Category Archives: 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

Measure for measure

The Brexit vote in the UK has produced a bizarre collection of desires of those Leavers eager to escape the poisonous grasp of the Brussels’ bureaucrats. At the top of their list is a return of the death penalty, a piece of errant stupidity that I shall leave largely uncommented here. Not far behind is the wish to abandon the metric system and to return to selling fruit and vegetables in pounds and ounces. This is particularly strange for a number of reasons. Firstly the UK went metric in 1965, six years before it joined the EU. Secondly EU regulations actually allows countries to use other systems of weights and measures parallel to the metric system, so there is nothing in EU law stopping greengrocers selling you a pound of carrots or bananas. Thirdly the country having gone metric in 1965, anybody in the UK under the age of about fifty is going to have a very hard time knowing what exactly pounds and ounces are.

Most readers of this blog will have now gathered that I have spent more than half my life living in Germany. Germany is of course one of the founding states of the EU and as such has been part of it from the very beginning in 1957. The various states that now constitute Germany also went metric at various points in the nineteenth century, the earliest in 1806-15, and the latest in 1868. However the Germans are a very pragmatic folk and I can and do buy my vegetables on the market place in Erlangen in pounds and half pounds. The Germans like most Europeans used variation of the predecessors to the so-called Imperial system of weights and measures and simple re-designated the pound (Pfund in German) to be half a kilo. The Imperial pound is actually approximately 454 grams and for practical purposes when buying potatoes or apples the 46-gram difference if negligible. Apparently the British are either too stupid or too inflexible to adopt such a pragmatic solution.

At the beginning of the month Tory dingbat and wanna be journalist Simon Heffer wrote an article in The Telegraph with the glorious title, Now that we are to be a sovereign nation again, we must bring back imperial units. I haven’t actually read it because one has to register in order to do so and I would rather drink bleach than register with the Torygraph. I shall also not link to the offending article, as it will only encourage them. Heffer charges into the fray thus:

But I know from my postbag that there is another infliction from the decades of our EU membership that many would like to be shot of, and that was the imposition of the metric system on large parts of our life. 

Consumer resistance ensured that our beer is still served in pints (though not in half-pint and pint bottles when bought in supermarkets: brewers please note), and that our signposts are still marked in miles.

As pointed out above it was not the EU who imposed the metric system on British lives but the British government before the UK joined the EU. According to EU regulations you can serve drinks in any quantities you like just as long as the glasses are calibrated, so keeping the traditional pint glasses and mugs in British pubs was never a problem. Alcohol is sold in Germany in a bewildering range of different size glasses depending on the local traditions. My beer drinking German friends (the Germans invented the stuff, you know) particularly like pints of beer because they say that they contain a mouthful more beer that a half litre glass. Sadly many bars in Franconia have gone over to selling beer in 0.4litre glasses to increase their profits, but I digress.

UK signposts are still marked in miles because the government could not afford the cost of replacing all of them when the UK went metric. Expediency not national pride was the motivation here.

Just before Heffer’s diatribe disappears behind the registration wall he spouts the following:

But we have been forced on to the Celsius temperature scale, which is less precise than Fahrenheit

When I read this statement I went back to check if the article had been published on 1 April, it hadn’t! Is the international scientific community aware of the fact that they have been conned into using an inaccurate temperature scale? (I know that scientist actually use the Kelvin temperature scale but it’s the same as the Celsius scale with a different zero point, so I assume by Heffer’s logic(!) it suffers from the same inaccuracy). Will all of those zillions of experiments and research programmes carried out using the Celsius/Kelvin scale have to be repeated with the accurate Fahrenheit scale? Does Simon Heffer actually get paid for writing this crap?


Anders Celcius Portrait by Olof Arenius Source: Wikimedia Commons


Daniel Gabriel Fahrenheit

Like myself on being confronted with the bring back imperial weights and measures madness lots of commentators pointed out that the UK went metric in 1965 but is this true? No, it isn’t! The UK actually went metric, by act of parliament over one hundred years earlier in 1864! The nineteenth century contains some pretty stirring history concerning the struggles between the metric and imperial systems and we will now take a brief look at them.

As soon as it became in someway necessary for humans to measure things in their environment it was fairly obvious that they would use parts of their body to do so. If we want a quick approximate measure of something we still pace it out or measure it with the length of an arm or the span of our fingers. So it was natural that parts of the body became the units of measurement, the foot, the forearm, the arm span and so on and so forth. This system of course suffers from the fact that we are not all the same size. My foot is shorter than yours; my forearm is longer than my partners. This led cultures with a strong central bureaucracy to develop standard feet and forearms. The various Fertile Crescent cultures developed sophisticated weights and measures systems, as did the Roman Empire and it is the latter that is the forefather of the imperial system. The Roman foot was between 29.5 and 30 cm, the pace was 2.5 feet and the Roman mile was 5000 feet. The word mile comes from the Latin for thousand, mille. The Roman military, which was very standardised, carried the Roman system of weights and measures to large parts of Europe thus establishing their standards overall.

With the collapse of the Roman Empire their standardised system of weights and measures slowly degenerated and whilst the names were retained their dimensions varied from district to district and from town to town. In the eighth and ninth centuries Karl der Große (that’s Charlemagne for the Brits) succeeded in uniting a substantial part of Europe under his rule. Although he was uneducated and illiterate he was a strong supporter of education and what passed at the time for science and amongst his reforms he introduced a unified system of weights and measures for his entire empire, another forefather of the imperial system. Things are looking quite grim for the anti-European supporters of the imperial system; it was born in Rome the birthplace of the EU and was reborn at the hands of a German, nothing very British here.

