Category Archives: History of Navigation

An inventor of instruments

Way back at the beginning of November I wrote what was intended to be the first of a series of posts about English mathematical practitioners, who were active at the end of the sixteenth and the beginning of the seventeenth centuries. I did not think it would be two months before I could continue that series with a second post, but first illness and then my annual Christmas trilogy got in the way and so it is only now that I am doing so. The subject of this post is a man for whom a whole series of mathematical instruments are named, Edmund Gunter (1581–1626).

Unfortunately, as is all to often the case with Renaissance mathematici, we know almost nothing about Gunter’s origins. His father was apparently a Welshmen from Gunterstown, Brecknockshire in South Wales but he was born somewhere in Hertfordshire sometime in 1581. Obviously from an established family he was educated at Westminster School as a Queen’s Scholar i.e., a foundation scholar (elected on the basis of good academic performance and usually qualifying for reduced fees). He matriculated at Christ Church Oxford 25 January 1599 (os). He graduated BA 12 December 1603 and MA 2 July 1606. He took religious orders and proceeded B.D. 23 November 1615. He was appointed Rector of St. George’s, Southwark and of St Mary Magdalen, Oxford in 1615, he retained both appointments until his death. 

Whilst still a student in 1603, he wrote a New Projection of the Sphere in Latin, which remained in manuscript until it was finally published in 1623. This came to the attention of Henry Briggs (1561–1630), who had been appointed professor of geometry at the newly founded Gresham College in 1596, and as such was very much a leading figure in the English mathematical community. Briggs was impressed by the young mathematician befriending him and becoming his mentor. The two men spent much time together at Gresham College discussing topics of practical mathematics. In 1606, Gunter developed a sector, about which later, and wrote a manuscript describing it in Latin, without a known title. This circulated in manuscript for many years and was much in demand. Gunter gave into that demand and finally published it also in 1623.

When the first Gresham professor of astronomy, Edward Brerewood (c. 1556–1613) died 4 November 1613, Briggs recommended Gunter as his successor. However, Thomas Williams another Christ Church graduate, of whom little is known, was appointed just seven days later 11 November 1613. When Williams resigned from the post 4 March 1619, for reasons unknown, Briggs once again supported his friend for the position, this time with success. Gunter was appointed just two days later, 6 March 1619. Like his two rectorships, he retained the Gresham professorship until his death. 

Gresham College, engraving by George Vertue, 1740 Source: Wikimedia Commons

Apparently, he was already spending so much time at Gresham College before being appointed that when the mathematician William Oughtred (1574–1660) visited Henry Briggs there in 1618, he thought that Gunter was already professor there.

In the Spring 1618 I being at London went to see my honoured friend Master Henry Briggs at Gresham College: who then brought me acquainted with Master Gunter lately chosen Astronomical lecturer there, and was at that time in Doctor Brooks his chamber. With whom falling into speech about his quadrant, I showed him my Horizontal Instrument. He viewed it very heedfully: and questioned about the projecture and use thereof, often saying these words, it is a very good one. And not long after he delivered to Master Briggs to be sent to me mine own Instrument printed off from one cut in brass: which afterwards I understood he presented to the right Honourable the Earl of Bridgewater, and in his book of the sector printed six years after, among other projections he setteth down this.

Gunter and Oughtred would go on to become firm friends.

William Oughtred engraving by Wenceslaus Hollar Source: Wikimedia Commons There are apparently no portraits of Briggs or Gunter

We now have the known details of the whole of Gunter’s life and can turn our attention to his mathematical output but before we do so there is an anecdote from Seth Ward (1617–1689), another mathematician and astronomer, concerning a position that Gunter did not get. In 1619, Henry Savile (1549–1622) established England’s first university chairs for mathematics the Savilian chairs for geometry and astronomy at Oxford. Savile’s first choice for the chair of geometry was Edmund Gunter and he invited him to an interview, according to John Aubrey (1626–1697) relating a report from Seth Ward:

[Gunter] brought with him his sector and quadrant, and fell to resolving triangles and doing a great many fine things. Said the grave knight [Savile], “Do you call this reading of geometry? This is showing of tricks, man!”, and so dismissed him with scorn, and sent for Henry Briggs.

So, Henry Briggs became England’s first university professor of geometry and not Edmund Gunter. One should point out that Ward can only have heard the story second hand as he was only two years old in 1619.

In 1614, John Napier (1550–1617) published his Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Canon of Logarithms, 1614), a new method of simplifying calculations. Edward Wright (1561–1615) produced an English translation, which was published posthumously in 1616. Napier’s logarithms were base:

NapLog(x) = –107ln (x/107)

Henry Briggs travelled all the way to Edinburgh to meet the inventor of this new calculating tool. After discussion with Napier, he received his blessing to produce a set of base ten logarithms. His Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.

Many people don’t realise that Napier’s logarithmic tables were not straight logarithms but logarithms of trigonometrical functions. These are of particular use for astronomers and navigators. It is almost certainly through Brigg’s influence that Gunter’s first publication was a set of base ten, seven figure logarithmic tables of sines and tangents. His Canon Triangulorum sive Tabulae Sinuum et Tangentium Artificialum was published in Latin in 1620. An English translation was published in the same year. The terms sine and tangent were already in use, but it was Gunter, who introduced the terms cosine and cotangent in this publication. Later, on his scale or rule he introduced the short forms sin and tan.

In 1623, Gunter finally published his New Projection of the Sphere written in his last year as an undergraduate. He also published his most important book, Description and Use of the Sector, the Crosse-staffe and other Instruments. This was one of the most important guides to the use of navigational instruments for seamen and became something of a seventeenth century best seller in various forms. David Waters in his The Art of Navigation say this, ” Gunter’s De Sectore & Radio must rank with Eden’s translation of Cortes’s Arte de Navegar and Wright’s Certain Errors as one of the three most important English books ever published for the improvement of navigation.” [1]

Waters opposite page 360

His various publications were collected into The Works of Edmund Gunter, which went through six editions by 1680. Each edition having extra content by other authors. Isaac Newton (1642-1727) bought a copy of the second edition. The title page of the fifth edition is impressive:

The Workers of Edmund Gunter 5th ed. Title page with diagrams of the sector on the fly leaf

The Works of Edmund Gunter:
Containing the description and Use of the
Sector, Cross-staff, Bow, Quadrant,
And other Instruments.
With a Canon of Artificial Sines and Tangents to a Radius of 10.00000 parts, and the Logarithms from Unite to 100000:
The Uses whereof are illustrated in the Practice of
Arithmetick, geometry, Astronomy, Navigation, Dialling and Fortification.
And some Questions in Navigation added by Mr. Henry Bond, Teacher of mathematicks in Ratcliff, near London.
To which is added,
The Description and Use of another Sector and Quadrant, both of them invented by Mr. Sam. Foster, Late Professor of Astronomy in Gresham Colledge, London, furnished with more Lines, and differing from those of Me. Gunter′s both in form and manner of Working.
The Fifth Edition,
Diligentyl Corrected, and divers necessary Things and Matters (pertinent thereunto) added, throughout the whole work, not before Printed.
By William Leybourne, Philomath.
London
Printed by A.C. for Francis Eglesfield at the Marigold in St. Pauls Church-yard. MDCLXXIII.

The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication, and division, geometry, and trigonometry, and for computing various mathematical functions, such as square and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. (Wikipedia)

The sector has many alleged inventors. The earliest was Fabrizio Mordente (1532–c. 1608). The invention is often credited to Galileo (1564–1642), who marketed a very successful variant in the early seventeenth century, including selling lessons and an instruction manual in its use. However, Galileo’s instrument was a development of one created by Guidobaldo dal Monte (1545–1607). It is not known if dal Monte developed the device independently or knew of Mordent’s. Thomas Hood (1556–1620) appear to have reinvented the instrument, a description of which he published in his Making and Use of the Sector, 1596.

Waters opposite page 345

Gunter developed Hood’s instruments adding addition scales, including a scale for use with Mercator’s new projection of the sphere. 

 

Water opposite page 361
Waters page 361

The French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin). 

Gunter image of a cross staff

Gunter’s book also describes the Gunter Quadrant, basically a horary quadrant for telling the time by taking the altitude of the sun but with some additional functions.

Boxwood Gunter-type sector, made by Isaac Carver and owned by George Lason; 1706 Whipple Museum
Illustration of a quadrant from Edmund Gunter’s Works (1653). Image © the Whipple Library.
Modern reproduction of the Gunter Quadrant Source

There is also a description of the crossbow an alternative to the backstaff that never became popular. 

; Navigation: an Astrolabe, a Cross-Staff, and a Back-Staff or Davis’s Sextant; Wellcome Collection; http://www.artuk.org/artworks/navigation-an-astrolabe-a-cross-staff-and-a-back-staff-or-daviss-sextant-241142
; Navigation: a Cross-Staff or Cross-Bow, and a Sailor Using the Device; Wellcome Collection; http://www.artuk.org/artworks/navigation-a-cross-staff-or-cross-bow-and-a-sailor-using-the-device-241141

Gunter’s most popular instrument was his scale. The Gunter scale or rule was a rule containing trigonometrical and logarithmic scales, which could be used with a pair of dividers to carry out calculations in astronomy and in particular navigations. The Gunter scale is basically a sector folded into a straight line without the hinge.Sailors simply referred to the rule as a Gunter. William Oughtred would go on to place two Gunter rules next to each other thus creating the slide rule and eliminating the need for dividers to carry out the calculations.

Gunter scale front side
Gunter scale back side

In 1622, Gunter engraved a new sundial at Whitehall, which carried many different dial plates supplying much astronomical data. At the behest of Prince Charles, he wrote and published an explanation of the dials, The Description and Use of His Majesties Dials in Whitehall, 1624. The sundial was demolished in 1697.

Gunter’s most well-known instrument was his surveyor’s chain, which became the standard English Imperial chain. 100 links and 22 yards (66 feet) long, there are 10 chains in a furlong and 80 chains to a mile. 

Although Gunter invented, designed, and described the use of several instruments, he didn’t actually make any of them. All of his instruments were produced by the London based, instrument maker Elias Allen (c. 1588–1652). Allen was born in Kent of unknown parentage and was apprenticed in 1602 to London instrument maker Charles Whitwell (c. 1568–1611) in the Grocer’s Company, serving his master for nine years. Following Whitwell’s death in 1611, Allen set up his own business. He rapidly became the foremost instrument maker in London, working mostly in brass, but occasionally in silver. He became very successful and made instruments for various aristocratic patrons and both James I and Charles I. Allen also produced the engravings in Gunter’s books, using them also as advertising in his shop.

He worked closely with various mathematicians including both Oughtred and Gunter. His workshop became a meeting place for discussion amongst mathematical practitioners. He was the first London instrument maker, who could make a living from just making instruments without working on the side as a map engraver or surveyor. His master Whitwell subsidised his income as a map engraver. He rose in status in the Grocers’ Company, becoming its treasurer in 1636 and its master for eighteen months in 1637-38. Over the years many of his apprentices became successful instrument maker masters in the own right, most notably Ralph Greatorex (1625–1675), who was associated with Oughtred, Samuel Pepys, John Evelyn, Samuel Hartlib, Christopher Wren, Robert Boyle, and Jonas Moore, the English scientific elite of the time. 

Allen had the distinction of being one of the few seventeenth-century artisans to have his portrait painted. The Dutch artist Hendrik van der Borcht the Younger (1614–1676) produced the portrait, now lost, in about 1640. It still exists as an engraving done by the Bohemian engraver, Wenceslaus Hollar (1607­–1677).

Edmund Gunter was not a mathematician as we understand the term today, but a mathematical practitioner, who exercised a large influence on the practical side of astronomy, navigation, and surveying in the seventeenth century through the instruments that he designed and the texts he wrote explaining how to use them. 

[1] David Walters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359

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

Renaissance Science – XLVIII

Using the simplest and widest definition as to what constitutes a scientific instrument, it is literally impossible to say who first created, devised, used a scientific instrument or when and where they did it. My conjecture would be that the first scientific instrument was some sort of measuring device, a rod, or a cord to standardise a unit of measurement, almost certainly taken from the human body: a forearm, the length of a stride or pace, maybe a foot, a unit that we still use today. It is obviously that all the early great civilisation, Indus valley, Yellow River, Yangtze River, Fertile Crescent and so on, definitely used measuring devices, possibly observational devices, instruments to measure or lay out angles, simple compasses to construct circles, all of them probably as much to do with architecture and surveying, as with anything we might now label science.

This is the Royal cubit rod of Amenemope – a 3320-year-old measuring rod which revealed that Egyptians used units of measurement taken from the human body. The basic unit was the cubit – the length from the elbow to the tip of the middle finger, about 45cm. Source: British Museum

Did the early astronomers in China, India, Babylon use some sorts of instruments to help them make their observations? We know that later people used sighting tubes, like a telescope without the lenses, to improve the quality of their observations, did those first astronomers already use something similar. Simple answer, we don’t really know, we can only speculate. We do know that Indian astronomers used a quadrant in their observation of solar eclipses around 1000 BCE. 

Turning to the Ancient Greeks we initially have a similar lack of knowledge. The first truly major Greek astronomer Hipparkhos (c. 190–c. 120 BCE) (Latin Hipparchus) definitely used astronomical instruments but we have no direct account of his having done so. Our minimal information of his instruments comes from later astronomers, such as Ptolemaios (c. 100–c. 170 CE). Ptolemaios tells us in his Mathēmatikē Syntaxis aka Almagest that Hipparkhos made observations with an equatorial ring.

The easiest way to understand the use of an equatorial ring is to imagine a ring placed vertically in the east-west plane at the Earth’s equator. At the time of the equinoxes, the Sun will rise precisely in the east, move across the zenith, and set precisely in the west. Throughout the day, the bottom half of the ring will be in the shadow cast by the top half of the ring. On other days of the year, the Sun passes to the north or south of the ring, and will illuminate the bottom half. For latitudes away from the equator, the ring merely needs to be placed at the correct angle in the equatorial plane. At the Earth’s poles, the ring would be horizontal. Source: Wikipedia

At another point in the book Ptolemaios talks of making observations with an armillary sphere and compares his observations with those of Hipparkhos, leading some to think that Hipparkhos also used an armillary sphere. Toomer in his translation of the Almagest say there is no foundation for this speculation and that Hipparkhos probably used a dioptra. [1]

Ptolemaios mentions four astronomical instruments in his book, all of which are for measuring angles: 

1) A double ring device and

Toomer p. 61

2) a quadrant both used to determine the inclination of the ecliptic.

Toomer p. 62

3) The armillary sphere, which he confusingly calls an astrolabe, used to determine sun-moon configurations. 

Toomer p. 218

4) His parallactic rulers, used to determine the moon’s parallax, which was called a triquetrum in the Middle Ages. 

Toomer p. 245

Ptolemaios almost certainly also used a dioptra a simple predecessor to the theodolite used for measuring angles both in astronomy and in surveying. As I outlined in the post on surveying, ancient cultures were also using instruments to carry out land measuring.

Graphic reconstruction of the dioptra, by Venturi, in 1814. (An incorrect interpretation of Heron’s description) Source: Wikimedia Commons

Around the same time as the armillary sphere began to emerge in ancient Greece it also began to emerge in China, with the earliest single ring device probably being used in the first century BCE. By the second century CE the complete armillary sphere had evolved ring by ring. When the armillary sphere first evolved in India is not known, but it was in full used by the time of Āryabhata in the fifth century CE.

Armillary sphere at Beijing Ancient Observatory, replica of an original from the Ming Dynasty

A parallel development to the armillary sphere was the celestial globe, a globe of the heavens marked with the constellations. In Greece celestial globes predate Ptolemaios but none of the early ones have survived.  In his Almagest, Ptolemaios gives instruction on how to produce celestial globes. Chinese celestial globes also developed around the time of their armillary spheres but, once again, none of the early ones have survived. As with everything else astronomical, the earliest surveying evidence for celestial globes in India is much later than Greece or China.

The Farnese Atlas holding a celestial globe is the oldest known surviving celestial globe dating from the second century CE Source: Wikimedia Commons

In late antiquity the astrolabe emerged, its origins are still not really clear. Ptolemaios published a text on the planisphere, the stereographic projection used to create the climata in an astrolabe and still used by astronomers for star charts today. The earliest references to the astrolabe itself are from Theon of Alexandria (c. 335–c. 414 CE). All earlier claims to existence or usage of astrolabes are speculative. No astrolabes from antiquity are known to have survived. The earliest surviving astrolabe is an Islamic instrument dated AH 315 (927-28 CE).

North African, 10th century AD, Planispheric Astrolabe Khalili Collection via Wikimedia Commons

Late Antiquity and the Early Middle Ages saw a steady decline in the mathematical sciences and with it a decline in the production and use of most scientific instruments in Europe until the disappeared almost completely. 

When the rapidly expanding Arabic Empire began filing their thirst for knowledge across a wide range of subjects by absorbing it from Greek, Indian and Chinese sources, as well as the mathematical disciplines they also took on board the scientific instruments. They developed and perfected the astrolabe, producing hundreds of both beautiful and practical multifunctional instruments. 

As well large-scale astronomical quadrants they produced four different types of handheld instruments. In the ninth century, the sine or sinical quadrant for measuring celestial angles and for doing trigonometrical calculations was developed by Muḥammad ibn Mūsā al-Khwārizmī. In the fourteenth century, the universal (shakkāzīya) quadrant used for solving astronomical problems for any latitude. Like astrolabes, quadrants are latitude dependent and unlike astrolabes do not have exchangeable climata. Origin unknown, but the oldest known example is from 1300, is the horary quadrant, which enables the uses to determine the time using the sun. An equal hours horary quadrant is latitude dependent, but an unequal hours one can be used anywhere, but its use entails calculations. Again, origin unknown, is the astrolabe quadrant, basically a reduced astrolabe in quadrant form. There are extant examples from twelfth century Egypt and fourteenth century Syria.

Horary quadrant for a latitude of about 51.5° as depicted in an instructional text of 1744: To find the Hour of the Day: Lay the thread just upon the Day of the Month, then hold it till you slip the small Bead or Pin-head [along the thread] to rest on one of the 12 o’Clock Lines; then let the Sun shine from the Sight G to the other at D, the Plummet hanging at liberty, the Bead will rest on the Hour of the Day. Source: Wikimedia Commons
Astrolabic quadrant, made of brass; made for latitude 33 degrees 30 minutes (i.e. Damascus); inscription on the front saying that the quadrant was made for the ‘muwaqqit’ (literally: the timekeeper) of the Great Umayyad Mosque of Damascus. AH 734 (1333-1334 CE) British Museum

Islamicate astronomers began making celestial globes in the tenth century and it is thought that al-Sufi’s Book of the Constellations was a major source for this development. However, the oldest surviving Islamic celestial globe made by Ibrahim Ibn Saîd al-Sahlì in Valencia in the eleventh century show no awareness of the forty-eight Greek constellations of al-Sufi’s book.

