# Category Archives: History of Navigation

## 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

## 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

## Isaac Newton: The Last Lone Genius?

The Friday before last, with much advanced publicity, the BBC broadcast a new documentary film biography of Isaac Newton with the title The Last Magician. This phrase is part of a famous quote by John Maynard Keynes, “not the first scientist but the last magician”, describing his feeling upon reading the Newtonian alchemical manuscripts that he acquired at the auction of the Portsmouth family Newton papers in 1936.  This of course together with the advanced advertising for the programme signalled that we were due for a fresh dose of “did you know that Newton was a secret alchemist?” A phenomenon that Rebekah “Becky” Higgitt has blogged on informatively in the past.

Based on quotes from Newton’s own writings and correspondence as well of those of his contemporaries the programme was in its basics factually correct. As usual for BBC historical documentaries it was well-produced and excellently filmed and thus pleasant to watch. The basic structure was the direct quotes being spoken by actors in costume and commented upon by five more or less experts. These were the historians of science Rob Iliffe head of the Newton Papers editing project and a genuine Newton expert, Patricia Fara author of an excellent book on the changing image of Newton down the centuries and Lisa Jardine expert on Renaissance history of science, as well as popular science writer James Gleick author of a competent popular Newton biography and astrophysicist turned novelist Stuart Clark.

Given all of these preconditions it should have been an excellent hours entertainment for a historian of science like myself, unfortunately it turned out to be a major disappointment for two reasons. The programme deliberately created two principle impressions that were and are fundamentally wrong.

The first of these turned up in the pre-programme publicity but also featured prominently fairly early in the documentary in what seems at first glance to be a fairly harmless statement:

By the age of 21, he had rejected 2,000 years of scientific orthodoxy

This brief phrase contains two claims one implicit and one explicit. The implicit claim is how wonderful Newton was to take such a bold step when he was only 21 years old. Anyone who has spent anytime at all looking at the history of mathematics knows that mathematicians tend to be very precocious. Pascal wrote the paper that gained him entry to the top flight of seventeenth century mathematics at the age of sixteen. In the nineteenth century the teenage William Rowan Hamilton was trotted out in public like a circus pony to display his brilliance. The stories are legion and there is absolutely nothing unusual in Newton intellectual development it’s par for the course for a highly talented mathematician.

As Becky put it very succinctly in a tweet what they are actually saying here is that there had been no science since Aristotle, which is of course complete rubbish. The scientific orthodoxy of the day, which was by the way on the verge of disappearing, of which more shortly, came into being in the thirteenth century when Albertus Magnus and his pupil Thomas Aquinas created a synthesis of Catholic theology and Aristotle’s philosophy with the addition of Ptolemaic geocentric astronomy. This synthesis is known as Scholastic or Aristotelian physics or natural philosophy. However as Edward Grant, one of the leading experts on medieval science, points out Aristotelian philosophy is not Aristotle’s philosophy. It is also important to note that Aristotelian philosophy was never carved in stone but in fact changed and developed continuously over the next four hundred years. Examples of major changes are the work of the Oxford Calculatores and the Paris Physicists in the fourteenth century. The Aristotelian physics of the fifteenth century is a very different beast to that of the thirteenth century. The geocentric astronomy produced in the middle of the fifteenth century by Peuerbach and Regiomontanus differed substantially from that of the first Ptolemaic translations of the twelfth century.

Added to all this change and development the first seeds of what would become modern science began to poke their slender stems out of the substrate of scientific innovation around the beginning of the fifteenth century. By 1661 when Newton went up to university Keplerian heliocentric astronomy had become the new orthodoxy and Aristotelian physics was being pushed out by the new physics developed by mathematicians such as Tartaglia and Benedetti in the sixteenth century and Stevin, Galileo, Borelli, Descartes, Pascal, Huygens and others in the seventeenth. One should bear in mind that the Leopoldina, the Accademia del Cimento, the Royal Society and the Acadédemie des Sciences all institutions dedicated to the propagation and development of the new science were founded in 1652, 1657, 1660 and 1666 respectively. The young Newton did not like some Carrollian hero draw his Vorpal Blade to slay the Jabberwock of ancient Greek science but like any bright young academic would do jumped on the band wagon of modern science that was speeding full speed ahead into the future.

We now turn to what I see as the most serious failing of the documentary expressed in the question posed in the title of this post. For the best part of an hour the documentary banged on about Newton’s solitude, his isolation his lone path to the secrets of nature. We were presented with the ultimate lone genius of the history of science. It went so far that the only other contemporary researchers mentioned by name were Descartes in passing and Hooke purely in a negative light. The way that the programme was structured created a totally false impression of Newton’s scientific endeavours.

