In episode XIV of this series, we surveyed the final intellectual efforts within Europe to hold the knowledge accrued during antiquity upright for future generations in the work of such figures as Boethius (c. 480–524), Cassiodorus (c. 485–c. 585) and Isidore of Seville (c. 560–636). Efforts that were at least partially successful as that knowledge did not die out completely but took, so to speak, a rest for several centuries. Important to note, I wrote there in opposition to a widespread popular myth, propagated by many militant atheists, Christianity and Christians were not responsible for the decline and loss of classical learning in late antiquity. In fact, the opposite is true, what survived in Europe did so because it was conserved and copied in monastery libraries, which is where much of it was found by the manuscript hunters during the Renaissance.
As we have seen in the following six episode, following the decline of knowledge production within Europe, which reached a deep point in the seventh century, beginning in the eighth century the newly emerging Islamic culture originating in Western Asia took up the baton of knowledge production, first collecting, then translating, and finally analysing, commenting on, and expanding, not just the knowledge from European antiquity but also that from Persia, India, and even China.
We now turn back to Europe and the gradual reawakening of the acquisition of knowledge beginning in the eight and ninth centuries, which slowly gained momentum down to the twelfth century and the so-called Scientific Renaissance during which much of the knowledge acquired, analysed, expanded, and improved by the scholars of the Islamic period was translated back into Latin and became available again, or in some cases for the first time, to European scholars. I shall here only offer an outline sketch, as I have already dealt in detail with this process in my Renaissance Science series to which I will here supply links at the appropriate points.
Before moving on I will briefly mention three authors from the Early Middle Ages, that I didn’t mention earlier, whose books, whilst on a fairly low academic level kept the knowledge of and interest in the mathematic sciences throughout the medieval period.
The first is Martianus Capella, a Roman citizen of Madaura in North Africa, who was active in the early fifth century and who wrote De nuptiis Philologiae et Mercurii (On the Marriage of Philology and Mercury) a Neoplatonic, allegorical tale describing the seven liberal arts, trivium and quadrivium, who appear as the bridesmaids at the title’s wedding.
Grammar teaching, from a 10th-century manuscript of De nuptiis Philologiae et Mercurii Source: Wikimedia Commons
The seven liberal arts provided the backbone of the curriculum in the medieval cathedral schools and for the undergraduate degrees at the newly emerging universities in the High Middle Ages. This book was highly popular and very widely read, as can be attested by the, at least, two hundred and forty-one surviving manuscripts. It was first printed in Vincenza in 1499 and there was an edition published in in 1539 just four years before the publication of Copernicus’ Derevolutionibus.
There were numerous commentaries on the text by leading medieval scholars. Perhaps the most intriguing aspect of the book is that Capella introduces a geo-heliocentric system, in the astronomy section, in which Mercury and Venus orbit the Sun which in turn with the remaining four planets orbits the Earth. This is the earliest known presentation of a geo-heliocentric system although Capella introduces in a way that seems to suggest that it was already known. He and his system get an honorary mention in De revolutionibus.
Capella’s cosmological model Manuscript Florence, Biblioteca Medicea Laurenziana, San Marco 190, fol. 102r (11. Jahrhundert) Source:: Wikimedia Commons
Our second is a near-contemporary of Capella’s, the Roman citizen, whose origins are unknown, Macrobius Ambrosius Theodosius, usually referred to as Macrobius, whose Commentarii in Somnium Scipionis (Commentary on Cicero’s Dream of Scipio) expounds a series of theories on the dream from a Neoplatonic background, on the mystic properties of the numbers, on the nature of the soul, on astronomy and on music. His commentary was essentially an encyclopaedic rendering of the Platonic interpretation of terrestrial and celestial science. Like Capella’s De nuptiis this work was widely read and commented on by medieval scholars.
Image from Macrobius Commentarii in Somnium Scipionis: The Universe, the Earth in the centre, surrounded by the classical planets, including the sun and the moon, within the zodiacal signs. Source: Wikimedia Commons
We leave the fifth-century Roman Empire and travel to Britain in the seventh and eighth centuries, where we find the monk Bede (672/3–735) in the monastery of Jarrow. Known as the Venerable Bede (Beda Venerabilis), he is best known for his Historia ecclesiastica gentis Anglorum (Ecclesiastical History of the English People) written about 731. However, he also wrote an important text on measuring time, his De temporum ratione (The Reckoning of Time). The book covers basic cosmological topics before going on to calendrics and its main theme computus, the calculation of the dates of Easter and the other movable Church feast days.
De temporum ratione: This manuscript was made around 1100, possibly in France.
The work of these three together with that of Boethius (c. 480–524), Cassiodorus (c. 485–c. 585), and Isidore of Seville (c. 560–636), who I introduced in an earlier episode, meant that an awareness of the mathematical sciences was kept alive in the Early Middle Ages, although at a very low level, following the decline of the Roman Empire. This meant that when a higher level of learning and knowledge began to emerge in Europe later in the Middle Ages, there was a foundation on which to build.
The next step in the reintroduction of learning into Europe came when Karl der Große (742–814) (known as Charlemagne in English) had completed the conquest and unification of a very large part of Europe by the Franks. Although Karl himself was illiterate, he and his heir Louis the Pious (778–840) introduced an education programme for priest and increased the spread of Latin on the continent.
The programme was basically not scientific, it had, however, an element of the mathematical sciences, some mathematics, computus (calendrical calculations to determine the date of Easter), astrology and simple astronomy due to the presence of Alcuin of York (c. 735–804) as the leading scholar at Karl’s court in Aachen. Through Alcuin the mathematical work of the Venerable Bede (c. 673–735), who was also the teacher of Alcuin’s teacher, Ecgbert, Archbishop of York, flowed onto the European continent and became widely disseminated.
Karl’s Court had trade and diplomatic relations with the Islamic Empire, in particular with Abu Ja’far Harun ibn Muhammad al-Mahdi (c. 764–809), better known as Harun al-Rashid, the fifth Abbasid caliph, and there was almost certainly some mathematical influence there in the astrology and astronomy practiced in the Carolingian Empire.
In the eleventh century the three Ottos, Otto I (912–973), Otto II (955–983), and Otto III (980–1002), increased the levels of learning on the Imperial court and in the monasteries through contact with Byzantium. This renaissance acquired a strong mathematical influence through Otto the Third’s patronage of Gerbert of Aurillac (c. 946–1003). A patronage that would eventually lead to Gerbert becoming Pope Sylvester II. From his time living in Spain Gerbert introduced some of the basics of Islamic astronomy and mathematics into the rest of Europe.
In the eleventh and twelfth centuries two developments furthered and accelerated to growth in knowledge within Europe. On the one hand groups of students seeking advanced instruction and groups of teachers seeking students to instruct set up the first European universities. The Latin term universitas “being a number of persons associated into one body, a society, company, community, guild, corporation, etc.” These bodies became sanctioned by the Church and by local rulers and adopted the seven liberal arts, as propagated by the scholars of the early Middle ages, such as Boethius and Capella as their undergraduate curriculum. They developed three post graduate faculties, theology, law, and medicine.
Bologna University is the oldest medieval European university. Interior view of the Porticum and Loggia of its oldest College, the Royal Spanish College. Source: Wikimedia Commons
The second development was that scholars began to travel to the areas dominated by Islamic culture to acquire and translate the knowledge of the ancient Greeks and their Islamic interpreters and commentators from Arabic into Latin, during what is know known as the Scientific Renaissance. Europe was now there where the Islamicate culture had been in the seventh century, with an education establishment and the material on which to build or better rebuild an academic and especially a scientific culture.
The beginning of Aristotle’s De anima in the Latin translation by William of Moerbek.. Manuscript Rome, Biblioteca Apostolica Vaticana, Vaticanus Palatinus lat. 1033, fol. 113r (Anfang des 14. Jahrhunderts) Source: Wikimedia Commons
I have already written an extensive blog post on the Scientific Renaissance in my series Renaissance Science, and also one on the emergence of the medieval university, so I won’t repeat them here. Next time I shall be looking at medieval contributions to the development of some areas of physics.
In the years following the publication of De Magnete in 1600 and the death of William Gilbert in 1603 a dispute developed between two leading English magnetists, William Barlow (1544 – 1625) and Dr Mark Ridley (1560–c. 1624), as to which of them was Gilbert’s true disciple.
We have already met William Barlow, son of a bishop, who was a successful career Church of England cleric, who never went to sea but became an expert on magnetism and navigation and was especially known for his mariner’s compass and variation compass designs. In 1605, he was appointed tutor and chaplain to Henry Frederick, Prince of Wales (1594–1612). Later, 1608 or 1609, the mathematician Edward Wright (1561–1615) was also appointed a tutor of Henry Frederick. Both Barlow and Wright were closely involved in the genesis of William Gilbert’s De Magnete. Barlow had also published a demonstration of Wright’s Mercator projection “obtained of a friend of mone of like professioin unto myself,” in his The Navigator’s Supply (1597). Both men lost their positions as tutor, when Henry Frederick died.
Prince Henry Frederick Portrait by Robert Peake the Elder, c. 1610 Source: Wikimedia Commons
We now leave Barlow for the moment and turn our attention the Mark Ridley, who we first met as one of the residents of Gilbert’s Wingfield house in London. In many ways Ridley’s career paralleled that of his erstwhile landlord. Ridley was born the second son of the six children of the Lancelot Ridley rector of Stretham in Cambridgeshire. Lancelot Ridley was an early prominent Protestant, promoted under Thomas Cranmer and favoured during the reign of Edward VI. He was subsequently deprived under Mary but rose again to prominence under Elizabeth I. Mark matriculated as a pensioner at Claire College Cambridge in 1577, graduating BA in 1581 and MA in 1584. He was licenced to practice medicine by the College of Physicians in 1590 and graduated MD in 1592.
