Category Archives: History of Navigation

Spicing up the evolution of the mathematical sciences

When we talk about the history of mathematics one thing that often gets forgotten is that from its beginnings right up to the latter part of the Early Modern Period almost all mathematics was developed to serve a particular practical function. For example, according to Greek legend geometry was first developed by the ancient Egyptians to measure (…metry) plots of land (geo…) following the annual Nile floods. Trade has always played a very central role in the development of mathematics, the weights and measures used to quantify the goods traded, the conversion rates of different currencies used by long distance traders, the calculation of final prices, taxes, surcharges etc. etc. A good historical example of this is the Islamic adoption of the Hindu place value decimal number system together with the associated arithmetic and algebra for use in trade, mirrored by the same adoption some time later by the Europeans through the trader Leonardo Pisano. In what follows I want to sketch the indirect impact that the spice trade had on the evolution of the mathematical sciences in Europe during the Renaissance.

The spice trade does not begin in the Renaissance and in fact had a long prehistory going back into antiquity. Both the ancient Egyptians and the Romans had extensive trade in spices from India and the Spice Islands, as indeed the ancient Chinese also did coming from the other direction.

Spices_in_an_Indian_market

The spice trade from India attracted the attention of the Ptolemaic dynasty, and subsequently the Roman empire. Source: Wikimedia Commons

Throughout history spice meant a much wider range of edible, medicinal, ritual and cosmetic products than our current usage and this trade was high volume and financially very rewarding. The Romans brought spices from India across the Indian Ocean themselves but by the Middle Ages that trade was dominated by the Arabs who brought the spices to the east coast of Africa and to the lands at the eastern end of the Mediterranean, known as the Levant; a second trade route existed overland from China to the Levant, the much fabled Silk Road. The Republic of Venice dominated the transfer of spices from the Levant into Europe, shipping them along the Mediterranean.

1920px-Silk_route

The economically important Silk Road (red) and spice trade routes (blue) blocked by the Ottoman Empire c. 1453 with the fall of the Byzantine Empire, spurring exploration motivated initially by the finding of a sea route around Africa and triggering the Age of Discovery. Source: Wikimedia Commons

Here I go local because it was Nürnberg, almost literally at the centre of Europe, whose traders collected the spices in Venice and distributed them throughout Europe. As Europe’s premier spice traders the Nürnberger Patrizier (from the Latin patrician), as they called themselves, grew very rich and looking for other investment possibilities bought up the metal ore mines in central Europe. In a short period of time they went from selling metal ore, to smelting the ore themselves and selling the metal, to working the metal and selling the finished products; each step producing more profit. They quite literally produced anything that could be made of metal from sewing needles to suits of armour. Scientific and mathematical instruments are also largely made of metal and so Nürnberg became Europe’s main centre for the manufacture of mathematical instruments in the Renaissance. The line from spice to mathematical instruments in Nürnberg is a straight one.

Scientific-Instruments-and-the-History-of-Medicine-Courtesy-of-GNM

Torquetum designed by Johannes Praetorius and made in Nürnberg

By the middle of the fifteenth century the Levant had become a part of the Ottoman Empire, which now effectively controlled the flow of spices into Europe and put the screws on the prices. The Europeans needed to find an alternative way to acquire the much-desired products of India and the Spice Islands, cutting out the middlemen. This need led to the so-called age of discovery, which might more appropriately be called the age of international sea trade. The most desirable and profitable trade goods being those spices.

The Portuguese set out navigating their way down the west coast of Africa and in 1488 Bartolomeu Dias succeeded in rounding the southern most tip of Africa and entering the Indian Ocean.

Bartolomeu_Dias,_South_Africa_House_(cut)

Statue of Bartolomeu Dias at the High Commission of South Africa in London. Source: Wikimedia Commons

This showed that contrary to the Ptolemaic world maps the Indian Ocean was not an inland sea but that it could be entered from the south opening up a direct sea route to India and the Spice Islands.

1920px-Claudius_Ptolemy-_The_World

A printed map from the 15th century depicting Ptolemy’s description of the Ecumene, (1482, Johannes Schnitzer, engraver). Showing the Indian Ocean bordered by land from the south Source: Wikimedia Commons

In 1497 Vasco da Gama took that advantage of this new knowledge and sailed around the Cape, up the east coast of Africa and then crossing the Indian Ocean to Goa; the final part of the journey only being made possible with the assistance of an Arab navigator.

875px-Gama_route_1.svg

The route followed in Vasco da Gama’s first voyage (1497–1499) Source: Wikimedia Commons

Famously, Christopher Columbus mistakenly believed that it would be simpler to sail west across, what he thought was, an open ocean to Japan and from there to the Spice Islands. So, as we all learn in school, he set out to do just that in 1492.

In fourteen hundred and ninety two

Columbus sailed the ocean blue.

The distance was of course much greater than he had calculated and when, what is now called, America had not been in the way he and his crews would almost certainly have all died of hunger somewhere out on the open seas.

Columbus_first_voyage

Columbus’ voyage. Modern place names in black, Columbus’s place names in blue Source: Wikimedia Commons

The Portuguese would go on over the next two decades to conquer the Spice Islands setting up a period of extreme wealth for themselves. Meanwhile, the Spanish after the initial disappointment of realising that they had after all not reached Asia and the source of the spices began to exploit the gold and silver of South America, as well as the new, previously unknown spices, most famously chilli, that they found there. In the following centuries, eager also to cash in on the spice wealth, the English and French pushed out the Portuguese in India and the Dutch did the same in the Spice Islands themselves. The efforts to establish sea borne trading routes to Asia did not stop there. Much time, effort and money was expended by the Europeans in attempts to find the North West and North East Passages around the north of Canada and the north of Russia respectively; these efforts often failed spectacularly.