We actually know very little about Newton’s time as a student though it is safe to say that he was more the type to curl up in front of the fire with a good book on a Friday evening than to go to the latest rave at which ever student hostelry was in that term. As a fellow we know that he communicated and worked together with other scholars such as Isaac Barrow so to talk of total solitude as the documentary did is wrong. After he emerged from obscurity at the beginning of the 1670s with his reflecting telescope and his famous paper on the phenomenon of colours he was in no way isolated. Even if Cambridge was somewhat off the beaten track in those days Newton corresponded with other scholars in Britain and also abroad as can easily be seen in his voluminous correspondence as edited by Turnbull. He was also often visited by other mathematical scholars such as Halley or John Collins. When he left Cambridge to go to London he became positively gregarious. Maintaining a town house with his niece Catherine Barton, a renowned social beauty, as his housekeeper where he received and entertained visitors. At the Royal Mint, which he attended daily, he was surrounded by a large staff. After 1703 he presided over the weekly meetings of the Royal Society and on other evenings surrounded by his acolytes he held court in one or other of the then fashionable London coffee bars.

More important for me was the totally false impression created by the documentary of Newton’s mathematical and scientific work. Anyone being introduced to Newton for the first time would come away with the impression that he revolutionised mathematics, physics and astronomy in a superhuman solo endeavour completely isolated from the rest of the late seventeenth century intellectual world.

We got presented with Newton in 1666 creating a completely new branch of mathematics, he only actually started it then and it took a number of years to develop. At no point was any other mathematician mentioned. The fact that Newton either, directly or indirectly, knew of and built on the previous work in this field of Kepler, Cavalieri, Fermat, Pascal, Descartes, van Schooten, Barrow and others was quietly swept under the carpet. Even worse no mention what so ever of Leibniz who independently developed the same mathematics almost at the same time from the same sources. This of course led eventually to the most notorious priority dispute in the history of science involving many of the leading mathematicians of Europe.

The same thing occurred with the presentation of his work in optics, no mention of Kepler, Schiener, Descartes, Grimaldi, Gregory, Hooke, Huygens or anybody for that matter. Isaac apparently did it all alone in isolation.

This form of presentation continued with his greatest work the Principia. We got each of the famous laws of motion presented individually but no hint of the fact that the first was taken from Beeckman by way of Descartes, the second from Huygens and the third from his readings in alchemy. We were told that he derived the law of gravity from his three laws but no mention was made of the fact that the concept of the law of gravity was common, much discussed intellectual property in academic circles at the time. No mention of the contributions made to the substance of the Principia by the work of Kepler, Galileo, Cassini, Halley and above all Flamsteed. We had the strange spectacle of Hooke famous accusation of Newton having stolen his law of gravity and plagiarised him delivered in a passionate speech to the Royal Society in 1660 but no mention what so ever that Hooke’s accusation had more than a little substance. Hooke and Newton had corresponded on the subject in the early 1680s and Hooke had already formulated a concept of universal gravity before Newton. This correspondence was with certainty one of the spurs that led Newton to write the Principia although Hook’s claims as to the extent of his contribution are wildly exaggerated.

Isaac Newton did not live and work in an intellectual vacuum as was very strongly implied either deliberately or accidently through bad scripting by this documentary. He was part of a strong multi-faceted scientific community who supplied both the scaffolding and a significant part of substance of Newton’s life work in mathematics, physics and astronomy. He was in no way a lone genius but a highly significant cog in a large intellectual endeavour.

There was a time some decades back when some historians of science went so far as to decry the Principia as purely a work of synthesis with only a very small original contribution from Newton. This view was shown to be exaggerated and invalid and has been dropped but the opposite point of view implied by this documentary of the Principia as being alone the work of Newton’s genius is even more false.

Before I close there are a couple of small points from the film that I think should be mentioned. As is all too often the case we had the tired old statement that after Newton became President of the Royal Society he produced no more original scientific work. This was as always made without explicit comment but with a strong implicit negative aura. Dear people, when Isaac Newton became President of the Royal Society in 1703 he was already sixty years old. He had written and published two of the most important major scientific works in the history of mankind, his Principia and his Optics, as well as vast quantities of, largely unpublished, absolutely world-class mathematics, which he did however circulate in manuscript amongst his acolytes. What more did you expect him to do (FFS)?