On 27 May 1594 he was appointed by Elizabeth, on the recommendation of William Cecil, to serve Feodor Ivanovich, the tsar of Russia as physician.
Tzar Feodar I Source: Wikimedia Commons
He worked for five years in Moscow and on the death of Tsar Feodor in 1599, he was appointed physician to of his successor, Boris Godunov. Elizabeth requested that he be allowed to return to London in that year and Boris Godunov wrote to her commending him for his faithful service and releasing him.
Ridley became an active member of the College of Physicians and like Gilbert before him rose in their ranks, being elected censor in 1607. Over the years he was regularly elected to various offices in the organisation. Interestingly, Ridley is perhaps more significant as the author of the two Russian-English dictionaries than for his writings on magnetism.
While living in Russia between 1594 and 1599, he compiled two manuscript dictionaries of Russian: a Russian-English dictionary of 7,203 entries entitled A dictionarie of the vulgar Russe tongue and an English-Russian dictionary of 8,113 entries entitled A dictionarie of the Englishe before the vulger Russe tonnge. The former includes a short grammar of Russian on the first eight folios. Both dictionaries are now held at theBodleian Library at the University of Oxford (MSS Laud misc. 47a and 47b). (Wikipedia)
Gilbert’s De Magnete was, of course, not without its critics. But in the early phase things remained fairly quiet, especially in England, where the book and its author were much admired. However, between 1603 and 1604 the splendidly named and titled Guillaume de Nautonier, sieur de Castel-Franc au haut Languedoc, Géographe du roi Henri IV (1560– 1620)
Guillaume de Nautonier
published the equally splendidly titled:
Mecometrie de leymant cest a dire La maniere de mesurer les longitudes par le moyen de l’eymant. Par laquelle est enseigné, un tres certain moyen, au paravant inconnu, de trouver les longitudes geographiques de tous lieux,–aussi facilement comme la latitude. Davantage, y est monstree la declinaison de la guideymant, pour tous lieux. Œuvre nécessaire aux admiraux, cosmographes, astrologues, geographes, pilotes, geometriens, ingenieux, mestres des mines, architectes, et quadraniers. (The mecometry of the loadstone or the way to determining the longitude by means of the loadstone…)
In this work Le Nautonier accepts Gilbert’s claim that the Earth is a magnet but claims that he discovered this independently, although, unlike Gilbert, he offers no experiments or other proofs to back up his claim. He was the first to state that the Earth is a tilted dipole, giving 67°N and 67°S for their latitudes and by modern reckoning approximately 30°E and 150°W as their longitudes. He stated that the Earth was a perfect sphere, and, as the book title states, resurrected the already debunked theory that magnetic variation was regular and using it one could determine longitude. He devoted a lot of space to refuting Gilbert’s explanations of the irregularities in variation. Initially there was no reaction to this book in England, although it would be thoroughly debunked in France by Didier Dounot (1574–1640), professor for mathematics on the Académies du roi, in his Confutation de l’invention des longitudes ou De la mecometrie de l’eymant. Cy devant mise en lumiere souz le nom de Guillaume le Nautonnier, sieur de Castel-Franc au haut Languedoc (1611)
The first reactions in England were triggered in 1608 by the publication by Anthony Linton, chaplain to Charles, Lord Howard of Effingham, who served as High Admiral from 1585–1618, of his Newes of the Complement of the Art of Navigation. And of the Mightie Empire of Cataia Together with the Straits of Anian.
In this rather strange volume, Linton, “after citing the criticisms of the art of navigation of Humphrey Gilbert, Thomas Digges, William Borough, Richard Polter, and Edward Wright, whose chart he praised, he pointed out that in navigation position-finding was still imperfect.”[1] Rather stating the obvious. He then claimed that any navigator could ‘make his conclusions of Latitude, Longitude, and Variation,’ as accurately ‘as is possible to be done in any other Mathematicall practice in use amongst us’ by ‘continued observation’, and by exploiting the existence of the two magnetic poles. By the use of certain globes and charts of his devising, obtainable at a price, and ‘in six other ways’, the navigator, knowing , ‘the vaiation of the Compasse and the Latitude of the place’ would find out by Aritmeticall calculation the true longitude of the same place’. However, for the satisfactory working of this admirable but obscurely worded system there appeared to be one serious drawback only, namely, that it required ‘professors of greater skill and practice in the Mathematics, then now commonly found’.[2] This very jumbled account obviously preaches the same gospel as Le Nautonier’s early work and raises the question, whether Linton had plagiarised it, to which we don’t know the answer.
Both of Henry Frederick’s navigation tutors now responded to Linton and Le Nautonier’s arguments. De Magnete was written in Latin and first got translated into English in the nineteenth century. This meant that his theories were not accessible to the mariners who couldn’t read Latin. Barlow wrote a manuscript presenting and explaining Gilbert’s ideas on magnetism and the compass in English. In this work he argued against and debunked the theory propagated by Linton and Le Nautonier. Barlow gave a copy of the manuscript to Sir Thomas Chaloner (1559–1615), a courtier and Governor of the Courtly College for the household of Prince Henry Frederick, so basically Barlow’s employer as chaplain and tutor to the prince. Chaloner manage to lose this manuscript as well as a second copy that he had agreed to have published. This was the situation in 1615, when Chaloner died.
Monument of Sir Thomas Chaloner St Nicolas’ Church Chiswick
Edward Wright simply refuted the argument in an appendix to the expanded second edition of 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 published in 1610, in which he listed the observed variation in many places. The volume was dedicated to “THE HIGH AND MIGHTIE PRINCE HENRY; eldest Son to our soueraigne Lord King Iames: Prince of Wales, Duke of Cornwell, Earle of Chester, &c.”
Ridley entered the fray in 1613 with the publication of his first book on magnetism:
A SHORT TREATISE of Magneticall Bodies and Motions. By Marke Ridley Dr in phisicke and Philosophie Latly Physition to the Emperour of Russia, and one of ye eight principals or Elects of the Colledge of Physitions in London. London Printed by Nicholas Okes. 1613.
Like Barlow he presented his theories in English for those who couldn’t read Latin. He debunked the various myths about the healing power of magnets etc and propagated the theories of Gilbert as presented in De Magnete. He then goes on to debunk the theories of Linton and Le Nautonier. After which he presents his own incorrect theory:
‘when travelling or sailing … it will be very necessary for thee to be stored with the Marriners Compasse for the sea … to know the way … and also to have the Inclinatory-needle truly placed in his ring, and the Directory needle, or a little flie Magneticall in the boxe, fastened at the bottome … for to know under what latitude thou art every day of thy voyage …’ Now one of the chief purposes of his book was to describe the benefits that would arise from the use of ‘the Directory-Magneticall-needle … for the description of Ports, Havens, Forelands, Capes, Bayes, and Rivers, for the more perfect making of Sea-cardes … and all Mathematicall instruments for measuring and surveying …’ and to explain the manner of using it. Yet the instrument was fundamentally unsound, for the mutual attraction and repulsion of the magnetical needles in close juxtaposition, such as he envisaged, foredoomed it to failure because of the resultant errors.[3]
MAGNETICALL Aduertisements : or DIVERS PERTINENT obserruations, and approued experiments concerning the nature and properties of the Load-stone: Very pleasant for knowledge, and most needful for practice, or trauelling, or framing of Instruments fir for trauellers both by Sea and Land.
Act. 17.26 He hath made of one bloud all nations of men for to dwell on the face of the earth, and hath determined the times before appointed, and the bounds of theior habitation, that they should seeke the Lord, &c.
LONDON; Printed by Edward Griffin for Timothy Barlow, and are to be sold at his shop in Pauls Church-yard at the signe of the Bull-head. 1616.
He didn’t name Ridley directly but referred to his “propositions set abroad in another man’s name and yet some of them not rightly understood by the partie usurping them.”[4] He wrote:
I was the first that made the inclinatory instrument transparent to be used pendant, with a glass on both sides, and a ring at the top … and moreover I hanged him in a compass box, wjere with two onces weight he will be fit for use at sea. I first found out and showed the difference between iron and steel, and their tempers for magnetical uses … I was also the first that showed the right way of touching needles …[5]
To demonstrate that he, not Ridley, was Gilbert’s heir he stated that he had been researching magnetism since 1576 and that Gilbert had appreciated his contributions. To prove this, he included a letter that Gilbert had sent to him in 1602. This is in fact the only letter of Gilbert’s that has survived:
To the Worshipfull my good friend, Mr. William Barlowe at Easton by Winchester.
Recommendations with many thanks for your paines and courtesies, for your diligence and enquiring, and finding diuers good secrets, I pray proceede with double capping your load-stone you speake of, I shall bee glad to see you, as you write, as any man, I will haue any leisure, if it were a moneth, to conferre with you, you have shewed mee more–and brought more light than any man hath done. Sir, I will commend you to my L. of Effingham, there is heere a wise learned man, a Secretary of Venice, he came sent by that State, and was honourably received by her Majesty, he brought me a lattin letter from a Gentle-man of Venice that is very well learned, whose name is Iohannes Franciscus Sagredus, he is a great Magneticall man, and writeth that hee hath conferred with diuers learned men in Venice and with Readers of Padua, and reporteth wonderfull liking of my booke, you shall have a copy of the letter: Sir, I propose to adioyne an appendix of six or eight sheets of paper to my booke after a while, I am in hand with it of some new inuentions and I would haue some of your experiments, in your name and inuention put into it, if you please, that you may be knowen for an augmener of that art. So for this time in haste I take my leaue the xiiyth of February.