Islamicate mathematical scholars developed and used many scientific instruments and when the developments in the mathematical sciences that they had made began to filter into Europe during the twelfth century scientific renaissance those instruments also began to become known in Europe. For example, the earliest astrolabes to appear in Europe were on the Iberian Peninsula, whilst it was still under Islamic occupation.  

Canterbury Astrolabe Quadrant 1388 Source Wikimedia Commons
Astrolabe of Jean Fusoris, made in Paris, 1400 Source: Wikimedia Commons

The medieval period in Europe saw a gradual increase in the use of scientific instruments, both imported and locally manufactured, but the use was still comparatively low level. There was some innovation, for example the French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin). 

…of a staff of 4.5 feet (1.4 m) long and about one inch (2.5 cm) wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars

Source
A Jacob’s staff, from John Sellers’ Practical Navigation (1672) Source: Wikimedia Commons

Also, the magnetic compass came into use in Europe in the twelfth century, first mentioned by Alexander Neckam (1157–1217) in his De naturis rerum at the end of the century.

The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.

Petrus Pereginus (fl. 1269) gave detailed descriptions of both the floating compass and the dry compass in his Epistola de magnete

However, it was first in the Renaissance that a widespread and thriving culture of scientific instrument design, manufacture, and usage really developed. The steep increase in scientific instrument culture was driving by the substantial parallel developments in astronomy, navigation, surveying, and cartography that began around fourteen hundred that I have already outlined in previous episodes of this series. Renaissance scientific instrument culture is too large a topic to cover in detail in one blog post, so I’ll only do a sketch of some major points and themes with several links to other earlier related posts.

Already, the first Viennese School of Mathematics, which was heavily involved in the development of both astronomy and cartography was also a source of scientific instrument design and manufacture.Johannes von Gmunden (c. 1380–1442) had a notable collection of instruments including an Albion, a multipurpose instrument conceived by Richard of Wallingford (1292–1336).

Albion front side Source: Seb Falk’s Twitter feed
Albion rear Source: Seb Falk’s Twitter feed

Georg von Peuerbach (1423–1461) produced several instruments most notably the earliest portable sundial marked for magnetic declination.

Folding sundial by Georg von Peuerbach

His pupil Regiomontanus (1436–1476) wrote a tract on the construction and use of the astrolabe and there is an extant instrument from 1462 dedicated to Cardinal Bessarion and signed IOHANNES, which is assumed to have been made by him. At least eleven other Regiomontanus style astrolabes from the fifteenth century are known.

Regiomontanus style astrolabe Source: Wikimedia Commons

Elements of his design were adopted by both Johannes Stöffler (1452–1531), the first professor of astronomy at the University of Tübingen, and by the Nürnberger mathematicus Georg Hartmann (1489–1564).

Stöffler also made celestial globes and an astronomical clock.

Celestial Globe, Johannes Stöffler, 1493; Landesmuseum Württemberg Source: Wikimedia Commons

Mechanical astronomical clocks began to emerge in Europe in the fourteenth century, but it would not be until the end of the sixteenth century that mechanical clocks became accurate enough to be used as scientific instruments. The earliest clockmaker, who reached this level of accuracy being the Swiss instrument maker, Jost Bürgi (1552–1632)

Bürgi made numerous highly elaborate and very decorative mechanical clocks, mechanised globes and mechanised armillary spheres that were more collectors items for rich patrons rather than practical instruments.

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society

This illustrates another driving force behind the Renaissance scientific instrument culture. The Renaissance mathematicus rated fairly low in the academical hierarchy, actually viewed as a craftsman rather than an academic. This made finding paid work difficult and they were dependent of rich patrons amongst the European aristocracy. It became a standard method of winning the favour of a patron to design a new instrument, usually a modification of an existing one, making an elaborate example of it and presenting it to the potential patron. The birth of the curiosity cabinets, which often also included collections of high-end instruments was also a driving force behind the trend. Many leading instrument makers produced elaborate, high-class instruments for such collections. Imperial courts in Vienna, Prague, and Budapest employed court instrument makers. For example, Erasmus Habermel (c. 1538–1606) was an incredibly prolific instrument maker, who became instrument maker to Rudolf II. A probable relative Josua Habermel (fl. 1570) worked as an instrument maker in southern Germany, eventually moving to Prague, where he probably worked in the workshop of Erasmus.

 1594 armillary sphere by Erasmus Habermel of Prague.

Whereas from Theon onwards, astrolabes were unique, individual, instruments, very often beautiful ornaments as well as functioning instruments, Georg Hartmann was the first instrument maker go into serial production of astrolabes. Also, Hartmann, although he didn’t invent them, was a major producer of printed paper instruments. These could be cut out and mounted on wood to produce cheap, functional instruments for those who couldn’t afford the expensive metal ones. 

Hartmann astrolabe front
Hartmann astrolabe rear
Paper and Wood Astrolabe Hartmann Source: HSM Oxford

Hartmann lived and worked in Nürnberg, which as I have sketched in an earlier post, was for more than a century the scientific instrument capital of Europe with a massive produce of instruments of all sorts.

One of the most beautiful sets on instruments manufactured in Nürnberg late 16th century. Designed by Johannes Pretorius (1537–1616), professor for astronomy at the Nürnberger University of Altdorf and manufactured by the goldsmith Hans Epischofer (c. 1530–1585) Germanische National Museum

As well as astrolabes and his paper instruments Hartmann also produced printed globes, none of which have survived. Another Nürnberger mathematicus, Johannes Schöner (1477–1547) launched the printed pairs of terrestrial and celestial globes onto the market.

Celestial Globe by Johannes Schöner c. 1534 Source

His innovation was copied by Gemma Frisius (1508–1555), whose student Gerard Mercator (1512–1594) took up globe making on a large scale, launching the seventeenth century Dutch globe making industry. 

Gemma Frisius set up a workshop producing a range of scientific instruments together with his nephew (?) Gualterus Arsenius (c. 1530–c. 1580).  

Astronomical ring dial Gualterus Arsenius Source

In France, Oronce Fine (1494–1555), a rough contemporary, who was appointed professor at the Collège Royal, was also influenced by Schöner in his cartography and like the Nürnberger was a major instrument maker. In Italy, Egnatio Danti (1536–1586) the leading cosmographer was also the leading instrument maker. 

Egnation Danti, Astrolabe, ca. 1568, brass and wood. Florence, Museo di Storia della Scienza Source: Fiorani The Marvel of Maps p. 49

A major change during the Renaissance was the emergence, for the first time in Early Modern Europe, of large-scale astronomical observatories, Wilhelm IV (1532–1592) in Hessen-Kassel beginning in about 1560 and Tycho Brahe (1546–1601) on the Island of Hven beginning in 1575. Both men commissioned new instruments, many of which were substantially improved in comparison with their predecessors from antiquity.

Sternwarte im Astronomisch-Physikalischen Kabinett, Foto: MHK, Arno Hensmanns Reconstruction of Wilhelm’s observatory
Tycho Brahe, Armillary Sphere, 1581 Source
Tycho Brahe quadrant

Their lead was followed by others, the first Vatican observatory was established in the Gregorian Tower in 1580.

View on the Tower of Winds (Gregorian tower) in Vatican City (with the dome of Saint Peter’s Basilica in the background). Source: Wikimedia Commons

In the early seventeenth century, Leiden University in Holland established the first European university observatory and Christian Longomontanus (1562–1647), who had been Tycho’s chief assistant, established a university observatory in Copenhagen 

Drawing of Leiden Observatory in 1670, seen on top of the university building. Source: Wikimedia Commons
Copenhagen University Observatory Source: Wikimedia Commons

As in all things mathematical England lagged behind the continent but partial filled the deficit by importing instrument makers from the continent, the German Nicolas Kratzer (c. 1487–1550) and the Netherlander Thomas Gemini (c. 1510–1562). The first home grown instrument maker was Humfrey Cole (c. 1530­–1591). By the end of the sixteenth century, led by John Dee (1527–c. 1608), who studied in Louven with Frisius and Mercator, and Leonard Digges (c. 1515–c. 1559), a new generation of English instrument makers began to dominate the home market. These include Leonard’s son Thomas Digges (c. 1546–1595), William Bourne (c. 1535–1582), John Blagrave (d. 1611), Thomas Blundeville (c. 1522–c. 1606), Edward Wright (1561–1615), Emery Molyneux (d. 1598), Thomas Hood (1556–1620), Edmund Gunter (1581–1626) Benjamin Cole (1695–1766), William Oughtred (1574–1660), and others.

The Renaissance also saw a large amount of innovation in scientific instruments. The Greek and Chinese armillary spheres were large observational instruments, but the Renaissance armillary sphere was a table top instrument conceived to teach the basic of astronomy.

Armillary Sphere by Carlo Plato, Rome, 1588 Museum of the History of Science

In navigation the Renaissance saw the invention various variations of the backstaff, to determine solar altitudes.

Davis quadrant (backstaff), made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons

Also new for the same purpose was the mariner’s astrolabe.

Mariner’s Astrolabe c. 1600 Source: Wikimedia Commons

Edmund Gunter (1581–1626) invented the Gunter scale or rule a multiple scale (logarithmic, trigonometrical) used to solve navigation calculation just using dividers.

Gunter scale front
Gunter scale back Source

William Oughtred (1574–1660) combined two Gunter scales to produce the slide rule.

New in surveying were the surveyor’s chain,

A Gunter chain photographed at Campus Martius Museum. Source: Wikimedia Commons

the plane table,

Surveying with plane table and surveyor’s chain

the theodolite

Theodolite 1590 Source:

and the circumferentor.

18th century circumferentor

All of which were of course also used in cartography. Another Renaissance innovation was sets of drawing instruments for the cartographical, navigational etc draughtsmen.

Drawing instruments Bartholomew Newsum, London c. 1570 Source

The biggest innovation in instruments in the Renaissance, and within its context one of the biggest instrument innovation in history, were of course the telescope and the microscope, the first scientific instruments that not only aided observations but increased human perception enabling researchers to perceive things that were previously hidden from sight. Here is a blog post over the complex story of the origins of the telescope and one over the unclear origins of the microscope.

The Renaissance can be viewed as the period when instrumental science began to come of age. 

[1] The information on Ptolemaios’ instruments and the diagrams are taken from Ptolemy’s Almagest, translated and annotated by G. J. Toomer, Princeton Paperbacks, 1998

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Filed under History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of Technology, Renaissance Science

THE MATHEMATICAL IEVVEL

Due to the impact of Isaac Newton and the mathematicians grouped around him, people often have a false impression of the role that England played in the history of the mathematical sciences during the Early Modern Period. As I have noted in the past, during the late medieval period and on down into the seventeenth century, England in fact lagged seriously behind continental Europe in the development of the mathematical sciences both on an institutional level, principally universities, and in terms of individual mathematical practitioners outside of the universities. Leading mathematical practitioners, working in England in the early sixteenth century, such as Thomas Gemini (1510–1562) and Nicolas Kratzer (1486/7–1550) were in fact immigrants, from the Netherlands and Germany respectively.

In the second half of the century the demand for mathematical practitioners in the fields of astrology, astronomy, navigation, cartography, surveying, and matters military was continually growing and England began to produce some home grown talent and take the mathematical disciplines more seriously, although the two universities, Oxford and Cambridge still remained aloof relying on enthusiastic informal teachers, such as Thomas Allen (1542–1632) rather than instituting proper chairs for the study and teaching of mathematics.

Outside of the universities ardent fans of the mathematical disciplines began to establish the so-called English school of mathematics, writing books in English, giving tuition, creating instruments, and carrying out mathematical tasks. Leading this group were the Welsh man, Robert Recorde (c. 1512–1558), who I shall return to in a later post, John Dee (1527–c. 1608), who I have dealt with in several post in the past, one of which outlines the English School, other important early members being, Dee’s friend Leonard Digges, and his son Thomas Digges (c. 1446–1595), who both deserve posts of their own, and Thomas Hood (1556–1620) the first officially appointed lecturer for mathematics in England.  I shall return to give all these worthy gentlemen, and others, the attention they deserve but today I shall outline the life and mathematical career of John Blagrave (d. 1611) a member of the landed gentry, who gained a strong reputation as a mathematical practitioner and in particular as a designer of mathematical instruments, the antiquary Anthony à Wood (1632–1695), author of Athenae Oxonienses. An Exact History of All the Writers and Bishops, who Have Had Their Education in the … University of Oxford from the Year 1500 to the End of the Year 1690, described him as “the flower of mathematicians of his age.”

John Blagrave was the second son of another John Blagrave of Bullmarsh, a district of Reading, and his wife Anne, the daughter of Sir Anthony Hungerford of Down-Ampney, an English soldier, sheriff, and courtier during the reign of Henry VIII, John junior was born into wealth in the town of Reading in Berkshire probably sometime in the 1560s. He was educated at Reading School, an old established grammar school, before going up to St John’s College Oxford, where he apparently acquired his love of mathematics. This raises the question as to whether he was another student, who benefitted from the tutoring skills of Thomas Allen (1542–1632). He left the university without graduating, not unusually for the sons of aristocrats and the gentry. He settled down in Southcot Lodge in Reading, an estate that he had inherited from his father and devoted himself to his mathematical studies and the design of mathematical instruments. He also worked as a surveyor and was amongst the first to draw estate maps to scale.

Harpsden a small parish near Henley-on-Thames Survey by John Blagrave 1589 Source

There are five known surviving works by Blagrave and one map, as opposed to a survey, of which the earliest his, The mathematical ievvel, from1585, which lends its name to the title of this post, is the most famous. The full title of this work is really quite extraordinary:

 THE MATHEMATICAL IEVVEL 

Shewing the making, and most excellent vse of a singuler Instrument So called: in that it performeth with wonderfull dexteritie, whatsoever is to be done, either by Quadrant, Ship, Circle, Cylinder, Ring, Dyall, Horoscope, Astrolabe, Sphere, Globe, or any such like heretofore deuised: yea or by most Tables commonly extant: and that generally to all places from Pole to Pole. 

The vse of which Ievvel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway (from the first steppe to the last) through the whole Artes of Astronomy, Cosmography, Geography, Topography, Nauigation, Longitudes of Regions, Dyalling, Sphericall triangles, Setting figures, and briefely of whatsoeuer concerneth the Globe or Sphere: with great and incredible speede, plainenesse, facillitie, and pleasure:

The most part newly founde out by the Author, Compiled and published for the furtherance, aswell of Gentlemen and others desirous or Speculariue knowledge, and priuate practise: as also for the furnishing of such worthy mindes, Nauigators,and traueylers,that pretend long voyages or new discoueries: By John Blagave of Reading Gentleman and well willer to the Mathematickes; Who hath cut all the prints or pictures of the whole worke with his owne hands. 1585•

Dig the spelling!
Title Page Source Note the title page illustration is an  armillary sphere and not the Mathematical Jewel

Blagrave’s Mathematical Jewel is in fact a universal astrolabe, and by no means the first but probably the most extensively described. The astrolabe is indeed a multifunctional instrument, al-Sufi (903–983) describes over a thousand different uses for it, and Chaucer (c. 1340s–1400) in what is considered to be the first English language description of the astrolabe and its function, a pamphlet written for a child, describes at least forty different functions. However, the normal astrolabe has one drawback, the flat plates, called tympans of climata, that sit in the mater and are engraved with the stereographic projection of a portion of the celestial sphere are limited in their use to a fairly narrow band of latitude, meaning that if one wishes to use it at a different latitude you need a different climata. Most astrolabes have a set of plates each engraved on both side for a different band of latitude. This problem led to the invention of the universal astrolabe.

Full-page figure of the rete of Blagrave’s Jewel (Peterborough A.8.13) For more illustration from The Mathematical Jewel go here

The earliest known universal astrolabes are attributed to Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī al-Tujibi (1029-1100), known simply as al-Zarqālī and in Latin as Arzachel, an Arabic astronomer, astrologer, and instrument maker from Al-Andalus, and another contemporary Arabic astronomer, instrument maker from Al-Andalus, Alī ibn Khalaf: Abū al‐Ḥasan ibn Aḥmar al‐Ṣaydalānī or simply Alī ibn Khalaf, about whom very little is known. In the Biographical Encyclopedia of Astronomers (Springer Reference, 2007, pp. 34-35) Roser Puig has this to say about the two Andalusian instrument makers: 

ʿAlī ibn Khalaf is the author of a treatise on the use of the lámina universal (universal plate) preserved only in a Spanish translation included in the Libros del Saber de Astronomía (III, 11–132), compiled by the Spanish King Alfonso X. To our knowledge, the Arabic original is lost. ʿAlī ibn Khalaf is also credited with the construction of a universal instrument called al‐asṭurlāb al‐maʾmūnī in the year 1071, dedicated to al‐Maʾmūn, ruler of Toledo. 

The universal plate and the ṣafīḥa (the plate) of Zarqalī (devised in 1048) are the first “universal instruments” (i.e., for all latitudes) developed in Andalus. Both are based on the stereographic meridian projection of each hemisphere, superimposing the projection of a half of the celestial sphere from the vernal point (and turning it) on to the projection of the other half from the autumnal point. However, their specific characteristics make them different instruments.

Al-Zarqālī’s universal astrolabe was known as the Azafea in Arabic and as the Saphaea in Europe.

A copy of al-Zarqālī’s astrolabe Source: Wikimedia Commons

Much closer to Blagrave’s time, Gemma Frisius (1508–1555) wrote about a universal astrolabe, published as the Medici ac Mathematici de astrolabio catholico liber quo latissime patientis instrumenti multiplex usus explicatur, in 1556. Better known than Frisius’ universal instrument was that of his one-time Spanish, student Juan de Rojas y Samiento (fl. 1540-1550) published in his Commentariorum in Astrolabium libri sex in 1551.

 

Although he never really left his home town of Reading and his work was in English, Blagrave, like the other members of the English School of Mathematics, was well aware of the developments in continental Europe and he quotes the work of leading European mathematical practitioners in his Mathematical Jewel, such as the Tübingen professor of mathematics, Johannes Stöffler (1452–1531), who wrote a highly influential volume on the construction of astrolabes, his Elucidatio fabricae ususque astrolabii originally published in 1513, which went through 16 editions up to 1620

or the works of Gemma Frisius, who was possibly the most influential mathematical practitioner of the sixteenth century. Blagrave’s Mathematical Jewel was based on Gemma Frisius astrolabio catholico.