I noted four major scientific/historical errors during the film, a fairly low quota; there may have been others. We of course get introduced to Newton’s reflecting telescope, the invention that first made him known to the world at large, but then we get informed that this instrument played a major role in marine navigation in the eighteenth century. Now whilst it is true that the reflecting telescope, mostly Gregorian’s and not Newtonian’s, had become the instrument of choice for astronomers by the middle of the eighteenth century they were for several good reasons not used for navigation on ships. Firstly reflecting telescopes whilst in principle smaller than refracting ones don’t telescope and so are more massive and cumbersome than the classical marine telescope. Secondly until the nineteenth century reflecting telescopes had metal mirrors made of so-called speculum metal an alloy that unfortunately was very susceptible to corrosion necessitating regular re-polishing. The salt-water atmosphere of sea voyages would have been very adverse for such mirrors requiring almost daily re-polishing and thus completely impractical.

The next error I spotted was a real howler. A voice over informed the viewer that, “for centuries light was considered the purest form of energy in the universe.” Really? Although etymologically derived from an ancient Greek word the physics concept of energy was first appeared in the nineteenth century, as did the recognition that light is a form of energy. Nuff said.

Moving along the historical time scale in the opposite direction voice over informed us the Newton’s Principia made possible the accurate prediction of comets and eclipses. Now the former is indeed true although the credit should properly go to Halley who first showed that some comets were periodical and obeyed Newton’s law of gravity. The latter is however again a real history of science howler. The Babylonians could accurately predict lunar eclipses in about the fifth century BCE and the ability to accurately predict solar eclipses was also developed in antiquity. No need to wait for Newton.

My final error is the one that as a historian of science causes me the most concern. Whilst discussing Newton’s alchemy voice over stated correctly Newton’s alchemical belief that light and matter are both products of some as yet undiscovered primal alchemical substance. The claim was immediately made that Newton had anticipated Einstein’s famous E = MC2! This claim being, to my surprise, repeated by Rob Iliffe an excellent historian of science. Now I’m not a big fan of the Kuhn/Feyerabend principle of the incommensurability of scientific theories. This says that one can’t compare scientific theories because the definitions of the concepts that they contain differ and are thus not comparable. Newton’s concept of force is not Maxwell’s concept of force for example. However I think that here we have a genuine case of incommensurability. The metaphysical concepts behind Newton’s alchemical theory and the metaphysical concepts behind Einstein’ theory of relativity are in no way comparable. It is not even comparing apples with oranges; it’s comparing apples with bicycles!

On the whole I think what was superficially a very good and certainly an excellently produced documentary failed miserably as a piece of history of science for the reasons that I have outlined above. Maybe I’m being too harsh but on the whole I don’t think so. For me the very strong emphasis of the biography of Newton as some sort of lone genius whether intended or an accidental product of ill considered scripting made this documentary next to worthless as a contribution to popular history of science.

## The Virgin Queen was in reality John Dee in drag.

The rumbling you can hear in the background is the HISTSCI HULK playing skittles with some skyscrapers. He’s all riled up and wants to place a big green foot in Carole Jahme’s butt and propel her into publishing purgatory. What has Ms Jahme done to provoke the wrath of the big green HISTSCI destroyer? Damon Albarn’s so-called Opera Dr Dee is being revived in London and Ms Jahme wrote an introductory preview posted last Monday on the Guardian’s website. This preview is unfortunately a mixture of exaggerations, half-truths and fantasies that is a blot on the Guardian’s reputation for good journalism. Now it could be argued in her defence that several of the false claims made in her article are also made in the video interview with the director of the piece Rufus Norris and the Public Astronomer at the Royal Observatory Marek Kukula at the head of the article and that they are also to blame for this piece of shoddy journalism. However there is a thing in writing in general and in journalism in particular that seems to be going out of fashion called fact checking, something that Ms Jahme apparently can’t be bothered to waste her time on. I did consider letting the big green monster loose on her but didn’t fancy the job of cleaning up the carnage so I’ve decided to expose some of Ms Jahme’s worst history of science sins myself.

Before I deal with any detail from the article I would like to address the premise given by Norris for the opera itself. He, and Albarn in previous interviews, create the impression that Dee is somehow a neglected figure, particularly as a mathematicus (which is what he was), I beg to differ. There are at least eight monographs that deal with large parts or the whole of Dee’s biography as well as several monographs that deal with wider contexts of Elizabethan culture that have Dee as a central figure. A couple of these works deal explicitly with Dee as a Renaissance scientific figure. There is also a volume of academic papers on Dee as well as academic annotated editions of his principle works. Already in the 1930s, as modern history of science was beginning to emerge, historians of astronomy, geography and navigation devoted quite a considerable amount of attention to Dee. There are articles on Dee in the Encyclopaedia Britannica, the Dictionary of Scientific Biography, the New Oxford dictionary of Biography and in the Internet at MacTutor and on Wikipedia, some of them quite substantial. I do not think Dee has been neglected, in fact I can’t think of another scientific figure of his stature who has been covered in anything approaching the expansive extant to which Dee has been. This brings us to the next problem, what is Dee’s scientific stature. Just as it is easy to underestimate Dee’s importance and influence in the development of the mathematical sciences in late sixteenth century England it is also possible to overestimate them and in my opinion both in the video and the article this is done. Dee played a role as a teacher and facilitator along with Robert Recorde, Leonard Digges, Thomas Digges, Thomas Harriot, Edward Wright and others in introducing the mathematical sciences into Britain but he made no original contributions to the mathematical sciences himself. He is not a Kepler, Galileo, Descartes or Huygens and he is certainly not one of the giants on whom shoulders Newton stood as claimed by Norris in the interview. Dee is an important figure but he is no more important than at least a dozen of his contemporaries who have received not even ten per cent of the scholarly attention that Dee has.