One major bone of contention between the two disciples of Gilbert was his embrace of Copernicanism with his assumption of a magnetic diurnal rotation of the Earth. As a conservative official of the Church, Barlow totally rejected this aspect of Gilbert’s work, remaining a staunch geocentrist. Ridley, however, going further than Gilbert, adopted a full heliocentric cosmology, as can be seen from his inclusion of the newest results from Galileo and Kepler in his book.
Barlow’s veiled accusation of plagiarism did not escape Ridley and he responded with a pamphlet: Magneticall Animadversions. Made by Dr Mark Ridley, Doctor in Physicke. Upon certain Magneticall Advertisements, lately published, From Maister William Barlow. (1617) His criticism was scathing:
‘There is almost no proposition in this book which most Mariners, Instrument-Makers, Compasse -makers, Cocke-makers, and Cutlers of the better and more understanding sort around London and the Suburbs have not known, practized, and made long before.’ His so-called inventions were ‘most of them in the Doctor Gilbert’s Booke, as I said before, or else such ordinary things that any ingenious workman hath or may easily invent or make; unles you hold all men Dulberts like your rare workman of Winchester.’[7]
Barlow’s response came immediately in his, A Briefe Discovery of the Idle Animadversions of Marke Ridley (1618):
This time it was personal. He tried to discredit Ridley, suggesting that he had morally compromised himself in order to ‘in so short a time become [the Russian] Empoerors principall Physition.’ In a double entendre to Ridley’s observations or ‘looks’ with the new-fangled telescope, he insinuated that the youthful Ridley had seduced the Czar, ‘for his lookes … are his meanes.’[8]
Ridley delivered a parting shot with his, Appendix or an Addition … unto his Magneticall Treatise in answer to M. Barlow (1618).
Despite Ridley’s attacks, Barlow reprinted his Magneticall Advertisements unchanged, except for a new title page, in 1618.
And so, the verbal war between the two heirs of William Gilbert ground to a halt. In their major publications, in this unpleasant exchange, both had made important contributions to the ongoing debate on magnetism and the compass, most importantly making much of Gilbert’s work accessible in English, for those unable to read Latin. However, at the same time they had made a public spectacle of themselves in their bitter dispute, a behaviour that was, unfortunately all too common amongst scholars during the Renaissance.
[1] David W. Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, New Haven, 1958, p. 274.
The magnetic compass was an important navigation instrument in the Early Modern Period, but it was not without its problems. In the last third of the sixteenth century a group of English navigators and scholars cooperated loosely in efforts to understand how the magnetic compass actually worked and to see if the known problems could be solved. The most famous of them was the physician William Gilbert[1] (1544?–1603), who published his ground-breaking De Magnete in 1600, an oft overlooked major contribution to the emergence of modern science in the seventeenth century.
William Gilbert artist unkown Source: Wikimedia Commons Title page De magnete 1st edition 1600 Source: Wikimedia commons
But Gilbert was by no means alone and as he himself acknowledges, in Book I Chapter I of his masterpiece, his work rests on the shoulders of a significant number of his countrymen:
There are other learned men who on long sea voyages have observed the difference of magnetic variation[2]; as that most accomplished scholar Thomas Harriot, Robert Hues, Edward Wright, Abraham Kendall, all Englishmen; others have invented and published magnetic instruments and already methods of observing, necessary for mariners and those who make long voyages: as William Borough in his little work the Variations of the Compass, William Barlo (Barlow) in his Supplement, Robert Norman in his New Attractive–the same Robert Norman, skilled navigator and ingenious artificer, who first discovered the dip[3] of the magnetic needle.[4]
Before I tackle Gilbert’s list of Englishmen, who contributed to the history of our understanding of magnetism and the magnetic compass, this episode will briefly deal with the history of the topic before the late sixteenth century.
We only know about magnetism because there are naturally occurring magnets. These are magnetised pieces of the mineral magnetite an iron ore with the chemical formula Fe2+(Fe3+)2O4, which when magnetised is known as lodestone. Magnetite is not naturally magnetic, and it is not actually known how pieces of magnetite become magnetised. The earth’s magnetic field is too weak to magnetise them, and the generally accepted theory is that they become magnetised by lightning strikes, a theory that is strengthened by the fact that lodestone is only found on or near the surface of the earth.
Lodestone attracting small bits of iron Source: Wikimedia Commons
The discovery of the magnetic property of lodestone by the Greeks is traditionally attributed to Thales (c. 624–c. 547 BCE) but as usually we have nothing on the topic from Thales himself. Aristotle (384–322 BCE), who in his On the Soul wrote:
Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he said that the magnet has a soul in it because it moves the iron.
Not exactly very informative. The earliest Chinese reference to magnetism is in the fourth-century BCE book Guiguzi, a collection of texts on rhetoric, named after its supposed author. The second-century annals Lüshi Chunqiu notes, the lodestone makes iron approach; some (force) is attracting it. The earliest mention of the attraction of a needle is in the first-century work Lunheng, A lodestone attracts a needle.
Lüshi Chunqiu Source: Wikimedia Commons
The earliest know compass was invented by the Chinese sometime between the second-century BCE and the first-century CE. This was not used for navigation by for geomancy and divination. They were almost certainly used in feng shui an ancient Chines practice which claims to use energy forces to harmonise individuals with their surrounding environment. In the Lunheng is the first reference to a spoon, thought to be made of lodestone pointing in a cardinal direction, but when the south-pointing spoon is thrown upon the ground, it comes to rest pointing south.
Model of a Han dynasty (206 BC–220 AD) south-indicating ladle or sinan made of magnetized lodestones. Source: Wikimedia Commons
The earliest Chinese reference to a magnetised needle is from the Dream Pool Essay (1088) written by the polymath Shen Kuo (1031–195). The earliest Chinese reference to the use of a magnetic compass on land for navigation dates to sometime before 1044 CE, and the first clear evidence of the use of the compass in maritime navigation is from Pingchow Table Talks (dated 1111 to 1117) by the maritime historian, Zhu Yu (960–1279).
The English theologian and writer, Alexander Neckam (1157–1217) published the earliest European reference to the use of the magnetic compass for navigation in his 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.
The earliest known reference to the use of the magnetic compass in navigation in the Muslim world was in the Jawāmi ul-Hikāyāt, a collection of stories from 1232. The reference is to a fish-shaped iron leaf, a typical early Chinese design, indicating a technology transfer. The earliest reference to a compass in the form of a magnetic needle floating in a bowl of water is in a book by Baylak al-Qibjāqī (fl. 1240–1282) written in 1282, relating a voyage he took from Syria to Alexandria in 1242. The Yemini astronomer Al‐Ashraf Umar (c. 1242–1296) wrote the first description of the use of a magnetic compass to determine the qibla (the direction of Mecca for prayer) in a text on astrolabes and sundials late in the thirteenth century.
Of interest is the fact that the Muslim use of the compass is fairly obviously a technology transfer from China, but the first known occurrence postdates the first reference for its use in Europe. Normally, in the Middle Ages, Europe acquired Chinese technology via the Muslim world. In this instance it appears not to be the case. It has suggested that, as with the invention of printing with movable type, that the European use of the compass was an independent reinvention.
Probably the most extraordinary document in the whole history of magnetism and the magnetic compass is the Epistola Petri Peregrini de Maricourt ad Sygerum de Foucaucourt, militem, de magnete (Letter of Peter the Pilgrim of Maricourt to Sygerus of Foucaucourt, Soldier, on the Magnet), one copy of the manuscript of which closes with Actum in castris in obsidione Luceriæ anno domini 1269º 8º die augusti (Done in camp during the siege of Lucera, August 8, 1269). Other than the information contained in the title and in the closing statement, we know absolutely nothing about Petrus Peregrinus or how he came to write is Epistola de magnete, as he and his text are commonly known. Despite the date and although it contains some unsubstantiated speculation this is a scientific study of the magnet and its application as a compass.
The Epistola is in two books the first having ten chapters and the second three. The first book describes the properties and effects of the lodestone. Peregrinus ignores all considerations of its occult powers. He was the first person to emphasise the bipolarity of the magnet and was probably the first to use the word polus (pole) for the magnet in analogy to the celestial poles with which, in his opinion, the free rotating lodestone aligns. Just as the celestial sphere has a north and south pole, so also does every magnet. Having suggested to Sygerus, the addressee of the Epistola, that he shape his lodestone like a sphere, Gilbert would later use the name terrella for such a magnet, he gives a method of finding the poles using an iron needle, basically using it to trace the lines of longitude on his sphere, the poles being where the lines cross.
Having found the poles, he then describes how by floating the magnet in a bowl of water one can distinguish the north and south poles. He describes the effect of one magnet on another, like poles repelling, unlike attracting. Having demonstrated that a magnet divided in the middle becomes two magnets he then correctly concludes that each part of a magnet is itself a magnet. There is more of the same, descriptions of the basic properties of the magnet, how to magnetise an iron needle etc in the first book.
In the second book he describes how to construct both the wet and dry compasses. The wet compass being a bowl of water in which a lodestone encased in a wooden sheath is floated. The dry compass if a magnetised needle pivoted on a pin in a bowl. For both bowls he suggests a transparent cover with graduations marking the cardinal points, to make reading off directions easier. The third chapter of the second book describes his attempt at constructing a magnetic perpetual motion machine.