So, you might by now be asking, what does all this have to do with the evolution of the mathematical science as announced in the title? When those first Portuguese and Spanish expedition set out their knowledge of navigation and cartography was to say the least very rudimentary. These various attempts to reach Asia and the subsequent exploration of the Americas led to an increased effort to improve just those two areas of knowledge both of which are heavily based on mathematics. This had the knock on effect of attempts to improve astronomy on which both navigation and cartography depend. It is not chance or coincidence that the so-called age of discovery is also the period in which modern astronomy, navigation and cartography came of age. Long distance sea trading drove the developments in those mathematically based disciplines.

This is not something that happened overnight but there is a steady curve of improvement in this disciplines that can be observed over the two plus centuries that followed Dias’ first rounding of the Cape. New instruments to help determine latitude and later longitude such as mariners’ astrolabe (which is not really an astrolabe, around 1500) the backstaff (John Davis, 1594) and the Hadley quadrant (later sextant, 1731) were developed. The Gunter Scale or Gunter Rule, a straight edge with various logarithmic and trigonometrical scales, which together with a pair of compasses was used for cartographical calculations (Edmund Gunter, early seventeenth century). William Oughtred would go on to lay two Gunter Scales on each other and invent the slide rule, also used by navigators and cartographers to make calculations.

New surveying instruments such as the surveyor’s chain (also Edmund Gunter), the theodolite (Gregorius Reisch and Martin Waldseemüller independently of each other but both in 1512) and the plane table (various possible inventors, middle of the sixteenth century). Perhaps the most important development in both surveying and cartography being triangulation, first described in print by Gemma Frisius in 1533.

Cartography developed steadily throughout the sixteenth century with cartographers adding the new discoveries and new knowledge to their world maps (for example the legendary Waldseemüller world map naming America) and searching for new ways to project the three-dimensional earth globe onto two-dimensional maps. An early example being the Stabius-Werner cordiform projection used by Peter Apian, Oronce Fine and Mercator.

THE_WORLD_MAP,_1524_(and_1564)_by_Petrus_Apianus

Cordiform projection in a map of the world by Apianus 1524 which is one of the earliest maps that shows America Source: Wikimedia Commons

This development eventually leading to the Mercator-Wright projection, a projection specifically designed for marine navigators based on Pedro Nunes discovery that a path of constant bearing is not a great circle but a spiral, known as a loxodrome or rhumb line. Nunes is just one example of a mathematical practitioner, who was appointed to an official position to develop and teach new methods of navigation and cartography to mariners, others were John Dee and Thomas Harriot.

pedro_nunes

Pedro Nunes was professor of mathematics at the University of Coimbra and Royal Cosmographer to the Portuguese Crown. Source: Wikimedia Commons

To outline all of the developments in astronomy, navigation and cartography that were driven by the demands the so-called age of discovery, itself triggered by the European demand for Asian spices would turn this blog post into a book but I will just mention one last thing. In his one volume history of mathematics, Ivor Grattan-Guinness calls this period the age of trigonometry. The period saw a strong development in the use of trigonometry because this is the mathematical discipline most necessary for astronomy, navigation and cartography. One could say a demand for spices led to a demand for geometrical angles.

 

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Filed under History of Astronomy, History of Cartography, History of Navigation, Renaissance Science, Uncategorized

Marine chronometer, lunar distance method or something else altogether?

Trying to find a method to determine longitude at sea was one of the greatest technical problems of the Early Modern Period. Quite a wide-range of ideas were floated of which the most were either totally impractical or simply false. In the end the two main competitors were: on the one hand the attempts to develop a clock reliable enough to carry time from a given starting point accurately enough through all the vicissitudes of a long sea voyage to be then compared with local time and thus to determine longitude, i.e. the marine chronometer. Or on the other to develop accurate tables of the Moon’s orbit respective a set of given fixed stars in order to be able to use the Moon’s position at any given time as a clock with which to calculate longitude, i.e. the lunar distant method. Both of these concepts were first presented in the sixteenth century but it took until the middle of the eighteenth century before they could be realised.

Around 1760, Tobias Mayer succeeded in delivering up a set of tables of the lunar orbit accurate enough to be used for determining longitude using the lunar distance method. Shortly after this John Harrison showed with his H4 that a solution with a chronometer was also possible. Unfortunately even with the naval almanac produced by Nevil Maskelyne to simplify the calculations the lunar distant method was mathematically difficult to execute. As I have written elsewhere although Harrison’s H4 showed that a chronometer solution was possible, the clock itself was too complex and too expensive to provide a real solution to the longitude problem. It would take well into the nineteenth century before enough affordable, accurate chronometers were available to make this a viable mass method. Many sources claim that in the mean time navigators used the lunar distant method, but did they?

It would appear that for the first fifty or so years following those breakthroughs seafarers relied on a mixture of navigational methods to help determine their longitude. Principally they relied on the old tried and trusted method of dead reckoning. This is the process of calculating the ships new position from a previous one based on compass direction, ship’s speed based on log line measurements, and knowledge of currents. In the period we are talking about, many navigators checked their dead reckoning results against chronometer or lunar distant determinations. Given the lack of reliability of the available chronometers the navigators often carried several watches, comparing or even averaging the results. Sometimes the lunar distant method was only used by landfall to correct or control the longitude determined by dead reckoning. In general it seems that the well-established dead reckoning was the principle method used, supplement by one or other or both of the new methods, although neither of them was really trusted by the navigators.

For a more detailed picture of the navigational methods used from the middle of the eighteenth century to the middle of the nineteenth by the various European sea going nations I can recommend Navigational Enterprises in Europe and its Empires, 1730–1850 (1) edited by Richard Dunn (@Lordoflongitude) and Rebekah Higgitt (@beckyfh) a set of academic papers that supplement their more popular, excellent Finding Longitude.