John Dee

Now to Ms Jahme who tells us that:

Dee was a larger-than-life magus figure. He was probably the inspiration for Christopher Marlowe’s character Doctor Faustus, Ben Jonson’s The Alchemist and Shakespeare’s Prospero.

We’ve been here before as the opera was premiered in Manchester but it is worth re-examining these claims. Marlow’s Faustus is of course based on the real life German magus Dr Johann Georg Faust whose fictionalised life story was a sixteenth century best seller. Ben Johnson’s The Alchemist is a satire on alchemy and alchemists in general, of which Dee was only one of many, and whilst Dee is not name-checked in the piece his medium Edward Kelly is. The claim that Dee is Prospero is old and there is no evidence to support it. Frances Yates one of the real experts for sixteenth century alchemy and magic thinks that Prospero is Giordano Bruno but addresses the claim for Dee pointing out that Dee and Bruno share many key characteristics. I think Prospero is probably a composite figure with elements of Bruno, Dee, Faust, Kelly, Robert Fludd, Cornelius Agrippa, Oswald Croll and a dozen other less well-known contemporary hermetic figures. Instantly identifying Prospero with Dee is in my opinion an act of hagiography and a failure to recognise just how widespread hermeticism was at the end of the sixteenth and beginning of the seventeenth centuries.

Ms Jahme informs us that:

Dee taught Raleigh and Drake “the perfect art of navigation” for calculating longitude from lunar distance observation, which helped facilitate the establishment of the British Empire.

Dee was certainly one of the mathematical practitioners teaching navigation and cartography to English sea captains in the sixteenth century along with Thomas Digges, Harriot, Wright and others but he did not teach Drake or Raleigh. I don’t actually know who, if anyone, taught Drake but if it had been Dee I’m sure I would have read about it in my studies and I haven’t. Raleigh and his ship’s captains were of course instructed not by Dee but by his friend Thomas Harriot who even accompanied the ill fated expedition to establish a colony on Roanoke Island in Virginia, as a sort of scientific officer. Dee instructed Martin Frobisher and other captains of the Muscovy Company in their attempts to discovery either a North-West or a North-East passage to China.

There is more to come Ms Jahme continues with the following:

Infamous in his lifetime, Dee was a risk-taker and exceptional scholar. With his eye on the court he rejected the comfort of university tenure at Cambridge, preferring to collate and categorise his data independently. A serious bibliophile, his private library became the largest in Britain. Dee charted the movement of the planets and in his early career toured Europe giving talks on astronomy – a form of science outreach that was entirely new.

We have here four claims of which two are true, one shows a complete lack of understanding of sixteenth century intellectual culture and one is complete rubbish. The first sentence and the statement about Dee’s love of books are both correct. The statement about university tenure is quite frankly bizarre. It seems to assume that Mediaeval Cambridge was like a modern university. Dee had a fellowship at Trinity but after graduating MA he left the university, as he apparently did not wish to study for a doctorate. Accepting a life as fellow and under-reader in Greek would have been tantamount to giving up before he started, not the comfort of university tenure but a dead end in badly paid futility. However it is the final sentence that this time takes the prize for wrongness. Jahme has exaggerated and misinterpreted a moderately false statement of Norris’ and made a real mess out of it.

