Mercator

Gerardus Mercator

After the biography are notes on the Mercator projection.

BIOGRAPHY

1512 Mercator was born Geert de Kremer or Kramer at Rupelmonde, Flanders on the 5th of March 1512. Some cite his first name as Gerherdt. His parents were German, to the degree that modern nationality has any meaning in the 16th century) and he did not stay long in Rupelmonde: But this has led to him being claimed as a national figure by three modern countries. He was the seventh child of Hubert Kremer and his wife Emerance. Their home town was Gangelt in the Princedom of Julich, now Germany. The family were visiting Hubert’s brother, Geert’s uncle, Gisbert de Kremer in Rupelmonde, Flanders- now Belgium- at the time of his birth. Hubert, his father, was of the artisan class, a cordwainer; Gisbert, whom they were visiting, was a Catholic cleric. Their stayed in Rupelmonde about half a year after which they returned to Gangelt and there Geert passed his infancy. Gangelt lies one and a half miles from the modern Dutch border where the closes town is Schinveld.

1518 Six years later, in 1518, the Kremers returned to Rupelmonde Flanders; some because Gangelt had been touched by plague, food shortages and the ensuing crime. Rupelmonde. Rupelmonde lies of the north bank of the Scheldt River and is now a district of Bazel, which has become a south west suburb of Antwerp . By the roads of the time, the two towns are about 200 km or 125 miles apart on almost exactly the same latitude: that is Rupelmonde is due west of Gangelt.

1520 circa: In this year, when Mercator was 8 years old: the German Erhard Etzlaub born 1461 died 1532) engraved miniature “compass maps”, about 100mm×80mm in size of Europe and Africa, from latitudes 67° north to the Equator- some say he produced a projection “identical to Mercator’s”

1522   In this year Geert was 10 years old, and in this year the Italic Script arrived in the Low Counties. Mercator was to become a great advocate of this script and wrote Literarum latinarum, an instruction manual and advocation of it. He must have written this many years after 1522, probably about the time he was engraving for his globe. It is said Mecator first used it on the globe of Gemma Frisius -which would have been in 1536.

1526    Geert de Kremer was 14 years old: Geert’s father Hubert died in 1526 and Gisbert, his uncle, became his guardian. It was anticipated by Gisbert that Geert might enter into the priesthood. Gisbert sent Geert to the School of the Brethren of the Common Life at Hertogenbosch in the Brabant province. This may well be the home town of the famous painter Jerome Bosch. Hertogenbosch is on the Merse River in modern day Netherlands and is north of, but equidistant from, Rupelmonde and Gangelt. Coincidentally the three towns form and almost exact equilateral triangle, when plotted. While at the school his headmaster was Georgius Macropedius (which seems to mean “big foot”; Geert studied the bible under him, as well as the Trivium and Pliny’s Natural History, and, most importantly, it has been said, the Geography of Ptolemy. Due to the Latin culture of 16th century education he took a Laminated version of his name and Geert de Kremer van Rupelmonde became, Gerardus Mercator Rupelmundanus (Gerard Merchant of Rupelmond). Mercator is the Latin translation of Kremer which means merchant. If that was the meaning of the family name, preposition “de” seems wrong. The Hertogenbosch school had a famous scriptorium and Mercator was particularly interest in cartography: later advocating certain scripts. Erasmus was an alumnus of this same school forty years before Mercator. (Erasmus’s biography actually records: Erasmus was educated in monastic and semi-monastic schools. At the age of nine, he and his brother Peter went to one of the best Latin schools in the Low Countries, at Deventer run by the chapter clergy of the Lebuïnuskerk; though some earlier biographies assert it was a school run by the Brethren of the Common Life. So could Hertogenbosch and Deventer refer to the same school? No Deventer is 80 miles north east up on the same parallel as Amsterdam. The truth seems to be that Erasmus and Mercator both attended schools which were run by the Brethren of the Common Life. Erasmus seems to have had nothing to say on the subject of geography or cartography)

