international research group of geophysicists and historians (including the author) is attempting to conduct the largest ever survey of the extant primary source material from the past centuries in order to build the best possible representation of the ever changing geomagnetic field. Thanks to the meticulous observance by diligent navigators, trying to cope with an incomprehensible problem, researchers can presently gather a unique data set spanning over four hundred years, allowing a better shot at understanding the inner workings of mother Earth.

 

The investigations were supported (in part) by the Foundation for Historical Sciences (SHW) with financial aid from the Netherlands Organization for Scientific Research (NWO).

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