Mioara Mandela, The Magnetic Declination: A History of the Compass, Springer, 2022 p. 28
There would not be another comparable study of the magnet, magnetism, and the magnetic compass until Gilbert wrote and published his own De Magnete in 1600, which borrowed much from Peregrinus, some of it acknowledged and some not.
Having established the history of the invention of the magnetic compass and the beginnings of its use for navigation, a brief note on its function. Nobody actually knew how or why the compass needle came to rest pointing along a north-south axis. Various unsubstantiated explanations were offered. Most common was that the compass needle pointed either to the North Celestial Pole or to the Pole star. For example, Peregrinus looked to the heavens in the belief that the poles of a magnet receive their virtue from the celestial poles. Other suggestions were an unknown island or an unknown magnetic mountain. Mercator’s largely fantasy map of the Arctic featured a RupesNigra (Black Rock) a phantom island believed to be a black rock located at theMagnetic North Pole or at the North Pole itself. Described by Mercator as 33 “French” miles in size, it purportedly explained why all compasses point to this location (Wikipedia).
Mioara Mandea, The Magnetic Declination: A History of the Compass, Springer, 2022 p. 37
Not long after Alexander Neckam’s description of the wet compass, in about 1240, the Belgian theologian Thomas of Cantimpré (1201–1271), a student of Albertus Magnus (c.1200–1280) and friend of Thomas Aquinas (1225–1274), wrote an account of mariners magnetising a needle and constructing a wet compass:
When clouds prevent sailors from seeing Sun or stars, they take a needle and press its point on the magnetic stone. Then they transfix it through a piece of straw and place it in a basin of water. The stone is then moved round and round the basin faster and faster until the needle, which follows it, is whirling swiftly. At that point the stone is suddenly snatched away, and the needle points towards the Stella Maris. From that position it does not move.
Stella Maris is an alternative name for Polaris or the Pole Star, which is associated with the Virgin Mary, so Thomas thought the compass needle pointed to the Pole Star.
Although they didn’t really know how or why it worked, European navigators at the beginning of the Early Modern Period, as they first began to venture out onto the high seas from the Iberian Peninsula, had a new tool that helped them orientate whilst out on the oceans. This instrument could help them find north and thus determine their sailing direction when the Sun and the stars were not visible. However, as they soon discovered there was a catch, isn’t there always. That catch is what we now call magnetic declination or as they knew it, magnetic variation.
What is magnetic variation? Magnetic variation is the fact that a compass needle does not actually point in the direction of the terrestrial North Pole but to a point some degrees distant from it. This would not be so slim if the amount of magnetic variation was constant, but it varies quite substantially depending on where you are on the earth’s surface, and as we will learn later in this series with time. That means if you determine the magnetic variation for say London in the year 2000 you will get a different value for it when you redetermine it in 2020. This makes the normal magnetic compass not the most reliable of navigation instruments.
As with almost all basic things magnetic, the Chinese are credited with being the first the discover magnetic variation sometime between 800 and 1100 CE. It is not known exactly when the Europeans first became aware of it but the earliest evidence that they had acquired that knowledge is on the compass of a portable sundial made by Georg von Peuerbach (1433–1461) in Vienna in 1451.
Georg von Peuerbach portable compass Vienna 1451
Portable sundials have a built-in compass to enable the user to orientate them correctly for use. Peuerbach’s 1451 portable sundial is the earliest known with a built-in compass. Other portable sundials from the period from Southern German, most notably Nürnberg, also were adjusted for magnetic variation with an average value of 10°E of true north.
Mioara Mandea, The Magnetic Declination: A History of the compass, Springer, 2022 p. 30
The compass makers of Antwerp obviously didn’t really understand variation and simply adopted the Nürnberg value for their compasses gluing the compass needle to the compass card offset by about 10°E. Awareness of variation obviously began to spread and the compass makers of Genoa began to follow the Antwerp model but with the needle offset only by 5°E.
Around 1500 the awareness of magnetic variation began to appear on maps. The famous 1500 Rome Pilgrimage Route Map of Erhard Etzlaub, the Nürnberger sundial maker, has a compass rose at the bottom with the variation marked on it.
Romweg” map, 1500. “South-up” display, as in all of Etzlaub’s maps. Source: Wikimedia Commons
Both the 1544 world map of Sebastian Cabot (c. 1474–c. 1557) and that of Gerard Mercator (1512–1594) from 1569 had information about magnetic variation in their cartouches.
The early Portuguese explorers only sailed down the coast of Africa, so the changes in magnetic variation initially did not play a significant role. However, as the Iberian explorers, beginning with Columbus in 1492, began to cross the Atlantic confusion set in together with a completely false hypothesis. The standard method of crossing the Atlantic was to sail down a latitude. To do this, a navigator sailed up or down the coast of Europe or Africa until the reached the latitude of their intended destination in the Americas. They then turned through ninety degrees and sailed across the ocean on that latitude. It was not the shortest route but in terms of not getting lost on the ocean the safest. Doing this they could measure how the magnetic variation varied as they sailed across. Then came a major shock. Up till now all magnetic variations determined in Europe had been east of true north. Suddenly east of the Azores they measured variations west of true north. E of true north variation became known as positive and W of true north negative variations. Also, around the longitude of the Azores they had made measurements of zero variation.
These discoveries led to João de Lisboa (c. 1470–1525) and Pedro Anes (c. 1475–?) putting forward the hypothesis in 1508, which João de Lisboa then published in his Tratado da agulha de marear (Treatise on the Nautical Compass) in 1514, that the true Azores meridian (25°W of Greenwich) was a zero meridian of magnetic variation and if one sailed 90°E or W of the Azores the variation would gradually rise to 45°. Here was a solution to the longitude problem! The measurements of variation that didn’t at least approximately fit this hypothesis were dismissed as operator or instrument error. This was widely accepted as there was a widespread belief anyway that variation didn’t really exist but was the product of operator or instrument error. Magnetic needles incorrectly mounted, lodestone by magnetisation wrongly applied, and so on and so forth. Perhaps surprisingly João de Lisboa’s theory became widely accepted in the Iberian Peninsula and was still going strong at the end of the sixteenth century, although already discredited. One major stumbling block for his theory is that when the Portuguese finally rounded the southern tip of Africa the compass needles swung wildly and also began to display W of true north variations. These were dismissed as the influence of a magnetic mountain. In Portuguese the Cape of Good Hope was called the Cap de Agulhas, the Cape of the Compass Needles!
In 1529, Pedro Nunes (1509–1578) was appointed Royal Cosmographer of Portugal and in 1537 professor for mathematics on the newly established University of Coimbra.
Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons
In 1537, he published both Tratado em defensam da carta de marear (Treatise Defending the Sea Chart) and Tratado sobre certas dúvidas da navegação (Treatise about some Navigational Doubts), containing his proof that a course of constant compass bearing on the globe is not a great circle but a spiral known as a loxodrome. He also argued that on a sea chart the meridians and parallels should be straight lines perpendicular to each other. This is, of course the information out of which Mercator constructed his 1569 chart. In 1546, Nunes also published a book on navigation in Latin, his De arte atque ratione navigandi, making his ideas available to a wider audience including William Gilbert. Nunes also invented a ‘shadow instrument,’ which made possible combined observation of magnetic direction and solar altitude. He trained navigators in its use.
Title page De arte atque ratione navigandi, 1573 Source: Wikimedia Commons
In 1538, the Portuguese government sent Nunes’ student, João de Castro (1500–1548), Chief Pilot of the Portuguese navy on a three-year voyage to the East Indies during which he made a survey of magnetic variation. In total he made forty-three accurate determinations, which varied wildly, and which totally blew João de Lisboa’s theory out of the water.
Retrato de João de Castro no Livro de Lisuarte de Abreu, c. 1560 Source: Wikimedia Commons
In 1545, the Spanish Royal Cosmographer, Pedro de Medina (1493–1567) published his Arte de Navegar (Art of Navigation) a widely used navigation manual, which maintained that compass needles pointed to the celestial poles and that variation was the product of operator or instrument error, at this point, a no longer viable argument. The Arte de Navegar (Art of Navigation), of his successor, Martin Cortés (1510–1582), published in 1551, and as we have already seen in earlier episodes the first navigation manual translated into English by Richard Eden (C. 1520–1576) in 1561, corrected Pedro de Medina’s view on variation.
In 1562, Jean Taisnier (1508–1562) a Wallonian musician, mathematician and astrologer, who taught in various European cities and universities and was the author of a number of cosmographical and divinatory texts, published an edition of Petrus Peregrinus’ Epistola de magnete together with the 1554 Demonstratio proportionum motuum localium (Treatise on the fall of bodies) by Giambattista Benedetti (1530–1590) under the title Opusculum perpetua memoria dignissimum, De Natura Magnetis et ejus effectibus, Item De Motu Continuo (A little work worthy of preservation, On the Nature of the Magnet and its Effects, and another On Perpetual Motion) without mentioning either author and with his own author portrait.
Woodcut: Author-portrait of Jan Taisnier, 1562, aged 53 (Wellcome Collection) via Wikimedia Commons
However, confusion still ruled on variation and its causes, as the English navigators and mathematici, who I shall be looking at in detail in future episodes of this series, began to tackle the problems of the magnet, magnetism, and the magnetic compass.