Blagrave’s Mathematical Jewel was obviously popular because Joseph Moxon (1627–1691), England first specialist mathematical publisher, cartographer, instrument, and globe maker republished it under the title:

The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer … ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P.

Engraved frontispiece to John Palmer (ed.), ‘The Catholique Planispaer, which Mr Blagrave calleth the Mathematical Jewel’ (London, Joseph Moxon, 1658); woman, wearing necklace, bracelet, jewels in her hair, and a veil, and seated at a table, on which are a design of a mathematical sphere, a compass, and an open book; top left, portrait of John Blagrave, wearing a ruff; top right, portrait of John Palmer; top centre, an angel with trumpets.
Engraving David Loggan Source: British Museum

John Palmer (1612-1679), who was apparently rector of Ecton and archdeacon of Northampton, is variously described as the author or the editor of the volume, which was first published in 1658 and went through sixteen editions up to 1973.

Following The Mathematical Jewel, Blagrave published four further books on scientific instruments that we know of: 

Baculum Familliare, Catholicon sive Generale. A Booke of the making and use of a Staffe, newly invented by the Author, called the Familiar Staffe (London, 1590)

Astrolabium uranicum generale, a necessary and pleasaunt solace and recreation for navigators … compyled by John Blagrave (London, 1596)

An apollogie confirmation explanation and addition to the Vranicall astrolabe (London, 1597)

None of these survive in large numbers.

Blagrave also manufactured sundials and his fourth instrument book is about this: 

The art of dyalling in two parts (London, 1609)

Source

Here there are considerably more surviving copies and even a modern reprint by Theatrum Orbis Terrarum Ltd., Da Capo Press, Amsterdam, New York, 1968.

People who don’t think about it tend to regard books on dialling, that is the mathematics of the construction and installation of sundials, as somehow odd. However, in this day and age, when almost everybody walks around with a mobile phone in their pocket with a highly accurate digital clock, we tend to forget that, for most of human history, time was not so instantly accessible. In the Early Modern period, mechanical clocks were few and far between and mostly unreliable. For time, people relied on sundials, which were common and widespread. From the invention of printing with movable type around 1450 up to about 1700, books on dialling constituted the largest genre of mathematical books printed and published. Designing and constructing sundials was a central part of the profession of mathematical practitioners. 

As well as the books there is one extant map:

Noua orbis terrarum descriptio opti[c]e proiecta secundu[m]q[ue] peritissimos Anglie geographos multis ni [sic] locis castigatissima et preceteris ipsiq[ue] globo nauigationi faciliter applcanda [sic] per Ioannem Blagrauum gen[er]osum Readingensem mathesibus beneuolentem Beniamin Wright Anglus Londinensis cµlator anno Domini 1596 

This is described as:

Two engraved maps, the first terrestrial, the second celestial (“Astrolabium uranicum generale …”). Evidently intended to illustrate Blagrave’s book “Astrolabium uranicum generale” but are not found in any copy of the latter.
The original is in the Bodleian Library.

When he died in 1611, Blagrave was buried in the St Laurence Church in Reading with a suitably mathematical monument. 

Blagrave is depicted surrounded by allegorical mathematical figures, with five women each holding the five platonic solids and Blagrave (in the center) depicted holding a globe and a quadrant.
The monument was the work of the sculptor Gerard Christmas (1576–1634), who later in life was appointed carver to the navy. It is not known who produced the drawing of the monument. 
Modern reconstruction of the armillary sphere from the cover of The Mathematical Jewel created by David Harber a descendent of John Blagrave

Blagrave was a minor, but not insignificant, participant in the mathematical community in England in the late sixteenth century. His work displays the typical Renaissance active interest in the practical mathematical disciplines, astronomy, navigation, surveying, and dialling. He seems to have enjoyed a good reputation and his Mathematical Jewel appears to have found a wide readership.  

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Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, Renaissance Science

History of science is global history

The simple statement that the history of science is global history is for me and, I assume, for every reasonably well-informed historian of science a rather trivial truism. So, I feel that James Poskett and the publishers Viking are presenting something of a strawman with the sensational claims for Poskett’s new book, HorizonsA Global History of Science[1]; claims that are made prominently by a series of pop science celebrities on the cover of the book. 

“Hugely Important,” Jim al-Khalili, really? 

“Revolutionary and revelatory,” Alice Roberts what’s so revolutionary about it?  

“This treasure trove of a book puts the case persuasively and compellingly that modern science did not develop solely in Europe,” Jim al-Khalili, I don’t know any sane historian of science, who would claim it did.

“Horizons is a remarkable book that challenges almost everything we know about science in the West. [Poskett brings to light an extraordinary array of material to change our thinking on virtually every great scientific breakthrough in the last 500 years… An explosive book that truly broadens our global scientific horizons, past and present.”] Jerry Brotton (The bit in square brackets is on the publisher’s website not on the book cover) I find this particularly fascinating as Brotton’s own The RenaissanceA Very Short Introduction (OUP, 2006) very much emphasises what is purportedly the main thesis of Horizons that science, in Brotton’s case the Renaissance, is not a purely Western or European phenomenon.

On June 22, Canadian historian Ted McCormick tweeted the following:

It’s not unusual for popular history to present as radical what has been scholarly consensus for a generation. If this bridges the gap between scholarship and public perception, then it is understandable. But what happens when the authors who do this are scholars who know better?

This is exactly what we have with Poskett’s book, he attempts to present in a popular format the actually stand amongst historian of science on the development of science over the last approximately five hundred years. I know Viking are only trying to drum up sales for the book, but I personally find it wrong that they use misleading hyperbole to do so. 

Having complained about the publisher’s pitch, let’s take a look at what Poskett is actually trying to sell to his readers and how he goes about doing so. Central to his message is that claims that science is a European invention/discovery[2] are false and that it is actually a global phenomenon. To back up his stand that such claims exist he reproduces a series of rather dated quotes making that claim. I would contend that very, very few historians of science actually believe that claim nowadays. He also proposes, what he sees as a new approach to the history of science of the last five hundred years, in that he divides the period into four epochs or eras, in which he sees science external factors during each era as the defining or driving force behind the scientific development in that era. Each is split into two central themes: Part One: Scientific Revolution, c. 1450–1700 1. New Worlds 2. Heaven and Earth, Part Two: Empire and Enlightenment, c. 1650–1800 3. Newton’s Slaves 4. Economy of Nature, Part Three:  Capitalism and Conflict, c. 1790–­1914 5. Struggle for Existence 6. Industrial Experiments, Part Four: Ideology and Aftermath, c. 1914–200 7. Faster Than Light 8. Genetic States.

I must sadly report that Part One, the area in which I claim a modicum of knowledge, is as appears recently oft to be the case strewn with factual errors and misleading statements and would have benefited from some basic fact checking.

New Worlds starts with a description of the palace of Emperor Moctezuma II and presents right away the first misleading claim. Poskett write:

Each morning he would take a walk around the royal botanical garden. Roses and vanilla flowers lined the paths, whilst hundreds of Aztec gardeners tended to rows of medicinal plants. Built in 1467, this Aztec botanical garden predated European examples by almost a century.[3]

Here Poskett is taking the university botanical gardens as his measure, the first of which was establish in Pisa in 1544, that is 77 years after Moctezuma’s Garden. However, there were herbal gardens, on which the university botanical gardens were modelled, in the European monasteries dating back to at least the ninth century. Matthaeus Silvaticus (c.1280–c. 1342) created a botanical garden at Salerno in 1334. Pope Nicholas V established a botanical garden in the Vatican in 1544. 

This is not as trivial as it might a first appear, as Poskett uses the discovery of South America to make a much bigger claim. First, he sets up a cardboard cut out image of the medieval university in the fifteenth century, he writes:

Surprisingly as it may sound today, the idea of making observations or preforming experiments was largely unknown to medieval thinkers. Instead, students at medieval universities in Europe spent their time reading, reciting, and discussing the works of Greek and Roman authors. This was a tradition known as scholasticism. Commonly read texts included Aristotle’s Physics, written in the fourth century BCE, and Pliny the Elder’s Natural History, written in the first century CE. The same approach was common to medicine. Studying medicine at medieval university in Europe involved almost no contact with actual human bodies. There was certainly no dissections or experiments on the working of particular organs. Instead, medieval medical students read and recited the works of the ancient Greek physician Galen. Why, then, sometime between 1500 and 1700, did European scholars turn away from investigating the natural world for themselves?[4]

His answer:

The answer has a lot to do with colonization of the New World alongside the accompanying appropriation of Aztec and Aztec and Inca knowledge, something that traditional histories of science fail to account for.[5]

Addressing European, medieval, medical education first, the practical turn to dissection began in the fourteenth century and by 1400 public dissections were part of the curriculum of nearly all European universities. The introduction of a practical materia medica education on a practical basis began towards the end of the fifteenth century. Both of these practical changes to an empirical approach to teaching medicine at the medieval university well before any possible influence from the New World. In general, the turn to empiricism in the European Renaissance took place before any such influence, which is not to say that that process was not accelerated by the discovery of a whole New World not covered by the authors of antiquity. However, it was not triggered by it, as Poskett would have us believe. 

Poskett’s next example to bolster his thesis is quite frankly bizarre. He tells the story of José de Acosta (c. 1539–1600), the Jesuit missionary who travelled and worked in South America and published his account of what he experienced, Natural and Moral History of the Indies in 1590. Poskett tells us: 

The young priest was anxious about the journey, not least because of what ancient authorities said about the equator. According to Aristotle, the world was divided into three climatic zones. The north and south poles were characterized by extreme cold and known as the ‘frigid zone’. Around the equator was the ‘torrid zone’, a region of burning dry heat. Finally, between the two extremes, at around the same latitudes as Europe, was the ‘temperate zone’. Crucially, Aristotle argued that life, particularly human life, could only be sustained in the ‘temperate zone’. Everywhere else was either too hot nor too cold.

Poskett pp. 17-18

Poskett goes on to quote Acosta:

I must confess I laughed and jeered at Aristotle’s meteorological theories and his philosophy, seeing that in the very place where, according to his rules, everything must be burning and on fire, I and all my companions were cold.

Poskett p. 18

Instead of commenting on Acosta’s ignorance or naivety, Aristotle’s myth of the ‘torrid zone’ had been busted decades earlier, at the very latest when Bartolomeu Dias (c. 1450–1500) had rounded the southern tip of Africa fifty-two years before Acosta was born and eight-two year before he travelled to Peru, Poskett sees this as some sort of great anti-Aristotelian revelation. He writes:

This was certainly a blow to classical authority. If Aristotle had been mistaken about the climate zones, what else might he have been wrong about?

Poskett p.18

This is all part of Poskett’s fake narrative that the breakdown of the scholastic system was first provoked by the contact with the new world. We have Poskett making this claim directly:

It was this commercial attitude towards the New World that really transformed the study of natural history. Merchants and doctors tended to place much greater emphasis on collecting and experimentation over classical authority.[6]

This transformation had begun in Europe well before any scholar set foot in the New World and was well established before any reports on the natural history of the New World had become known in Europe. The discovery of the New World accelerated the process but it in no way initiated it as Poskett would have his readers believe. Poskett once again paints a totally misleading picture a few pages on:

This new approach to natural history was also reflected in the increasing use of images. Whereas ancient texts on natural history tended not to be illustrated, the new natural histories of the sixteenth and seventeenth centuries were full of drawings and engravings, many of which were hand-coloured. This was partly a reaction to the novelty of what had been discovered. How else would those in Europe know what a vanilla plant or a hummingbird looked like?

Poskett pp.29-30

Firstly, both ancient and medieval natural history texts were illustrated, I refer Mr Proskett, for example, to the lavishly illustrated Vienna Dioscorides from 512 CE. Secondly, the introduction of heavily illustrated, printed herbals began in the sixteenth century before any illustrated natural history books or manuscripts from the New World had arrived in Europe. For example, Otto Brunfels’ Herbarium vivae eicones three volumes 1530-1536 or the second edition of Hieronymus Bock’s Neu Kreütterbuch in 1546 and finally the truly lavishly illustrated De Historia Stirpium Commentarii by Leonhard Fuchs published in 1542. The later inclusion of illustrations plants and animals from the New World in such books was the continuation of an already established tradition. 

Poskett moves on from natural history to cartography and produced what I can only call a train wreck. He tells us:

The basic problem, which was now more pressing [following the discovery of the New World], stemmed from the fact that the world is round, but a map is flat. What then was the best way to represent a three-dimensional space on a two-dimensional plane? Ptolemy had used what is known as a ‘conic’ projection, in which the world is divided into arcs radiating out from the north pole, rather like a fan. This worked well for depicting one hemisphere, but not both. It also made it difficult for navigators to follow compass bearings, as the lines spread outwards the further one got from the north pole. In the sixteenth century, European cartographers started experimenting with new projections. In 1569, the Flemish cartographer Gerardus Mercator produced an influential map he titled ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’. Mercator effectively stretched the earth at the poles and shrunk it in the middle. This allowed him to produce a map of the world in which the lines of latitude are always at right angles to one another. This was particularly useful for sailors, as it allowed them to follow compass bearings as straight lines.

Poskett p. 39

Where to begin? First off, the discovery of the New World is almost contemporaneous with the development of the printed terrestrial globe, Waldseemüller 1507 and more significantly Johannes Schöner 1515. So, it became fairly common in the sixteenth century to represent the three-dimensional world three-dimensionally as a globe. In fact, Mercator, the only Early Modern cartographer mentioned here, was in his time the premium globe maker in Europe. Secondly, in the fifteenth and sixteenth centuries mariners did not even attempt to use a Ptolemaic projection on the marine charts, instead they used portulan charts–which first emerged in the Mediterranean in the fourteenth century–to navigate in the Atlantic, and which used an equiangular or plane chart projection that ignores the curvature of the earth. Thirdly between the re-emergence of Ptolemy’s Geographia in 1406 and Mercator’s world map of 1569, Johannes Werner published Johannes Stabius’ cordiform projection in 1514, which can be used to depict two hemispheres and in fact Mercator used a pair of cordiform maps to do just that in his world map from 1538. In 1508, Francesco Rosselli published his oval projection, which can be used to display two hemispheres and was used by Abraham Ortelius for his world map from 1564. Fourthly, stereographic projection, known at least since the second century CE and used in astrolabes, can be used in pairs to depict two hemispheres, as was demonstrated by Mercator’s son Rumold in his version of his father’s world map in 1587. Fifthly, the Mercator projection if based on the equator, as it normally is, does not shrink the earth in the middle. Lastly, far from being influential, Mercator’s ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’, even in the improved version of Edward Wright from 1599 had very little influence on practical navigation in the first century after it first was published. 

After this abuse of the history of cartography Poskett introduces something, which is actually very interesting. He describes how the Spanish crown went about creating a map of their newly won territories in the New World. The authorities sent out questionnaires to each province asking the local governors or mayors to describe their province. Poskett notes quite correctly that a lot of the information gathered by this method came from the indigenous population. However, he once again displays his ignorance of the history of European cartography. He writes:

A questionnaire might seem like an obvious way to collect geographical information, but in the sixteenth century this idea was entirely novel. It represented a new way of doing geography, one that – like science more generally in this period – relied less and less on ancient Greek and Roman authority.

Poskett p. 41

It would appear that Poskett has never heard of Sebastian Münster and his Cosmographia, published in 1544, probably the biggest selling book of the sixteenth century. An atlas of the entire world it was compiled by Münster from the contributions from over one hundred scholars from all over Europe, who provided maps and texts on various topics for inclusion in what was effectively an encyclopaedia. Münster, who was not a political authority did not send out a questionnaire but appealed for contributions both in publications and with personal letters. Whilst not exactly the same, the methodology is very similar to that used later in 1577 by the Spanish authorities. 

In his conclusion to the section on the New World Poskett repeats his misleading summation of the development of science in the sixteenth century:

Prior to the sixteenth century, European scholars relied almost exclusively on ancient Greek and Roman authorities. For natural history they read Pliny for geography they read Ptolemy. However, following the colonization of the Americas, a new generation of thinkers started to place a greater emphasis on experience as the main source of scientific knowledge. They conducted experiments, collected specimens, and organised geographical surveys. This might seem an obvious way to do science to us today, but at the time it was a revelation. This new emphasis on experience was in part a response to the fact that the Americas were completely unknown to the ancients.

Poskett p. 44

Poskett’s claim simply ignores the fact that the turn to empirical science had already begun in the latter part of the fifteenth century and by the time Europeans began to investigate the Americas was well established, those investigators carrying the new methods with them rather than developing them in situ. 

Following on from the New World, Poskett takes us into the age of Renaissance astronomy serving up a well worn and well know story of non-European contributions to the Early Modern history of the discipline which has been well represented in basic texts for decades. Nothing ‘revolutionary and revelatory’ here, to quote Alice Roberts. However, despite the fact that everything he in presenting in this section is well documented he still manages to include some errors. To start with he attributes all of the mechanics of Ptolemy’s geocentric astronomy–deferent, eccentric, epicycle, equant–to Ptolemy, whereas in fact they were largely developed by other astronomers–Hipparchus, Apollonius–and merely taken over by Ptolemy.  

Next up we get the so-called twelfth century “scientific Renaissance” dealt with in one paragraph. Poskett tells us the Gerard of Cremona translated Ptolemy from Arabic into Latin in 1175, completely ignoring the fact that it was translated from Greek into Latin in Sicily at around the same time. This is a lead into the Humanist Renaissance, which Poskett presents with the totally outdated thesis that it was the result of the fall of Constantinople, which he rather confusingly calls Istanbul, in 1453, evoking images of Christians fleeing across the Adriatic with armfuls of books; the Humanist Renaissance had been in full swing for about a century by that point. 

Following the introduction of Georg of Trebizond and his translation of the Almagest from Greek, not the first as already noted above as Poskett seems to imply, up next is a very mangled account of the connections between Bessarion, Regiomontanus, and Peuerbach and Bessarion’s request that Peuerbach produce a new translation of the Almagest from the Greek because of the deficiencies in Trebizond’s translation. Poskett completely misses the fact that Peuerbach couldn’t read Greek and the Epitome, the Peuerbach-Regiomontanus Almagest, started as a compendium of his extensive knowledge of the existing Latin translations. Poskett then sends Regiomontanus off the Italy for ten years collecting manuscripts to improve his translation. In fact, Regiomontanus only spent four years in Italy in the service of Bessarion collecting manuscripts for Bessarion’s library, whilst also making copies for himself, and learning Greek to finish the Epitome.