In the period of his life that he dedicated to the study of the mathematical sciences Dee made three trips to the European continent; these were not lecture but study tours. Such tours were common practice in the High Middle Ages and the Renaissance with young scholars travelling from university to university to study manuscripts not available in their home university libraries and to meet, study under and discuss or dispute with other scholars. Norris says that this was unique for an English mathematical practitioner at this time and although rare it was not unique. Henry Savile, who would later use his fortune to found the chairs for geometry and astronomy in Oxford, is a contemporary of Dee’s who also undertook such a study tour of the continent. Norris also claims that this was a lecture tour and it is this that Jahme falsely makes unique. On his first trip of only a few months in 1547 Dee studied in Louvain under Gemma Frisius and Gerald Mercator. He returned to Louvain for further studies in 1548 and staid until 1550. Here I would like to correct another of Norris’ false statements. He claims in the video interview that Dee’s range of subjects mathematics, astronomy, astrology, geography, cartography, navigation and history was unusually wide and unique. This is simply not true. This is the normal range of study of the Renaissance mathematicus and is exactly what Dee would have studied with Frisius and Mercator in Louvain. When he left Louvain Dee went to Paris were he did indeed lecture, not on astronomy, but Euclidian geometry. Again this is not out of the ordinary, the visiting scholar demonstrating his own learning to his hosts, nothing new or unusual here. His third trip abroad in 1562 to 1564 was to visit other scholars such as Gesner in Switzerland or the Italian mathematician Commandino with whom he published the translation of a Greek mathematical text.

He was opposed to a tiered system of education where those without classical scholarship were held back, so when his translation of Euclid’s mathematics was complete he made the arcane information accessible to non-university-taught artisans and craftsmen. In his General and Rare Memorials Pertaining to the Perfect Arte of Navigation, he advocated the usefulness of mathematics as a “Publick Commodity”.

In the above quote Jahme has got something right for a change. Dee, following Robert Recorde, is one of the founders of the so-called English School of Mathematics; a group of mathematical practitioners who made their knowledge available in the vernacular. However Dee, unlike Digges for example, also wrote extensively in Latin for an educated public. The paragraph does however contain one serious error. Although Dee wrote his very famous preface for the first English translation of Euclid’s Elements, the translation itself was not by Dee but by Henry Billingsley.

We now come to what I regard as the weirdest claim made by Jahme:

His students include Francis Bacon, promoter of the “scientific method”, and the astronomer Thomas Diggs, who believed the universe to be infinite.

Thomas Digges was not only Dee’s student but also his foster son and he was indeed the first modern astronomer to propose an infinite universe. Although Dee was instrumental in spreading knowledge of Copernican heliocentricity in England he does not appear to have been a totally convinced Copernican. Digges, however, was a totally convinced Copernican who also published the first ever partial translation into the vernacular of De revolutionibus. Now I wouldn’t claim to be an expert on either Dee or Bacon but I have read an awful lot about and by both of them and I have never ever come across the claim that Bacon was a student of Dee’s. If we look at this rationally it also seems highly unlikely. Dee was absolutely convinced that mathematics was the most important discipline of all and was the number one propagator of the works of Copernicus in Britain. Bacon rejected both mathematics and heliocentricity so it does no appear very likely that he was Dee’s student. I will happily admit that I haven’t really researched this properly but a quick search revealed that Dee mentions Bacon just once in his diary. The then 21 year old accompanied somebody else who was visiting Dee in Mortlake in 1583. Bacon never mentions Dee at all in his voluminous writings! I did stumble across one website that actually claimed the fact of Dee’s absence from Bacon’s writings as proof that Bacon was Dee’s disciple! On that basis I could prove literally anything!

It is to the enigmatic Dr John Dee that we must look for the origins of Britain’s contribution to modern Western science, yet Dee has been largely left out of the history books – why?

Both of the claims made in the quote above are simply false and two wrongs definitively do not make a right. This post is already over long but there are two short claims made by Ms Jahme that I wish to include before I close my demolition of her pitifully bad piece of history of science journalism. She writes:

In 1600, astronomer Giordano Bruno was burnt at the stake for daring to say the sun was a star.

And a few lines further on:

Within Dee’s lifetime Copernicus’s sun-centric theories would be strengthened by Galileo’s discoveries.

Giordano Bruno was not an astronomer and he was burnt for his religious opinions and not for his cosmological ones. The reports are not totally in agreement but Dee died in either 1608 or 1609. Galileo first published his telescopic discoveries in 1610 so not in Dee’s lifetime.

It would appear that one qualifies as a history of science writer these days when one is good at making things up so I’ve decided to stop being a pedant and to go with the flow. My next work will be the sensational discovery that Elizabeth the Virgin Queen was in reality Renaissance magus John Dee in drag! Remember you read it here first.

## Living and dying in Cook’s shadow

As I have no intention of getting up in the middle of the night to stare at the clouds preventing me from seeing the last half hour of the transit of Venus I thought instead I would write a, for the meantime, last short post about the history of this event.

For the English the most well known of all expeditions to observe a transit of Venus is the Tahiti expedition of 1769. It is the most famous because it was the first of James Cook’s three expeditions to explore and map the Pacific Ocean. Expeditions that would make Cook one of the most famous British explorers of all time. The articles written and published in recent months on the history of the transit observations have heavily featured the Cook Tahiti expedition but in doing so all of them have made a serious error of omission. They all talk about the Tahiti expedition as if it was Cook’s expedition, it wasn’t, Cook was actually only the driver, the scientific leader of the expedition was Charles Green.