The Bretheren of the Common Life, or Fratres Vitae Communis in Latin was a Catholic community from the Low Countries. They had an ancient origin but ran schools in the 1500’s. They were founded on the teachings of the earlier Gerard Groote, 1340- 1384 who, after a life changing experience, had began to preach living by simple devotion to Christ. These were not formal monks for they did not take full vows. They were one of proto-socialist groups which so interested Marx in his works such as “The German Ideology”, as a template for his idea of how a society might be ordered. They were a working order- not simply contemplative and had science laboratories, observatories, workshops and scriptoria. The ate in common as so displayed many aspects of life which are reflected in the university college. One might call theirs didactic literate and artisan based religious community.

1529 Lemma and Gaspar Van der Heyden, future teachers of Mercator from whom he learned instrument engineering, completed a terrestrial globe in his year.

1530 Mercator was 18 in this year- reaching adulthood. Mercator was born into a family which broadly kept to the Catholic faith at a time when Luther’s Protestantism was gaining ground. Old Testament Creationism was always extolled in his publications and occupied large sections of his atlases. It might be said that he wasted his talents on calculations of specious time lines based on Old Testament texts. Yet he must have accepted Copericus- there must have been conflict between his religious upbringing, his scientific leaning and empirical knowledge. However sympathies for some of Luther’s ideas were to force him to flee Leuven where he had been imprisoned for “Lutheran Heracy” by Inquisitionists at the University of Leuven.

1530 From school, Mercator, as he was now called, entered to the University of Leuven, where his Latin name appears in the study records of 1530. He lived in the teaching institution, the Castle College. Fellow students included the anatomist Andrea Vesalius, the statesman Antoine Perrenot, and the theologian George Cassander. The “Bachelor” degree was, at Leuven, called “Magister”. And the core Trivium were: Philosophy, Ancient Greek and Theology; Greek Philosophy was Aristotelian. The Trivium was complemented by the lay subjects, the Quadrivium: Arithmetic, Music Astronomy, and Geometry. These subjects were secondary to Theology and Philosophy . Mercator graduated from Leuven as “Magister” in 1532.

1532 Mercator, aged 20, left the University of Leuven.

1532 -1534 Aged 20 to 22, Mercator was at Antwerp. Normally any good student having graduated as Magister might have gone on to study in one of the four faculties at Leuven: Theology, Medicine, and Law (Canon or Roman). Gisbert hoped Mercator would further study Theology and enter the Church but this did not happen. The dates suggest that meeting a young lady, Barbara Schellekens, may have ended this aspiration. There were also academic problems trying to reconcile Aristotelian Philosophy, Church teaching and his own empirical scientific observation and mathematical proofs. A particular problem arose with the Genesis Creation. Conflict leads to doubt, and doubt was heretical. He avoided the worst consequences of this intellectual conflict because he was not publishing in print. He went to Antwerp to study Philosophy. At Antwerp, Mercator exchanged views with the Franciscan monk Monachism of Mechelen- hardly a name, more a nom-de plume of anonymity for Monachus just means “monk”. This cloak over his identity was due to his humanism and challenging of the Aristotelian model of the world: he himself investigated and recorded observations. It is to be wondered that a pagan such as Aristotle would hold sway with the Catholic Church. Mercator studied Monachus’ map collection including the globe he had constructed for Jean Carondelet, Court Advisor to Charles V. The armature of the globe was built by Gaspar van der Heyden of Leuven (1495–1550). Later would be apprenticed to him.

1534 Mercator is 22 years old and leaves Antwerp University. He married Barbara Schellekens. (but other accounts say the marriage was in September 1536 when he was 24). Their children were: Arnold, Emerentia, Dorothes, Bartholomew, Rumold, Cartharina.