Poskett correctly points out that the Epitome was an improved, modernised version of the Almagest drawing on Greek, Latin and Arabic sources. Poskett now claims that Regiomontanus introduced an innovation borrowed from the Islamic astronomer, Ali Qushji, that deferent and epicycles could be replaced by the eccentric. Poskett supports this argument by the fact that Regiomontanus uses Ali Qushji diagram to illustrate this possibility. The argument is not original to Poskett but is taken from the work of historian of astronomy, F. Jamil Ragip. Like Ragip, Poskett now argues thus:

In short, Ali Qushji argued that the motion of all the planets could be modelled simply by imagining that the centre of their orbits was at a point other than the Earth. Neither he nor Regiomontanus went as far as to suggest this point might in fact be the Sun. By dispensing with Ptolemy’s notion of the epicycle, Ali Qushji opened the door for a much more radical version of the structure of the cosmos.[7]

This is Ragip theory of what motivated Copernicus to adopt a heliocentric model of the cosmos. The question of Copernicus’s motivation remains open and there are numerous theories. This theory, as presented, however, has several problems. That the planetary models can be presented either with the deferent-epicycle model or the eccentric model goes back to Apollonius and is actually included in the Almagest by Ptolemy as Apollonius’ theorem (Almagest, Book XII, first two paragraphs), so this is neither an innovation from Ali Qushji nor from Regiomontanus. In Copernicus’ work the Sun is not actually at the centre of the planetary orbits but slightly offset, as has been pointed out his system is not actually heliocentric but more accurately heliostatic. Lastly, Copernicus in his heliostatic system continues to use the deferent-epicycle model to describe planetary orbits.

Poskett is presenting Ragip’s disputed theory to bolster his presentation of Copernicus’ dependency on Arabic sources, somewhat unnecessary as no historian of astronomy would dispute that dependency. Poskett continues along this line, when introducing Copernicus and De revolutionibus. After a highly inaccurate half paragraph biography of Copernicus–for example he has the good Nicolaus appointed canon of Frombork Cathedral after he had finished his studies in Italy, whereas he was actually appointed before he began his studies, he introduces us to De revolutionibus. He emphasis the wide range of international sources on which the book is based, and then presents Ragip’s high speculative hypothesis, for which there is very little supporting evidence, as fact:

Copernicus suggested that all these problems could be solved if we imagined the Sun was at the centre of the universe. In making this move he was directly inspired by the Epitome of the Almagest. Regiomontanus, drawing on Ali Qushji, had shown it was possible to imagine that the centre of all the orbits of the planets was somewhere other than the Earth. Copernicus took the final step, arguing that that this point was in fact the Sun.[8]

We simply do not know what inspired Copernicus to adopt a heliocentric model and to present a speculative hypothesis, one of a number, as the factual answer to this problem in a popular book is in my opinion irresponsible and not something a historian should be doing. 

Poskett now follows on with the next misleading statement. Having, a couple of pages earlier, introduced the Persian astronomer Nasir al-Din al-Tusi and the so-called Tusi couple, a mathematical device that allows linear motion to be reproduced geometrically with circles, Poskett now turns to Copernicus’ use of the Tusi couple. He writes:

The diagram in On the Revolution of the Heavenly Spheres shows the Tusi couple in action. Copernicus used this idea to solve exactly the same problem as al-Tusi. He wanted a way to generate an oscillating circular movement without sacrificing a commitment to uniform circular motion. He used the Tusi couple to model planetary motion around the Sun rather than the Earth. This mathematical tool, invented in thirteenth-century Persia, found its way into the most important work in the history of European astronomy. Without it, Copernicus would not have been able to place the Sun at the centre of the universe.[9] [my emphasis]

As my alter-ego the HISTSCI_HULK would say the emphasised sentence is pure and utter bullshit!

The bizarre claims continue, Poskett writes:

The publication of On the Revolution of the Heavenly Spheres in 1543 has long been considered the starting point for the scientific revolution. However, what is less often recognised is that Nicolaus Copernicus was in fact building on a much longer Islamic tradition.[10]

When I first read the second sentence here, I had a truly WTF! moment. There was a time in the past when it was claimed that the Islamic astronomers merely conserved ancient Greek astronomy, adding nothing new to it before passing it on to the Europeans in the High Middle Ages. However, this myth was exploded long ago. All the general histories of astronomy, the histories of Early Modern and Renaissance astronomy, and the histories of Copernicus, his De revolutionibus and its reception that I have on my bookshelf emphasise quite clearly and in detail the influence that Islamic astronomy had on the development of astronomy in Europe in the Middle Ages, the Renaissance, and the Early Modern period. Either Poskett is ignorant of the true facts, which I don’t believe, or he is presenting a false picture to support his own incorrect thesis.

Having botched European Renaissance astronomy, Poskett turns his attention to the Ottoman Empire and the Istanbul observatory of Taqi al-Din with a couple of pages that are OK, but he does indulge in a bit of hype when talking about al-Din’s use of a clock in an observatory, whilst quietly ignoring Jost Bürgi’s far more advanced clocks used in the observatories of Wilhelm IV of Hessen-Kassel and Tycho Brahe contemporaneously. 

This is followed by a brief section on astronomy in North Africa in the same period, which is basically an extension of Islamic astronomy with a bit of local colouration. Travelling around the globe we land in China and, of course, the Jesuits. Nothing really to complain about here but Poskett does allow himself another clangour on the subject of calendar reform. Having correctly discussed the Chinese obsession with calendar reform and the Jesuit missionaries’ involvement in it in the seventeenth century Poskett add an aside about the Gregorian Calendar reform in Europe. He writes:

The problem was not unique to China. In 1582, Pope Gregory XIII had asked the Jesuits to help reform the Christian Calendar back in Europe. As both leading astronomers and Catholic servants, the Jesuits proved an ideal group to undertake such a task. Christoph Clavius, Ricci’s tutor at the Roman College [Ricci had featured prominently in the section on the Jesuits in China], led the reforms. He integrated the latest mathematical methods alongside data taken from Copernicus’s astronomical tables. The result was the Gregorian calendar, still in use today throughout many parts of the world.[11]

I have no idea what source Poskett used for this brief account, but he has managed to get almost everything wrong that one can get wrong. The process of calendar reform didn’t start in 1582, that’s the year in which the finished calendar reform was announced in the papal bull Inter gravissimas. The whole process had begun many years before when the Vatican issued two appeals for suggestion on how to reform the Julian calendar which was now ten days out of sync with the solar year. Eventually, the suggestion of the physician Luigi Lilio was adopted for consideration and a committee was set up to do just that. We don’t actually know how long the committee deliberated but it was at least ten years. We also don’t know, who sat in that committee over those years; we only know the nine members who signed the final report. Clavius was not the leader of the reform, in fact he was the least important member of the committee, the leader being naturally a cardinal. You can read all of the details in this earlier blog post. At the time there were not a lot of Jesuit astronomers, that development came later and data from Copernicus’ astronomical tables were not used for the reform. Just for those who don’t want to read my blog post, Clavius only became associated with the reform after the fact, when he was commissioned by the pope to defend it against its numerous detractors.  I do feel that a bit of fact checking might prevent Poskett and Viking from filling the world with false information about what is after all a major historical event. 

The section Heaven and Earth closes with an account of Jai Singh’s observatories in India in the eighteenth century, the spectacular instruments of the Jantar Mantar observatory in Jaipur still stand today. 

Readers of this review need not worry that I’m going to go on at such length about the other three quarters of Poskett’s book. I’m not for two reasons. Firstly, he appears to be on territory where he knows his way around better than in the Early Modern period, which was dealt with in the first quarter Secondly, my knowledge of the periods and sciences he now deals with are severely limited so I might not necessarily have seen any errors. 

There are however a couple more train wrecks before we reach the end and the biggest one of all comes at the beginning of the second quarter in the section titled Newton’s Slaves. I’ll start with a series of partial quote, then analyse them:

(a) Where did Newton get this idea [theory of gravity] from? Contrary to popular belief, Newton did not make his great discovery after an apple fell on his head. Instead in a key passage in the Principia, Newton cited the experiments of a French astronomer named Jean Richer. In 1672, Richer had travelled to the French colony of Cayenne in South America. The voyage was sponsored by King Louis XIV through the Royal Academy of Science in Paris.

[…]

(b) Once in Cayenne, Richer made a series of astronomical observations, focusing on the movements of the planets and cataloguing stars close to the equator.

[…]

(c) Whilst in Cayenne, Richer also undertook a number of experiments with a pendulum clock.

[…]

(d) In particular, a pendulum with a length of just one metre makes a complete swing, left to right, every second. This became known as a ‘seconds pendulum’…

[…]

(e) In Cayenne, Richer noticed that his carefully calibrated pendulum was running slow, taking longer than a second to complete each swing.

[…]

(f) [On a second voyage] Richer found that, on both Gorée and Guadeloupe, he needed to shorten the pendulum by about four millimetres to keep it running on time.

[…]

(g) What could explain this variation?

[…]

(h) Newton, however, quickly realised the implications the implications of what Richer had observed. Writing in the Principia, Newton argued that the force of gravity varied across the surface of the planet. 

[…]

(i) This was a radical suggestion, one which seemed to go against common sense. But Newton did the calculations and showed how his equations for the gravitational force matched exactly Richer’s results from Cayenne and Gorée. Gravity really was weaker nearer the equator.

[…]

(j) All this implied a second, even more controversial, conclusion. If gravity was variable, then the Earth could not be a perfect sphere. Instead, Newton argued, the Earth must be a ‘spheroid’, flattened at the poles rather like a pumpkin. 

[…]

(k) Today, it is easy to see the Principia as a scientific masterpiece, the validity of which nobody could deny. But at the time, Newton’s ideas were incredibly controversial.

[…]

(l) Many preferred the mechanical philosophy of the French mathematician René Descartes. Writing in his Principles of Philosophy (1644), Descartes denied the possibility of any kind of invisible force like gravity, instead arguing that force was only transferred through direct contact. Descartes also suggested that, according to his own theory of matter, the Earth should be stretched the other way, elongated like an egg rather than squashed like a pumpkin.

[…]

(m) These differences were not simply a case of national rivalry or scientific ignorance. When Newton published the Principia in 1687, his theories were in fact incomplete. Two major problems remained to be solved. First, there were the aforementioned conflicting reports of the shape of the Earth. And if Newton was wrong about the shape of the Earth, then he was wrong about gravity.[12]

To begin at the beginning: (a) The suggestion or implication that Newton got the idea of the theory of gravity from Richer’s second pendulum experiments is quite simply grotesque. The concept of a force holding the solar system together and propelling the planets in their orbits evolved throughout the seventeenth century beginning with Kepler. The inverse square law of gravity was first hypothesised by Ismaël Boulliau, although he didn’t believe it existed. Newton made his first attempt to show that the force causing an object to fall to the Earth, an apple for example, and the force that held the Moon in its orbit and prevented it shooting off at a tangent as the law of inertia required, before Richer even went to Cayenne.

(c)–(g) It is probable that Richer didn’t make the discovery of the difference in length between a second pendulum in Northern Europe and the equatorial region, this had already ben observed earlier. What he did was to carry out systematic experiments to determine the size of the difference.

(l) Descartes did not suggest, according to his own theory of matter, that the Earth was an elongated spheroid. In fact, using Descartes theories Huygens arrived at the same shape for the Earth as Newton. This suggestion was first made by Jean-Dominique Cassini and his son Jacques long after Descartes death. Their reasoning was based on the difference in the length of one degree of latitude as measured by Willebrord Snel in The Netherlands in 1615 and by Jean Picard in France in 1670. 

This is all a prelude for the main train wreck, which I will now elucidate. In the middle of the eighteenth century, to solve the dispute on the shape of the Earth, Huygens & Newton vs the Cassinis, the French Academy of Science organised two expeditions, one to Lapland and one to Peru in order to determine as accurately as possible the length of one degree of latitude at each location. Re-enter Poskett, who almost completely ignoring the Lapland expedition, now gives his account of the French expedition to Peru. He tells us:

The basic technique for conducting a survey [triangulation] of this kind had been pioneered in France in the seventeenth century. To begin the team needed to construct what was known as a ‘baseline’. This was a perfectly straight trench, only a few inches deep, but at least a couple of miles long.[13]

Triangulation was not first pioneered in France in the seventeenth century. First described in print in the sixteenth century by Gemma Frisius, it was pioneered in the sixteenth century by Mercator when he surveyed the Duchy of Lorraine, and also used by Tycho Brahe to map his island of Hven. To determine the length of one degree of latitude it was pioneered, as already stated, by Willebrord Snell. However, although wrong this is not what most disturbed me about this quote. One of my major interests is the history of triangulation and its use in surveying the Earth and determining its shape and I have never come across any reference to digging a trench to lay out a baseline. Clearing the undergrowth and levelling the surface, yes, but a trench? Uncertain, I consulted the book that Poskett references for this section of his book, Larrie D Ferreiro’s Measure of the EarthThe Enlightenment Expedition that Reshaped the World (Basic Books, 2011), which I have on my bookshelf. Mr Ferreiro make no mention of a baseline trench. Still uncertain and not wishing to do Poskett wrong I consulter Professor Matthew Edney, a leading expert on the history of surveying by triangulation, his answer:

This is the first I’ve heard of digging a trench for a baseline. It makes little sense. The key is to have a flat surface (flat within the tolerance dictated by the quality of the instruments being used, which wasn’t great before 1770). Natural forces (erosion) and human forces (road building) can construct a sufficiently level surface; digging a trench would only increase irregularities.[14]

The problems don’t end here, Poskett writes:

La Condamine did not build the baseline himself. The backbreaking work of digging a seven-mile trench was left to the local Peruvian Indians.[15]

This is contradicted by Ferreiro who write:

Just as the three men completed the alignment for the baseline, the rest of the expedition arrived on the scene, in time for the most difficult phase of the operation. In order to create a baseline, an absolutely straight path, seven miles long and just eighteen inches wide, had to be dug into, ripped up from, and scraped out of the landscape. For the scientists, who had been accustomed to a largely sedentary life back in Europe, this would involve eight days of back breaking labour and struggling for breath in the rarefied air. “We worked at felling trees,” Bouguer explained in his letter to Bignon, “breaking through walls and filling in ravines to align [a baseline] of more than two leagues.” They employed several Indians to help transport equipment, though Bouguer felt it necessary that someone “keep an eye on them.”[16]

Poskett includes this whole story of the Peruvian Indians not digging a non-existent baseline trench because he wants to draw a parallel between the baseline and the Nazca Lines, a group of geoglyphs made in the soil of the Nazca desert in southern Peru that were created between 500 BCE and 500 CE. He writes:

The Peruvian Indians who built the baseline must have believed that La Condamine wanted to construct his own ritual line much like the earlier Inca rulers.[17]

Also:

Intriguingly some are simply long straight lines. They carry on for miles, dead straight, crossing hills and valleys. Whilst their exact function is still unclear, many historians now believe they were used to align astronomical observations, exactly as La Condamine intended with his baseline.[18]

The Nazca lines are of course pre-Inca. The ‘many historians’ is a bit of a giveaway, which historians? Who? Even if the straight Nazca lines are astronomically aligned, they by no means serve the same function as La Condamine’s triangulation baseline, which is terrestrial not celestial.  

To be fair to Poskett, without turning the baseline into a trench and without having the Indians dig it, Ferreiro draws the same parallel but without the astronomical component: 

For their part, the Indians were also observing the scientists, but to them “all was confusion” regarding the scientists’ motives for this arduous work. The long straight baseline the had scratched out of the ground certainly resembled the sacred linear pathways that Peruvian cultures since long before the Incas, had been constructing.[19]

Poskett’s conclusion to this section, in my opinion, contains a piece of pure bullshit.

By January 1742, the results were in. La Condamine calculated that the distance between Quito and Cuenca was exactly 344,856 metres. From observations made of the stars at both ends of the survey, La Condamine also found that the difference in latitude between Quit and Cuenca was a little over three degrees. Dividing the two, La Condamine concluded that the length of a degree of latitude at the equator was 110,613 metres. This was over 1,000 metres less than the result found by the Lapland expedition, which had recently returned to Paris. The French, unwittingly relying on Indigenous Andean science [my emphasis] had discovered the true shape of the Earth. It was an ‘oblate spheroid’, squashed at the poles and bulging at the equator. Newton was right.[20]

Sorry, but just because Poskett thinks that a triangulation survey baseline looks like an ancient, straight line, Peruvian geoglyph doesn’t in anyway make the French triangulation survey in anyway dependent on Indigenous Andean science. As I said, pure bullshit. 

The next section deals with the reliance of European navigators of interaction with indigenous navigators throughout the eighteenth century and is OK. This is followed by the history of eighteenth-century natural history outside of Europe and is also OK. 

At the beginning of the third quarter, we again run into a significant problem. The chapter Struggle for Existence open with the story of Étienne Geoffroy Saint-Hilaire, a natural historian, who having taken part in Napoleon’s Egypt expedition, compared mummified ancient Egyptian ibises with contemporary ones in order to detect traces of evolutions but because the time span was too short, he found nothing. His work was published in France 1818, but Poskett argues that his earliest work was published in Egyptian at the start of the century and so, “In order to understand the history of evolution, we therefore need to begin with Geoffroy and the French army in North Africa.” I’m not a historian of evolution but really? Ignoring all the claims for evolutionary thought in earlier history, Poskett completely blends out the evolutionary theories of Pierre Louis Maupertuis (1751), James Burnett, Lord Monboddo, (between 1767 and 1792) and above all Darwin’s grandfather Erasmus, who published his theory of evolution in his Zoonomia (1794–1796). So why do we need to begin with Étienne Geoffroy Saint-Hilaire?

Having dealt briefly with Charles Darwin, Poskett takes us on a tour of the contributions to evolutionary theory made in Russia, Japan, and China in the nineteenth century, whilst ignoring the European contributions. 

Up next in Industrial Experiments Poskett takes us on a tour of the contributions to the physical sciences outside of Europe in the nineteenth century. Here we have one brief WTF statement. Poskett writes:

Since the early nineteenth century, scientists had known that the magnetic field of the Earth varies across the planet. This means that the direction of the north pole (‘true north’) and the direction that the compass needle points (‘magnetic north’) are not necessarily identical, depending on where you are.[21]

Magnetic declination, to give the technical name, had been known and documented since before the seventeenth century, having been first measured accurately for Rome by Georg Hartmann in 1510, it was even known that it varies over time for a given location. Edmund Halley even mapped the magnetic declination of the Atlantic Ocean at the end of the seventeenth century in the hope that it would provide a solution to the longitude problem. 

In the final quarter we move into the twentieth century. The first half deals with modern physics up till WWII, and the second with genetic research following WWII, in each case documenting the contribution from outside of Europe. Faster than Light, the modern physics section, move through Revolutionary Russia, China, Japan, and India; here Poskett connects the individual contributions to the various revolutionary political movements in these countries. Genetic States moves from the US, setting the background, through Mexico, India, China, and Israel.  I have two minor quibbles about what is presented in these two sections.