Navigation001

After an excellent general introduction to the subject by the editors follow eleven papers covering a wide range of aspects of the subject, all of which maintain a very high level of scholarship.

Navigation002

Navigation003

My only real quibble with the book is the unfortunately usual high price putting it beyond my humble resources and probably those of most others interested in reading and learning from this highly informative volume.

(1) Ricard Dunn & Rebekah Higgitt eds., Navigational Enterprises in Europe and its Empires, 1730–1850, Palsgrave Macmillan, 2015

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Getting names right is rather important in the history of science

“Have you seen my new Rolls Royce?”

“But that’s not a Rolls Royce; it’s a Fiat Bambino!”

“It’s got four wheels, an internal combustion engine and it gets you from a to b so it’s a Rolls Royce, isn’t it?”

“Well, no it isn’t.”

The little dialogue above would probably seem pretty ridiculous to any of my readers but today BBC News achieved something similar concerning scientific instruments. On the BBC website they posted a story with the following title, Astrolabe: Shipwreck find ‘earliest navigation tool’

The story is about the find of a scientific instrument found by marine archaeologists in 2014, in the wreck of a Portuguese ship that sank in 1503. Not just in the title, but also throughout the article the discovered instrument is simply referred to as an astrolabe. The article went on to say that astrolabes are relatively rare, and this is the only the 108th to be confirmed catalogued. It is also the earliest known example by several decades.

As it stood this was patent rubbish. There are more than 900 hundred known astrolabes between the earliest known dated instrument from 927 CE and 1900 CE. However the problem is not in the historical accuracy but in the name. The instrument that had been discovered is not an astrolabe but a mariner’s astrolabe a more than somewhat different instrument.

Astrolabe Renners Arsenius 1569
Source: Wikimedia Commons

Mariner’s Astrolabe Francisco de Goes 1608 Source: Istituto e Museo di Storia della Scienza, Firenze

As I explained to someone on Twitter, as I had just corrected the tweet linking to the article for about the zillionth time, a mariner’s astrolabe is a very simplified form of the astrolabe specifically made for use on ships with just one function, the measuring of the altitude of a star or the sun in order to determine latitude. The astrolabe, however, is a very complex instrument with hundreds of different function in astronomy, chronology and surveying.

Following my protests, and those of others, the article has been changed very slightly for the majority of the article it still refers to the instrument as an astrolabe but about three quarters of the way through, the sentence that I have quoted above now starts “Mariners’ astrolabes” instead of simply astrolabes. So everything is now OK? Well, actually no.

All of the references to astrolabe should have been changed to mariner’s astrolabe and above all the click bait title should have been changed, as it also has a second major problem. It states, shipwreck find ‘earliest navigation tool’. This is complete rubbish. Mariner’s astrolabes are quite late developments in the history of navigation and there are many navigation tools that predate it, such as the quadrant, the sea chart, the compass etc. etc. This blatant hyperbolic error is corrected in the subtitle, which reads: An artefact excavated from a shipwreck off the coast of Oman has been found to be the oldest know example of a type of navigation tool [my emphasis]. But of course by now the damage has been done for the casual reader who just glances at the title.

This article is a mess and a lousy piece of history of science communication for which there is absolutely no excuse whatsoever.

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The House of Blaeu vs.The House of Hondius – The Battle of the Globes and Atlases

There is a South to North trajectory in the evolution of the modern mathematical cartography in Europe over the two hundred years between fourteen hundred and sixteen hundred. Ptolemaic mathematical cartography re-entered Europe in Northern Italy with the first translation into Latin of his Geographia by Jacobus Angulus in 1406. Following this the first modern first modern cartographers, including Paolo dal Pozzo Toscanelli, were also situated in Northern Italy. By the middle of the fifteenth century the main centre of cartographical activity had moved north to Vienna and was centred around Kloster-Neuburg and the University with its First Viennese School of Mathematics, Georg von Peuerbach and Johannes Regiomontanus. Towards the end of the century printed editions of Ptolemaeus’ work began to appear both north and south of the Alps. The beginning of the sixteenth century saw the main centres of cartographic development in the Southern German sphere. Two principle schools are identifiable, the Nürnberg-Vienna school, whose main figures are Johannes Stabius, Peter Apian and Johannes Schöner, and the South-Western school with Waldseemüller and Ringmann in Saint-Dié-des-Vosges and Sebastian Münster in Basel. Again by the middle of the century the centre had once again moved northwards to Leuven and the Flemish school founded by Gemma Frisius and including the two great atlas makers Abraham Ortelius and Gerard Mercator. At the start of the seventeenth century the final step northwards had been taken and the new state of The United Provinces (The Netherlands) had taken the lead in modern cartography. This final step is the subject of this post.

Willem Janszoon Blaeu was born into a prosperous herring trading family in Alkmaar or Uitgeest in 1471. As would have been expected he was sent at an early age to Amsterdam to learn the family trade but it did not appeal to him and he worked instead as a carpenter and clerk in the office of his cousin. In late 1595 his life took a radical turn when he travelled to Hven to study astronomy under Tycho Brahe. It is not known what level of foreknowledge Blaeu took to Hven with him but he spent six months there studiously learning astronomy, instrument making, geodesy and cartography with Tycho and his staff. When he started his observing marathon Tycho had had a large brass globe constructed on which he, over the years, engraved the positions of all the stars that he had measured. Blaeu was given permission to transfer this data to a globe of his own. In 1596 he returned to Alkmaar and his wife Maertgen Cornilisdochter who bore his eldest son Joan on 21 September. On 21 February 1598 Blaeu in Alkmaar and Tycho in Hamburg both observed a lunar eclipse to determine the relative longitude of the two cities.