1534 At the end of 1534, aged 24, Mercator returned to Leuven and studied Geography, Astronomy and Mathematics informally under Gemma Frisius. Mercator’s natural gift for geography was not matched by his mathematical ability and he struggled for two years to master the basics, after which Leuven University permitted him to take some private pupils. Gemma had designed mathematical instruments and it was from him that Mercator learnt how to manufacture his own instruments. The other craft skill necessary was engraving on copper, and, particularly with cartography, the engraving of a mirror script: for this form of printing is intaglio and cannot be off-set.

1535. Mercator is 23 years old. Gemma, Van der Heyden and Mercator, planned a new globe to show their latest geographical discoveries. The paper elliptical panels, called gores, were to be engraved on copper, not wood, and the text was in the italic script, replacing the older Roman lettering formerly employed. Gemma produced the mapping, Van der Heyden engraved the geography and Mercator engraved the wording and scripts, including a title cartouche which published his name for the first time.

1536 Mercator is 24 years old. The Gemma, Heyden,Mercator globe was finished in 1536 and they produced its celestial partner a year later. Widely lauded, these were expensive and sales provided Mercator with additional income (to add to his sales of mathematical instruments and from teaching fees). Thus he was able to marry.

1536 Mercator’s marriage to Barbara Schellekens was in September 1536. (others cite 1534). In this year Mercator first used the Italic Script on the globe of Gemma.

1537. Arnold, the first child of Geert and Barbara Mercator was born. They were eventually to have six children; and, in 1537, aged 25, Mercator cemented his reputation with his Map of the Holy Land” which he researched, engraved, printed and partly published in league with others. It was dedicated to Francis van Cranevelt who was a member of the Mechelen Grand Council.

1537 Mercator is 25 years old in this year. The Portuguese cosmographer Pedro Nunes, who was born 1502 and died in 1578, became the first to describe the loxodrome and show its use in navigation. He argued for a marine atlas of several sheets in a cylindrical equidistant projection as, he pointed out, this would minimize distortion of directions (Rhumb lines). An assemblage of these would substantially produce a Mercator projection

1538 Mercator, aged 26, produced his first Map of the World called the Orbis Imago. It was dedicated to Johannus Drosius, a colleague and a student who became a radical priest and may have had Luthern sympathies. It has been contended that some of the symbolism on the Orbis Imago World map were hidden references to Mercator’s Lutheran sympathies. Mercator was putting himself in some danger from the Catholic theologians of Leuven University.

1540 Aged 28, Mercator made a Map of Flanders dedicated to the Emperor.

1540 Benjamin Mercator, Geert’s second son, was born in this year.

1541 Aged 29, Mercator made a terrestrial globe. All these early works were admired and sold well. The globe was dedicated to Nicholas Perronet, the Emperor’s chief advisor.

1542 In this year Mercator was thirty year old . Leuven was besieged by the troops of the Duke of Cleves, a Lutheran supporter but supported by the French, he was taking advantage of religious strife unrest for the advantage of both parties. Ten years later Mercator would petition the Duke of Cleves for aid. After the siege Leuven was impoverished and its merchants, traders and artisans suffered greatly- one of whom was Mercator. But of more seriousness for a young man whoi had flirted with Lutheran ideas, the Inquisition arrived in this year.

1543 Mercator was 31 years old in this year. His family had links to Molanus, a religious reformer who would later fled Leuven. He was also a friend of Melanchthon, the Lutheran reformer, and wrote to him. Mercator knew the free thinking Franciscans of Mechelen well and visited them. He may have, through these acts, come to the attention of Inquisition practitioners from the University of Leuven- notable Ruard Tappen and Jacob Latomer. Through them, Mercator was added to a list of 52 heretics of Leuven. The others were arrested, but Mercator was at Rupelmonde executing the will of Gisbert and managing his estate: Gisbet, his uncle, was recently deceased.

Mercator was arrested in Rupelmonde and imprisoned in the castle. He was accused of correspondence with the Franciscans of Mechelen but proof was not forthcoming. Some friends petitioned for his release, which happened after seven months, say some accounts; others say six months. Many of the 52 arrestees were tortured, two were burnt at the stake, one beheaded and two women were entombed alive, three others died in custody.