Firstly, in both sections, instead of a chronological narrative of the science under discussion we have a series of biographical essays of the figures in the different countries who made the contribution, which, of course, also outlines their individual contributions. I have no objections to this, but something became obvious to me reading through this collection of biographies. They all have the same muster. X was born in Y, became interested in topic Z, began their studies at some comparatively local institute of higher education, and then went off to Heidelberg/Berlin/Paris/London/Cambridge/Edinburg… to study with some famous European authority, and acquire a PhD. Then off to a different European or US university to research, or teach or both, before to returning home to a professorship in their mother country. This does seem to suggest that opposed to Poskett’s central thesis of the global development of science, a central and dominant role for Europe.  

My second quibble concerns only the genetics section. One of Poskett’s central theses is that science in a given epoch is driven by an external to the science cultural, social, or political factor. For this section he claims that the external driving force was the Cold War. Reading through this section my impression was that every time he evoked the Cold War he could just have easily written ‘post Second World War’ or even ‘second half of the twentieth century’ and it would have made absolutely no difference to his narrative. In my opinion he fails to actually connect the Cold War to the scientific developments he is describing.

The book closes with a look into the future and what Poskett thinks will be the force driving science there. Not surprisingly he chooses AI and being a sceptic what all such attempts at crystal ball gazing are concerned I won’t comment here.

The book has very extensive end notes, which are largely references to a vast array of primary and mostly secondary literature, which confirms what I said at the beginning that Poskett in merely presenting in semi-popular form the current stand in the history of science of the last half millennium. There is no separate bibliography, which is a pain if you didn’t look to see something the first time it was end noted, as in subsequent notes it just becomes Smith, 2003, sending you off on an oft hopeless search for that all important first mention in the notes. There are occasional grey scale illustrations and two blocks, one of thirteen and one of sixteen, colour plates. There is also an extensive index.

So, after all the negative comments, what do I really think about James Poskett, highly praised volume. I find the concept excellent, and the intention is to be applauded. A general popular overview of the development of the sciences since the Renaissance is an important contribution to the history of science book market. Poskett’s book has much to recommend it, and I personally learnt a lot reading it. However, as a notorious history of science pedant, I cannot ignore or excuse the errors than I have outlined in my review, some of which are in my opinion far from minor. The various sections of the book should have been fact checked by other historians, expert in the topic of the section, and this has very obviously not been done. It is to be hoped that this will take place before a second edition is published. 

Would I recommend it? Perhaps surprisingly, yes. James Poskett is a good writer and there is much to be gained from reading this book but, of course, with the caveat that it also contains things that are simply wrong. 


[1] James Poskett, Horizons: A Global History of Science, Viking, 2022 

[2] Take your pick according to your personal philosophy of science.

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of botany, History of Cartography, History of Geodesy, History of Islamic Science, History of Navigation, Natural history, Renaissance Science

The Wizard Earl’s mathematici 

In my recent post on the Oxford mathematician and astrologer Thomas Allen, I mentioned his association with Henry Percy, 9th Earl of Northumberland, who because of his strong interest in the sciences was known as the Wizard Earl.

HENRY PERCY, 9TH EARL OF NORTHUMBERLAND (1564-1632) by Sir Anthony Van Dyck (1599-1641). The ‘Wizard Earl’ was painted posthumously as a philosopher, hung in Square Room at Petworth. This is NT owned. via Wikimedia Commons

As already explained there Percy actively supported four mathematici, or to use the English term mathematical practitioners, Thomas Harriot (c. 1560–1621), Robert Hues (1553–1632), Walter Warner (1563–1643), and Nathaniel Torporley (1564–1632). Today, I’m going to take a closer look at them.

Thomas Harriot is, of course, the most well-known of the four; I have already written a post about him in the past, so I will only brief account of the salient point here.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

He graduatied from Oxford in 1580 and entered the service of Sir Walter Raleigh (1552–1618) in 1583. At Raleigh’s instigation he set up a school to teach Raleigh’s marine captains the newest methods of navigation and cartography, writing a manual on mathematical navigation, which contained the correct mathematical method for the construction of the Mercator projection. This manual was never published but we can assume he used it in his teaching. He was also directly involved in Raleigh’s voyages to establish the colony of Roanoke Island.

Sir Walter Ralegh in 1588 artist unknown. Source: Wikimedia Commons

In 1590, he left Raleigh’s service and became a pensioner of Henry Percy, with a very generous pension, the title to some land in the North of England, and a house on Percy’s estate, Syon House, in Middlesex.[1] Here, Harriot lived out his years as a research scientist with no obligations.

Syon House Attributed to Robert Griffier

After Harriot, the most significant of the Wizard Earl’s mathematici was Robert Hues. Like Harriot, Hues attended St Mary’s Hall in Oxford, graduating a couple of years ahead of him in 1578. Being interested in geography and mathematics, he was one of those who studied navigation under Harriot in the school set up by Raleigh, having been introduced to Raleigh by Richard Hakluyt (1553–1616), another student of Thomas Allen and a big promoter of English colonisation of North America.  

Hakluyt depicted in stained glass in the west window of the south transept of Bristol Cathedral – Charles Eamer Kempe, c. 1905. Source: Wikimedia Commons

Hues went on to become an experienced mariner. During a trip to Newfoundland, he came to doubt the published values for magnetic declination, the difference between magnetic north and true north, which varies from place to place.

In 1586, he joined with Thomas Cavendish (1560–1592), a privateer and another graduate of the Harriot school of navigation, who set out to raid Spanish shipping and undertake a circumnavigation of the globe, leaving Plymouth with three ships on 21 July. After the usual collection of adventures, they returned to Plymouth with just one ship on 9 September 1588, as the third ever ship to complete the circumnavigation after Magellan and Drake. Like Drake, Cavendish was knighted by Queen Elizabeth for his endeavours.

Thomas Cavendish An engraving from Henry Holland’s Herōologia Anglica (1620). Animum fortuna sequatur is Latin for “May fortune follow courage.” Source: Wikimedia Commons

Hues undertook astronomical observations throughout the journey and determined the latitudes of the places they visited. In 1589, he served with the mathematicus Edward Wright (1561–1615), who like Harriot worked out the correct mathematical method for the construction of the Mercator projection, but unlike Harriot published it in his Certaine Errors in Navigation in 1599.

Source: Wikimedia Commons

In August 1591, he set out once again with Cavendish on another attempted circumnavigation, also accompanied by the navigator John Davis (c. 1550–1605), another associate of Raleigh’s, known for his attempts to discover the North-West passage and his discovery of the Falkland Islands.

Miniature engraved portrait of navigator John Davis (c. 1550-1605), detail from the title page of Samuel Purchas’s Hakluytus Posthumus or Purchas his Pilgrimes (1624). Source: Wikimedia Commons

Cavendish died on route in 1592 and Hues returned to England with Davis in 1683. On this voyage Hues continued his astronomical observations in the South Atlantic and made determinations of compass declinations at various latitudes and the equator. 

Back in England, Hues published the results of his astronomical and navigational research in his Tractatus de globis et eorum usu (Treatise on Globes and Their Use, 1594), which was dedicated to Raleigh.

The book was a guide to the use of the terrestrial and celestial globes that Emery Molyneux (died 1598) had published in 1592 or 1593.

Molyneux CEltial Globe Middle Temple Library
A terrestrial globe by Emery Molyneux (d.1598-1599) is dated 1592 and is the earliest such English globe in existence. It is weighted with sand and made from layers of paper with a surface coat of plaster engraved with elaborate cartouches, fanciful sea-monsters and other nautical decoration by the Fleming Jodocus Hondius (1563-1611). There is a wooden horizon circle and brass meridian rings.

Molyneux belong to the same circle of mariners and mathematici, counting Hues, Wright, Cavendish, Davis, Raleigh, and Francis Drake (c. 1540–1596) amongst his acquaintances. In fact, he took part in Drake’s circumnavigation 1577–1580. These were the first globes made in England apparently at the suggestion of John Davis to his patron the wealthy London merchant William Sanderson (?1548–1638), who financed the construction of Molyneux’s globes to the tune of £1,000. Sanderson had sponsored Davis’ voyages and for a time was Raleigh’s financial manager. He named his first three sons Raleigh, Cavendish, and Drake.

Molyneux’s terrestrial globe was his own work incorporating information from his mariner friends and with the assistance of Edward Wright in plotting the coast lines. The circumnavigations of Drake and Cavendish were marked on the globe in red and blue line respectively. His celestial globe was a copy of the 1571 globe of Gerard Mercator (1512–1594), which itself was based on the 1537 globe of Gemma Frisius (1508–1555), on which Mercator had served his apprenticeship as globe maker. Molyneux’s globes were engraved by Jodocus Hondius (1563–1612), who lived in London between 1584 and 1593, and who would upon his return to the Netherlands would found one of the two biggest cartographical publishing houses of the seventeenth century.

Hues’ Tractatus de globis et eorum usu was one of four publications on the use of the globes. Molyneux wrote one himself, The Globes Celestial and Terrestrial Set Forth in Plano, published by Sanderson in 1592, of which none have survived. The London public lecturer on mathematics Thomas Hood published his The Vse of Both the Globes, Celestiall and Terrestriall in 1592, and finally Thomas Blundeville (c. 1522–c. 1606) in his Exercises containing six treatises including Cosmography, Astronomy, Geography and Navigation in 1594.

Hues’ Tractatus de globis has five sections the first of which deals with a basic description of and use of Molyneux’s globes. The second is concerned with matters celestial, plants, stars, and constellations. The third describes the lands, and seas displayed on the terrestrial globe, the circumference of the earth and degrees of a great circle. Part four contains the meat of the book and explains how mariners can use the globes to determine the sun’s position, latitude, course and distance, amplitudes and azimuths, and time and declination. The final section is a treatise, inspired by Harriot’s work on rhumb lines, on the use of the nautical triangle for dead reckoning. Difference of latitude and departure (or longitude) are two legs of a right triangle, the distance travelled is the hypotenuse, and the angle between difference of latitude and distance is the course. If any two elements are known, the other two can be determined by plotting or calculation using trigonometry.

The book was a success going through numerous editions in various languages. The original in Latin in 1593, Dutch in 1597, an enlarged and corrected Latin edition in 1611, Dutch again in 1613, enlarged once again in Latin in 1617, French in 1618, another Dutch edition in 1622, Latin again in 1627, English in 1638, Latin in 1659, another English edition also in 1659, and finally the third enlarged Latin edition reprinted in 1663. There were others.

The title page of Robert Hues (1634) Tractatvs de Globis Coelesti et Terrestri eorvmqve vsv in the collection of the Biblioteca Nacional de Portugal via Wikimedia Commons

Hues continued his acquaintance with Raleigh in the 1590s and was one of the executors of Raleigh’s will. He became a servant of Thomas Grey, 15th Baron Gray de Wilton (died 1614) and when Grey was imprisoned in the Tower of London for his involvement in a Catholic plot against James I & VI in 1604, Hues was granted permission to visit and even to stay with him in the Tower. From 1605 to 1621, Northumberland was also incarcerated in the Tower because of his family’s involvement in the Gunpowder Plot. Following Grey’s death Hues transferred his Tower visits to Northumberland, who paid him a yearly pension of £40 until his death in 1632.

He withdrew to Oxford University and tutored Henry Percy’s oldest son Algernon, the future 10th Earl of Northumberland, in mathematics when he matriculated at Christ’s Church in 1617.

Algernon Percy, 10th Earl of Northumberland, as Lord High Admiral of England, by Anthony van Dyck. Source: Wikimedia Commons

In 1622-23 he would also tutor the younger son Henry.

Oil painting on canvas, Henry Percy, Baron Percy of Alnwick (1605-1659) by Anthony Van Dyck Source: Wikimedia Commons

During this period, he probably visited both Petworth and Syon, Northumberland’s southern estates. He in known to have had discussion with Walter Warner on reflection. He remained in Oxford discussing mathematics with like minded fellows until his death.

Compared to the nautical adventures of Harriot and Hues, both Warner and Torporley led quiet lives. Walter Warner was born in Leicestershire and educated at Merton College Oxford graduating BA in 1579, the year between Hues and Harriot. According to John Aubrey in his Brief Lives, Warner was born with only one hand. It is almost certain that Hues, Warner, and Harriot met each other attending the mathematics lectures of Thomas Allen at Oxford. Originally a protégé of Robert Dudley, 1st Earl of Leicester, (1532–1588), he entered Northumberland’s household as a gentleman servitor in 1590 and became a pensioner in 1617. Although a servant, Warner dined with the family and was treated as a companion by the Earl. In Syon house, he was responsible for purchasing the Earl’s books, Northumberland had one of the largest libraries in England, and scientific instruments. He accompanied the Earl on his military mission to the Netherlands in 1600-01, acting as his confidential courier.       

Like Harriot, Warner was a true polymath, researching and writing on a very wide range of topics–logic, psychology, animal locomotion, atomism, time and space, the nature of heat and light, bullion and exchange, hydrostatics, chemistry, and the circulation of the blood, which he claimed to have discovered before William Harvey. However, like Harriot he published almost nothing, although, like Harriot, he was well-known in scholarly circles. Some of his work on optics was published posthumously by Marin Mersenne (1588–1648) in his Universæ geometriæ (1646).

Source: Google Books

It seems that following Harriot’s death Warner left Syon house, living in Charing Cross and at Cranbourne Lodge in Windsor the home of Sir Thomas Aylesbury, 1st Baronet (!576–1657), who had also been a student of Thomas Allen, and who had served both as Surveyor of the Navy and Master of the Mint. Aylesbury became Warner’s patron.

This painting by William Dobson probably represents Sir Thomas Aylesbury, 1st Baronet. 
Source: Wikimedia Commons

Aylesbury had inherited Harriot’s papers and encouraged Warner in the work of editing them for publication (of which more later), together with the young mathematician John Pell (1611–1685), asking Northumberland for financial assistance in the endeavour.

Northumberland died in 1632 and Algernon Percy the 10th Earl discontinued Warner’s pension. In 1635, Warner tried to win the patronage of Sir Charles Cavendish and his brother William Cavendish, enthusiastic supporters of the new scientific developments, in particular Keplerian astronomy. Charles Cavendish’s wife was the notorious female philosopher, Margaret Cavendish. Warner sent Cavendish a tract on the construction of telescopes and lenses for which he was rewarded with £20. However, Thomas Hobbes, another member of the Cavendish circle, managed to get Warner expelled from Cavendish’s patronage. Despite Aylesbury’s support Warner died in poverty. 

Nathaniel Torporley was born in Shropshire of unknow parentage and educated at Shrewsbury Grammar Scholl before matriculating at Christ Church Oxford in 1581. He graduated BA in 1584 and then travelled to France where he served as amanuensis to the French mathematician François Viète (1540–1603).

François Viète Source: Wikimedia Commons

He is thought to have supplied Harriot with a copy of Viète’s Isagoge, making Harriot the first English mathematician to have read it.

Source

Torporley returned to Oxford in 1587 or 1588 and graduated MA from Brasenose College in 1591. 

He entered holy orders and was appointed rector of Salwarpe in Worcestershire, a living he retained until 1622. From 1611 he was also rector of Liddington in Wiltshire. His interest in mathematics, astronomy and astrology attracted the attention of Northumberland and he probably received a pension from him but there is only evidence of one payment in 1627. He was investigated in 1605, shortly before the Gunpowder Plot for having cast a nativity of the king. At some point he published a pamphlet, under the name Poulterey, attacking Viète. In 1632, he died at Sion College, on London Wall and in a will written in the year of his death he left all of his books, papers, and scientific instrument to the Sion College library.

Although his papers in the Sion College library contain several unpublished mathematical texts, still extant today, he only published one book his Diclides Coelometricae; seu Valuae Astronomicae universales, omnia artis totius munera Psephophoretica in sat modicis Finibus Duarum Tabularum methodo Nova, generali et facillima continentes, (containing a preface, Directionis accuratae consummata Doctrina, Astrologis hactenus plurimum desiderata and the Tabula praemissilis ad Declinationes et coeli meditations) in London in 1602.

Source

This is a book on how to calculate astrological directions, a method for determining the time of major incidents in the life of a subject including their point of death, which was a very popular astrological method in the Renaissance. This requires spherical trigonometry, and the book is interesting for containing new simplified methods of solving right spherical triangles of any sort, methods that are normally attributed to John Napier (1550–1617) in a later publication. The book is, however, extremely cryptic and obscure, and almost unreadable. Despite this the surviving copies would suggest that it was widely distributed in Europe.

Our three mathematici came together as executors of Harriot’s will. Hues was charged with pricing Harriot’s books and other items for sale to the Bodleian Library. Hues and Torporley were charged with assisting Warner with the publication of Harriot’s mathematical manuscripts, a task that the three of them managed to bungle. In the end they only managed to publish one single book, Harriot’s algebra Artis Analyticae Praxis in 1631 and this text they castrated.

Source

Harriot’s manuscript was the most advanced text on the topic written at the time and included full solutions of algebraic equations including negative and complex solutions. Either Warner et al did not understand Harriot’s work or they got cold feet in the face of his revolutionary new methods, whichever, they removed all of the innovative parts of the book making it basically irrelevant and depriving Harriot of the glory that was due to him.

For myself the main lesson to be learned from taking a closer look at the lives of this group of mathematici is that it shows that those interested in mathematics, astronomy, cartography, and navigation in England the late sixteenth and early seventeenth centuries were intricately linked in a complex network of relationships, which contains hubs one of which was initially Harriot and Raleigh and then later Harriot and Northumberland. 


[1] For those who don’t know, Middlesex was a small English county bordering London, in the South-West corner of Essex, squeezed between Hertfordshire to the north and Surry in the South, which now no longer exists having been largely absorbed into Greater London. 

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Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of Optics, History of science, Renaissance Science

Around the World in One Thousand and Eighty-three Days 

Growing up in the UK in the 1950s, history lessons in primary school, that’s elementary school for Americans, still consisted to a large extent of a glorification of the rapidly fading British Empire. The classroom globes were still covered in swathes of pink and there, at least, the sun never set on the empire that was. Another popular theme, in this collection of fairy tales and myths, was the great period of European exploration and discovery in the Early Modern Period, in which Columbus, Vasco da Gama and Magellan were presented as larger than life, heroic, visionary adventurers, who respectively discovered America, became the first European to sail to India, and, perhaps the greatest achievement of all, circumnavigated the globe. 