The quote I brought at the beginning of this essay from William Gilbert’s De magnete (1600), listing some but not all of the people I shall be dealing with, is followed by an incredible chauvinistic rant about the efforts of the Early Modern Europeans to make sense of magnetism, the compass, and variation some of which I have sketched above:
Many others I pass by of purpose: Frenchmen, Germans, and Spaniards of recent times who in their writings, mostly composed in their vernacular languages, either misuse the teachings of others, and like furbishers send forth ancient things dressed with ne names and tricked in an apparel of new words as in prostitutes’ finery; or who publish things not even worthy of record; who, pilfering some book, grasp for themselves from other authors, and go a-begging for some patron, or go a-fishing among the inexperienced and the young for a reputation; who seem to transmit from hand to hand, as it were, erroneous teachings in every science and out of their own store now and again to add somewhat of error.[5]
[1] I have to make the obligator comment that William Gilbert and I attended the same grammar school, he was a couple of year ahead of me.
All of these books went through several editions, showing that there was an eager and expanding market for vernacular literature on navigation in the period. A market that was also exploited by the gentlemanly humanist scholar Thomas Blundeville (c. 1522–c. 1606), probably writing for a different, more popular, readership than the others.
Thomas was born in the manor house of Newton Flotman in Norfolk, a small village about 13 km south of Norwich. He was the eldest of four sons of Edward Blundevill (1492–1568) and Elizabeth Godsalve. He had one sister and two half-brothers from his father’s second marriage to Barbara Drake. Unfortunately, as is all too often the case, that is all we know about his background, his upbringing, or his education.
The authors of Athenae Cantabrigienses claim that he studied at Cambridge but there are no details of his having studied there. He is said to have been in Cambridge at the same time as John Dee (1527–c. 1608) but there is no corroboration of this, although they were friends in later life. However, based on his publications Blundeville does appear to have obtained a good education somewhere, somehow. Blundeville seems to have lived in London for some time before returning to live in Newton Flotman Manor, which he inherited, when his father died in 1568. Much of his writing also seems to indicate that he spent some time in Italy.
Blundeville was well connected, along with his acquaintances with John Dee, Edward Wright, and Edmund Gunter he was also friends with Henry Briggs (1561–1630). Elizabeth I’s favourite Robert Dudley, 1st Earl of Leicester, who took a great interest in the expanding field of exploration and maritime trade, investing in many companies and endeavours, was one of his patrons. He was also, for a time, mathematics tutor to Elizabeth Bacon, daughter of Sir William Bacon (1510–1579, Lord Keeper of the Great Seal, and elder half sister of Francis Bacon (1561–1626), 1st Viscount St Alban. He was also mathematics tutor in the household of the judge Francis Wyndham (d. 1592) of Norwich. We will return to his tutorship later.
Blundeville only turned to writing on mathematics, astronomy, and navigation late in life having previously published books on a wide range of topics.
Blundeville’s first publication, 1561, was a partial verse translation of Plutarch’s Moralia, entitled Three Moral Treatises, which was to mark the accession of Elizabeth I to the throne and one of which was dedicated to her:
‘Three Morall Treatises, no less pleasant than necessary for all men to read, whereof the one is called the Learned Prince, the other the Fruites of Foes, the thyrde the Porte of Rest,’ The first two pieces are in verse, the third in prose; the first is dedicated to the queen. Prefixed to the second piece are three four-line stanzas by Roger Ascham.
About the same time, he published The arte of ryding and breakinge greate horses, an abridged and adapted translation of Gli ordini di cavalcare by Federico Grisone a Neapolitan nobleman and an early master of dressage.
Grisone’s book was the first book on equitation published in early modern Europe and Blundeville’s translation the first in English. Blundeville followed this in 1565/6 with The fower chiefyst offices belonging to Horsemanshippe, which included a revised translation of Grisone together with other treatises.
In 1570, under the title A very briefe and profitable Treatise, declaring howe many Counsels and what manner of Counselers a Prince that will governe well ought to have. he translated into English, Alfonso d’Woa’s Italian translation of a Spanish treatise by Federigo Furio Ceriól. He now followed up with historiography, his True Order and Methode (1574) was a loose translation and summery of historiographical works by the Italians Jacopo Aconcio (c. 1520–c. 1566) and Francesco Patrizzi (1529–1597). The first work emphasised the importance of historiography as a prerequisite for a counsellor. Both volumes were dedicated to the Earl of Leicester.
In 1575 he wrote Arte of Logike, which was first published in 1599. Strongly Ramist it displays the influences Galen (129–216 CE), De Methodo (1558) of Jacopo Aconcio (c. 1520–c. 1566), Philip Melanchthon (1497–1560), and Thomas Wilson (1524–1581).
Arte of Logike Plainely taught in the English tongue, according to the best approved authors. Very necessary for all students in any profession, how to defend any argument against all subtill sophisters, and cauelling schismatikes, and how to confute their false syllogismes, and captious arguments. By M. Blundevile.
It contains a section on fallacies and examples of Aristotelian and Copernican arguments on the motion of the Earth.
This is very typical of Blundeville’s publications. He is rather more a synthesist of the works of others than an original thinker. This is very clear in his mathematical and geographical works. Blunderville published three mathematical works covering a wide range including cartography, studies in magnetism, astronomy, and navigation. The first of these works was his A Briefe Description of Universal Mappes and Cardes
This contains the following interesting passage:
For mine owne part, having to seek out, in these latter Maps, the way by sea or land to any place I would use none other instrument by direction then half a Circle divided with lines like a Mariner’s Flie [compass rose] [my emphasis]. Truly, I do thinke the use of this flie a more easie and speedy way of direction, then the manifold tracing of the Maps or Mariners Cards, with such crosse lines as commonly are drawn therein…
What Blundeville is describing here is the humble geometrical protractor, which we all used at school to draw or measure angles. This is the earliest known reference to a protractor, and he is credited with its invention.
Blundeville’s second mathematical work, is the most important of all his publications, M. Bludeville His exercises… or to give it its full title:
M. BLVNDEVILE
His Exercises, containing sixe Treatises, the titles wherof are set down
in the next printed page: which Treatises are verie necessarie to be read and learned of all yoong Gentlemen that haue not bene exercised in such disciplines, and yet are desirous to haue knowledge as well in Cosmographie, Astronomie, and Geographie, as also in the Arte of Navigation, in which Arte it is impossible to profite without the helpe of these, or such like instructions. To the furtherance of which Arte of Navigation, the said M. Blundevile speciallie wrote the said Treatises and of meere good will doth dedicate the same to all the young Gentlemen of this Realme.
This is a fat quarto volume of 350 pages, which covers a lot of territory. Blundeville is not aiming for originality but has read and synthesised the works of Martín Cortés de Albacar(1510–1582), Pedro de Medina (1493–1567), William Bourne (c. 1535–1582), Robert Norman (before 1560–after 1596), William Borough (1536–1599), Michel Coignet (1549–1623), and Thomas Hood (1556–1620) and is very much up to date on the latest developments.
The first treatise:
First, a verie easie Arithmeticke so plainlie written as any man of a mean capacitie may easilie learn the same without the helpe of any teacher.
What cause first mooved the Author to write this Arithmeticke, and with what order it is here taught, which order the contents of the chapters therof hereafter following doe plainly shew.
I Began this Arithmeticke more than seuen yeares since for a vertuous Gentlewoman, and my verie deare frend M. Elizabeth Bacon, the daughter of Sir Nicholas Bacon Knight, a man of most excellent wit, and of most deepe iudgment, and sometime Lord Keeper of the great Seale of England, and latelie (as shee hath bene manie yeares past) the most loving and faithfull wife of my worshipfull friend M. Iustice Wyndham, not long since deceased, who for his integritie of life, and for his wisedome and iustice daylie shewed in gouernement, and also for his good hospitalitie deserued great commendation. And though at her request I had made this Arithmeticke so plaine and easie as was possible (to my seeming) yet her continuall sicknesse would not suffer her to exercise her selfe therein. And because that diuerse having seene it, and liking my plaine order of teaching therein, were desirous to haue copies thereof, I thought good therefore to print the same, and to augment it with many necessarie rules meet for those that are desirous to studie any part of Cosmographie, Astronomie, or Geographie, and speciallie the Arte of Navigation, in which without Arithmeticke, as I haue said before, they shall hardly profit.
And moreover, I haue thought good to adde vnto mine Arithmeticke, as an appendix depending thereon, the vse of the Tables of the three right lines belonging to a circle, which lines are called Sines, lines tangent, and lines secant, whereby many profitable and necessarie conclusions aswell of Astronomie, as of Geometrie are to be wrought only by the help of Arithmeticke, which Ta∣bles are set downe by Clauius the Iesuite, a most excellent Mathematician, in his booke of demonstrations made vpon the Spherickes of Theodosius, more trulie printed than those of Monte Regio, which booke whilest I read at mine owne house, together with a loving friend of mine, I took such delight therein, as I mind (God willing) if God giue me life, to translate all those propositions, which Clauius himselfe hath set downe of his owne, touching the quantitie of Angles, and of their sides, as well in right line triangles, as in Sphericall triangles: of which matter, a Monte Regio wrote diffusedlie and at large, so Copernicus wrote of the same brieflie, but therewith somewhat obscurelie, as Clauius saith. Moreover, in reading the Geometrie of Albertus Durcrus, that excellent painter, and finding manie of his conclusions verie obscurelie interpreted by his Latine interpreter (for he himselfe wrote in high Dutch) I requested a friend of mine, whome I knewe to haue spent some time in the studie of the Mathematicals, not onelie plainelie to translate the foresaide Durerus into English, but also to adde thereunto manie necessary propositions of his owne, which my request he hath (I thanke him) verie well perfourmed, not onely to my satisfaction, but also to the great commo∣ditie and profite of all those that desire to bee perfect in Architecture, in the Arte of Painting, in free Masons craft, in Ioyners craft, in Carvers craft, or anie such like Arte commodious and serviceable in any common Wealth, and I hope that he will put the same in print ere it be long, his name I conceale at his owne earnest intreatie, although much against my will, but I hope that he will make himselfe known in the publishing of his Arithmeticke, and the great Arte of Algebra, the one being almost finished, and the other to bee vndertaken at his best leasure, as also in the printing of Durerus, vnto whom he hath added many necessary Geometrical conclusions, not heard of heretofore, together with divers other of his workes as wel in Geometrie as as in other of the Mathe∣maticall sciences, if he be not called away from these his studies by other affaires. In the mean time I pray al young Gentlemen and seamen to take these my labours already ended in good part, whereby I seeke neither praise nor glorie, but onely to profite my countrey.