1545 Mercator was 33 in this year. Nicholas Perrenot recommended him to the Emperor, to make a set of instruments. The order was for Compasses, Globes, Astrolabes and Astronomical plane-rings. The work was finished in 1545 and Mercator was granted “Royal Approval” for his atelier. The instruments were to be lost on military campaign and Mercator had to make a second set, the whereabouts of which is not known.

1545 He returned to his major project for a highly detailed Wall Map of Europe. He had said on his 1538 world map, that this project was well advanced, but the map was not to appear until 1555.

1551 In this year, when 39 years old, Mercator’s Celestial Globe was finished It was the accompanying project to the 1541 Terrestrial Globe- and from this date, they were sold as a pair. Mercator globes were never updated but were still valued some ½ a century after the gore plates were cut.

1552 In this year, aged 40, Mercator moved from Leuven to Duisburg in Cleves. New teachers were required by the recently opened university there. Due to his birth he had not been granted full citizenship in Leuven. In Duisburg, Mercator established himself as a publisher of maps, and a maker of instruments and globes. He made globe for John Dee. Mercator became a friend of Walter Ghim, the twelve times mayor of Duisburg and, later, Mercator’s biographer. Duke Wilhelm of Duisburg appointed Mercator to the position of his Court Cosmographer. Mercator worked for the Duke to survey a disputed boundary between Duisburg, the County of Mark and Westphalia, a neighbouring Duchy.

1555 Mercator is 43 years old. The Detailed Wall map of Europe was published. It had been started in about 1534. Some give its publication year as 1554. It was dedicated to Antoine Perrenot, now a Cardinal. Some say it had been a 12 year project which would make its commencement 1542 (from 1554) It sold in large quantities for the rest of the century with a second edition in 1572 and a third edition in the atlas of 1595. Some Mercator maps are seen on the walls in Vermeer Van Delf’s paintings of the 17th century.

1558 Mercator is 46 years old. Arnold, the eldest, son of Mercator produced his first map. It showed Iceland, in this year. Years later Arnold took over the Mercator map globe and instrument business.

1559 When Mercator was 47, the Akademisches Gymnasium was founded in Duisburg when the Duke and the Duchy’s authorities finally lost interest in the planned University after years of Papal obfuscation. The Gymnasium did not require papal authority. In this year Mercator was asked to teach mathematics and cosmography.

1560 In this year, aged 48, Mercator was involved in the appointment of Jan Vermeulen, whose name was latinised to Molanus, as rector at the Gymnasium. Vermeulen then married Emerantia, Mercator’s daughter.

1562 Mercator is 50 years old. Bartholomew Mercator, Geert’s second son, took over the teaching of his father’s three year lecture-course at the Gymnasium which- Mercator had only taught once. Bartholomew was 22 years old.

1564 In the year 1564, when 52 years old, Mercator published his Map of Great Britain, a map of greatly improved accuracy which far surpassed any of his previous representations of the island. This map predated the Union of England and Scotland and in 1564, the English monarch was Elizabeth who had acceded to the throne following the death of her half sister Mary Tudor in 1558. This fact rather scotches some cartographic historian’s notions that it was anti Henry VIII, but the circumstances were certainly unusual . The fact that it is not dedicated suggests that the cartographer on the ground would have been at risk from such an acknowledgement. Mercator says in the script that it was not his map but that he engraved it for a “good friend”. Some say it was drawn by a Scots Catholic priest called John Elder, who smuggled it to a French priest who passed it to Antoine Petitioner, a friend of Mercator’s. Such subterfuge may not have been necessary if the source was in Scotland and this tale again seems to avoid the fact that the Kingdoms were not then united. Smuggling of texts would not have been necessary between Scotland and the Low Countries. The map is said to have been Catholic in its bias. It showed Pre Reformation institutions and none of the Tudor monarch’s “replacements”. The legends on it play down English history in favour of Scottish and Irish events- but this may just show the nationality of the cartographer. Hidden sources may also have been to protect Benjamin Mercator who was working in publishing houses in London in this Elizabethan age. Some say it proved to be an important document in the preparation for invasion by Phillip II of Spain with his Armada: but that project was wrecked by storms and the seamanship of Drake and the English Navy.