At grammar school history became modern European history–Napoleon, Vienna Conference, Franco-Prussian War, unification of German, First World War, rise of Fascism and Hitler, and Second World War–my generation was after all born in and grew up in the aftermath of WWII. The “heroes” of the so-called age of discovery faded into the background, becoming nothing more than a handful of half-remembered facts–1492 Columbus sailed the ocean blue. Somewhere down the line those early tales of daring do became tarnished by inconvenient facts, such as the information that the Vikings almost certainly got to America before Columbus or that Vasco da Gama only managed to sail from Africa to India because he employed a local navigator, who knew how to get there. On the whole it was not a topic that particularly interested me in the early part of my adult life. As far as history went, it didn’t seem to me at that time to be part of the history of mathematics, boy was I wrong on that, so I largely ignored it. 

However, I was aware of the gradual dethroning of Columbus, who having been appointed governor by the Spanish Crown of the islands he had discovered was later stripped of his title because of incompetence and brutality towards the indigenous population. Also, that de Gama had had to use military force to persuade the Indians to trade with him. These men were not the saints they had been painted as in my youth. However, through it all Magellan remained a heroic role model, the first man to circumnavigate the globe. 

I first became more interested in more detail about the so-called age of discovery about fifteen years ago when I became aware that the Renaissance mathematici, who now occupied a large part of my historical activities, were not mathematicians in anything like the modern sense of the word but were, as the English term has it, mathematical practitioners. That is, that they were actively engage in particle mathematics, not to be confused with the modern term applied mathematics, which included navigation and map making, as well as the design and production of mathematical instruments for navigation, surveying, and cartography. All of these activities have, of course, a direct and important connection to those voyages of discovery. This was brought home to me when I discovered that one of my favourite mathematici, the Nürnberger Johannes Schöner (1477–1547 most well known as a pioneer in the production of printed globes, had probably produced a terrestrial globe in 1523 displaying Magellan’s circumnavigation. As I wrote in a blog post from 2010:

So, what does all of this have to do with Magellan and the first circumnavigation? As Schöner was in Kirchehrenbach in his banishment he tried to curry favour with his Bishop in that he dedicated his newest terrestrial globe to him, produced in 1523 this globe featured the route of Magellan’s circumnavigation only one year after those 18 seamen struggled back to Spain. At least we think he did! The accompanying cosmographia for the globe exists but none of the globes has survived the ravages of time. How did Schöner manage to transfer the knowledge of this epic voyage so quickly into a printed globe? In this day and age where the news of Ms Watson’s achievement is blasted around the globe in all form of media within seconds of her landfall, we tend to forget that such news sometimes took years to permeate through Europe in the 16th century. At the instigation of Cardinal Matthäus Lang a great sponsor of science in this age Maximilianus Transylvanus interviewed the survivors in Spain and published his account of the voyage in 1523 and it was this account, which Schöner, who made sure to always acquire the latest travel reports through a network of contacts, used to make his globe. I said that none of his Magellan globes have survived but there is a set of globe gores in New York that appear to be those of Schöner’s 1523 globe. Globes were printed on gores, these are strips of paper shaped like segments of an orange that were then glued on to a papier mâché sphere and coloured by hand. The set of gores in New York have Schöner’s cartographical style and Magellan’s route printed on them and although there are some dissenting voices, in general the experts think that they are Schöner’s original.

Included in this quote in the information that only a very small number of the 237 seamen, who set out on this much acclaimed voyage actually made it back to Spain, and only one of the original five ships. Moreover, Magellan was not amongst the survivors having been killed in an imperial attack on indigenous natives on the island of Mactan, who refused to accept the authority of the king of Spain. I had personally garnered this information somewhere down the line.

I became increasingly interested in the mathematical aspects of the so-called age of discovery and became embroiled in an Internet debate on the naming of America with a famous, British pop historian, who was erroneously claiming that it was far more likely that America was named after the Welsh merchant, Richard Ap Meric, an investor in John Cabot’s voyages of discovery, than after Amerigo Vespucci. Being well aware of the reasons why Waldseemüller and Ringmann had named America after Vespucci on their 1507 map of the world, I wrote a long blog post challenging this twaddle. 

As part of my study of this piece of history I acquired my first book by historian extraordinary of exploration, Felipe Fernández-Armesto, his excellent biography of Vespucci, AmerigoThe Man who Gave His Name to America.[1] This was quickly followed by his equally good biography of Columbus,[2] and somewhat later by his PathfindersA Global History of Exploration.[3] So, when it was announced that Felipe Fernández-Armesto’s latest book, he’s incredibly prolific, was to be a biography of Magellan, I immediately ordered a copy and this blog post is a review of  his STRAITSBeyond the myth of Magellan.[4]

I will start by saying that Fernández-Armesto does not disappoint, and this biography of the man and his infamous voyage is up to his usual very high standards. If you have a serious interest in the topic, then this is definitely a book you should read. Although this is a trade book rather than an academic tome, Fernández-Armesto has scrupulously researched his topic and all of the book’s statements and claims are backed up by detailed endnotes. While we are by the apparatus the book also has an extensive and very comprehensive index but no general bibliography. This is one of several new books that I have without a general bibliography, meaning that if you become interested in a referenced volume and it’s not the first reference, then you have to plough your way back through the endnotes, desperately searching for that all important first reference, which contains the details that you require to actually find the book. Staying briefly with the general description, each chapter has a frontispiece consisting of a contemporary print with a detailed descriptions that related to the following chapter. There are also five grey tone maps scattered throughout the book showing places referred to in the narrative.

One thing that Fernández-Armesto makes very clear throughout his book is that the sources for actual hard information about Magellan are very thin and those that do exist are often contradictory. Because he very carefully qualifies his statements concerning Magellan, weighing up the sources and explaining why he believes the one version rather than the other, this makes the book, whilst not a hard read, shall we say a very intense read. Put another way, Fernández-Armesto doesn’t present his readers with a smooth novel like narrative, lulling them into thinking that we know more than we do, but shows the reader how the historian is forced to construct their narrative despite inadequate sources. This is a lesson that other trade book authors could learn.

The central myth of the Magellan story that Fernández-Armesto tackles in his book is that of the inspirational figure, who set out to circumnavigate the world. Not only did Magellan personally fail to do so, a fact that is so often swept under the carpet in the simple claim that he was the first man to do so, but that he in fact never had the intention of doing so. 

In the somewhat less than first half of his book Fernández-Armesto takes the reader through the details of what we know about Magellan’s life before that infamous voyage. His origins, his life and education on the Portuguese court, his service for the Portuguese Crown both as a seaman and a soldier. His reasons for leaving Portugal and moving to Spain, where he offered his services to the Spanish Crown instead. All of this leads up to his plans for that voyage and the motivation behind it. His intended aim was not to sail around the world but to find a passage through the Americas from the Atlantic to the Pacific, or Southern Sea, as it was generally known then, and then to sail across the Pacific to the Moluccas (Spice Islands), today known as the Maluka Islands, and hopefully demonstrate that they lay in the Spanish half of the globe, as designated by the Pope’s Tordesillas Treaty. Having done so to then return to Spain by the same route. Nobody actually knew in which half of the globe the Moluccas lay, as the treaty only specified the demarcation line or meridian in the Atlantic and it was not known where the anti-meridian lay in the Pacific, which in general everybody, including Magellan, thought was much smaller than it actually is.

Due to the uncertainties that this plan, was there even a passage through the Americas joining the two oceans, was it possible to cross the Pacific by ship, did the Moluccas actually lay within the Spanish hemisphere, the negotiations to set up the voyage and the persuade the Spanish Crown to finance it were tough and complex and Fernández-Armesto takes the reader through them step by step. Having succeeded, we then set sail with Magellan on a voyage that was an unmitigated disaster every single sea mile of the way.

The somewhat more than second half of Fernández-Armesto’s narrative is a detailed account, as far as it is possible to reconstruct it, of what might be described, with only slight exaggeration, as the voyage to hell and back with long periods in purgatory. Possibly the only thing that is admirable about Magellan and the voyage is his tenacity in the constant face of doom and disaster, although that tenacity takes on more and more maniacal traits as the voyage proceeds.

Fernández-Armesto’s biography of the man and his voyage is a total demolition of the myths that have been created and propagated over the last five centuries, leaving no trace of valour, heroism, or gallant endeavour. The voyage was an unmitigated disaster perpetrated by a ruthless, driven monomaniac. At the end of his excellent tome Fernández-Armesto illustrates how the myth of Magellan and his circumnavigation was put into the world, starting almost as soon as the Victoria, the only one of the five ships to complete the circumnavigations, docked in Spain more than a thousand days after it set sail with only a handful of the crews that started that voyage. Fernández-Armesto also list some of the myriad of organisations, objects, institutes, prizes etc. that proudly bear Magellan’s name, his attitude to all this being summed up perhaps by his comment on the Order of Magellan awarded by the Circumnavigators Club of New York:

Though it seems astonishing that an award for “world understanding should be named for a failed conqueror who burned villages ad coerced and killed people. (p. 277)

As a final comment on this possibly definitive biography, I learnt in reading this book that the early explorers, Columbus, da Gamma, Magellan et al identified both themselves and their endeavours with the heroic knights in the medieval tales of chivalry and romance, riding their ships out on quests of discovery that would bring the fame, fortune, and honour. Magellan’s quest was about as far removed from this image as it was possible to get. 


[1] Felipe Fernández-Armesto, AmerigoThe Man who Gave His Name to America, Weidenfeld & Nicolson, London, 2006.

[2] Felipe Fernández-Armesto, Columbus, OUP, Oxford & London, 1991, ppb Duckworth, London, 1996

[3] Felipe Fernández-Armesto, PathfindersA Global History of Exploration, W W Norton, New York, 2006, ppb 2007

[4] Felipe Fernández-Armesto, STRAITSBeyond the myth of Magellan, Bloomsbury, London, Oxford, New York, New Delhi, Sydney, 2022

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Filed under Book Reviews, History of Navigation, Renaissance Science

Renaissance science – XXVIII

In the last episode of this series, we explored the history of the magnetic compass in Europe and marine cartography from the Portolan chart to the Mercator Projection. We will now turn our attention to the other developments in navigation at sea in the Renaissance. As already stated in the last episode, the need to develop new methods of navigation and the instruments to carry them out was driven by what I prefer to call the Contact Period, commonly called the Age of Discovery or Age of Exploration. The period when the Europeans moved out into the rest of the world and exploited it. 

This movement in turn was motivated by various factors. Curiosity about lands outside of Europe was driven both by travellers’ tales such as The Travels of Marco Polo c. 1300 and The Travels of Sir John Mandeville, which first appeared around 1360, both of which were highly popular throughout Europe, and also by new cartographical representation of the know world, known to the Europeans that is, in particular Ptolemaeus’ Geographia, which first became available in the early fifteenth century. Another development was technological, the development by the Portuguese, who as we shall see led the drive out of Europe into the rest of the world, of a new type of ship, the caravel, which was more manoeuvrable than existing vessels and because of its lateen sails was capable of sailing windward, making it more suitable for long ocean voyages, as opposed to coastal sailing.

The Portuguese invention of the caravel, which was maneuverable and able to undertake ocean voyages, was essential to European maritime exploration. The present image shows the “Caravela Vera Cruz“, navigating the Tagus river, Lisboa. Source: Wikipedia Commons
Depending on the situation, different intervals between tacking can be used. This does not influence the total distance travelled (though may impact the time required). Sailing from point A to point B, path P1 involves more turns but only requires a narrow channel. Path P2 involves fewer turns but a wider channel. Path P3 requires only a single turn but covers comparatively the widest channel. Source: Wikimedia Commons

The final and definitely most important factor was trade or perhaps more accurately greed. The early sailors, who set out to investigate the world outside of Europe, were not the romantic explorers or discoverers, we get taught about in school, but hard-headed businessmen out to make a profit by trade or if necessary, theft. 

The two commodities most desired by these traders, were precious metals, principally gold but also silver and copper, and spices. The metal ore mines of Middle Europe could not fill the demands for precious metals, so other sources must be found. This is perhaps best illustrated by the search in South America, by the Spanish, for the mythical city of gold, El Dorado, during the sixteenth century. Spices had been coming into Europe from the East over the Indian Ocean and then overland, brought by Arab traders, to the port cities of Northern Italy, principally Venice and Genoa, from where there were distributed overland throughout Europe since the eleventh century. The new generation of traders thought they could maximise profits by cutting out the middlemen and going directly to the source by the sea route. This was the motivation of both Vasco da Gama (c. 1460–1524), sailing eastwards, and Christopher Columbus (1451–1506), sailing westward. Their voyages are, however, one end point of a series of voyages, which began with the Portuguese capture of Ceuta, in North Africa, from the Arabs, in 1415.

Having established a bridgehead in North Africa the Portuguese, who were after all situated on the Atlantic coast of the Iberian Peninsula, argued that they could bypass the middleman, their trading partners the Arabs, and sail down the coast to Sub-Saharan West Africa and fetch for themselves, the gold and the third great trading commodity of the Contact Period, slaves, who they had previously bought from Arab traders. It is fair to ask why other countries, further north, with Atlantic coasts did not lead the expansion into unknown territory? The first decades of the Portuguese Atlantic ventures were still very much coastal sailing progressively further down the African coast; other northern European countries, such as Britain did sail north and south along the Atlantic coast, but their journeys remained within Europe. 

Starting in 1520, Portuguese expeditions worked their way down the west coast of Africa until the end of the sixteenth century.

The gradual Portuguese progress down the West Coast of Africa Source: Wikipedia Commons

The Nürnberger Martin Behaim (1459–1507), responsible for the creation of the oldest surviving terrestrial globe and member of the Portuguese Board of Navigation (to which we will return), claimed to have sailed with Diogo Cão, who made two journeys in the 1480s, which is almost certainly a lie. At the time of Cão’s first voyage along the African coast Behaim is known to have been in Antwerp. On his second voyage Cão erected pillars at all of his landing places naming all of the important members of the crew, who were on the voyage, Martin Behaim is not amongst them. 

The two most significant Portuguese expedition were that of Bartolomeu Dias (c. 1450–1500) in 1488, which was the first to round the Cape of Good Hope, actually Diogo Cão’s aim on his two voyages, which he failed to achieve, and, of course, Vasco da Gama’s voyage of 1497, which took him not only up the east African coast but all the way to India with the help of a local navigator. The two voyages also showed that the Indian Ocean was open to the south, whereas Ptolemaeus had shown it to be a closed sea in his Geographia. 

Much earlier in the century the Portuguese had ventured out into the Atlantic and when blown off course by a storm João Gonçalves Zarco (c. 1390 –1471) and Tristão Vaz Teixeira (c. 1395–1480) discovered the archipelago of Madeira in 1420 and one expedition discovered the Azores, 1,200 km from the Portuguese coast in 1427. The Canaries had already been discovered in the early fourteenth century and were colonised by the Spanish in 1402. The Cap Verde archipelago was discovered around 1456. The discovery of the Atlantic islands off the coasts of the Iberian Peninsula and Africa was important in two senses. Firstly, there developed myths about other islands further westward in the Atlantic, which encouraged people to go and look for them. Secondly, by venturing further out into the Atlantic sailors began to discover the major Atlantic winds and currents,, known as gyres essential knowledge for successful expeditions.

The Atlantic Gyres influenced the Portuguese discoveries and trading port routes, here shown in the India Run (“Carreira da Índia“), which would be developed in subsequent years. Source: Wikipedia Commons

Dias could only successfully round the Cape because he followed the prevailing current in a big loop almost all the way to South America and then back past the southern tip of Africa. Sailors crossing the Indian Ocean between Africa and India had long known about the prevailing winds and currents, which change with the seasons, which they had to follow to make successful crossings. The Spanish and the Portuguese would later discover the currents they needed to follow to successfully sail to the American continent and back.

The idea of island hopping to travel westwards in the Atlantic that the discoveries of the Azores and the other Southern Atlantic islands suggested was something already been followed in the North Atlantic by fishing fleets sailing out of Bristol in Southwest England in the fifteenth century. They would sail up the coast of Ireland going North to the Faroe Islands, settled by the Vikings around 800 CE and then onto Iceland, another Viking settlement, preceding to Greenland and onto the fishing grounds off the coast of Newfoundland. This is the route that Sebastian Cabot (c. 1474–c. 1557) would follow on his expedition to North America in the service of Henry VIII. It is also probable that Columbus got his first experience of navigating across the Atlantic on this northern route. 

Columbus famously made his first expedition to what would be erroneously named America in 1492, in an attempt to reach the Spice Islands of Southeast Asia by sailing westward around the globe. This expedition was undertaken on the basis of a series of errors concerning the size of the globe, the extent of the oikumene, the European-Asian landmass known to the Greek cartographers, and the distance of Japan from the Asian mainland. Columbus thought he was undertaking a journey of about 3,700 km from the Canary Islands to Japan instead of the actual 19,600 km! If he hadn’t bumped into America, he and his entire crew would have starved to death on the open sea. Be that as it may, he did bump into America and succeeded in returning safely, if only by the skin of his teeth. With Columbus’ expedition to America and da Gama’s to India, the Europeans were no longer merely coastal sailors but established deep sea and new approaches to navigation had to be found.

The easiest way to locate something on a large open area is to use a geometrical coordinate system with one set of equally spaced lines running from top to bottom and a second set from side to side or in the case of a map from north to south and east to west. We now call such a grid on a map or sea chart, lines of longitude also called meridians, north to south, and lines of latitude also called parallels, east to west. The earliest know presentation of this idea is attributed to the Greek polymath Eratosthenes (c. 276­–c. 195 BCE).

A perspective view of the Earth showing how latitude (𝛟) and longitude (𝛌) are defined on a spherical model. The graticule spacing is 10 degrees.

The concept was reintroduced into Early Modern Europe by the discovery of Ptolemaeus’ Geographia. It’s all very well to have a location grid on your maps and charts but it’s a very different problem to determine where exactly you are on that grid when stuck in the middle of an ocean. However, before we consider this problem and its solutions I want to return to the Portuguese Board of Navigation, which I briefly mentioned above.

Both the Portuguese and the Spanish realised fairly early on as they began to journey out onto the oceans that they needed some way of collecting and collating new geographical and navigation relevant information that their various expeditions brought back with them and also a way of imparting the relevant information and techniques to navigators due to set out on new expeditions. Both countries established official institutions to fulfil these tasks and also appointed official cosmographers to lead these endeavours. Pedro Nunes (1502–1578), who we met in the first episode on navigation, as the discoverer of the loxodrome, was appointed Portugal’s Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547, a post he held until his death.

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The practice of establishing official organisations to teach cartography and navigation, as well as the mathematics they needed to carry them out to seamen was followed in time by France, Holland, and Britain as they too began to send out deep sea marine expeditions. 