Karl’s attempt to impose a unified system of weights and measures on his empire was not a great success and soon after his death each district and town went back to their own local standards, if they ever left them. Throughout the Middle Ages and deep into the Early Modern Period traders had to live with the fact that a foot in Liège was not the same as a foot in Venice and a pound in Copenhagen was not a pound in Vienna.

This chaos provided work for the reckoning masters producing tables of conversions or actually doing the conversions for the traders, as well as running reckoning schools for the apprentice traders where they taught the arithmetic and algebra necessary to do the conversions, writing the textbooks for the tuition as well. The lack of unity in currency and mensuration in medieval Europe was a major driving force in the development algebra – the rule of three ruled supreme.

At the beginning of the seventeenth century Simon Stevin and Christoph Clavius introduced decimal fractions and the decimal point into European mathematics, necessary requirements for a decimal based metric system of mensuration. Already in the middle of the seventeenth century just such a system emerged and not from the dastardly French but from a true blue English man, who was an Anglican bishop to boot, polymath, science supporter, communicator, founding member of the Royal Society and one of its first secretaries, John Wilkins (1614–1672).

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Asked by the society to devise a universal standard of measure he devoted four pages of his monumental An Essay towards a Real Character and a Philosophical Language (1668) to the subject.


Title Page Source: Wikimedia Commons

He proposed a decimal system of measure based on a universal measure derived from nature for use between ‘learned men’ of various nations. He considered atmospheric pressure, the earth’s meridian and the pendulum as his universal measure, rejecting the first as susceptible to variation, the second as immeasurable and settled on the length of the second pendulum as his measure of length. Volume should be the cubic of length and weight a cubic standard of water. To all extents and purposes he proposed the metric system. His proposal fell, however, on deaf ears.


European units of length in the first third of the 19th century Part 1


European units of length in the first third of the 19th century Part 2

As science developed throughout the seventeenth and eighteenth century it became obvious that some sort of universal system of measurement was a necessity and various people in various countries addressed to subject. In 1790 the revolutionary Assemblée in France commissioned the Académie to investigate the topic. A committee consisting of Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Nicolas de Condorcet, all leading scientific figures, recommended the adoption of a decimal metric system based on one ten-millionth of one quarter of the Earth’s circumference. The proposal was accepted by the Assemblée on 30 March 1791. Actually determining the length of one quarter of the Earth circumference turned into a major project fraught with difficulties, which I can’t do justice to here in an already overlong blog post, but if you are interested then read Ken Adler’s excellent The Measure of All Things: The Seven-Year Odyssey That Transformed The World.


Standard meter on the left of the entrance of the french Ministère de la Justice, Paris, France. Source: Wikimedia Commons

However Britain needed a unified system of mensuration, as they still had the problem that every town had different local standards for foot, pound etc. John Herschel the rising leading scientific figure wanted a new decimal imperial system based on the second pendulum but in the end parliament decide to stick with the old imperial system taking a physical yard housed in the Houses of Parliament as the standard for the whole of the UK. Unfortunately disaster struck. The Houses of Parliament burnt down in 1834 and with it the official standard yard. It took the scientists several years to re-establish the length of the official yard and meanwhile a large number were still advocating for the adoption of the metric system.


The informal public imperial measurement standards erected at the Royal Observatory, Greenwich, London, in the 19th century: 1 British yard, 2 feet, 1 foot, 6 inches, and 3 inches. The inexact monument was designed to permit rods of the correct measure to fit snugly into its pins at an ambient temperature of 62 °F (16.66 °C) Source: Wikimedia Commons

The debate now took a scurrile turn with the introduction of pyramidology! An English writer, John Taylor, developed the thesis that the Great Pyramid was constructed using the imperial system and that the imperial system was somehow divine. Strangely his ideas were adopted and championed by Charles Piazzi Smyth the Astronomer Royal of Scotland and even received tacit and indirect support from John Herschel, who rejected the pyramidology aspect but saw Taylor’s pyramid inch as the natural standard of length.

However wiser heads prevailed and the leaders of the British Victorian scientific community made major contributions to the expansion of the metric system towards the SI system, used internationally by scientists today. They applied political pressure and in 1864 the politicians capitulated and parliament passed the Metric (Weights and Measures) Act. This permitted the use of weights and measures in Britain. Further acts followed in 1867, 1868, 1871 and 1873 extending the permitted use of the metre. However the metric system could be used for scientific purposes but not for business. For that, Britain would have to wait another one hundred and one years!

Interestingly, parallel to the discussion about systems of mensuration in the nineteenth century, a discussing took place about the adoption of a single prime meridian for cartographical, navigational, and time purposes. In the end the two main contenders were the observatories in Paris and Greenwich. Naturally neither Britain nor France was prepared to concede to the other. To try and solve the stalemate it was suggested that in exchange for Paris accepting Greenwich as the prime meridian London should adopt the metric system of measurement. By the end of the nineteenth century both countries had nominally agreed to the deal without a formal commitment. Although France fulfilled their half of this deal sometime early in the twentieth century, Britain took until 1965 before they fulfilled their half.

Should the Leavers get their wish and the UK returns to the imperial system of measurement then they will be joining an elite group consisting of the USA, Myanmar and Liberia, the only countries in the world that don’t have the metric system as their national system of measurement for all purposes.


Filed under History of Mathematics, History of Navigation, History of science, Uncategorized

Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus.

There is a strong tendency, particularly in the popular history of science, to write about or present scientists as individuals. This leads to a serious distortion of the way that science develops and in particular propagates the lone genius myth. In reality science has always been a collective endeavour with its practitioners interacting in many different ways and on many different levels. In the Renaissance, when travelling from one end of Europe to the other would take weeks and letters often even longer, one might be excused for thinking that such cooperation was very low level but in fact the opposite was the truth, with scholars in the mathematical sciences exchanging information and ideas throughout Europe. A particularly strong mathematical nexus existed in the Southern German speaking area between the cities of Nürnberg, Ingolstadt and Vienna in the century between 1450 and 1550. Interestingly two of the paintings of the Northern Renaissance artist Hans Holbein the Younger open a door into this nexus.