1564. This was the year when Mercator began engraving his Lorraine Map. After the Map of Britain was published Mercator was asked to survey and map Lorraine or Lotharingia and it was formerly called. This was the first time he was required to travel and undertaken surveying and information gathering “in the field” himself. He was not a traveller or surveyor. He set out, aged 52, accompanied by his second son, the academic, Bartholomew. Mercator undertook the work and produced through triangulated measurements in the wooded, and deep valleys of the region. His son claimed that the expedition “gravely imperilled (his father’s) life and weakened him so much that he came very close to a serious physical and mental breakdown: a derangement of his senses- brought about by those terrifying experiences.” Mercator returned home weak and ill and took to his bed. Bartholomew was left to continue in the field and collate the material back in Duisburg. No published map resulted, perhaps the Duke never intended the material to be commonly published. Slowly Mercator regained his health and spirits.

1565-1569 Mercator was 53 in 1565 and between these dates he was engaged on what he considered his most important work: a very large scholarly piece which would today be considered of no historical merit at all: the “Chronologia”,comprising a supposed table of the significant events since the beginning of the world compiled according to a literal reading of the Old Testament and 123 other sources: consisting of histories, genealogies and accounts of all regimes, empires and dynasties that, to his knowledge, had ever existed. Mercator made the first attempt to link recorded history to records of solar and lunar eclipses, calculated by him according to his understanding of the motions of the sun, moon and Earth. He linked in dates from other calendars and events recorded according to them: events from Babylon, Israel, Ancient Greece, the Annals of Rome. He married the eclipsed recorded by them with those known to him and calculated by him in the past. Adam and Eve were expelled from Eden, he reckoned, some 3,965 years before the birth of Jesus. The 400 page word was lauded and its false chronology was still being cited in the late 19th century by Bible commentators- ironically, mainly fundamentalist non-conformists. Mercator considered this his greatest achievement. Back in Leuven the Catholic Authorities placed it on the prohibited list because it included the acts of Protestant reformers and Luther. This greatly added to the work’s attraction – for there was some prestige in being on the “Index Librorum Prohibitorum”

The Chronologia developed into an even wider project: the Cosmographia, his description of the Universe. Mercator’s outline was (1st) the creation of the world; (2nd) the description of the heavens (astronomical and astrological); (3rd) the earth comprising modern geography, the geography of Ptolemy and the geography of the ancients; (4th) genealogies and history of the known states; and (5th) The Chronology. Of these: the Chronology had already been accomplished, the account of the creation and the modern maps would appear in the atlas of 1595,

This period around 1565 must be about the last time when the idea that one could essentially publish the combined knowledge of the World – even in outline form- in one work- could be entertained. It is interesting that this is contemporary to Shakespeare of whom, it has been said, that he was the last person to have read all (non-trivial) works available in the English Language.

1568 Mercator is 56 years old. Bartholomew, Mercator’s second son, died aged 28, died. He had taken over some of his father’s courses at the Duisburg Gymnasium.

In 1587 Rumold, Mercator’s third son, returned to Duisburg and later, in 1594, it fell to his lot to publish Mercator’s works posthumously. Rumold would spend a large part of his life in London’s publishing houses providing for Mercator a vital link to the new discoveries of the Elizabethan age. In 1587 Mercator was 75 years old.