To determine latitude and longitude are two very different problems and I will start with the easier of the two, the determination of latitude. For the determination of longitude or latitude you first need a null point, for latitude this is the equator. In the northern hemisphere your latitude is how many degrees you are north of the equator. You can determine your latitude using either the Sun during the day or the North Star at night. At night you need to observe the North Star with some sort of angle measuring device then measure the angle that makes to the horizon and that angle is your latitude in degrees. During the day you need to observe the Sun at exactly noon with an angle measuring device then the angle to makes with a vertical plumb line is your latitude. This is only strictly true for the date of the two equinoxes. For other days of the year, you have to calculate an adjustment using tables. For these observations mariners initially used either a quadrant,

Geometric quadrant with plumb bob. Source: Wikimedia Commons

which had been in use since antiquity or a Jacob’s Staff or Cross Staff, the invention of which is attributed to the French astronomer Levi Ben Gershon (1268–1344).

A sailor uses a ‘Jacob’s Staff’ to calculate the angle between a star and the horizon Source

Contrary to many claims, astrolabes were never used on ships for this purpose. However, around the end of the fifteenth century a much-simplified version of the astrolabe, the mariner’s astrolabe began to be used for this purpose. 

Mariner’s astrolabe Source: Wikimedia Commons

Because looking directly into the Sun is not good for the eyes, the backstaff was developed over time. With a backstaff the mariner stands with his back to the Sun and a shadow is cast onto the angle measuring scale. Thomas Harriot (c. 1560–1621) is credited with being the originator of the concept. The mariner John Davis (c. 1550–1605) introduced the double quadrant or Davis quadrant in his book on practical navigation, The Seaman’s Secrets in 1594, a device that evolved over time.

Davis quadrant, made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons
How a Davis Quadrant is used Source includes a video of how to use one

In 1730, John Hadley invented the reflecting octant, which incorporated a mirror to reflect the image of the Sun, whilst the user observed the horizon.

John Hadley Source: Wikimedia Commons
Hadley Octant Source includes video

This evolved into the sextant the device still used today to “shoot the Sun” as it is called. Here we see an evolution of instruments used to fulfil a specific function.

The determination of longitude at sea is a much more difficult problem. First, there is no natural null point, and any meridian can be and indeed was used until the Greenwich Meridian was chosen as the international null point for the determination of longitude at the International Meridian Conference in Washington in 1884. Because the Earth revolves once in twenty-four hours the determination of the difference in longitude between two locations is equivalent to the difference in local time between them, one degree of longitude equals four minutes of time difference, so the determination of longitude is basically the determination of time differences, which is easy to state but much more difficult to carry out.

The various European sea going nations–Spain, Portugal, France, Holland, Britain–all offered financial awards to anybody who could come up with a practical solution for determining longitude at sea. 

In antiquity, the difference in longitude between two locations was determined by calculating the difference in the observation times of major astronomical events such as lunar or solar eclipses. Then, if one had determined the difference in longitude between two given locations and their respective distances from a third location, it was possible to calculate the difference in longitude for the third location geometrically. Using these methods, astronomers, and cartographers gradually built-up tables of longitude for large numbers of towns and cities such as the one found in Ptolemaeus’ Geographia. This method is, of course, not practical for mariners at sea.

Starting in the early sixteenth century, various methods were suggested for determining time differences in order to determine longitude. The Nürnberger mathematicus Johannes Werner (1468 – 1522) in his In hoc opere haec continentur Nova translatio primi libri geographiae Cl’ Ptolomaei … (Nürnberg 1514) proposed the so-called lunar distance method. In this method an accurate table of the position of the Moon relative to a given set of reference stars for a given location for the entire year needs to be created.

Source: Wikimedia Commons

The mariner then has to observe the position of the Moon relative to the reference stars for his local time and then calculate the time difference to the given location from the tables. Unfortunately, because the Moon is pulled all over the place by the gravitational influence of both the Sun and the Earth, its orbit is highly irregular and the preparation of such tables proved beyond the capabilities of sixteenth century astronomers and indeed of seventeenth century astronomers, when the method was proposed again by Jean-Baptiste Morin (1583–1656). There was also the problem of an instrument accurate enough to measure the position of the Moon on a moving ship. It was Tobias Mayer (1723–1762), who first managed to produce accurate tables and Hadley’s octant or rather the sextant that evolved out of it solved the instrument problem. 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.

Portrait of Nevil Maskelyne by Edward Scriven Source: Wikimedia Commons
Source: Library of Congress Washington

The next solution to the problem of determining longitude suggested during the Renaissance by Gemma Frisius (1508–1555) was the clock, published in his De principiis astronomiae et cosmographiae. (Antwerp, 1530).

Gemma Frisius 17th C woodcut by E. de Boulonois Source: Wikimedia Commons

The mariner should take a clock, capable of maintaining accurate time over a long period under the conditions that prevail on a ship on the high seas, set to the time of the point of departure. By comparing local time with the clock time, the longitude difference could then be calculated. The problem was that although mechanical clocks had been around for a couple of centuries when Gemma Frisius made his suggestion, they were incapable of maintaining the required accuracy on land, let alone on a ship at sea. Jean-Baptiste Morin thought it would never be possible, “I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.” A view apparently shared by Isaac Newton, when he sat on the English Board of Longitude.

Only when Christiaan Huygens (1629–1695) had the first pendulum clock constructed by Salomon Coster (c. 1620–1659) accord his design in 1657 that Frisius’ idea began to seem realistic.

Christiaen Huygens II (1629-1695) signed C.Netscher / 1671 Source: Wikimedia Commons
Spring-driven pendulum clock, designed by Huygens and built by Salomon Coster (1657),  with a copy of the Horologium Oscillatorium (1673), at Museum Boerhaave, Leiden. Source: Wikimedia Commons

One of Huygens’ clocks was actually sent on sea trials but failed the test. In what is, thanks to Dava Sobel[1], probably the most well-known story in the history of technology John Harrison (1693–1776)

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

finally succeeded in producing a clock capable of fulfilling the demands with his H4 in 1761, slightly later than the successful fulfilment of the lunar distance method. In one sense the problem was still not really solved because the H4 was too complex and too expensive for it to be mass produced at a reasonable cost for use in sea transport. It was only really in the nineteenth century, after further developments in clock technology, that the marine chronometer became a real solution to the longitude problem.

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

Back tacking, at the beginning of the seventeenth century with the discovery of the four largest moons of Jupiter another method suggested itself. These moons, Io, Europa, Ganymede, and Callisto, have orbital periods of respectively, 1.77, 3.55, 7.15, and 16.6 days.

A montage of Jupiter and its four largest moons (distance and sizes not to scale) Source: Wikimedia Commons

This means that one or other of them is being fairly often eclipsed by Jupiter. Galileo argued that is one could calculate the orbits accurately enough they could be used as a clock to determine longitude. He tried to sell the idea to the governments of both Spain and the Netherlands without success. The principal problem was the difficulty of observing them with a telescope on a moving ship. Galileo worked on an idea of an observing chair with the telescope mounted on a helmet, but the idea never made it off the paper. Later in the seventeenth century Jean-Dominique Cassini (1625–1712) produced tables of the orbits accurate enough for them to be used to determine longitude and he and Jean Picard (1620–1682) used the method on land to accurately determine the borders of France, leading Louis XVI to famously quip that he had lost more territory to the cartographers than he ever lost to his enemies.

Map showing both old and new French coastlines Source: Wikimedia Commons

In the first part of this account of navigation I described the phenomenon of magnetic variations or declination, which is the fact that that a compass does not point to true north but to magnetic north, which is somewhat removed from true north. I also mentioned that magnetic declination is not constant but varies from location to location. This led to the thought that if one were to map the magnetic inclination for the entire Atlantic one could use the data to determine longitude, whilst at sea. Edmond Halley (1556–1742) did in fact create such a map on a voyage from1699 to 1700. However, this method of determining longitude was never really utilised. 

Portrait of Halley (c. 1690) by Thomas Murray Source: Wikimedia Commons
Halley’s 1701 map showing isogonic lines of equal magnetic declination in the Atlantic Ocean. Source: Wikimedia Commons

Although the methods eventually developed to determine longitude on the high seas all came to fruition long after the Renaissance, they all have their roots firmly planted in the practical science of the Renaissance. This brief sketch also displays an important aspect of the history of science and technology. A lot of time can pass, and very often does, between the recognition of a problem, the suggestion of one or more solutions to that problem, and the realisation or fulfilment of those solutions.

Having gone to great lengths to describe the principal methods suggested and eventually realised for determining longitude, there were others ranging from the sublime to the ridiculous that I haven’t described, there remains the question, how did mariners navigate when far away from the coast during the Early Modern Period? There are two answers firstly latitude sailing and secondly dead reckoning. In latitude sailing, instead of, for example, trying to cross the Atlantic by the most direct course from A to B, the navigator first sails due north or south along the coast until he reaches the latitude of his planned destination. They then turn their ship through ninety degrees and maintain a course along that latitude. This, of course, nearly always means a much longer voyage but one with less risk of getting lost. 

In dead reckoning, the navigator, starting from a fixed point, measures the speed and direction of his ship over a given period of time transferring this information mathematically to a sea chat to determine their new position. The direction is determined with the compass, but the determination of the ship’s speed is at best an approximation, which was carried out in the following manner. A log would be thrown overboard at the front of the ship and the mariners would measure how long it took for the ship to pass the log, and the result recorded in a book, which became known as the logbook. The term logbook expanded to include all the information recorded on a voyage on a sip and then later on planes and even lorries. Of note, the word blog is an abbreviation of the term weblog, a record of web or internet activity, but I’m deviating from the topic.

An example of dead reckoning Columbus’ return voyage Source

The process of measuring the ships speed evolved over time. The log was thrown overboard attached to a long line and using an hourglass, the time how long the line needed to pay out was recorded. Later the line was knotted at regular intervals and the number of knots were recorded for a given time period. This is, of course, the origin of the term knots for the speed of ships and aircraft. Overtime the simple log of wood was replaced with a so-called chip-log, which became standardised:

The shape is a quarter circle, or quadrant with a radius of 5 inches (130 mm) or 6 inches (150 mm), and 0.5 inches (13 mm) thick. The logline attaches to the board with a bridle of three lines that connect to the vertex and to the two ends of the quadrant’s arc. To ensure the log submerges and orients correctly in the water, the bottom of the log is weighted with lead. This provides more resistance in the water, and a more accurate and repeatable reading. The bridle attaches in such a way that a strong tug on the logline makes one or two of the bridle’s lines release, enabling a sailor to retrieve the log. (Wikipedia)

Model of chip log and associated kit. The reel of log-line is clearly visible. The first knot, marking the first nautical mile is visible on the reel just below the centre. The timing sandglass is in the upper left and the chip log is in the lower left. The small light-coloured wooden pin and plug form a release mechanism for two lines of the bridle. From the Musée de la Marine, Paris. Source: Wikimedia Commons

The invention of the log method of determining a ship’s speed is attributed to the Portuguese mariner Bartolomeu Crescêncio at the end of the fifteenth century. The earliest known published account of using a log to determine a ship’s speed was by William Bourne (c. 1535–1582) in his A regiment of the Sea in 1574, which went through 11 English editions up to 1631 and at least 3 Dutch edition from 1594. 

Dead reckoning is a process that is prone to error, as it doesn’t take into account directional drift caused by wind and currents. Another problem was that not all mariners processed the necessary mathematical knowledge to transfer the data to a sea chart. Those mariners, who disliked and rejected the mathematical approach used a traverse board, which uses threads and pegs to record direction and speed of a ship. William Bourne writing in 1571 said:

I have known within these 20 years that them that were ancient masters of shippes hathe derided and mocked them that have occupied their cards and plattes and also the observation of the Altitude of the Pole saying; that they care not for their sheepskinne for he could keepe a better account upon a board.

This blog post is already far too long, so I’ll skip a detailed description of the traverse board, but you can read one here.

We have one last Renaissance contribution to the art of navigation from the English mathematical practitioner, Edmund Gunter (1581–1626), who we have already met as the inventor of the standard English surveyor’s chain in the episode on surveying. Gunter invented the Gunter scale or rule, simply known as the “gunter” by mariners, which he published in his Description and Use of the Sector, the Crosse-staffe and other Instrumentsin 1623. Developed shortly after the invention of logarithms, the scale is usually somewhat more than a half metre long and about 40 mm broad. It is engraved on both sides with various scales or lines. Usually, on the one side are natural line, chords, sines, tangents, rhumbs etc., and on the other scales of the logarithms of those functions. Navigational mathematical problems were then worked through using a pair of compasses. 

Gunter scale front
Gunter scale back Source

Despite its drawbacks, uncertainties, and errors dead reckoning was used for centuries by European mariners to crisscross the oceans and circumnavigate the globe. It continued to be used well into the nineteenth century, long after the perfection of the marine chronometer and the lunar distance method. 

This over long blog post is but a sketch of the contributions made by the Renaissance mathematical practitioners to the development of methods of deep-sea navigation required by the European mariners during the Contact Period, when they swarmed out to investigate the world beyond Europe and exploit it. Those contributions were in the form of theories, publications, instruments, charts, and practical instruction (which I haven’t really expanded upon here). For a more detailed version of the story, I heartily recommend Margaret Scotte’s excellent Sailing School: Navigation Science and Skill, 1550–1800 (Johns Hopkins University Press, 2019).


[1] Sobel’s account of the story is somewhat less than historically accurate and as always, I recommend instead Dunne and Higgitt, Finding LongitudeHow ships, clocks and stars helped solve the longitude problem (Collins, 2014)

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Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of Navigation, Renaissance Science

WRONG, WRONG, WRONG…

I think the Internet has finally broken the HISTSCI_HULK; he’s lying in the corner sobbing bitterly and mumbling wrong, wrong, wrong… like a broken record. What could have felled the mighty beast? 

29 January was the anniversary of the birth (1611) and death (1687) of the Danzig astronomer Johannes Hevelius and numerous people, including myself, posted or reposted articles about him on the Internet. One of those articles was the 2018 article, The 17th-Century Astronomer Who Made the First Atlas of the Moon by Elizabeth Landau, with the lede Johannes Hevelius drew some of the first maps of the moon, praised for their detail, from his homemade rooftop observatory in the Kingdom of Poland, in the Smithsonian Magazine.

Johannes Hevelius by Daniel Schultz Source: Wikimedia Commons

I suppose that I’m really to blame because I let him read it. He was chugging along quite happily, nodding his head, and burbling to himself, on the lookout, as always, for history of science errors and howlers, when he let out a piercing scream, NOOOOOO!!!!!! And collapsed in a sobbing heap on the floor. I’ve tried everything but I haven’t been able to console the poor beast.

So, what was it that caused this total breakdown? The first six paragraphs of the article are harmless enough, with only some very minor questionable statements, not really worth bothering about, but then comes this monstrosity:

Mapping the moon was one of Hevelius’s first major undertakings. The seafaring nations at the time were desperately searching for a way to measure longitude at sea, and it was thought that the moon could provide a solution. The idea was that during a lunar eclipse, if sailors observed the shadow of the moon crossing a particular point on the surface at 3:03 p.m., but they knew that in another location, such as Paris, the same crossing would occur at 3:33 p.m., then they could calculate their degrees of longitude away from the known location of the city. More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

One can only assume that it is an attempt to describe the lunar distance method for determining longitude but apart from the word moon, it has absolutely nothing in common with the actual lunar distance method. Put very mildly it is a complete travesty that should never have seen the light of day, let alone been published. 

Lunar eclipses had already been used for many centuries to determine the longitude difference between two locations, but you don’t need either a map of the moon or a telescope to do so. Two observers, in their respective locations, merely record the local time of the beginning and/or the end of the eclipse (initial and final contacts) and the resulting time difference gives the difference in longitude. Lunar eclipses are impractical as a method of determining longitude for navigation, as they occur too infrequently; there will only be a total of 230 lunar eclipses in the whole of the twenty-first century, of which only eighty-five will be total lunar eclipses. For example, if you were sitting in the middle of the Atlantic Ocean on 6 June 2022 and wished to determine your longitude, you would have to wait until 8 November for the next total lunar eclipse. After that you would have to wait until 14 March 2025 for the next total lunar eclipse, although there are a couple of partial and penumbral eclipses in between. 

Early Modern explorers did use solar and lunar eclipses combined with an ephemeris, a book of astronomical tables, to determine longitude on land, to establish their location and to draw maps. Columbus, famously, used his knowledge of the total lunar eclipse on 1 March 1504, taken from an ephemeris, to intimidate the natives on the island of Jamaica into continuing to feed his hungry stranded crew.

The lunar distance method of determining longitude is something completely different. It was first proposed by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524. For reasons that I will explain in a minute, it was found impractical, but was proposed again in 1634 by the French astronomer Jean-Baptiste Morin (1586–1656), but once again rejected as impractical. 

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. 

We now turn our attention to Landau’s closing statement in this horror paragraph:

More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

Historically, tables of the necessary accuracy were produced by Tobias Meyer (1723–1762) in 1755. However, 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 (1732–1811) produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766. One does not need a telescope to make the necessary observations. A sextant is sufficient to measure the distance between the moon and the reference stars and that had been invented by John Hadley (1682–1744) in 1731. The lunar distance method was in fact ready for practical use before the marine chronometer. 

One question that I have, is did Landau extract this heap of nonsense out of her own posterior or is she paraphrasing somebody else’s description? Throughout her article she gives links to various books with the information she is using, so did she take this abomination from another source? If so, it is still out there somewhere creating confusion for anybody unlucky enough to read it. On the question of sources, Dava Sobel’s Longitude, which, despite her prejudices against it, contains a correct description of the lunar distance method was published in 2005 and the much better Finding Longitude by Rebekah Higgitt and Richard Dunn was published in 2014, so there is no real excuse for Landau’s load of bovine manure in 2018. 

I don’t know how many people have subscriptions to the Smithsonian Magazine, but it has over 300,000 followers on Twitter. If we look at the Wikipedia article on the Smithsonian Institutions it starts thus, “The Smithsonian Institution, or simply, the Smithsonian, is a group of museums and education and research centers, the largest such complex in the world, created by the U.S. government for the increase and diffusion of knowledge (my emphasis), so why is the Smithsonian Magazine diffusing crap?

I’m hoping that with plenty of sweet tea and digestive biscuits, I’ll be able to restore the HISTSCI_HULK to his normal boisterous self. 