Portrait of Willem Janszoon Blaeu Artist unknown

Sometime in 1598/9 Blaeu took his family to Amsterdam and set up shop as a printer, instrument maker, globe maker and cartographer; making his first celestial globe, 34 cm diameter, for Adriaan Anthoniszoon, using Tycho’s data; this was the first publication of that data. However Blaeu’s new career was not going to be simple as he had an established competitor, Jocodus Hondius.

Jocodus Hondius was born Joost de Hondt in Wakken and grew up in Ghent, both now in Belgium, on 14 October 1563. He received an education in mathematics and learnt engraving, drawing and calligraphy. He had already established himself as a successful engraver when he was forced by the Spanish, as a Calvinist, to flee to London in 1584. In London he worked for and with Richard Hakluyt and Edward Wright and expanded his knowledge of geography and cartography through contact with the English explorers Francis Drake, Thomas Cavendish and Walter Raleigh. Around 1589 he published a wall map in London showing Drake’s voyage around the world. In 1593 he moved back to The Netherlands, establishing himself in Amsterdam.

Self-portrait of Jodocus Hondas taken from one of his maps

Portrait of Francis Drake by Jodocus Hondas from his Drake world map

He formed an alliance with the Plantin printing house in Leiden for who he made several globes. In 1602 he matriculated at the University of Leiden to study mathematics. In 1604 he made the most important decision of his career in that he bought the copper printing plates of the of both Mercator’s edition of Ptolemaeus’ Geographia and Mercator’s Atlas from his heirs.He published a new edition of Mercator’s Ptolemaeus, Claudïï Ptolemaeï Alexandrini geographicae libri octo graecog latini, in the same year. He set up his own publishing house in Amsterdam in December 1604. In the sixteenth century Mercator’s Atlas had failed to establish itself in a market dominated by Ortelius’ Theatum Orbis Terrarum, however Hondius republished it in 1606 with 36 new maps and it became a best seller.

Atlas sive Cosmographiae Meditationes de Fabrica Mundi et Frabicati Figura
Mercator (left) and Hondius (right) shown working together on tittle page of 1630 Atlas
Slightly ironical as they never met and both were dead by then.

Meanwhile Blaeu had established himself as a globe maker and astronomer. Following the tradition established by Johannes Schöner and continued by Mercator Blaeu issued a pair of 23.5 cm globes, terrestrial and celestial, in 1602. His rival Hondius introduced the southern constellation on a celestial globe produced in cooperation with the astronomer-cartographer Petrus Plancius in 1598. Blaeu followed suite in 1603. Hondius produced a pair of 53.5 cm globes in 1613; Blaeu countered with a pair of 68 cm globes in 1616, which remained the largest globes in production for over 70 years.

Hondas celestial globe 1600
Source: Linda Hall Library

A matching pair of Blaeu globes

As an astronomer Blaeu discovered the star P Cygni, only the third variable star to be discovered. In 1617 Willebrord Snellius published his Eratosthenes Batavus (The Dutch Eratosthenes) in which he described his measurement of a meridian arc between Alkmaar and Bergen op Zoom. This was done in consultation with Blaeu, who had learnt the art of triangulation from Tycho, using a quadrant, with a radius of more than 2 metres, constructed by Blaeu. Blaeu specialised in publishing books on navigation beginning in 1605 with his Nieuw graetbouck and established himself as the leading Dutch publisher of such literature.

Source: Wikimedia Commons

Title page
Source: Wikimedia Commons

Quadrant constructed by Blaeu for Snellius now in Museum Boerhaave in Leiden
Source: Wikimedia Commons

Jodocus Hondius died in 1612 and his sons Jodocus II and Henricus took over the publish house later going into partnership with Jan Janszoon their brother in law. They continued to publish new improved version of the Mercator-Hondius Atlas. Blaeu had already established himself as the successful publisher of wall maps when he began planning a major atlas to rival that of the house of Hondius. That rivalry is also reflected in a name change that Blaeu undertook in 1617. Up till then he had signed his work either Guilielmus Janssonius or Willem Janszoon, now he started add the name Blaeu to his signature probably to avoid confusion with Jan Janszoon (Janssonius), his rival.

Jan Janszoon Original copperplate from his Atlas Novus 1647

In 1630 the strangest episode in the battle of the globes and atlases took place when Jodocus II’s widow sold 37 of the copper plates of the Mercator-Hondius Atlas to Willem Blaeu. He published them together with maps of his own in his Atlantic Appendix in 1631. In 1636 Blaeu published the first two volumes of his own planned world atlas as Atlas Novus or Theatrum Orbis Terrarum, thus reviving the old Ortelius name.

In 1633 the States General (the government of the United Provinces) appointed Blaeu mapmaker of the Republic. In the same year he was appointed cartographer and hydrographer of the Vereenighde Oostindische Compagnie (VOC) – The Dutch East India Company. His son Joan inherited the VOC position, as did his grandson Joan II; The Blaeu family held this prestigious position from 1633 till 1712.

Willem Blaeu had great plans to publish several more volumes of his world atlas but he didn’t live to see them realised, dying 21 October 1638. The publishing house passed to his two sons Joan (1596-1673) and Cornelis (c.1610-1644). The last two volumes prepared by Willem appeared in 1640 and 1645. Joan completed his father’s atlas with a sixth volume in 1655.

Along with all his other achievements Willem Janszoon Blaeu made a substantial improvement to the mechanical printing press by adding a counter weight to the pressure bar in order to make the platen rise automatically. This ‘Blaeu’ or ‘Dutch’ press became standard throughout the low countries and was also introduced into England. The first printing press introduced into America in 1639 was a Blaeu press.