1569    Mercator was 57 years old. The most important date in the history of Mercator’s cartography. This was the year of the publication of the Mercator projection which mapped the surface of the earth flat, as if on a cylinder not a sphere and so created as to make the Rhumb lines remain accurate and straight- for navigation. This type of map projection is often described as the “cylindrical projection”. The meridians (of longitude) are equally spaced, parallel vertical lines, and the parallels of latitude are parallel, horizontal straight lines, spaced increasingly far apart as they distance themselves from the Equator. The projection is widely used for navigation charts, because a straight line is a line of “constant true bearing” enabling a navigator to plot straight-line courses. It is less practical for world maps because the scale is distorted; areas farther away from the equator appear disproportionately large. Mercator’s 1569 map using his new projection was a large flat projection measuring 79 1/2 inches by 49 inches. He called this his “new and augmented description of Earth corrected for the use of sailors”.

1569 Perhaps his most famous World Map was published in this year. It was accompanied by about 5100 words of engraved script arranged on 15 panels or explanations. Contemporary to the World map, Mercator published: Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata (A new and more complete representation of the terrestrial globe properly adapted for the use of navigation (or sailors). In a preface to a map series. Mercator cites Atlas, the mythical king of Mauritania, not the Titan, who was his father. Mercator read of this Atlas as having been a learned figure and skilled in the geographical sciences of his (mythical) age, “Atlas, a King notable for his erudition, humaneness, and wisdom” so much so as to form a “model for my imitation.” Hence the modern term “Atlas” is coined.

1570 Around 1570 the Military Commander of Julich asked Mercator, then aged 58, to prepare a suite of Regional Maps of Europe to accompany Johnannes, the Heir to Julich on a tour. This has been called the Atlas of Europe, though Mercator did not coin that title. Some of the pages were parts of large Mercator wall maps and some were not by Mercator at all: such as the 30+ maps from Abrahamus Ortelius’s “Theatre of the Sphere of the World”: Theatrum Orbis Terrarum. At this time the word for a map collection was hovering between Atlas (Blaeu and Mercator’s term, and “Theatre” used by Ortelius and most of the English 16th century cartographers.

1578 Mercator, aged 66, published an edition of Ptolemy’s Geography. This was the world as described in toponyms and a kind of grid reference by the Romano Egyptian geographer from Alexandria.

1578 Mercator’s Mauretania map appears in the greater folio.

1578 Mercator’s 28 maps of Ptolemy appeared. The work has been described as an “Epitaph to Ptolemy”. Ptolemy had worked on two projections and listed the supposed latitude and longitude of over 8,000 sites: usually towns, promontories, islands, river mouths. The 28 map project had started in 1568 and had lasted 10 years- with breaks for other commissions. Ptolemy, an Egyptian of Alexandria, wrote in Greek.

1585 In 1585 Mercator, aged 73, published a folio of 51 maps of France, Germany and the Netherlands.

1586: Barbara Schellekens, Mercator’s first wife died. Mercator was 74; his eldest son Arnold was to die in the following year leaving Rumold and Arnold’s sons to continue the family firm. The deaths prompted an interest in philosophy philosophy and theology. Three written works appears at this time. “On the Harmonisation of the Gospels”, and Commentaries on the New Testament Epistles of Paul and the Old Testament Book of Ezekiel.

1587. Arnolf, Mercator’s 1st son died a year after his mother. Mercator was 75 years old.

1587 In 1587 Rumold ,Mercator’s third son, returned to Duisburg from England. Later, in 1594, he published Mercator’s last works works posthumously, having finished them, or readied them for publication.

Rumold, spent many years in London, working in publishing houses. This is said to have furnished Mercator with much geographical information from the navigators of the English Elizabethan age. It is interesting to speculate on which cartographers he may have met: certainly Saxon, perhaps Lord Burghley his patron, possibly Rudd, probably not Speed.

1589 Mercator married a second wife: Gertrude Fingerlings. He was 77 years old. Mercator had a new zest for life. Gertrude Vierlings, was the widow of a mayor of Duisburg. Rumold married her daughter at the same time.