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

Renaissance science – XXVII

Early on in this series I mentioned that a lot of the scientific developments that took place during the Renaissance were the result of practical developments entering the excessively theoretical world of the university disciplines. This was very much the case in the mathematical sciences, where the standard English expression for the Renaissance mathematicus is mathematical practitioner. In this practical world, areas that we would now regard as separate disciples were intertwined is a complex that the mathematical practitioners viewed as one discipline with various aspects, this involved astronomy, cartography, navigation, trigonometry, as well as instrument and globe making. I have already dealt with trigonometry, cartography and astronomy and will here turn my attention to navigation, which very much involved the other areas in that list.

The so-called Age of Discovery or Age of Exploration, that is when Europeans started crossing the oceans and discovering other lands and other cultures, coincides roughly with the Renaissance and this was, of course the main driving force behind the developments in navigation during this period. Before we look at those developments, I want to devote a couple of lines to the terms Age of Discovery and Age of Exploration. Both of them imply some sort of European superiority, “you didn’t exist until we discovered you” or “your lands were unknown until we explored them.” The populations of non-European countries and continents were not sitting around waiting for their lands and cultures to be discovered by the Europeans. In fact, that discovery very often turned out to be highly negative for the discovered. The explorers and discoverers were not the fearless, visionary heroes that we tend to get presented with in our schools, but ruthless, often brutal chancers, who were out to make a profit at whatever cost.  This being the case the more modern Contact Period, whilst blandly neutral, is preferred to describe this period of world history.

As far as can be determined, with the notable exception of the Vikings, sailing in the Atlantic was restricted to coastal sailing before the Late Middle Ages. Coastal sailing included things such as crossing the English Channel, which, archaeological evidence suggests, was done on a regular basis since at least the Neolithic if not even earlier. I’m not going to even try to deal with the discussions about how the Vikings possibly navigated. Of course, in other areas of the world, crossing large stretches of open water had become common place, whilst the European seamen still clung to their coast lines. Most notable are the island peoples of the Pacific, who were undertaking long journeys across the ocean already in the first millennium BCE. Arab and Chinese seamen were also sailing direct routes across the Indian Ocean, rather than hugging the coastline, during the medieval period. It should be noted that European exploited the navigation skills developed by these other cultures as they began to take up contact with the other part of the world. Vasco da Gamma (c. 1460–1524) used unidentified local navigators to guide his ships the first time he crossed the Indian Ocean from Africa to India. On his first voyage of exploration of the Pacific Ocean from 1768 to 1771, James Cook (1728–1779) used the services of the of the Polynesian navigator, Tupaia (c. 1725–1770), who even drew a chart, in cooperation with Cook, Joseph Banks, and several of Cooks officer, of his knowledge of the Pacific Ocean. 

Tupaia’s map, c. 1769 Source: Wikimedia Commons

There were two major developments in European navigation during the High Middle Ages, the use of the magnetic compass and the advent of the Portolan chart. The Chinese began to use the magnetic properties of loadstone, the mineral magnetite, for divination sometime in the second century BCE. Out of this they developed the compass needle over several centuries. It should be noted that for the Chinese, the compass points South and not North. The earliest Chinese mention of the use of a compass for navigation on land by the military is before 1044 CE and in maritime navigation in 1117 CE.

Diagram of a Ming Dynasty (1368–1644) mariner’s compass Source: Wikimedia Commons

Alexander Neckam (1157–1219) reported the use of the compass for maritime navigation in the English Channel in his manuscripts De untensilibus and De naturis rerum, written between 1187 and 1202.

The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.

This and other references to the compass suggest that it use was well known in Europe by this time.

A drawing of a compass in a mid 14th-century copy of Epistola de magnete of Peter Peregrinus. Source: Wikimedia Commons

The earliest reference to maritime navigation with a compass in the Muslim world in in the Persian text Jawāmi ul-Hikāyāt wa Lawāmi’ ul-Riwāyāt (Collections of Stories and Illustrations of Histories) written by Sadīd ud-Dīn Muhammad Ibn Muhammad ‘Aufī Bukhārī (1171-1242) in 1232. There is still no certainty as to whether there was a knowledge transfer from China to Europe, either direct or via the Islamic Empire, or independent multiple discovery. Magnetism and the magnetic compass went through a four-hundred-year period of investigation and discovery until William Gilbert (1544–1603) published his De magnete in 1600. 

De Magnete, title page of 1628 edition Source: Wikimedia Commons

The earliest compasses used for navigation were in the form of a magnetic needle floating in a bowl of water. These were later replaced with dry mounted magnetic needles. The first discovery was the fact that the compass needle doesn’t actually point at the North Pole, the difference is called magnetic variation or magnetic declination. The Chinese knew of magnetic declination in the seventh century. In Europe the discovery is attributed to Georg Hartmann (1489–1564), who describes it in an unpublished letter to Duke Albrecht of Prussia. However, Georg von Peuerbach (1423–1461) had already built a portable sundial on which the declination for Vienna is marked on the compass.

NIMA Magnetic Variation Map 2000 Source: Wikimedia Commons

There followed the discovery that magnetic declination varies from place to place. Later in the seventeenth century it was also discovered that declination also varies over time. We now know that the Earth’s magnetic pole wanders, but it was first Gilbert, who suggested that the Earth is a large magnet with poles. The next discovery was magnetic dip or magnetic inclination. This describes the fact that a compass needle does not sit parallel to the ground but points up or down following the lines of magnetic field. The discovery of magnetic inclination is also attributed to Georg Hartmann. The sixteenth century English, seaman Robert Norman rediscovered it and described how to measure it in his The Newe Attractive (1581) His work heavily influenced Gilbert. 

Illustration of magnetic dip from Norman’s book, The Newe Attractive Source: Wikimedia Commons

The Portolan chart, the earliest known sea chart, emerged in the Mediterranean in the late thirteenth century, not long after the compass, with which it is closely associated, appeared in Europe. The oldest surviving Portolan, the Carta Pisana is a map of the Mediterranean, the Black Sea and part of the Atlantic coast.

Source: Wikimedia Commons

The origins of the Portolan chart remain something of a mystery, as they are very sophisticated artifacts that appear to display no historical evolution. A Portolan has a very accurate presentation of the coastlines with the locations of the major harbours and town on the coast. Otherwise, they have no details further inland, indicating that they were designed for use in coastal sailing. A distinctive feature of Portolans is their wind roses or compass roses located at various points on the charts. These are points with lines radiating outwards in the sixteen headings, on later charts thirty-two, of the mariner’s compass.

Central wind rose on the Carta Pisana

Portolan charts have no latitude or longitude lines and are on the so-called plane chart projection, which treats the area being mapped as flat, ignoring the curvature of the Earth. This is alright for comparatively small areas, such as the Mediterranean, but leads to serious distortion, when applied to larger areas.

During the Contact Period, Portolan charts were extended to include the west coast of Africa, as the Portuguese explorers worked their way down it. Later, the first charts of the Americas were also drawn in the same way. Portolan style charts remained popular down to the eighteenth century.

Portolan chart of Central America c. 1585-1595 Source:

A central problem with Portolan charts over larger areas is that on a globe constant compass bearings are not straight lines. The solution to the problem was found by the Portuguese cosmographer Pedro Nunes (1502–1578) and published in his Tratado em defensam da carta de marear (Treatise Defending the Sea Chart), (1537).

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The line is a spiral known as a loxodrome or rhumb lines. Nunes problem was that he didn’t know how to reproduce his loxodromes on a flat map.

Image of a loxodrome, or rhumb line, spiraling towards the North Pole Source: Wikimedia Commons

The solution to the problem was provided by the map maker Gerard Mercator (1512–1594), when he developed the so-called Mercator projection, which he published as a world map, Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata (New and more complete representation of the terrestrial globe properly adapted for use in navigation) in 1569.

Source: Wikimedia Commons
The 1569 Mercator world map Source: Wikimedia Commons.

On the Mercator projection lines of constant compass bearing, loxodromes, are straight lines. This however comes at a price. In order to achieve the required navigational advantage, the lines of latitude on the map get further apart as one moves away from the centre of projection. This leads to an area distortion that increases the further north or south on goes from the equator. This means that Greenland, slightly more than two million square kilometres, appear lager than Africa, over thirty million square kilometres.

Mercator did not publish an explanation of the mathematics used to produce his projection, so initially others could reproduce it. In the late sixteenth century three English mathematicians John Dee (1527–c. 1608), Thomas Harriot (c. 1560–1621), and Edward Wright (1561–1615) all individually worked out the mathematics of the Mercator projection. Although Dee and Harriot both used this knowledge and taught it to others in their respective functions as mathematical advisors to the Muscovy Trading Company and Sir Walter Raleigh, only Wright published the solution in his Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected. (The Voyage of the Right Ho. George Earle of Cumberl. to the Azores, &c.) published in London in 1599. A second edition with a different, even longer, title was published in the same year. Further editions were published in 1610 and 1657. 

Source: Wikimedia Commons
Wright explained the Mercator projection with the analogy of a sphere being inflated like a bladder inside a hollow cylinder. The sphere is expanded uniformly, so that the meridians lengthen in the same proportion as the parallels, until each point of the expanding spherical surface comes into contact with the inside of the cylinder. This process preserves the local shape and angles of features on the surface of the original globe, at the expense of parts of the globe with different latitudes becoming expanded by different amounts. The cylinder is then opened out into a two-dimensional rectangle. The projection is a boon to navigators as rhumb lines are depicted as straight lines. Source: Wikimedia Commons

His mathematical solution for the Mercator projection had been published previously with his permission and acknowledgement by Thomas Blundeville (c. 1522–c. 1606) in his Exercises (1594) and by William Barlow (died 1625) in his The Navigator’s Supply (1597). However, Jodocus Hondius (1563–1612) published maps using Wright’s work without acknowledgement in Amsterdam in 1597, which provoked Wright to publish his Certaine Errors. Despite its availability, the uptake on the Mercator projection was actually very slow and it didn’t really come into widespread use until the eighteenth century.

Wright’s “Chart of the World on Mercator’s Projection” (c. 1599), otherwise known as the Wright–Molyneux map because it was based on the globe of Emery Molyneux (died 1598) Source: Wikimedia Commons

Following the cartographical trail, we have over sprung a lot of developments in navigation to which we will return in the next episode. 

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

The black sheep of the Provence-Paris group

I continue my sketches of the seventeenth century group pf mathematicians and astronomers associated with Nicolas-Claude Fabri de Peiresc (1580-1637) in Provence and Marin Mersenne (1588–1648) in Paris with Jean-Baptiste Morin (1583–1656), who was born in Villefranche-sur-Saône in the east of France.

Jean-Baptiste Morin Source: Wikimedia Commons

He seems to have come from an affluent family and at the age of sixteen he began his studies at the University of Aix-en-Provence. Here he resided in the house of the Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix and Peiresc’s observing partner. For the last two years of his time in Aix, the young Pierre Gassendi, also lived in Gaultier de la Valette’s house and the two became good friends and observing partners.

In 1611, Morin moved to the University of Avignon, where he studied medicine graduating MD in 1613. For the next eight years, until 1621, he was in the service of Claude Dormy (c.1562–1626) the Bishop of Boulogne, in Paris, who paid for him to travel extensively in Germany, Hungary and Transylvania to study the metal mining industry. As well as serving Dormy as physician, he almost certainly acted as his astrologer, this was still in the period when astro-medicine or iatromathematics was the mainstream medical theory.

The tomb of Claude Dormy Source

From 1621 to 1629 he served Philip IV, King of Spain, and Duke of Luxembourg, also probably as astrologer. 

In 1630, he was indirectly asked by Marie de’ Medici, the Queen Mother, to cast a horoscope for her son, Louis XIII, who was seriously ill and whose doctor had predicted, on his own astrological reading, that he would die. Morin’s astrological analysis said that Louis would be severely ill but would survive. Luckily for Morin, his prediction proved accurate, and Marie de’ Medici used her influence to have him appointed professor for mathematics at the Collège Royal in Paris, a position he held until his death in 1656.

Marie de Médici portrait by Frans Pourbus, the Younger Source: Wikimedia Commons

In Paris, Morin he took up his friendship with Gassendi from their mutual student days and even continued to make astronomical observations with him in the 1630s, at the same time becoming a member of the group around Mersenne. However, in my title I have labelled Morin the black sheep of the Provence-Paris group and if we turn to his scholarly activities, it is very clear why. Whereas Peiresc, Mersenne, Boulliau, and Gassendi were all to one degree or another supporters of the new scientific developments in the early seventeenth century, coming to reject Aristotelean philosophy and geocentric astronomy in favour of a heliocentric world view, Morin stayed staunchly conservative in his philosophy and his cosmology.

Already in 1624, Morin wrote and published a defence of Aristotle, and he remained an Aristotelian all of his life. He rejected heliocentricity and insisted that the Earth lies at the centre of the cosmos and does not move. Whereas the others in the group supported the ideas of Galileo and also tried to defend Galileo against the Catholic Church, Morin launched an open attack on Galileo and his ideas in 1630, continuing to attack him even after his trial and house arrest. In 1638, he also publicly attacked René Descartes and his philosophy, not critically like Gassendi, but across-the-board, without real justification. He famously wrote that he knew that Descartes philosophy was no good just by looking at him when they first met. This claim is typical of Morin’s character, he could, without prejudice, be best described as a belligerent malcontent. Over the years he managed to alienate himself from almost the entire Parisian scholarly community. 

It would seem legitimate to ask, if Morin was so pig-headed and completely out of step with the developments and advances in science that were going on around him, and in which his friends were actively engaged, why bother with him at all? Morin distinguished himself in two areas, one scientific the other pseudo-scientific and it is to these that we now turn.

The scientific area in which made a mark was the determination of longitude. With European seamen venturing out into the deep sea for the first time, beginning at the end of the fifteenth century, navigation took on a new importance. If you are out in the middle of one of the Earth’s oceans, then being able to determine your exact position is an important necessity. Determining one’s latitude is a comparatively easy task. You need to determine local time, the position of the Sun, during the day, or the Pole Star, during the night and then make a comparatively easy trigonometrical calculation. Longitude is a much more difficult problem that relies on some method of determining time differences between one’s given position and some other fixed position. If one is one hour time difference west of Greenwich, say, then one is fifteen degrees of longitude west of Greenwich. 

Finding a solution to this problem became an urgent task for all of the European sea going nations, including France, and several of them were offering substantial financial rewards for a usable solution. In 1634, Morin suggested a solution using the Moon as a clock. The method, called the lunar distance method or simply lunars, was not new and had already suggested by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524.

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. Another method that was under discussion was taking time with you in the form of an accurate clock, as first proposed by Gemma Frisius (1508–1555), Morin did not think much of this idea:

“I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.”

Morin was well aware of the difficulties involved and suggested a comprehensive plan to overcome them. Eager to win the offered reward money, Morin put his proposal to Cardinal Richelieu (1585–1642), Chief Minister and most powerful man in France. Morin suggested improved astronomical instruments fitted out with vernier scales, a recent invention, and telescopic sights, also comparatively new, along with improvements in spherical trigonometry. He also suggested the construction of a national observatory, with the specific assignment of collected more accurate lunar data. Richelieu put Morin’s proposition to an expert commission consisting of Étienne Pascal (1588–1651), the father of Blaise, Pierre Hérigone (1580–1643), a Parisian mathematics teacher, and Claude Mydorge (1585–1647), optical physicist and geometer. This commission rejected Morin’s proposal as still not practical, resulting in a five year long dispute between Morin and the commission. It would be another century before Tobias Mayer (1723–1762) made the lunar distance method viable, basically following Morin’s plan.

Although his proposal was rejected, Morin did receive 2000 livre for his suggestion from Richelieu’s successor, Cardinal Mazarin (1602–1661) in 1645. Mazarin’s successor Jean-Baptiste Colbert (1619–1683) set up both the Académie des sciences in 1666 and the Paris Observatory in 1667, to work on the problem. This led, eventually to Charles II setting up the Royal Observatory in Greenwich, in 1675 for the same purpose.

Today, Morin is actually best known as an astrologer. The practice of astrology was still acceptable for mathematicians and astronomers during Morin’s lifetime, although it went into steep decline in the decades following his death. Although an avid astronomer, Peiresc appears to have had no interest in astrology. This is most obvious in his observation notes on the great comet of 1618. Comets were a central theme for astrologers, but Peiresc offers no astrological interpretation of the comet at all. Both Mersenne and Gassendi accepted the scientific status of astrology and make brief references to it in their published works, but neither of them appears to have practiced astrology. Boulliau also appear to have accepted astrology, as amongst his published translations of scientific texts from antiquity we can find Marcus Manilius’ Astronomicom (1655), an astrological poem written about 30 CE, and Ptolemaeus’ De judicandi jacultate (1667). Like Mersenne and Gassendi he appears not to have practiced astrology.

According to Morin’s own account, he initially thought little of astrology, but around the age of thirty he changed his mind and then spent ten years studying it in depth.

Jean-Baptiste Morin’s with chart as cast by himself

He then spent thirty years writing a total of twenty-six volumes on astrology that were published posthumously as one volume of 850 pages in Den Hague in 1661, as Astrologia Galllica (French Astrology). Like Regiomontanus, Tycho Brahe, and Kepler before him, he saw astrology as in need of reformation and himself as its anointed reformer. 

Source: Wikimedia Commons

The first eight volumes of Astrologia Galllica hardly deal with astrology at all but lay down Morin’s philosophical and religious views on which he bases his astrology. The remaining eighteen volumes then deal with the various topics of astrology one by one. Central to his work is the concept of directio in interpreting horoscopes. This is a method of determining the times of major events in a subject’s life that are indicated in their birth horoscope. Originally, to be found in Ptolemaeus’ Tetrabiblos, it became very popular during the Renaissance. The standard text was Regiomontanus’ Tabulae Directionum, originally written in 1467, and large numbers of manuscripts can still be found in libraries and archives. It was published in print by Erhard Ratdolt in Augsburg in 1490 and went through eleven editions, the last being published in 1626. Aware of Kepler’s rejection of both the signs of the zodiac and the system of houses, Morin defends both of them.

Coming, as it did at a time when astrology was in decline as an accepted academic discipline, Morin’s Astrologia Galllica had very little impact in the seventeenth century, but surprisingly, in English translation, it enjoys a lot of popularity amongst modern astrologers.

Morin was cantankerous and belligerent, which cost him most of his contacts with the contemporary scholars in Paris and his adherence to Aristotelian philosophy and a geocentric world view put him out of step with the rest of the Provence-Paris group, but he certainly didn’t suffer from a lack of belief in his own abilities as he tells us in this autobiographical quote:

“… I am excessively inclined to consider myself superior to others on account of my intellectual endowments and scientific attainments, and it is very difficult for me to struggle against this tendency, except when the realization of my sins troubles me, and I see myself a vile man and worthy of contempt. Because of all this my name has become famous throughout the world.”

 

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Filed under History of Astrology, History of Astronomy, History of medicine, History of Navigation