Although he held a doctorate in law, Joan devoted his life to the family cartographic publishing business. In 1662 he set the high point of the atlas battle with the House of Hondius with the publication of the Atlas Maior; containing 600 double page maps and 3,000 pages of text it was the most spectacular atlas of all time. Along with its lavish maps the Atlas Maior contained a map of Hven and pictures of the house and stellar observatory on the island where Willem Janszoon Blaeu first learnt his trade. Whereas Willem was careful not to take sides in the dispute between the different systems for the cosmos – geocentric, heliocentric, geo-heliocentric – in the Atlas Maior, Joan committed to heliocentricity.

Joan Blaeu. By J.van Rossum
Source: Wikimedia Commons

Blaeu Atlas Maior 1662-5, Volume 1
Nova Et Accvratissima Totius Terrarvm Orbis Tabvla
Source: National Library of Scotland

The rivalry between the Houses of Hondius and Blaeu, pushing each other to new heights of quality and accuracy in their maps and globes led to them totally dominating the European market in the first half of the sixteenth century, particularly in the production of globes where they almost had a monopoly. Globes in the period, which weren’t from one of the Amsterdam producers, were almost always pirated copies of their products.

As an interesting footnote, as with all things mathematical England lagged behind the continent in cartography and globe making. Although there had been earlier single globes made in on the island, England’s first commercial producer of terrestrial and celestial globes, Joseph Moxon, learnt his trade from Willem Janszoon Blaeu in Amsterdam. In 1634 Blaeu had published a manual on how to use globes, Tweevoudigh onderwijs van de Hemelsche en Aerdsche globen (Twofold instruction in the use of the celestial and terrestrial globes). In the 1660s, Moxon published his highly successful A Tutor to Astronomie and Geographie. Or an Easie and speedy way to know the Use of both the Globes, Cœlestial and Terrestrial : in six Books, which went through many editions, however the first edition was just an English translation of Blaeu’s earlier manual.

The Dutch painter Jan Vermeer often featured globes and maps in his paintings and it has been shown that these are all reproductions of products from the Blaeu publishing house.

Vermeer’s Art of Painting or The Allegory of Painting (c. 1666–68)
With Blaeu Wall Map
Google Art Project Source: Wikimedia Commons

Jan Vermeer The Astronomer with Blaeu celestial globe and right on the wall a Blaeu wall map
Source: Wikimedia Commons

Jan Vermeer The Geographer with Blaeu terrestrial globe and again right a Blaeu wall map
Source: Wikimedia Commons

The Blaeu wall map used in Vermeers’ The Astronomer and The Geographer

We tend to emphasise politicians, artists and big name scientists, as the people who shape culture in any given age but the cartographic publishing houses of Hondius and Blaeu made significant contributions to shaping the culture of The United Provinces in the so-called Dutch Golden Age and deserve to be much better known than they are.

 

 

 

 

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All at sea

As I’ve said more than once in the past, mathematics as a discipline as we know it today didn’t exist in the Early Modern Period. Mathematics, astronomy, astrology, geography, cartography, navigation, hydrography, surveying, instrument design and construction, and horology were all facets or sub-disciplines of a sort of mega-discipline that was the stomping ground of the working mathematicus, whether inside or outside the university. The making of sea charts – or to give it its technical name, hydrography – combines mathematics, geography, cartography, astronomy, surveying, and the use of instruments so I am always happy to add a new volume on the history of sea charts to my collection of books on cartography and hydrography.

I recently acquired the “revised and updated” reissue of Peter Whitfield’s Charting the Oceans, a British Library publication.

The original edition from 1996 carried the subtitle Ten Centuries of Maritime Maps (missing from the new edition) and this is what Whitfield delivers in his superb tome. The book has four sections: Navigation before Charts, The Sea-Chart and the Age of Exploration, Sea-Charts in Europe’s Maritime Age and War, Empire and Technology: The Last 200 years. As can be seen from these section titles Whitfield not only deals with the details of the hydrography and the charts produced but defines the driving forces behind the cartographic developments: explorations, trade, war and colonisation. This makes the book to a valuable all round introduction of the subject highly recommended to anybody looking for a general overview of the topic.

However, what really makes this book very special is the illustrations.

The Nile Delta, c. 1540, from Piri Re’is Kitab-i Bahriye
Charting the Oceans page 90

A large format volume, more than fifty per cent of the pages are adorned with amazing reproductions of the historical charts that Whitfield describes in his text.

Willem van de Velde II, Dutch Ships in a Calm, c. 1665
Charting the Oceans page 132

Beautifully photographed and expertly printed the illustrations make this a book to treasure. Although not an academic text, in the strict sense, there is a short bibliography for those, whose appetites wetted, wish to delve deeper into the subject and an excellent index. Given the quality of the presentation the official British Library shop price of £14.99 is ridiculously low and a real bargain. If you love maps all I can say is buy this book.

Title page to the English edition of Lucas Janszoon Waghenaer’s Spiegheel der Zeevaert, 1588
Charting the Oceans page 109

The A Very Short Introduction series of books published by the Oxford University Press is a really excellent undertaking. Very small format 11×17 and a bit cm, they are somewhere between 100 and 150 pages long and provide a concise introduction to a single topic. One thing that distinguishes them is the quality of the authors that OUP commissions to write them; they really are experts in their field. The Galileo volume, for example, is authored by Stillman Drake, one of the great Galileo experts, and The Periodic Table: A Very Short Introduction was written by Mr Periodic Table himself, Eric Scerri. So when Navigation: A Very Short Introduction appeared recently I couldn’t resist. Especially, as it is authored by Jim Bennett a man who probably knows more about the topic then almost anybody else on the surface of the planet.

Mr Bennett does not disappoint, in a scant 135-small-format-pages he delivers a very comprehensive introduction to the history of navigation. He carefully explains all of the principal developments down the centuries and does not shy away from explaining the intricate mathematical and astronomical details of various forms of navigation.