Holbein (c. 1497–1543) was born in Augsburg the son of the painter and draughtsman Hans Holbein the Elder. As a young artist he lived and worked for a time in Basel where he became acquainted with Erasmus and worked for the printer publisher Johann Froben amongst others. Between 1526 and 1528 he spent some time in England in the household of Thomas More and it is here that he painted the second portrait I shall be discussing. The next four years find him living in Basel again before he returned to England in 1532 where he became associated with the court of Henry VIII, More having fallen out of favour. It was at the court that he painted, what is probably his most well know portrait, The Ambassadors in 1533.

Hans Holbein The Ambassadors Source: Wikimedia Commons

Hans Holbein The Ambassadors
Source: Wikimedia Commons

The painting shows two courtiers, usually identified as the French Ambassador Jean de Dinteville and Georges de Selve, Bishop of Lavaur standing on either side of a set of shelves laden with various books and instruments. There is much discussion was to what the instruments are supposed to represent but it is certain that, whatever else they stand for, they represent the quadrivium, arithmetic, geometry music and astronomy, the four mathematical sciences taught at European medieval universities. There are two globes, on the lower shelf a terrestrial and on the upper a celestial one. The celestial globe has been positively identified, as a Schöner globe and the terrestrial globe also displays characteristics of Schöner’s handwork.

Terrestrial Globe The Ambassadors Source Wikimedia Commons

Terrestrial Globe The Ambassadors
Source Wikimedia Commons

Celestial Globe The Ambassadors Source Wikimedia Commons

Celestial Globe The Ambassadors
Source Wikimedia Commons

Johannes Schöner (1477–1547) was professor for mathematics at the Egidienöberschule in Nürnberg, the addressee of Rheticus’ Narratio Prima, the founder of the tradition of printed globe pairs, an editor of mathematical texts for publication (especially for Johannes Petreius the sixteenth centuries most important scientific publisher) and one of the most influential astrologers in Europe. Schöner is a central and highly influential figure in Renaissance mathematics.

On the left hand side of the lower shelf is a copy of Peter Apian’s Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen (published in Ingolstadt in 1527) held open by a ruler. This is a popular book of commercial arithmetic, written in German, typical of the period. Peter Apian (1495–1552) professor of mathematics at the University of Ingolstadt, cartographer, printer-publisher and astronomer was a third generation representative of the so-called Second Viennese School of Mathematics. A pupil of Georg Tannstetter (1482–1535) a graduate of the University of Ingolstadt who had followed his teachers Johannes Stabius and Andreas Stiborious to teach at Conrad Celtis’ Collegium poetarum et mathematicorum, of which more later. Together Apian and Tannstetter produced the first printed edition of the Optic of Witelo, one of the most important medieval optic texts, which was printed by Petreius in Nürnberg in 1535. The Tannstetter/Apian/Petreius Witelo was one of the books that Rheticus took with him as a present for Copernicus when he visited him in 1539. Already, a brief description of the activities of Schöner and Apian is beginning to illustrate the connection between our three cities.

Apian's Arithmetic Book The Ambassadors Source: Wikimedia Commons

Apian’s Arithmetic Book The Ambassadors
Source: Wikimedia Commons

When Sebastian Münster (1488–1552), the cosmographer, sent out a circular requesting the cartographers of Germany to supply him with data and maps for his Cosmographia, he specifically addressed both Schöner and Apian by name as the leading cartographers of the age. Münster’s Cosmographia, which became the biggest selling book of the sixteenth century, was first published by Heinrich Petri in Basel in 1544. Münster was Petri’s stepfather and Petri was the cousin of Johannes Petreius, who learnt his trade as printer publisher in Heinrich’s printing shop in Basel. The Petri publishing house was also part of a consortium with Johann Amerbach and Johann Froben who had employed Hans Holbein in his time in Basel. Wheels within wheels.

The, mostly astronomical, instruments on the upper shelf are almost certainly the property of the German mathematician Nicolaus Kratzer (1487–1550), who is the subject of the second Holbein portrait who will be looking at.

Nicolas Kratzer by Hans Holbein Source: Wikimedia Commona

Nicolas Kratzer by Hans Holbein
Source: Wikimedia Commona

Born in Munich and educated at the universities of Cologne and Wittenberg Kratzer, originally came to England, like Holbein, to become part of the Thomas More household, where he was employed as a tutor for More’s children. Also like Holbein, Kratzer moved over to Henry VIII’s court as court horologist or clock maker, although the clocks he was responsible for making were more probably sundials than mechanical ones. During his time as a courtier Kratzer also lectured at Oxford and is said to have erected a monumental stone sundial in the grounds of Corpus Christi College. One polyhedral sundial attributed to Kratzer is in the Oxford Museum for the History of Science.

Polyhedral Sundial attributed to Nicolas Kratzer Source: MHS Oxford

Polyhedral Sundial attributed to Nicolas Kratzer
Source: MHS Oxford

In 1520 Kratzer travelled to Antwerp to visit Erasmus and here he met up with Nürnberg’s most famous painter Albrecht Dürer, who regular readers of this blog will know was also the author of a book on mathematics. Dürer’s book contains the first printed instructions, in German, on how to design, construct and install sundials, so the two men will have had a common topic of interest to liven there conversations. Kratzer witnessed Dürer, who was in Antwerp to negotiate with the German Emperor, painting Erasmus’ portrait and Dürer is said to have also drawn a portrait of Kratzer that is now missing. After Kratzer returned to England and Dürer to Nürnberg the two of them exchanged, at least once, letters and it is Kratzer’s letter that reveals some new connections in out nexus.