Blundeville obviously prefers the trigonometry of Christoph Clavius over that of Johannes Regiomontanus but is well acquainted with both. More interesting is the fact that he took his geometry from Albertus Durcrus or Durerus, who is obviously Albrecht Dürer and his Underweysung der Messung mit dem Zirkel und Richtscheyt(Instruction in Measurement with Compass and Straightedge, 1525. Blundeville even goes so far as to have an English translation made from the original German (high Dutch!), as he considers the Latin translation defective.
Title page of Albrecht Dürer’s Underweysung der Messung mit dem Zirkel und Richtscheyt
The second treatise:
Item the first principles of Cosmographie, and especi∣ally a plaine treatise of the Spheare, representing the shape of the whole world, together with the chiefest and most necessarie vses of the said Spheare.
The third treatise:
Item a plaine and full description of both the Globes, aswell Terrestriall as Celestiall, and all the chiefest and most necessary vses of the same, in the end whereof are set downe the chiefest vses of the Ephemerides of Iohan∣nes Stadius, and of certaine necessarie Tables therein con∣tained for the better finding out of the true place of the Sunne and Moone, and of all the rest of the Planets vpon the Celestiall Globe.
A plaine description of the two globes of Mercator, that is to say, of the Terrestriall Globe, and of the Celestiall Globe, and of either of them, together with the most necessary vses thereof, and first of the Terrestriall Globe, written by M. Blundeuill.
This ends with A briefe description of the two great Globes lately set forth first by M. Sanderson, and the by M. Molineux.
The first voyage of Sir Francis Drake by sea vnto the West and East Indies both outward and homeward.
The voyage of M. Candish vntothe West and East Indies, described on the Terrestriall Globe by blew line.
Johannes Stadius’ ephemerides were the first ephemerides based on Copernicus’ De revolutionibus.
The fourth treatise:
Item a plaine and full description of Petrus Plancius his vniversall Mappe, lately set forth in the yeare of our Lord 1592. contayning more places newly found, aswell in the East and West Indies, as also towards the North Pole, which no other Map made heretofore hath, whereunto is also added how to find out the true distance betwixt anie two places on the land or sea, their longitudes and la∣titudes being first knowne, and thereby you may correct the skales or Tronkes that be not trulie set downe in anie Map or Carde.
This map was published under the title, Nova et exacta Terrarum Orbis Tabula geographica ac hydrographica.
Petrus Plancius’ world map from 1594
The fifth treatise:
Item, A briefe and plaine description of M. Blagraue his Astrolabe, otherwise called the Mathematicall Iewel, shewing the most necessary vses thereof, and meetest for sea men to know.
Title Page Source Note the title page illustration is an armillary sphere and not the Mathematical Jewel
The sixth treatise:
Item the first & chiefest principles of Navigation more plainlie and more orderly taught than they haue bene heretofore by some that haue written thereof, lately col∣lected out of the best modern writers, and treaters of that Arte.
Towards the end of this section, we find the first published account of Edward Wright’s mathematical solution of the construction of the Mercator chart
in the meane time to reforme the saide faults, Mercator hath in his vniuersal carde or Mappe made the spaces of the Parallels of latitude to bée wider euerie one than other from the E∣quinoctiall towards either of the Poles, by what rule I knowe not, vnlesse it be by such a Table, as my friende M. Wright of Caius colledge in Cambridge at my request sent me (I thanke him) not long since for that purpose, which Table with his consent, I haue here plainlie set downe together with the vse thereof as followeth.
The Table followeth on the other side of the leafe.
The first edition was published in 1594 and was obviously a success with a second edition in 1597, a third in 1606, and a fourth in 1613. The eighth and final edition appeared in 1638. Beginning with the second edition two extra treatises were added. The first was his A Briefe Description of Universal Mappes and Cardes. The second, the true order of making Ptolomie his Tables.
Blundeville’s Exercises contains almost everything that was actual at the end of the sixteenth century in mathematics, cartography, and navigation.
Blundeville’s final book was The Theoriques of the Seuen Planets written with some assistance from Lancelot Browne (c. 1545–1605) a friend of William Gilbert (c. 1544–1603), and like Gilbert a royal physician, published in 1602:
THE Theoriques of the seuen Planets, shewing all their diuerse motions, and all other Accidents, cal∣led Passions, thereunto belonging. Now more plainly set forth in our mother tongue by M. Blundeuile, than euer they haue been heretofore in any other tongue whatsoeuer, and that with such pleasant demonstratiue figures, as eue∣ry man that hath any skill in Arithmeticke, may easily vnderstand the same. A Booke most necessarie for all Gentlemen that are desirous to be skil∣full in Astronomie, and for all Pilots and Sea-men, or any others that loue to serue the Prince on the Sea, or by the Sea to trauell into forraine Countries.
Whereunto is added by the said Master Blundeuile, a breefe Extract by him made, of Maginus his Theoriques, for the better vnderstanding of the Prutenicall Tables, to calculate thereby the diuerse mo∣tions of the seuen Planets.
There is also hereto added, The making, description, and vse, of two most ingenious and necessarie Instruments for Sea-men, to find out thereby the latitude of any Place vpon the Sea or Land, in the darkest night that is, without the helpe of Sunne, Moone, or Starr. First inuented by M. Doctor Gilbert, a most excellent Philosopher, and one of the ordinarie Physicians to her Maiestie: and now here plainely set downe in our mother tongue by Master Blundeuile.
LONDON, Printed by Adam Islip. 1602.
A short Appendix annexed to the former Treatise by Edward Wright, at the motion of the right Worshipfull M. Doctor Gilbert.
To the Reader.
Being aduertised by diuers of my good friends, how fauorably it hath pleased the Gentlemen, both of the Court and Country, and specially the Gentlemen of the Innes of Court, to accept of my poore Pamphlets, entituled Blundeuiles Exercises; yea, and that many haue earnestly studied the same, because they plainly teach the first Principles, as well of Geographie as of Astronomie: I thought I could not shew my selfe any way more thankfull vnto them, than by setting forth the Theoriques of the Planets, vvhich I haue collected, partly out of Ptolomey, and partly out of Purbachius, and of his Commentator Reinholdus, also out of Copernicus, but most out of Mestelyn, whom I haue cheefely followed, because his method and order of writing greatly contenteth my humor. I haue also in many things followed Maginus, a later vvriter, vvho came not vnto my hands, before that I had almost ended the first part of my booke, neither should I haue had him at all, if my good friend M. Doctor Browne, one of the ordinarie Physicians to her Maiestie, had not gotten him for me…
It is interesting to note the sources that Blundeville consulted to write what is basically an astronomy-astrology* textbook. He names Ptolemy, Georg von Peuerbach’s Theoricae novae planetarum and Erasmus Reinhold’s commentary on it, Copernicus, but names Michael Mästlin as his primary source. Although Copernicus is a named source, the book is, as one would expect at the juncture, solidly geocentric. *Blundeville never mentions the word astrology in any of his astronomy texts, but it is clear from the contents of his books that they were also written for and expected to be used by astrologers.
The Theoriques contains an appendix on the use of magnetic declination to determine the height of the pole very much state of the art research.
Because the making and vsing of the foresaid Instrument, for finding the latitude by the declination of the Mag∣neticall Needle, will bee too troublesome for the most part of Sea-men, being notwithstanding a thing most worthie to be put in daily practise, especially by such as vndertake long voyages: it was thought meet by my worshipfull friend M. Doctor Gilbert, that (ac∣cording to M. Blundeuiles earnest request) this Table following should be hereunto adioined; which M. Henry Brigs (professor of Geometrie in Gre∣sham Colledge at London) calculated and made out of the doctrine and ta∣bles of Triangles, according to the Geometricall grounds and reason of this Instrument, appearing in the 7 and 8 Chapter of M. Doctor Gilberts fift booke of the Loadstone. By helpe of which Table, the Magneticall declination being giuen, the height of the Pole may most easily be found, after this manner.
It is very clear that Thomas Blundeville was a very well connected and integral part of the scientific scene in England at the end of the sixteenth century. An obviously erudite scholar he distilled a wide range of the actual literature on astronomy, cartography, and navigation in popular form into his books making it available to a wide readership. In this endeavour he was obviously very successful as the numerous editions of The Exercises show.