1590 In this year Mercator, aged 78, has a seizure or stroke and was left incapacitated. He tried to finish his remaining map projects, so religious works and a new account of the Creation of the World, which was finished. It was, to him the philosophical and theological background to all his map making and underpinned his oeuvre and atlas.

1594. Mercator, aged 82, died after two strokes in this year. It was 4 years after his first stroke (if he had not suffered and undiagnosed one on his field trip of 1564. He was buried in St. Salvatore’s Church in Duisburg. He died on the 2nd of December at the age of 82. Then Duisburg was in the United Duchy of Cleves, Berg and Julich- a part of the Empire.

1644 A memorial to Mercator was placed in St Salvatore’s, Duisburg 50 years after his death. The inscription praises him for his excellence in mathematics and for his globes which “represented the heaven from beneath and the Earth from above. He was man of erudition in theology.”

1595 Mercator’s Atlas of smaller maps with 100 new maps bound: his previous maps had tended to be large for wall hanging. This Atlas has some 100 pages of maps and 20 pages of illustrated titles. Then many pages are given over to an explanation of the creation of the Universe. He then describes the countries shown. His chronology is about 400 pages long and cites dates from the Biblical Creation. He also codifies Ruling families and dynasties, Battles and War, events of social import, notes eruptions of volcanoes, eclipses of the Sun, notable earthquakes etc.

1598 The death of Ortelius in 1598 but his atlas, the Theatrum continued to sell well and this is considered to have hampered sales of Mercator’s atlas and works. Ortelius produced more decorative work. An analogy might be made between Saxton and Speed maps in England.

1599 Rumbold Mercator died.

1599 The English mathematician Edward Wright, born in 1558, died in 1615, published tables for the construction of an accurate Mercator type projection from 1599 to 1610.This was, of course, after Mercator’s map.

1600 An English mathematicians called Thomas Harriot, who was born in 1560–and who died in 1621,independently associated the Mercator projection with its logarithmic formula, a connection later demonstrated by calculus.

1602 The existent family posthumously produced a second volume of the atlas in which texts were changed but no addition cartography was produced.

1604 The sale in Leyden in the Netherlands of Mercator’s Library which is said to have shown that the existent family were in some financial trouble. A book of particular interest from this library is Mercator’s self annotated copy of Copernicus’s book “De Revolutionibus Orbium Coelestium “which is now housed in Glasgow.

1604 The Mercator family sold his copper plates to Jodocus Hondius in this year; Hondius re-edited the atlas with 40 more maps, including Portugal and Spain.

1606 In 1606 a new edition of the posthumous atlas appeared, now with Hondius as author; he did still acknowledge the authorship of those maps drawn by Mercator.

1645 English mathematician Henry Bond, born 1600–died 1678, independently in 1645 calculated and linked the Mercator projection to its modern logarithmic formula.

MERCATOR’S PROJECTION

Mercator’s 1569 map showed a large rendering of the earth on a flat surface measuring 79 ½ inches by 49 inches, printed originally on eighteen leaves. It is a cylindrical projection in which parallels and meridians are straight and perpendicular to each other. So at every point location the east-west scale is the same as the north-south scale, making the projection “conformal”, and on such a projection, angles are preserved from any location.

Because the linear scale of a Mercator map increases with latitude, it distorts the size of objects far from the equator, an effect which can be alleviated- particularly locally with a Secant Projection.  At latitudes greater than 70° north or south the Mercator projection is impractical: the linear scale becomes infinitely long at the poles. This form of Mercator map can never fully show the polar regions but a Transverse Mercator projection can. The Ordnance Survey uses the Transverse Mercator Projection for its survey of Great Britain- however on such a projection rhumb lines are no long straight but arc.

All lines of so-called rhumb lines or loxodromes are straight on a standard Mercator map. The two properties, conformality and straight loxodromes, make this projection most suited for marine navigation.