Albrecht Dürer selfportrait Source: Wikimedia Commons

Albrecht Dürer selfportrait
Source: Wikimedia Commons

In his letter, from 1524, Kratzer makes inquires about Willibald Pirckheimer and also asks if Dürer knows what has happened to the mathematical papers of Johannes Werner and Johannes Stabius who had both died two years earlier.

Willibald Pirckheimer (1470–1530) a close friend and patron of Dürer’s was a rich merchant, a politician, a soldier and a humanist scholar. In the last capacity he was the hub of a group of largely mathematical humanist scholars now known as the Pirckheimer circle. Although not a mathematician himself Pirckheimer was a fervent supporter of the mathematical sciences and produced a Latin translation from the Greek of Ptolemaeus’ Geōgraphikḕ or Geographia, Pirckheimer’s translation provided the basis for Sebastian Münster’s edition, which was regarded as the definitive text in the sixteenth century. Stabius and Werner were both prominent members of the Pirckheimer circle.

Willibald Pirckheimer by Albrecht Dürer Source: Wikimedia Commons

Willibald Pirckheimer by Albrecht Dürer
Source: Wikimedia Commons

The two Johanneses, Stabius (1450–1522) and Werner (1468–1522), had become friends at the University of Ingolstadt where the both studied mathematics. Ingolstadt was the first German university to have a dedicated chair for mathematics. Werner returned to his hometown of Nürnberg where he became a priest but the Austrian Stabius remained in Ingolstadt, where he became professor of mathematics. The two of them continued to correspond and work together and Werner is said to have instigated the highly complex sundial on the wall of the Saint Lorenz Church in Nürnberg, which was designed by Stabius and constructed in 1502.

St Lorenz Church Nürnberg Sundial 1502 Source: Astronomie in Nürnberg

St Lorenz Church Nürnberg Sundial 1502
Source: Astronomie in Nürnberg

It was also Werner who first published Stabius’ heart shaped or cordiform map projection leading to it being labelled the Werner-Stabius Projection. This projection was used for world maps by Peter Apian as well as Oronce Fine, France’s leading mathematicus of the sixteenth century and Gerard Mercator, of whom more, later. The network expands.

Mercator cordiform world map 1538 Source: American Geographical Society Library

Mercator cordiform world map 1538
Source: American Geographical Society Library

In his own right Werner produced a partial Latin translation from the Greek of Ptolemaeus’ Geographia, was the first to write about prosthaphaeresis (a trigonometrical method of simplifying calculation prior to the invention of logarithms), was the first to suggest the lunar distance method of determining longitude and was in all probability Albrecht Dürer’s maths teacher. He also was the subject of an astronomical dispute with Copernicus.

Johannes Werner Source: Wikimedia Commons

Johannes Werner
Source: Wikimedia Commons

Regular readers of this blog will know that Stabius co-operated with Albrecht Dürer on a series of projects, including his famous star maps, which you can read about in an earlier post here.

Johannes Statius Portrait by Albrecht Dürer Source: Wikimedia Commons

Johannes Statius Portrait by Albrecht Dürer
Source: Wikimedia Commons

An important non-Nürnberger member of the Pirckheimer Circle was Conrad Celtis (1459–1508), who is known in Germany as the arch-humanist. Like his friend Pirckheimer, Celtis was not a mathematician but believed in the importance of the mathematical sciences. Although already graduated he spent time in 1489 on the University of Kraków in order to get the education in mathematics and astronomy that he couldn’t get at a German university. Celtis had spent time at the humanist universities of Northern Italy and his mission in life was to demonstrate that Germany was just as civilised and educated as Italy and not a land of barbarians as the Italians claimed. His contributions to the Nuremberg Chronicle can be viewed as part of this demonstration. He believed he could achieve his aim by writing a comprehensive history of Germany including, as was common at the time its geography. In 1491/92 he received a teaching post in Ingolstadt, where he seduced the professors of mathematics Johannes Stabius and Andreas Stiborius (1464–1515) into turning their attention from astrology for medicine student, their official assignment, to mathematical cartography in order to help him with his historical geography.

Conrad Celtis Source: Wikimedia Commons

Conrad Celtis
Source: Wikimedia Commons

Unable to achieve his ends in Ingolstadt Celtis decamped to Vienna, taking Stabius and Stiborius with him, to found his Collegium poetarum et mathematicorum as mentioned above and with it the so-called Second Viennese School of Mathematics; the first had been Peuerbach and Regiomontanus in the middle of the fifteenth century. Regiomontanus spent the last five years of his life living in Nürnberg, where he set up the world’s first scientific publishing house. Stiborius’ pupil Georg Tannstetter proved to be a gifted teacher and Peter Apian was by no means his only famous pupil.

The influence of the Nürnberg–Ingolstadt–Vienna mathematicians reached far beyond their own relatively small Southern German corridor. As already stated Münster in Basel stood in contact with both Apian and Schöner and Stabius’ cordiform projection found favour with cartographers throughout Northern Europe. Both Apian and Schöner exercised a major influence on Gemma Frisius in Louvain and through him on his pupils Gerard Mercator and John Dee. As outlined in my blog post on Frisius, he took over editing the second and all subsequent editions of Apian’s Cosmographia, one of the most important textbooks for all things astronomical, cartographical and to do with surveying in the sixteenth century. Frisius also learnt his globe making, a skill he passed on to Mercator, through the works of Schöner. Dee and Mercator also had connections to Pedro Nunes (1502–1578) the most important mathematicus on the Iberian peninsular. Frisius had several other important pupils who spread the skills in cosmography, and globe and instrument making that he had acquired from Apian and Schöner all over Europe.