Now most of the people reading this have almost certainly never heard of Charles Green and it is Green’s historical fate that he has been swallowed up by the immense shadow cast by the heroic profile of James Cook.

The Royal Society had decided to sponsor an expedition to the Pacific to observe the 1769 transit, which would not be visible from most of Europe. With this intention they petitioned the King, George III, to order the Royal Navy to supply the necessary transport for the expedition. The King agreed and issued the necessary royal warrants. This then led to the question, who should be in command of the ship? The Royal Society wanted the command of the ship to be in the hands of the astronomer assigned to the expedition, the Royal Navy did not concur.

In 1698 the astronomer Edmond Halley had been given command of a Royal Navy vessel, The Paramour, in order to conduct a survey of the variation of the compass in the Atlantic. The idea was that should these variation turns out to confirm to a pattern, as had been believed by many people since their discovery in the preceding centuries, then they could be used to determine longitude. Halley the landlubber and the Royal Navy seamen did not see eye to eye and Halley was forced to return to England and charged his crew with insubordination. The result of the court case can best be regarded as a draw the crew being given a mild rebuke and Halley a temporary commission to finish his scientific investigations. The Royal Navy had not forgotten this incident and was not keen to give another astronomer command of one of their vessels.

In the end a compromise was found and a young naval lieutenant with experience in cartography and thus astronomy, James Cook, was appointed ships captain and Charles Green was appointed the scientific leader of the expedition. Green himself had earlier been an assistant astronomer at the Royal Observatory in Greenwich under both Bradley and Bliss but on the appointed of Nevil Maskeline to the post of Astronomer Royal in 1765 he had left the observatory and joined the navy as a purser. Green had in 1763/4 conducted the second sea trial of John Harrison’s H4 chronometer on a sea voyage to Barbados with Maskelyne as his assistant and the two men apparently did not get on. The relative status of the two naval astronomers, Green and Cook, on Tahiti is reflected in their gratuities from the Royal Society for the transit observations; Green was awarded 200 guineas whereas Cook only received 100 guineas. This was Green’s transit of Venus expedition and not Cook’s.

The two men apparently got on well and Cook commented favourably in his ship’s log on Green’s abilities as an astronomer. On Tahiti they successfully observed the transit of Venus together with a young Joseph Banks, the expeditions natural historian, who would go on to become one of the dominant figures of the British scientific establishment in the second half of the eighteenth century and on into the nineteenth.

After completing their observations came the historical moment in which Cook opened his secret orders and instead of returning to Britain set off to explore the Southern Pacific in search of the great southern continent. Green had no choice but to continue the journey and together they circumnavigated New Zealand charting the coastline as they went and then explored and mapped the east coast of Australia where Cook named Green Island after his astronomical companion.

They headed home via Indonesia and whilst refitting in Batavia Charles Green took ill and died on the home leg of the voyage on 29th January 1771. Cook would go on to great fame and a secure place in the history books whilst Green has become lost in his shadows. When we think of the history of eighteenth century astronomy we should remember that it was Charles Green’s expedition to Tahiti to observe the transit of Venus, James Cook was just the driver.

As a footnote to this story I want to point out another of those historical horrors in accounts of the transit of Venus observations. Phys.Org has a piece by a Dr Tony Phillips on “Cook’s” voyage to Tahiti to observe the transit, which is littered with the usual minor errors and which only mentions Charles Green in passing as one of those who died after to stopover in Batavia. All of this is par for the course for such pieces but the good Dr Phillips manages one error that would cause consternation in the British cultural establishment. He writes:

Their mission was to reach Tahiti before June 1769, establish themselves among the islanders, and construct an astronomical observatory. Cook and his crew would observe Venus gliding across the face of the Sun, and by doing so measure the size of the solar system. Or so hoped England’s Royal Academy, [my emphasis] which sponsored the trip.

Now the Royal Academy had been granted its charter by George III in 1768 so it is of course just possible that they had sponsored the trip. However as they are a society dedicated to promoting the creation, enjoyment and appreciation of the visual arts through exhibitions, education and debate it is highly unlikely. The expedition was, as I have already written above, of course sponsored by the Royal Society a completely different body dedicated to the promotion of the natural sciences.

## It’s not the Mercator projection; it’s the Mercator-Wright projection!

500 years ago on 5th March 1512 Gerard de Kremer was born in Rupelmonde, in those days a town in the Spanish Netherlands today in Belgium. He is of course much better known through his Latinised pseudonym Mercator.