Map showing position of Gravesend on the ThamesGravesend in the 18th century
As with many minor figures from the sixteenth century, we know very little about the man and his life. He was the son of another William Bourne who died in 1560 and the first mention of him is in the first charter of incorporation of Gravesend, granted 22 July 1562, where he appears on the list of jurats of the town. A jurat is a councilman or alderman. He was listed in the same office again in the second charter, granted 5 June 1568. There is a note in the town archives that indicate that he was an innkeeper. He got fined for serving short measure. In the dedication to Admiral Sir William Wynter (c. 1521–1589), Surveyor and Rigger of the Navy and Master of Navy Ordnance, in his Treasure for Travellers(1572/3) he writes:
I have most largely tasted of your benevolence towards me, being as a poore gunner serving under your worthiness…
Later in book iii Chapt. 9 he writes:
I am neither Naupeger or Ship-carpenter, neither usual Seaman.
A Naupeger is a shipwright. Treasure for Travellers is a manual on the maintenance and repair of ships. He was probably a shore based naval gunner most likely serving in the Gravesend Bulwark or Blockhouse or across the river in Tilbury Fort.
Engraving from 1588 showing the defences along the River Thames, including Gravesend Blockhouse (centre) and the boom Source: Wikimedia Commons
He wrote two books on gunnery in 1572/73, one of which, William Bourns booke of artillery, remained in manuscript. The other, Art of Shooting in Great Ordnance, was published in 1572 and saw new editions in 1578, 1587, and 1643. He later became a skilled surveyor and served was port-reeve for Gravesend. When he died, he left a widow and four sons. The Poet Gabriel Harvey (c. 1552–1631), writing in 1593 said, “a gunner…unlectured in Schooles or unlettered in bookes…”
His first printed book, published in 1567, of which no copies survive was, An Almanack and Prognostication for iii yeres, with serten Rules of Navigation.
Almanacs and prognostica were amongst the most frequently published texts in the first two hundred and fifty years of publishing. Gutenberg printed and published a single sheet astronomical/astrological wall calendar before he published his famous bible. The first English almanac, a translation of a French work, The Kalendayr of shyppers, which contained a calendar and a description of the Ptolemaic cosmos, was published in 1503, and went through numerous editions. There were almanacs conceived for astronomer, physicians, scholars and students, and simpler ones for the less educated, which included ship-masters. There were broadsheet editions and pocket almanacs, which contained a calendar and simple astronomical information and weather forecasts. Full scale almanacs, which contained the chief astronomical events of the year and the terrestrial events dependent upon them–including conjunctions and oppositions of the sun and moon for the year, tables of the sun’s declination, some star positions, rules for using the North Star, and rules for compilation of the calendar. The day started at noon and the year at the vernal equinox.
Such almanacs often covered a period of four years, because the year is approximately 3651/4 and not 365 days long, sun declination tables have to be recalculated after four years.
Prognostica were rare in England until the repeal of the 1541 Act against sorcery in 1547. Later almanacs were published bound together with a prognostica, as in the case of Bourne’s 1567 text. By now almanacs often had lunar tables, tide tables, solar declination tables, descriptions of methods for determining latitude and other information of use for mariners, so Bourne’s edition of rules for navigators was a natural progression. There had been a flood of new almanacs on the English market since Leonard Digges (c. 1515–c. 1559) had first published his A Prognostication everlasting in 1556. In a later edition of which, in 1576, his son Thomas Digges (c. 1546–1595) published the first English account of Copernican astronomy his A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved.
Source: Water’s Art of NavigationSource: Water’s Art of Navigation
Bourne, as we will see, belonged to the circle of Dee and the Digges. Thomas Digges became Dee’s foster son following the death of his father. As such Bourne’s publications on navigation belong to the rapidly widening awareness of the importance of practical mathematics in England the last quarter of the sixteenth century.
Bourne reissued his almanac in 1571, An Almanac and Prognostication for Three Years. Why three years rather than four is not clear. It contains sixteen rules for navigators. The title of this blog post is the first sentence of the first rule, which is:
The first rule is of a good Navigator.
Of all sciences that is used with us in England, Navigation is one of the principall and most necessary for the benefite of our Realme and native country and also most defencible against our enemies, because we lie environed rounde aboute with the sea.
Rule two explains the compass, three and four the computation of the tides. Five and six deal with the zodiac and the declination of the sun, seven and eight how to take the altitude of the sun and the pole star. Nine deals with the distance to raise or lay a degree, and eleven and twelve dealt with longitude. Thirteen and fourteen give the longitude and latitude of English towns and of fixed stars. Fifteen explained how to sail by the globe. Finally rule ten dealt with sounding and sixteen how to find the hours of the day by compass, both rules being useful for both pilots and navigators.
This publication had a major impact on the acceptance and the recognition of the importance of the mathematical science in England. In the preface Dee presented detailed analysis of the arts of hydrography and navigation. This almost certainly inspired Bourne to expand his rules for navigation into a full-blown handbook for navigation, his A Regiment for the Sea, in 1574 when the three years covered by his almanac had run their course. Here regiment is a synonym for rule.
Source: Water’s Art of Navigation
Bourne said his best contribution to his country would be a simple manual of navigation for the simplest sort of seafaring man. He stated that Regiment for the Sea was “as it were a Nosegay whose Floures are of myne owne gathering” and that it contained nothing already in Matin Cortes’ Arte of Navigation. However, it is obviously inspired by the earlier work but was not a paraphrase, as it contains much that is original.
The Regiment for the Sea is basically a much-expanded version of his sixteen rules from his almanac but also contains original material. Apart from anything else it contains very detailed accounts of how to determine latitude in norther waters during the summer when the sun never sets.
Source: Water’s Art of Navigation
Perhaps, the most interesting new content is the first published description of the use of the recently invented log-line for determining the speed of the ship. At the time a somewhat controversial and disputed instrument that would become a standard navigation instrument from about the second quarter of the seventeenth century onwards.
Source: E.G.R. Taylor & M.W. Richey, The Geometrical Seaman: a book of early nautical instruments, (Hollis & Carter for the Institute of Navigation , 1962)
David Waters in his Art of Navigation summarises the Regiment for the Sea thus:
The Regiment was a practical manual, written by a man who, if not practiced in the art of the sea, had the sea-breeze in his nostrils, seamen at his elbows, and the rare faculties of quick comprehension and lucid exposition. Its essential feature was that it supplemented Cortes’s Arte of Navigation in exactly the right way–where it is weakest. Cortes’s manual was valuable to the navigator chiefly for its detailed descriptions of how to make the principal instruments for navigation; Bourne’s manual, apart from its innovations and simplifications, was valuable chiefly for its detailed instructions on how to use the instruments[2].
A regiment for the Sea was a major success and went through at least eleven editions to 1631, the 1592 edition was edited by Thomas Hood (1556–1629). It was also translated into Dutch with the first edition appearing in 1594, this was followed by at least two further editions.
Another book is Bourne’s Inventions or Devises. Very Necessary for all Generalles and Captaines, as wel by Sea as by Land which was published in 1578 and contains 113 numbered devices. Much of the material is a continuation of his Treasure for Travellers and his Art of Shooting in Great Ordnance, as well as a lot of military advice for sieges etc. However, the book contains some truly fascinating entries. The 21. Deuise is a fairly detailed description of log-line, the invention of which he attributes to Humfray Cole (died 1591) one of the earliest scientific instrument makers in England and a native unlike Thomas Gemini (c. 1515–1562), who was a Flemish refugee, and Nicolas Kratzer (1487–around 1550), who was German.
Source: Wikimedia Commons
The 18. Deuise is one of the earliest descriptions of how to construct a submarine:
ANd also it is possible to make a Ship or a Boate that may goe vnder the water vnto the bottome, and so to come vp againe at your pleasure, as this, as I haue decla∣red in my Booke called The Treasure for trauellers,in the 4. Booke called Staticke, that any thing that sinketh, is hea∣uier than the proportion of so much water, and if it bee lighter than the magnitude of so much water, then it swimmeth or appeareth aboue the water, according vnto the proportion of weight, and then this being true, as it is most certaine, then any magnitude or body that is in the water, if that the quantity in bignesse, hauing alwaies but one weight, may bee made bigger or lesser, then it shall swimme when you would, and sinke when you list: and for to make any thing doo so, then in the ioyntes or places that doo make the thing bigger and lesser, must be of lea∣ther, and in the inside to haue Skrewes to winde it in and also out againe: and for to haue it sinke, they must winde it in to make the thing lesse, and then it sinketh vnto the bottome: and to haue it swimme, then to winde the sides out againe, to make the thing bigger, and it will swimme, according vnto the body of the thing in the water. And to make a small Ship or Barke or Boate, do this, the Barke being made of purpose, let there be good store of Balest in the bottome of hir, and ouer the Balest as lowe as may be, let there be a close Orloppe, such a one, that no water may come into it, and then in like manner at a sufficient heigth, to haue another close Orlop that no water may come through it, and that being done, then bore both the sides full of holes betweene the two close Orlops: and that being done, then make a thing like the side of the Barke or Ship that may goe vnto the side of the Ship, the one for the one side, and the other for the other side, and that must be made so tight and close, that no water may come thorough it, and that done, then take leather, such a quan∣titie as is sufficient for to serue your purpose, and that lea∣ther must bee nayled close, with such prouision, that no water may soake thorough it, and to be of that largenesse, that the thing may goe close vnto the Barke or Ship side when you would, and come in againe, to let sufficient wa∣ter in, that it shall not be able to swimme. And now this being done, then you must make prouision of Skrewes or other engines, to winde the two things on the insides of the Barke or Ships, that you may winde them in or out at your pleasure and that done, then for the hatch or Skotel, that you must goe in or out, you must haue leather round about it, that you may bring that together as a pursse mouth, and so with a small Skrewe, you may winde it so close together, that being in the bottome of the water, there shal no water come in, and that done, then you must haue one Mast, that must bee of such sufficient bignesse, that it must haue a hole bored thorough the one end vnto the other, as a Pompe hath: and that done, then when that you list to nnke, then you must sound the deepenesse of the water, and foresee that the water will not rise higher than the top of the Mast, for the hole that goeth thorough the Mast must giue you ayre, as man cannot liue without it: & now when you would sinke, then with your Skrewes winde the two sides inwards, and water will come into the holes, and so the Ship or Barke will sinke vnto the bottome, and there it may rest at your pleasure: and then when that you would haue it swimme, then with the Skrewes winde out the things on both the sides, and that will thrust the water out againe at the holes, and so it will rise and come vp aboue the water, and swimme as it did before, &c.