Famously Rheticus came to Nürnberg to study astrology at the feet of Johannes Schöner, who maintained close contacts to Philipp Melanchthon Rheticus patron. Schöner was the first professor of mathematics at a school designed by Melanchthon. Melanchthon had learnt his mathematics and astrology at the University of Tübingen from Johannes Stöffler (1452–1531) another mathematical graduate from Ingolstadt.

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica Source: Wikimedia Commons

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica
Source: Wikimedia Commons

Another of Stöffler’s pupils was Sebastian Münster. During his time in Nürnberg Rheticus became acquainted with the other Nürnberger mathematicians and above all with the printer-publisher Johannes Petreius and it was famously Rheticus who brought the manuscript of Copernicus’ De revolutionibus to Nürnberg for Petreius to publish. Rheticus says that he first learnt of Copernicus’s existence during his travels on his sabbatical and historians think that it was probably in Nürnberg that he acquired this knowledge. One of the few pieces of astronomical writing from Copernicus that we have is the so-called Letter to Werner. In this manuscript Copernicus criticises Werner’s theory of trepidation. Trepidation was a mistaken belief based on faulty data that the rate of the precession of the equinoxes is not constant but varies with time. Because of this highly technical dispute amongst astronomers Copernicus would have been known in Nürnberg and thus the assumption that Rheticus first heard of him there. Interestingly Copernicus includes observations of Mercury made by Bernhard Walther (1430–1504), Regiomontanus partner, in Nürnberg; falsely attributing some of them to Schöner, so a connection between Copernicus and Nürnberg seems to have existed.

In this brief outline we have covered a lot of ground but I hope I have made clear just how interconnected the mathematical practitioners of Germany and indeed Europe were in the second half of the fifteenth century and the first half of the sixteenth. Science is very much a collective endeavour and historians of science should not just concentrate on individuals but look at the networks within which those individual operate bringing to light the influences and exchanges that take place within those networks.


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of science, Renaissance Science

Retelling a story – this time with all the facts

Before 1995 probably only a handful of people interested in the history of navigation had ever heard of the English clockmaker John Harrison and the role he played in the history of attempts to find a reliable method of determining longitude at sea. This situation changed radically when Dava Sobel published her book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time[1] in that year. This volume caught the public imagination and very rapidly became one of the most successful popular history of science and technology books of all time. It was followed just three years later by a lavishly illustrated expanded edition. Just one year after that followed the equally lavish television documentary film based on the book. By the year 2000 at the latest John Harrison had become a household name and a British scientific hero on a level with Newton and Darwin.

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,

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,

All of this would have been well and good if Sobel had actually adhered to the first three words of her subtitle, The True Story…, but unfortunately she sacrificed historical accuracy to the expediency of telling a good story, basically reducing a complex historical narrative to the fairy tale of a poor honest hero, John Harrison, overcoming adversity to finally triumph against the evil machination of his dishonest scheming opponent the Astronomer Royal, Nevil Maskelyne. Sobel’s lurid narrative proved, as already stated, commercially very successful but left its readers with a highly distorted view of what actually took place in the long eighteenth century in the endeavours to find a method of determining longitude and the role that the various people involved played in those endeavours. In particular Nevil Maskelyne was left in the popular public imagination looking rather like the devil’s evil cousin.


Rev. Dr Nevil Maskelyne Source Wikimedia

Rev. Dr Nevil Maskelyne
Source Wikimedia

About five years ago a major historical research project, under the auspices of the Arts & Humanities Research Council, was set up by Cambridge University and the National Maritime Museum in Greenwich on the history of the British Board of Longitude, the official body set up to oversee and direct the search for a method to determine longitude at sea in the eighteenth century. Led by Simon Schaffer for the University of Cambridge and Richard Dunn and Rebekah Higgitt for the National Maritime Museum this project featured a cast of excellent doctoral and post doctoral researchers some of whose findings can be found on the excellent Longitude Project Blog. To date this research project has produced a remarkable list of achievements. Alongside a volume of papers on the much maligned Nevil Maskelyne, which has just appeared and which I am looking forward very much to reading,


the whole of the Board of Longitude archive has been digitized and made available online to researchers. Currently on at the Museum in Greenwich is a major exhibition Ships, Clocks and Stars: The Quest for Longitude, which you can still visit if you hurry, it closes on the 4th of January 2015. If you are uncertain whether or not it’s worth visiting, it has just been awarded the British Society for the History of Science Great Exhibitions Award for 2014! If like myself you are unable for some reason to make the journey to Greenwich do not despair you can bring the exhibition into your own living room by acquiring the accompanying book Finding Longitude: How Ships, clocks and stars helped solve the longitude problem[2] by Richard Dunn and Rebekah Higgitt, a review of which is the actually subject of this post.

Finding Longitude001

My review is actually very simple this book is magnificent. If you have any interest in the histories of navigation, sea voyages, astronomy, clocks, John Harrison, Nevil Maskelyne, Tobias Mayer, and a whole ship’s cargo of other related and interrelated topics then buy this book! I guarantee you that you won’t regret it for one second. It combines thorough research, first class scholarship, excellent writing, unbelievably lavish illustrations, fascinating narratives and historical accuracy in one superb and, for what it is, surprisingly low priced large format volume. Unlike Sobel’s, from a historians standpoint, ill-starred volume, this work really does tell the true story of the solution of the longitude problem with all its complex twists and turns giving all the participants their dues. Although written for the general reader this book should also find a home on the bookshelves of any working historian of navigation, astronomy, horology, sea voyages or just the science and technology of the long eighteenth century.

This book will take you on a voyage through the choppy waters of eighteenth century science, politics and technology and deliver you up on the shores of the nineteenth century much more knowledgeable then you were when you boarded ship and entertain and delight you along the way. It will also make for a first class Christmas present.