In German a Kremer or Krämer is a shopkeeper, a grocer and Latinised it becomes Mercator, the root of course of the English words merchant, mercantile, merchandise etc. In modern German a Krämerladen is a corner-shop. Mercator turns up for the first time in a scientific context as an assistant globe-maker to Gemma Frisius in Leuven between 1534 and 1537. Gemma Frisius was professor of medicine at the University of Leuven and was a leading European mathematicus.

Under his tuition Mercator learnt mathematics, astronomy, astrology, surveying, instrument and globe making and cartography. As a pupil and later colleague of Frisius Mercator became part of an important circle of mathematical practitioners that included the Englishman John Dee and the Dutchman Abraham Ortelius.

In his own right Mercator became one of the leading European instrument and globe makers, surveyors, and cartographers but in this post I just want to take a brief look at the thing for which he is most famous the Mercator projection.

As you probably know it is impossible to cut open a sphere and spread it out flat. This is a major problem for cartographer because of course the world is a sphere, at least theoretically. In reality it resembles a rather lumpy distorted potato but cartographers treat it as an idealised oblate spheroid. Over the centuries cartographers developed mathematical methods of transferring the surface of the sphere onto a flat sheet of paper, parchment or what ever. These methods are known as projections because that is exactly what they are. On selects a viewpoint inside or outside the sphere and projects the points on its surface along the lines of sight onto a flat surface. One such projection is the cylindrical projection in which the sphere is conceived of as being inside a cylinder and all points on the spheres surface are projected from the middle of the sphere onto the inside of the cylinder which is then rolled out flat.

The problem is that all projections distort if some way the surface of the sphere. A cartographer has to choose the projection, which best conserves that aspect of the map that he wishes to emphasise.

In the Renaissance the age of exploration, which had been kick-started by the Portuguese King Henry the Navigator (who coincidentally was born on 4th March 1394) in the 15th century,

the mathematicians were called upon to develop new methods of astral and mathematical navigation and new forms of cartography. Mercator’s teacher Gemma Frisius for example invented triangulation for surveying and cartography and first suggested the chronometer method of determining longitude. One of the central problems that needed to solved was what path does a compass bearing follow on a globe and how would it be possible to represent that compass bearing as a straight line on a sea chart?

The first part of the problem was solved by the Portuguese mathematicus Pedro Nunes one of the leading mathematical practitioners of the age. Nunes was professor of mathematics at the University of Coimbra and Royal Cosmographer to the Portuguese Crown.

Nunes demonstrated that a constant compass bearing on a globe follows a segment of a spiral and not a great circle as had been previously assumed. Such lines are technically known as loxodromes or rhumb lines.He also knew that in order to make a constant compass bearing on a sea-chart a straight line then the lines of longitude and latitude must be straight parallel lines but he was not able to work out how the lines of latitude needed to be spaced. This was the problem that was first solved by Mercator and led to the Mercator projection.

The Mercator projection is basically a cylindrical projection in which the distances between the lines of latitude are adjusted according to a special mathematical formula.

Mercator printed and published a world map constructed according to this method of projection in 1569 but he did not explain the mathematical rules on which it was based. He was a professional cartographer and globe maker and he probably hoped that if he kept his method secret then the people who wished to take advantage of this new development would have to order their maps and charts from him.

We know from their unpublished papers that both of the English mathematicians John Dee

and Thomas Harriot

independently solved the mathematical problem of the projection but like Mercator neither of them made the knowledge public. We can however assume that both of them made use of this knowledge when teaching navigation and cartography, Dee to the pilots of the Muscovy Company and Harriot to Walter Raleigh’s sea captains.

The first person to publish the mathematical method of constructing such a chart was another English mathematicus Edward Wright in his book Certaine Errors in Navigation, first published in 1599.

It is because of this that modern historians of cartography say that the correct name for this type of map projection is the Mercator-Wright Projection.

If you go to John D. Cook’s Endeavour Blog and follow the links you can find out all about the maths of the Mercator-Wright projection. There’s a link to a Mercator projection xkcd cartoon too!

## How far the moon?

Anyone coming to the history of the search for a method to accurately determine longitude through Dava Sobel’s Longitude might be forgiven for thinking that the lunar distance method was just some sort of excuse dreamed up by Neville Maskelyne to prevent John Harrison receiving his just deserts. This is far from being the case. The lunar distance method first explicated by Johannes Werner in Nürnberg at the beginning of the 16th century was the method supported by nearly all astronomers since at least Newton as they were of the opinion that it would not be possible to construct a clock sturdy enough to survive a rough sea voyage and extreme changes of temperature and accurate enough to keep its time over several weeks in the foreseeable future. It should be remembered that it was the astronomers, responsible for keeping track of time since the dawn of civilisation, who had invented and developed the mechanical clock and it was the astronomical instrument makers who were the leading clock makers of the period so they really did know what they were talking about. For these highly knowledgeable men the lunar distance method genuinely seemed to offer more hope of a solution to the problem.