Mercator’s 1569 world map was entitled “Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata”: “A New and Improved Description of the Sphere of the Earth Corrected for the Use of Navigators (sailors)”. Although the method of construction is not explained by the author, Mercator probably used a manual graphic method, transferring a sample of rhumb lines, plotted on a globe, to a grid formed out of lines of latitude and longitude, and then adjusting the spacing between parallels so that those lines became straight.

It was much ahead of its time: the old navigational techniques were not compatible with its use in navigation. Two factors prevented its immediate adoption: the impossibility of determining the longitude at sea accurately; and, that magnetic directions, not geographical directions, were used in navigation. Only in the 18th century, when the marine chronometer was perfected by Harrison- which led to the distribution of magnetic declination being known, could Mercator’s projection be adopted.

For maps, the ellipsoid of the Earth is approximated to a sphere of of a given radius x. Many different methods exist for calculating x. They throw up variations of about 21 miles which for most maps may be ignored, and one arrives at mean values giving a radius of 3959 miles and circumference of 24,873 miles. Cylindrical projections: The spherical Earth with radius “x” can be modelled by a sphere internal to a cylinder of radius “r”, which determines the scale of the map. The cylinder is unrolled to give the planar map.

Since the cylinder is tangential to the globe at the equator, the scale between globe and cylinder is completely accurate on equator but nowhere else.

A classic way of showing the distortion inherent in a Mercator projection is to use Tissot’s indicatrix. Nicolas Tissot (1824-1897) was a French cartographer who noted that for cylindrical projections the scale factors at a point, define an ellipse at that point of the projection. The axes of the ellipse are aligned to the meridians and parallels. His distortion circles, show the level of distortion at any latitude from accurate at the Equator to very elongated eclipses near the poles.

One measure of a map’s accuracy is a comparison of the length of corresponding lines on the map and globe. Therefore, by construction, the Mercator projection is perfectly accurate along the equator and nowhere else. At a latitude of 25 degrees north or south of the Equator it is about 1.1 of the equatorial length, and therefore the projection may be deemed accurate to within 10% in a strip of width 50° 9north and south and centred on the equator). Therefore, the Mercator projection is adequate for mapping countries close to the equator: hence the development of the secant Mercator variant.

In a Secant Mercator projection the globe is projected to a cylinder which passes without the sphere at two parallel latitudes in the north and south hemispheres. The scale is now true at these latitudes whereas parallels between these latitudes (near the equator) are contracted by the projection and their scale factor there must be less than one. The result is that deviation of the scale from unity is reduced over a wider range of latitudes.

The scale on the equator is less than 1:1; and is dead accurate at the two secant latitudes, where the sphere touches the cylinder. But the inaccuracy is generally reduced and spread over a wider band of latitudes.

Therefore, the projection has a better general accuracy compared with the standard Mercator projection, particularly for seas beyond the tropics.

Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. The scale varies with latitude.

The distinction between rhumb (sailing) distance and great circle (true) distance was well understood by Mercator. He stated that the rhumb line distance is an acceptable approximation for true great circle distance only for courses of short or moderate length, and particularly so at lower latitudes. He said: “When the great circle distances to be measured are in the vicinity of the equator do not exceed 20 degrees of a great circle, or 15 degrees near Spain and France, or 8 and even 10 degrees in northern parts it is convenient to use rhumb line distances”.

In his general descriptions of usage, he e thus divided the world known to him into three zones of navigation:

1:  “Northern”, which meant  British  Isles , North Germany, the Baltic etc.

2.  France and Spain.

3. Tropics.

On the equator: Scale is correct on the equator. Therefore, interpreting ruler measurements on the equator is simple: True distance  equals ruler distance.

On a meridian: A meridian of the map is a great circle on the globe but the continuous variation of scale as one travels s=north or south of the Equator means ruler measurement cannot show the true distance between points on the meridian. However, if the map is marked with an accurate and finely spaced latitude scale from which the latitude may be read directly—as is the case on three of the 18 plates which form the Mercator 1569 world map,  and on all subsequent nautical charts.