Navigation: A Very Short Introduction page 50

The book contains a very useful seven page Glossary of Terms, a short but very useful annotated bibliography, which includes the first edition of Whitfield’s excellent tome, and a comprehensive index. One aspect of the annotated bibliography that particularly appealed to me was his comments on Dava Sobel’s Longitude; he writes:

“[It] …has the disadvantage of being very one-sided despite the more scrupulous work found in in earlier books such as Rupert T. Gould, The Marine Chronometer: Its History and Development (London, Holland Press, 1960); and Humphrey Quill, John Harrison: The Man Who Found Longitude (London, John Baker, 1966)”

I have read both of these books earlier and can warmly recommend them. He then recommends Derek Howse, Greenwich Time and the Discovery of Longitude (Oxford, Oxford University Press, 1980), which sits on my bookshelf, and Derek Howse, Nevil Maskelyne: The Seaman’s Astronomer, (Cambridge, Cambridge University Press, 1989), which I haven’t read. However it was his closing comment that I found most interesting:

“A welcome recent corrective is Richard Dunn and Rebekah Higgitt, Ships, Clocks, and Stars: The Quest for Longitude (Collins: Glasgow, 2014)”. A judgement with which, regular readers of this blog will already know, I heartily concur.

The flyleaf of the Navigation volume contains the following quote:

‘a thoroughly good idea. Snappy, small-format…stylish design…perfect to pop into your pocket for spare moments’ – Lisa Jardine, The Times

Another judgement with which I heartily concur. Although square centimetre for square centimetre considerably more expensive than Whitfield’s book the Bennett navigation volume is still cheap enough (official OUP price £7.99) not to break the household budget. For those wishing to learn more about the history of navigation and the closely related mapping of the seas I can only recommend that they acquire both of these excellent publications.

 

 

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Filed under History of Cartography, History of Mathematics, History of Navigation

The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

The title of this post is the subtitle of Dava Sobel’s Longitude, her mega bestselling account of the life and work of the eighteenth-century clock maker John Harrison; probably the biggest selling popular #histSTM book of all time.

I’m quite happy to admit that when I first read it I was very impressed by her account of a man I didn’t know from a period of history with which I was not particularly well acquainted. However, because I was very impressed, I went looking for more information about the history of John Harrison and the marine chronometer. I found and read quite a lot of academic literature on both topics and came to the realisation that Sobel’s account was not really the true story and that she had twisted the facts to make for a more exciting story but quite far removed from the true narrative.

P.L. Tassaert’s half-tone print of Thomas King’s original 1767 portrait of John Harrison, located at the Science and Society Picture Library, London
Source: Wikimedia Commons

The next segment of the subtitle is also not true. Harrison was supported and encouraged in his endeavours by George Graham, possibly the greatest eighteenth-century English clockmaker, and James Short, almost certainly the greatest telescope maker in the world in the eighteenth century. Both men were important and highly influential figures in the scientific and technological communities of the period. Their support of Harrison rather gives the lie to the claim that Harrison was a lone genius.

George Graham
Source: Wikimedia Commons

The final segment of the subtitle is also highly inaccurate. The problem that Harrison and others were working on in the eighteenth century was a reliable method of determining longitude at sea. They were trying to solve a technological problem not a scientific one. The scientific problem had already been solved in antiquity. Scholars in ancient Greece already knew that to determine the difference in longitude between two locations, one ‘merely’ had to determine the local time difference between them; knowing this the problem was how to determine that time difference, as I said a technological problem.

In antiquity and up to the early modern period cartographers and astronomers (usually the same person) used astronomical phenomena such as solar or lunar eclipses. Observers determined the local time of the occurrence of a given astronomical phenomenon at two different locations and it was then possible to determine their longitudinal difference. Unfortunately eclipses are not very frequent occurrences and so this method has rather limited usefulness. Something else had to be developed.

In the early seventeenth century both Galileo Galilei and Simon Marius discovered the four largest moons of Jupiter and Galileo realised that the orbits of these moons and their appearances and disappearances as the circled Jupiter could, if tabulated accurately enough, be used as a clock to determine longitude. Towards the end of the seventeenth century Giovanni Domenico Cassini and Ole Rømer succeeded in producing the necessary tables and Galileo’s idea could be put into practice. Whilst this method was very successful for cartographers on land, on a rolling ship it was not possible to observe the Jupiter moons accurately enough with a telescope to be able to apply this method; something else had to be used.

The two solutions that came to be developed in the eighteenth century and form the backbone of Sobel’s book, the lunar distance method (lunars) and the marine chronometer, were both first suggested in the sixteenth century, the former by Johannes Werner and the latter by Gemma Frisius. Other methods were suggested but proved either impractical or downright impossible. For lunars you need accurate lunar orbit tables and an accurate instrument to determine the position of the moon. Tobias Mayer provided the necessary tables and John Hadley the instrument with his sextant. For the clock method you require a clock that has a high level of accuracy over a long period of time and which retains that accuracy under the often very adverse conditions of a sea voyage; this is the technological problem that Harrison solved. Sobel presents the two methods as in competition but for navigators they are in fact complimentary and they were both used. As my #histsci soul sister Rebekah ‘Becky’ Higgitt constantly repeats, with the marine chronometer you can carry longitude with you, but if you chronometer breaks down you can’t find it, whereas with lunars you can find longitude, as James Cook did in fact do on one of his voyages.

As I said above, I began to seriously doubt the veracity of Sobel’s account through my own study of the academic accounts of the story, these doubts were then confirmed as I began to follow the blog of the Longitude Board research project set up by Cambridge University and the Maritime Museum in Greenwich, of which Becky Higgitt was one of the lead researchers. For a more balanced and accurate account of the story I recommend Finding Longitude the book written by Becky and Richard Dunn to accompany the longitude exhibition at the Maritime Museum, one of the products of the research project.