[1] Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Fourth Estate, London, 1995

[2] Richard Dunn & Rebekah Higgitt, Longitude: How Ships, clocks and stars helped solve the longitude problem, Collins and Royal Museums Greenwich, London 2014


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

Planetary Tables and Heliocentricity: A Rough Guide

Since it emerged sometime in the middle of the first millennium BCE the principal function of mathematical astronomy was to provide the most accurate possible predictions of the future positions of the main celestial bodies. This information was contained in the form of tables calculated with the help of the mathematical models, which had been derived by the astronomers from the observed behaviour of those bodies, the planets. The earliest Babylonian models were algebraic but were soon replaced by the Greeks with geometrical models based on spheres and circles. To a large extent it did not matter if those models were depictions of reality, what mattered was the accuracy of the prediction that they produced; that is the reliability of the associated tables. The models of mathematical astronomy were judge on the quality of the data they produced and not on whether they were a true reproduction of what was going on in the heavens. This data was used principally for astrology but also for cartography and navigation. Mathematical astronomy was a handmaiden to other disciplines.

Before I outline the history of such tables, a brief comment on terminology. Data on the movement of celestial bodies is published under the titles planetary tables and ephemerides (singular ephemeris). I know of no formal distinction between the two names but as far as I can determine planetary tables is generally used for tables calculated for quantitatively larger intervals, ten days for example, and these are normally calculated directly from the mathematical models for the planetary movement. Ephemeris is generally used for tables calculated for smaller interval, daily positions for example, and are often not calculated directly from the mathematical models but are interpolated from the values given in the planetary tables. Maybe one of my super intelligent and incredibly well read readers knows better and will correct me in the comments.

The Babylonians produced individual planetary tables, in particular of Venus, but we find the first extensive set in the work of Ptolemaeus. He included tables calculated from his geometrical models in his Syntaxis Mathematiké (The Almagest), published around 150 CE, and to make life easier for those who wished to use them he extracted the tables and published them separately, in extended form with directions of their use, in what is known as his Handy Tables. This publication provided both a source and an archetype for all future planetary tables.

The important role played by planetary tables in mathematical astronomy is illustrated by the fact that the first astronomical works produced by Islamic astronomers in Arabic in the eighth-century CE were planetary tables known in Arabic as zījes (singular zīj). These initial zījes were based on Indian sources and earlier Sassanid Persian models. These were quickly followed by those based on Ptolemaeus’ Handy Tables. Later sets of tables included material drawn from Islamic Arabic sources. Over 200 zījes are known from the period between the eighth and the fifteenth centuries. Because planetary tables are dependent on the observers geographical position most of these are only recalculation of existing tables for new locations. New zījes continued to be produced in India well into the eighteenth-century.

With the coming of the European translators in the twelfth and thirteenth centuries and the first mathematical Renaissance the pattern repeated itself with zījes being amongst the first astronomical documents translated from Arabic into Latin. Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was originally better known in Europe for his zīj than for The Compendious Book on Calculation by Completion and Balancing” (al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala), the book that introduced algebra into the West. The Toledan Tables were created in Toledo in the eleventh-century partially based on the work of Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī, known in Latin as Arzachel. In the twelfth-century they were translated in Latin by Gerard of Cremona, the most prolific of the translators, and became the benchmark for European planetary tables.

In the thirteenth- century the Toledan Tables were superseded by the Alfonsine Tables, which were produced by the so-called Toledo School of Translators from Islamic sources under the sponsorship of Alfonso X of Castile. The Alfonsine Tables remained the primary source of planetary tables and ephemerides in Europe down to the Renaissance where they were used by Peuerbach, Regiomontanus and Copernicus. Having set up the world’s first scientific press Regiomontanus produced the first ever printed ephemerides, which were distinguished by the accuracies of their calculations and low level of printing errors. Regiomontanus’ ephemerides were very popular and enjoyed many editions, many of them pirated. Columbus took a pirate edition of them on his first voyage to America and used them to impress some natives by accurately predicting an eclipse of the moon.

By the fifteenth-century astronomers and other users of astronomical data were very much aware of the numerous inaccuracies in that data, many of them having crept in over the centuries through frequent translation and copying errors. Regiomontanus was aware that the problem could only be solved by collecting new basic observational data from which to calculate the tables. He started on such an observational programme in Nürnberg in 1470 but his early death in 1475 put an end to his endeavours.

When Copernicus published his De revolutionibus in 1543 many astronomers hoped that his mathematical models for the planetary orbits would lead to more accurate planetary tables and this pragmatic attitude to his work was the principle positive reception that it received. Copernicus’ fellow professor of mathematic in Wittenberg Erasmus Reinhold calculated the first set of planetary tables based on De revolutionibus. The Prutenic Tables, sponsored by Duke Albrecht of Brandenburg Prussia (Prutenic is Latin for Prussian), were printed and published in 1551. Ephemerides based on Copernicus were produced by Johannes Stadius, a student of Gemma Frisius, in 1554 and by John Feild (sic), with a forward by John Dee, in 1557. Unfortunately they didn’t live up to expectations. The problem was that Copernicus’ work and the tables were based on the same corrupted data as the Alfonsine Tables. In his unpublished manuscript on navigation Thomas Harriot complained about the inaccuracies in the Alfonsine Tables and then goes on to say that the Prutenic Tables are not any better. However he follows this complaint up with the information that Wilhelm IV of Hessen-Kassel and Tycho Brahe on Hven are gathering new observational data that should improve the situation.