The lunar distance method is one of several ‘astronomical clock’ methods of determining longitude. The theory says that if one has a set of tables detailing the position of the moon respective to a given star or group of stars for accurately determined time intervals for a given fixed position then by observing the moon’s distance from said star or stars locally and noting the local time it should be possible to calculate the time difference of the two observations, real and tabular, and thus determine the longitude of the current position relative to the fixed position in the tables. Four minute of time difference equal one degree of longitude difference.

Two lunar observations taken at the same true local times

with the observers separated by 90 degrees of longitude

To make this system viable one needs two things, an instrument capable of accurately determining the lunar distance on a moving ship and accurate lunar distance tables. The first problem was solved by the English mathematician and instrument maker John Hadley who I’ve written about before and the second by the German cartographer and astronomer Tobias Mayer who died two hundred and fifty years ago today on 20th February 1762, aged just 39.

Tobias Mayer

Mayer was born on in 17th February 1723 in Marbach but his family moved to Esslingen less than two years later.

Mayer’s place of birth in Marbach

Now the Mayer Museum

He grew up in comparative poverty and when his father died in 1731 Tobias was placed in an orphanage. He received only very basic schooling and was a mathematical autodidact. However at the age of eighteen he had already published a book on geometry and a town plan of Esslingen. In 1743 he moved to Augsburg where he worked for the Pfeffel publishing house and where he published a Mathematical Atlas and a book on fortification. His publications led to him being appointed to a senior position at the Homanns Erben cartographical publishing house in Nürnberg, one of the leading cartography companies in Europe, in 1745.

Mayer’s workplace in Nürnberg home of the Homanns Erben publishing house

Today the museum of the history of the city of Nürnberg Fembo Haus

In his six years in Nürnberg Mayer published about thirty maps and numerous astronomical papers with a special emphasis on lunar research. It was during his time in Nürnberg that Mayer laid the foundations of his lunar tables for the lunar distance method.

By 1751 Mayer enjoyed a reputation as one of the leading European astronomers and he was offered the chair of mathematics at Göttingen and the directorship of the university observatory. During the next ten years Mayer would publish extensively on astronomy, mathematics, geodetics, mensuration and the design and construction of scientific instruments. He died on 20th February 1762 of typhoid.

Although the moon obeys Kepler’s laws of planetary motion, because it is fairly large and lays between the earth and the sun it gets pulled all over the place by the force of gravity and as a result its orbit is a very ragged and irregular affair. In both the systems of Ptolemaeus and of Copernicus the models for the moon’s orbit are less than successful. Kepler ignored the problem and did not supply a lunar model in his system. This omission was corrected by the young English astronomer Jeremiah Horrocks who proved that the moon also has, at least in theory, an elliptical Keplerian orbit and delivered the best lunar model up till that time. Even the great Newton had immense difficulties with the moon and although he based his efforts on Horrocks’ work he was unable to show that the moon really conforms to his gravitation theory. It would have to wait for Simon Laplace to tame the moons orbit at the end of the eighteenth century. Before Laplace none of the mathematical models of the moons orbit was accurate enough to deliver tables that could be used for the lunar distance method.

Mayer took a novel approach, he argued that what was needed was not a new model but more accurate observations and more accurate calculations based on those observations and set to work to deliver and deliver he did. Over several years Mayer made very exact observations of the moons positions and very accurate calculations for his tables and thus he succeeded where others had failed. In 1752 he published his first set of lunar tables and in 1755 he submitted them to the Board of Longitude in London. With his tables it was possible to determine the position of the moon within five seconds of arc making it possible to determine longitude to within half a degree.

I am the more unwilling my tables should lie any longer concealed; especially as the most celebrated astronomers of almost every age have ardently wished for a perfect theory of the Moon … on account of its singular use in navigation. I have constructed theses tables … with respect to the inequalities of motions, from that famous theory of the great Newton, which that eminent mathematician Eulerus first elegantly reduced to general analytic equations.

Mayer’s preface to the 1760 edition of his tables.

Combined with Hadley’s quadrant now modified to a sextant the problem of longitude was effectively solved, although only for days when the moon was visible. After trials and a new improved set of tables, published posthumously, the Board awarded Mayer’s widow a prize of £3000 a very large sum of money in the eighteenth century although only a fraction of the sum awarded to Harrison. The calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766.