Recently I have become fully aware of another aspect of the Harrison story that Sobel does not cover. I say fully aware because I already knew something of it before reading David S. Landes’ excellent Revolution in Time: Clocks and the making of the Modern World (Harvard University Press, 1983). Landes covers the whole history of the mechanical clock from the Middle Ages through to the quartz wristwatch. One of his central themes is the increasing accuracy of clocks down the ages in which the invention of the marine chronometer played a central role, so he devotes a whole chapter to Harrison’s endeavours.

Landes quite correctly points out that after a lifetime of experimentation and ingenious invention John Harrison did indeed produce a solution to the technological problem of determining longitude with a clock. An astute reader with a feel for language might have noticed that in the previous sentence I wrote ‘a solution’ and not ‘the solution’ and therein lies the rub. Over the years that he worked on the problem Harrison produced many ingenious innovations in clock making in order to achieve his aim, an accurate, reliable, highly durable timepiece, however the timepiece that he finally produced was too complex and too expensive to be practicable for widespread everyday service at sea. Harrison had, so to speak, priced himself out of the market.

Harrison’s “Sea Watch” No.1 (H4), with winding crank
Source: Wikimedia Commons

Harrison was by no means the only clock maker working on a viable marine chronometer in the eighteenth century and it is actually his competitors who in the end carried away the laurels and not Harrison. Two clockmakers who made important contributions to the eventual development of a mechanically and financially viable marine chronometer were the Frenchman Pierre Le Roy and Swiss Ferdinand Berthoud, who were bitter rivals.

Pierre Le Roy (1717–1785)
Source: Wikimedia Commons

Plans of Le Roy chronometer
Source: Wikimedia Commons

Ferdinand Berthoud (1727–1807)
Source: Wikimedia Commons

Berthoud marine clock no.2, with motor spring and double pendulum wheel, 1763
Source: Wikimedia Commons

Neither of them can be said to have solved the problem but the work of both of them in different ways led in the right direction. Another contributor was George Graham’s one time apprentice, Thomas Mudge, his highly praised marine chronometer suffered from the same problem as Harrison’s too complex and thus too expensive to manufacture.

The two English clock makers, who actually first solved the problem of a viable marine chronometer were John Arnold and Thomas Earnshaw, who also became bitter rivals. This rivalry involved accusations of theft of innovations and disputes over patents. In the end it was John Arnold and Thomas Earnshaw, who became the most successful of the early clock makers, who worked on the development of the marine chronometer.


Chronometer-maker John Arnold (1736–1799) (attributed to Mason Chamberlin, ca. 1767)
Source: Wikimedia Commons

Thomas Earnshaw (!749–1829)
Source: Wikimedia Commons

Earnshaw chronometer No. 506
Source: Wikimedia Commons

I don’t intend to go into the details of which innovations in clock manufacture each of the man listed above contributed to the development of the marine chronometer that would go on to become an essential navigation tool in the nineteenth century. What I wish to make clear is exactly the same point as my essay on the history of the reflecting telescope for AEON made. From its first conception by Gemma Frisius in the sixteenth century, through the failure of Christiaan Huygens to realise it with his pendulum clock in the late seventeenth century (not discussed here), over its first successful realisation by John Harrison and on to the creation of a viable model by a succession of eighteenth-century clock makers, the marine chronometer was not the product of a single man’s (John Harrison’s) genius but a tool that evolved through the endeavours of a succession of dedicated inventors and innovators. Scientific and technological progress is teamwork.

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Filed under History of Navigation, History of Technology, Myths of Science

One line to rule them all

A standard concept in the modern politico-military terminology is that of mission creep. This describes the, in the last sixty or seventy years often observed, phenomenon of a military intervention by a dominant power that starts with a so-called police action with a couple of hundred combatants and then within a couple of years grows to a full scale military operation involving thousands of troops and the expenditure of sums of money with an eye watering large number of zeros at the end. Famous examples of mission creep were the Americans in Viet Nam and the Russians in Afghanistan. In fact since the Second World War the American have become world champions in mission creep.

As a historian I, and I strongly suspect virtually all of my historian colleagues, experience a form of mission creep in every field of study to which I turn my attention. In fact the progress of my entire career as a historian of science has been one massive example of mission creep. It all started, at the age of sixteen, when I first learned that Isaac Newton was the (co)discoverer/inventor[1] of the calculus that I so loved at school. (Yes, I know that makes me sound a little bit strange but there’s no accounting for taste). This of course set me off on the trail of the whole history of mathematics, but that is not what I want to talk about here; let us stick with Newton. At some point I started to wonder why Newton, whom I saw as very much the theoretical mathematician and physicist, should have invented a telescope. This set me on the trail of the entire history of the telescope and because the telescope is an optical instrument, with time, the history of optics, not just in the early modern period but backwards through time into the European Middle Ages, the Islamic Empire and Antiquity. Of course Newton is most well known as physicist and astronomer and at some point I started investigating the pre-history of his work in astronomy. This eventually led me back to the Renaissance astronomers, not just Copernicus but all those whose work provided the foundations for Copernicus’s own work.

At some point it became very clear to me that to talk of Renaissance astronomers was in some sense a misnomer because those who pursued the study of astronomy in this time did so within a discipline that encompassed not just astronomy but also astrology, cartography (with a large chunk of geography and history in the mix), navigation, surveying, geodesy as well as the mathematical knowledge necessary to do all of these things. These were not separate disciplines as we see them now but different facets of one discipline. Over the years my studies have expanded to cover all of these facets and one into which I have delved very deeply is the history of cartography with the associated history of surveying. All of this is a rather longwinded explanation of why I have been reading Charles Withers’ new book Zero Degrees[2]

 

This book describes the history of how the Greenwich Meridian became the Prime Meridian.