As a young astronomer the Danish aristocrat, Tycho Brahe, was indignant that the times given in both the Alfonsine and the Prutenic tables for a specific astronomical event that he wished to observe were highly inaccurate. Like Regiomontanus, a hundred years earlier, he realised that the problem lay in the inaccurate and corrupted data on which both sets of tables were based. Like Regiomontanus he started an extensive programme of astronomical observations to solve the problem, initially at his purpose built observatory financed by the Danish Crown on the island of Hven and then later, through force of circumstances, under the auspices of Rudolph II, the Holy Roman German Emperor, in Prague. Tycho devoted almost thirty years to accruing a vast collection of astronomical data. Although he was using the same observational instruments available to Ptolemaeus fifteen hundred years earlier, he devoted an incredible amount of time and effort to improving those instruments and the methods of using them, meaning that his observations were more accurate by several factors than those of his predecessors. What was now needed was somebody to turn this data into planetary tables, enter Johannes Kepler. Kepler joined Tycho in Prague in 1600 and was specifically appointed to the task of producing planetary tables from Tycho’s data. Contrary to popular belief he was not employed by Tycho but directly by Rudolph.

Following Tycho’s death, a short time later, a major problem ensued. Kepler was official appointed Imperial Mathematicus, as Tycho’s successor, and still had his original commission to produce the planetary tables for the Emperor, however, legally, he no longer had the data; this was Tycho’s private property and on his death passed into the possession of his heirs. Kepler was in physical possession of the data, however, and hung on to it during the protracted, complicated and at times vitriolic negotiations with Tycho’s son in law, Frans Gansneb Genaamd Tengnagel van de Camp, over their future use. In the end the heirs granted Kepler permission to use the data with the proviso that any publications based on them must carry Tengnagel’s name as co-author. Kepler then proceeded to calculate the tables.

Put like this, it sounds like a fairly straightforward task, however it was difficult and tedious work that Kepler loathed intensely. It was not made any easier by the personal and political circumstances surrounding Kepler over the years he took to complete the task. Wars, famine, usurpation of the Emperor’s throne (don’t forget the Emperor was his employer) and family disasters all served to make his life more difficult.

Finally in 1626, twenty-six years after he started Kepler had finally reduced Tycho’s thirty years of observations into planetary tables for general use, now he only had to get them printed. Drumming up the financial resources for the task was the first hurdle that Kepler successfully cleared. He then purchased the necessary paper and settled in Linz to complete the task of turning his calculations into a book. As the printing was progressing all the Protestants in Linz were ordered to leave the city, Kepler, being Imperial Mathematicus, and his printer were granted an exemption to finish printing the tables but then Wallenstein laid siege to the city to supress a peasants uprising. In the ensuing chaos the printing shop and the partially finished tables went up in flames.

Leaving Linz Kepler now moved to Ulm where, starting from the beginning again, he was finally able to complete the printing of the Rudophine Tables, named after the Emperor who had originally commissioned them but dedicated to the current Emperor, Ferdinand II. Although technically not his property, because he had paid the costs of having them printed Kepler took the finished volumes to the book fair in Frankfurt to sell in September 1627.

Due to the accuracy of Tycho’s observational data and the diligence of Kepler’s mathematical calculations the new tables were of a level of accuracy never seen before in the history of astronomy and fairly quickly became the benchmark for all astronomical work. Perceived to have been calculated on the basis of Kepler’s own elliptical heliocentric astronomy they became the most important artefact in the general acceptance of heliocentricity in the seventeenth century. As already stated above systems of mathematical astronomy were judged on the data that they produced for use by astrologers, cartographers, navigators et al. Using the Rudolphine Tables Gassendi was able to predict and observe a transit of Mercury in 1631, as Jeremiah Horrocks succeeded in predicting and observing a transit of Venus for the first time in human history based on his own calculations of an ephemeris for Venus using Kepler’s tables, it served as a confirming instance of the superiority of both the tables and Kepler’s elliptical astronomy, which was the system that came to be accepted by most working astronomers in Europe around 1660. The principle battle in the war of the astronomical systems had been won by a rather boring set of mathematical tables, Johannes Kepler’s Tabulae Rudolphinae.

Rudolphine Tables Frontispiece

Rudolphine Tables Frontispiece




Filed under History of Astrology, History of Astronomy, History of Cartography, History of Navigation, History of science, Renaissance Science

Cartographical Claptrap!

The AEON magazine website has a long essay[1] by Kurt Hollander simply titled Middle Earth that takes as its subject not the fantasy realm of J. R. R. Tolkien but the equator, the imaginary line marking the middle of the Earth’s sphere. Unfortunately this essay is severely marred by a series of errors, myths and falsities about the history of cartography and geodesy. I have selected some of the worst here for critical analysis and correction.

Our author gets off to a flying start with the biggest geodesic myth of them all:

Medieval Christian mapmakers, familiar only with a small corner of the planet, worked within strict horizons that were fixed by the Church’s interpretation of the Bible. Their Earth was flat.

My friend Darrin Hayton (@dhayton) has written several posts on the excellent PACHS blog over the years criticising the people who still insists on propagating the myth that the Europeans in the Middle Ages believed that the world was flat. Just once more for those that haven’t been listening, they didn’t. That the world was a sphere was probably first recognised by the Pythagoreans in the sixth century BCE and almost all educated people accepted this fact from at the latest the fourth century BCE up to the present.

First created in the 7th century, the Christian orbis terrarum (circle of the Earth) maps, known for visual reasons as ‘T-and-O’ maps, included only the northern hemisphere.

T and O maps actually have their roots in Greek geography and cartography and only display part of the northern hemisphere because that was all that their creators knew about.

The T represented the Mediterranean ocean, which divided the Earth’s three continents — Asia, Africa, and Europe — each of which was populated by the descendants of one of Noah’s three sons. Jerusalem usually appeared at the centre, on the Earth’s navel (ombilicum mundi), while Paradise (the Garden of Eden) was drawn to the east in Asia and situated at the top portion of the map. The O was the Ocean surrounding the three continents; beyond that was another ring of fire.