A brief explanation for those who are not really clear what a meridian is; a meridian (or line of longitude) is any ‘straight’ line on the globe of the of the earth connecting the North Pole with the South Pole, where here straight means taking the shortest path between the two poles, as a meridian is by nature curved because it lies on the surface of the globe. Meridians are by their very nature arbitrary, abstract and non-real. We can chose to put a meridian wherever we like, they are an artificial construct and not naturally given. The Prime Meridian is a singular, unique, universally accepted meridian from which all other meridians (lines of longitude) are measured. The recognition of the necessity for a Prime Meridian is a fairly recent one in human history and Withers’ book deals with the history of the period between that recognition in the Early Modern Period to the realisation of a Prime Meridian at the beginning of the twentieth century.

The first thing that Withers made me aware of is that a meridian is not a singular object but one that has at least four separate functions and at least two different realisations. Meridians are used for navigation, for time determination, for cartography and for astronomy. The latter is because astronomers project our latitude and longitude coordinate system out into space in order to map the heavens. Nothing says that one has to use the same meridians for each of these activities and for much of the period of history covered by Withers people didn’t.

On the realisation of meridians Withers distinguishes two geographical and observed. The majority of meridians in use before the late seventeenth century were geographical. What does this mean? It meant that somebody simply said that they make their measurements or calculations from an imaginary line, the meridian, through some given geographical point on the surface of the earth. Ptolemaeus to whom we own our longitude and latitude coordinate system, although he had predecessors in antiquity, used the Azores as his zero meridian although he didn’t know with any real accuracy where exactly the Azores lay. Also the Azores is a scattered island group and he doesn’t specify exactly where within this island group his zero meridian ran. We have a lovely example of the confusion caused by this inaccuracy. On 4 May 1493 Pope Alexander VI issued the papal bull Inter caetera, which granted the Crowns of Castile and Aragon all the lands to the west and south of a meridian 100 leagues and south of the Azores or the Cape Verde islands.

This led to a whole series of treaties and papal bulls carving up the globe between Spain (Castile and Aragon) and Portugal. The 1494 Treaty of Tordesillas moved the line to a meridian 370 leagues west of the Portuguese Cape Verde islands now explicitly giving Portugal all new discoveries east of this meridian. I’m not going to go into all the gory details but this led to all sorts of problems because nobody actually knew where exactly this meridian or its anti-meridian on the other side of the globe lay. Ownership disputes in the Pacific between Spain and Portugal were pre-programmed. These are classical examples of geographical meridians.

The Cantino planisphere of 1502 shows the line of the Treaty of Tordesillas.
Source: Wikimedia Commons

The first observed meridian in the Early Modern Period was the Paris Meridian surveyed by Jean-Félix Picard in the 1660s. Such meridians are called observed because their exact position on the globe is determined astronomically using a transit telescope.

In the Early Modern Period there was no consensus as to which meridian should be used for which purpose and on the whole each country used its own zero meridian. I fact it was not unusual for several different zero meridians to be used for different purposes or even the same purpose, with one country. For geographers, cartographers and navigators crossing borders chaos ruled. The awareness that a single Prime Meridian would be beneficial for all already existed in the seventeenth century but it wasn’t until the nineteenth century that serious moves were made to solve the problem.

The discussion were long and very complicated and involved scientific, political and pragmatic considerations, which often clashed with each other. On the political level nationalism, of course, raised its ugly head. Surprisingly, at least for me, there was also a very heated discussion as to whether the Prime Meridian should be a geographical or an observed meridian. I personally can discern no reasons in favour of a geographical Prime Meridian but various participants in the discussions could. Another problem was one or more Prime Meridians? Separate ones for cartography, navigation, astronomy and time determination.

Withers deals with all of these topics in great detail and very lucidly in his excellent summery of all of the discussions leading up to the International Meridian Conference in Washington in 1884, which forms the climax of his book.

The delegates to the International Meridian Conference in Washington in 1884
Source: Wikimedia Commons

This is a truly fascinating piece of the history of science and in Withers it has found a more than worthy narrator and I recommend his book whole-heartedly for anybody who might be interested in the topic. Very important is his penultimate chapter Washington’s Afterlife. Every year in October people in the Internet announce that on this day in 1884 (I can’t be bothered to look up the exact date) the Greenwich Meridian became the world’s Prime Meridian and every year my #histsci soul sisterTM Rebekah ‘Becky’ Higgitt (who played a significant role in the genesis of Withers’ book, as can be read in the acknowledgements) announces no it didn’t, the resolutions reached in Washington were non-binding. In fact the acceptance of Greenwich as the Prime Meridian took quite some time after the Washington Conference, some even accepting it initial only for some but not all the four functions sketched above. France, whose Paris Meridian was the main contender against Greenwich, only finally accepted Greenwich as the Prime Meridian in 1912.

I do have a couple of minor quibbles about Withers’ book. In the preface he outlines the structure of the book saying what takes place in each section. He repeats this in greater detail in the introduction. Then he starts each chapter with a synopsis of the chapter’s contents, often repeating what he has already said in the introduction, and closes the chapter with a summary of its contents. It was for this reader a little bit too much repetition. My second quibble concerns the illustrations and tables of which there are a fairly large number in the book. These are all basically black and white but are in fact printed black on a sort of pastel grey. I assume that the book designer thinks this makes them somehow artistically more attractive but I personally found that it makes it more difficult to determine the details, particularly on the many maps that are reproduced. Whatever I wouldn’t let these rather personal minor points interfere with my genuine whole-hearted recommendation.

[1] Chose the word that best fits your personal philosophy of mathematics

[2] Charles W. J. Withers, Zero Degrees: Geographies of the Prime Meridian, Harvard University Press, Cambridge Massachusetts, London England, 2017

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Filed under History of Cartography, History of Navigation, History of science