Given that the Greeks, the originators of the geography on which the T and O maps are based, lived in the Mediterranean Sea (not ocean!) they were of course well aware of the fact that it is not T shaped. The T on T and O maps actually represents in schematic form the Mediterranean and the Don and Nile rivers, as the dividing lines between the three known continents.

For the Catholic Church, the Equator marked the border of civilisation, beyond which no humans (at least, no followers of Christ) could exist. In The Divine Institutes (written between 303 and 311CE), the theologian Lactantius ridiculed the notion that there could be inhabitants in the antipodes ‘whose footsteps are higher than their heads’. Other authors scoffed at the idea of a place where the rain must fall up. In 748, Pope Zachary declared the idea that people could exist in the antipodes, on the ‘other side’ of the Christian world, heretical..

As has been pointed out by numerous people writing about the flat earth myth, Lactantius had almost no supporters of his theories.

This medieval argument was still rumbling on when Columbus first sailed southwest from Spain to the ‘Indies’ in 1492. Columbus, who had seen sub-Saharans in Portuguese ports in west Africa, disagreed with the Church: he claimed that the Torrid Zone was ‘not uninhabitable’.

Our author appears to be prejudiced against the Portuguese. Throughout the fifteenth century in a series of expeditions, started by Henry the Navigator (1394 – 1460), a succession of Portuguese explorers had been venturing further and further down the West African coast reaching the Gulf of Guinea, which lies on the equator, in 1460. These expeditions reached a climax in 1488, four years before Columbus set sail to the Indies, when Bartolomeu Dias rounded the tip of South Africa proving that one could reach the Indian Ocean by sea and pathing the way for Vasco de Gama’s 1497 voyage to India.

Although he never actually crossed the Equator, he did go beyond the borders of European maps when he inadvertently sailed to the Americas. To navigate, Columbus used, among others, the Imago Mundi (1410), a work of cosmography written by the 15th-century French theologian Pierre d’Ailly, which included one of the few T-and-O maps with north situated at the top.

The importance of Pierre d’Ailley’s Imago Mundi for Columbus lay not in the orientation of its T and O map but in the fact that d’Ailley severely underestimated the circumference of the globe thus making Columbus’ attempt to sail westward to the Indies seem more plausible than it in reality was.

Columbus’s eventual ‘discovery’ of America stretched the horizons of the European mind. The Equator was gradually reimagined: no longer the extreme limit of humanity, a geographical hell on Earth, it became simply the middle of the Earth.

In particular, Cobo has problems with the direction that mapmaking has taken. In 150AD, Ptolemy drew the first world map with north placed firmly at the top.

Earlier Greek geographers such as Eratosthenes, who also drew world maps, almost certainly also drew their maps with north at the top. Ptolemaeus is not the beginning but the culmination of Greek cartography.

This orientation has become the standard one for maps everywhere. The preeminence of north derives from the use of Polaris, also known as the North Star, as the guiding light for sailors.

This is a piece of pure fantasy on the part of out author. To quote Jerry Brotton from his excellent A History of the World in Twelve Maps, “Why north ultimately triumphed as the prime direction in the Western geographical tradition, especially considering its initial negative connotations for Christianity […], has never been fully explained. Later Greek maps and early medieval sailing charts, or portolans, were drawn using magnetic compasses, which probably established the navigational superiority of the north-south axis over an east-west one; but even so there is little reason why south could not have been adopted as the simplest point of cardinal orientation instead, and indeed Muslim mapmakers continued to draw maps with south at the top long after the adoption of the compass.”[2] I would add to this the fact that many European Renaissance maps also had south at the top.

Yet Polaris, or any other star for that matter, is not a fixed point. Because of the Sun and Moon’s gravitational attraction, the Earth actually moves like a wobbling top. This wobble, known to astronomers as the precession of the Equator, represents a cyclical shift in the Earth’s axis of rotation. It makes the stars seem to migrate across the sky at the rate of about one degree every 72 years. This gradual shift means that Polaris will eventually cease to be viewed as the North Star, and sailors will have to orient themselves by other means.

In 1569, the Flemish cartographer Gerardus Mercator, the first to mass-produce Earth and star globes,

Geradus Mercator (1512 – 1594) was not the first to mass-produce Earth and star globes Johannes Schöner  (1477 – 1547) was.

devised a system for projecting the round Earth onto a flat sheet of paper.

Our author, probably unintentionally or at least I hope so, creates the impression that Mercator was the first to devise a map projection from the sphere onto a flat sheet of paper; he, of course, wasn’t. This achievement is usually credited to Eratosthenes in the third century BCE. Ptolemaeus’ Geographia (about 150 CE) outlines three different map projections.

His ‘new and augmented description of Earth corrected for the use of sailors’ made the Earth the same width at the Equator and the poles, thus distorting the size of the continents. Although Mercator created his projection (still used today in almost all world maps) for navigation purposes, his scheme led to a bloated sense of self for the northern countries, located at the top of the map, while diminishing the southern hemisphere’s sense of size and importance.

Our author is rather vague about how or why this distortion occurs. Because the distance between the parallels of longitude in the Mercator projection increases the further one moves from the equator, landmasses become distorted in area (larger than they are in reality) the further they are away from the equator. Because the major landmasses in the northern hemisphere are further removed from the equator than those in the southern hemisphere they take on an illusionary physical dominance.

Might I, not so politely, suggest to Mr Hollander that if he wishes to write about the history of cartography in the future that he indulges in some proper research of the subject before he puts finger to keyboard.

[1] I’m not sure whether I should thank or curse Richard Carter FCD (@friendsofdarwin) for drawing my attention to this essay. Whichever, he is to blame for the existence of this post.

[2] Jerry Brotton, A History of the World in Twelve Maps, Allen Lane, London, 2012, p. 11


Filed under History of Cartography, History of Navigation, History of science, Myths of Science, Renaissance Science