Bourne never attempted to construct this craft.
The 19. Deuise is a description of how to construct a boat powered by paddle wheels.
ANd furthermore, you may make a Boate to goe without oares or Sayle, by the placing of certaine wheeles on the outside of the Boate, in that sort, that the armes of the wheeles may goe into the water, and so turning the wheeles by some prouision, and so the wheeles shall make the Boate to goe.
The 23. Deuise is a diving suit:
ANd furthermore, they may make such prouision that any man may goe downe vnto the bottome of the wa∣ter, and remaine there at his pleasure, as this: first pre∣pare leather, and make a case of it in this manner. First for his head, and that must bee made large ynough, and then there must bee two holes for his eyes, and then set in Glasse, and make it tight round aboutes it, and so make the body and the sleeues for his armes, and to bee closed so close, that no water may come into it. And that done, then there must bee a long Truncke made of Leather that must bee hollowe within, that must bee longer than the deepenesse of the water, and that must bee tighte too, and then at the vppermost ende or top there must bee a bowle, or such a thing that will swimme, that through the Truncke that is like a rope, the ayre may passe downe vnto him that is in the bottome of the water, and so the man that is put in∣to the case of Leather, and that beeing made tyght, that no water may come in vnto him, and especiallie vnto his Mouth and Nose, and so to haue ayre to come downe thorough the Trunck of leather, then he hauing sight thorough the Glasse, hee shall bee able to endure to tarrie in the water, and also to see in the water how for to make ropes fast vnto any thing that is sonke in the wa∣ter, &c.
Entries 107, 109, and 110 take us into the world of sixteenth-century optics.
The 109. Deuise explains the use of burning lenses.
AS it is not vnknowne in respect vnto all persons, that you may burne any thing that is apt to burne with a glasse at hand, which is done by the Sunne beams pearsing through the glasse, for that the Sunne beames bee vnited and knit all together in the center thereof, which is the ve∣ry cause that it burneth, and as we doo reade that Archi∣medes burned the Romane Nauie at Syracusa in the Iland of Sicilia, some haue supposed that he did burne thē with such kind of glasses, which is most vnpossible: wherfore it must needes be, that they were burned with diuers glasses, and the reflection of the Sunne beames turned vnto them. But this is to be noted, that it is possible that fewer glasses may serue to burne any thing there in that Latitude, than that it will doo here in this Latitude, for that the Sunne beames be more hoter: for the Latitude of Syracusa is but fiue and thirtie degrees and a halfe, and to burne anything any great distance off with glasses, it requireth to haue some sight in Geometrie, or els it is not possible for to doo it, and for to burne any thing that is apt to burne, it must bee thus handled: they must prepare a number of glasses made of mettall, such as the common people call of steele, made of purpose, and well polished, and to place those glasses to burne, as if that it were gunne powder, flaxe or towe, or occom, pitch, tarre, or such like things that will take fire quickly, the Sunne shining very bright: then set the glasse against the Sunne, and then turne the reflection beame or shadowe to the place assigned that you would burne, and then place another glasse in the like manner, and turne the reflection beame or shadow vnto that place in like manner, right vppon the first ende of the beame or shadowe, and so to place more glasses, and to bee sure that all the reflected beames or shadowes doo rest vppon one place, and so by a great number of glasses to multiply the heate, that in the ende it will bee set on fire and burne: but you must be sure that all the reflected beames or sha∣dowes doo rest in one place, or else it will be vnto no pur∣pose, and at a great distance you shall haue much to doo to decerne or see it, &c. Wherefore you must haue the ayde of Geometry, to vse it according vnto the distance, and to place the glasses in a frame, which I doo omit at this time for breuitie.
Both the 107. Device and the 110. Device appear to describe some form of proto-telescope.
The 107. Deuise appears to me to be a possible description of a camara obscura but I wouldn’t bet on it.
ANd furthermore, it is possible for to place a glasse in a chamber or a parler in a house, for to see any thing a∣broade in the fields, or if that it be neere vnto any hauen or riuer where as shippes or boates doo passe too and fro, that they may see in the glasse within the house, the things that are abroade, as playnely as if that they should goe abroade and get them vp vnto some high hill, or high tower, for to see them of purpose, the which thing is ve∣ry necessarie, either for men of Honour or Gentlemen for to beholde in their chambers what is abroade in some such partes of their ground, as they haue any plea∣sure for to beholde and see into it, what is stirruing: there∣fore that quantitie that it will shewe as their Deere in their parkes, or cattell in their pastures, or what persons that there is stirring in their Gardens or Orchardes: and also it is very necessarie for a Captaine or the Generall of a Towne, Forte or Castell, whether that it be in such pla∣ces, that is, within the lande, or that they haue any charge to looke towards the sea or hauen, or riuer, it is very ne∣cessary for them, for that the glasses may be so placed, that they may see if that there bee any ships comming or go∣ing in the sea, riuer or Hauen, or any persons in the high way. But the greatest impediment that the glasses haue, you shall see no great circuite of grounde in compasse, ex∣cept that the glasses be very large, and also the windowe that the sight commeth in at, be large in like manner, &c. And furthermore▪ for the placing of a glasse in a cham∣ber or parlour, to see the things abroade, it must bee thus done, first you must prepare diuers glasses of a great pro∣portion, that are very perfect and good looking glasses, either of steele or Christall, and that done, the place must bee viewed where that it must stand, for it is not possible to place a glasse in some chabers to see any thing abroad, but it must be in such a chamber as is conuenient for the purpose, that hath a very high roufe, and that hath win∣dowes that are of a great heigth from the floore, or else some high Tower neare vnto it, &c. And if that the place be conuenient for that purpose, then this you must doo first, the place must bee assigned that you would see in the glasse, and then whether the place bee farre of or nearer, then you must place the first glasse alofte against a win∣dowe that is open vnto that place, and that done, if that it be very high, then turne the shadowe of the glasse ac∣cordingly as you doe see cause for your purpose, bring∣yng the beame downewardes: and agaynst that glasse place an other glasse to receyue the beame or shadowe, of the thyngs abroade, and that done, you may turne the beame or shadowe of that glasse downewardes vn∣to what place that you liste, and so place an other glasse agaynst that at your discretion, and so to place as many glasses, vntill that you haue brought it vnto the place that you woulde bryng it vntill, and then to sette all the glasses fast, for if that any of them bee sturred neuer so little, then the beame or shadowe will be turned out of the glasse, &c. And by this meanes you may conuey the beame or shadow of any thyng by glasses made of due proportion from one place vnto an other, vntill that you haue brought it vnto what place you doe desire at your pleasure, and so by that meanes to see in a house what things be abroade.
The 110. Deuise there is much debate in the literature on what exactly Bourne is describing here.
FOr to see any small thing a great distance of from you, it requireth the ayde of two glasses, and one glasse must be made of purpose, and it may be made in such sort, that you may see a small thing a great distance of, as this, to reade a letter that is set open neare a quarter of a myle from you, and also to see a man foure or fiue miles from you, or to view a Towne or Castell, or to see any window or such like thing sixe or seauen myles from you. And to declare what manner of glasses that these must bee, the one glasse that must be made of purpose, is like the small burning glasses of that kinde of glasse, and must bee round, and set in a frame as those bee, but that it must bee made very large, of a foote, or 14. or 16. inches broade, and the broader the better: and the propertie of this glasse, is this, if that you doo behold any thing thorow the glasse, then your eye being neare vnto it, it sheweth it selfe accor∣ding vnto the thing, but as you doo goe backwardes, the thing sheweth bigger and bigger, vntill that the thing shall seeme of a monstrous bignesse: but if that you doo goe to farre backe, then it will debate and be smal & turne the fashion downewards. But now to vse this glasse, to see a small thing a great distance, then doo this, the thing or place that you would view and discerne, set that glasse fast, and the middle of the glasse to stand right with the place assigned, and be sure that it doo not stand oblique or awry by no meanes, and that done, then take a very fayre large looking glasse that is well polished, & set that glasse directly right with the polished side against the first glasse, to the intent to receiue the beame or shadow that cōmeth thorow the first placed glasse, and set it at such a distance off, that the thing shall marke the beame or shadowe so large, that it may serue your turne, and so by that meanes you shall see in the looking glasse a small thing a great di∣stance, for if that the first placed glasse be well made, and very large, you may descerne and knowe the fauour or phisnomie of a man a mile of from you: wherefore in my opinion, this is very necessary in diuers respects, as the viewing of an army of men, and such other like causes, which I doo omit, &c.
Fred Watson in his book Stargazer: the life and times of the Telescope (Da Capo Press, 2004) thinks that Bourne is describing a “window telescope” as marketed in the 1920s but I have my doubts.
Source: Watson Stargazer
There is a more extensive text on optics from Bourne A treatise on the properties and qualities of glasses fror optical purposes, according to the making, polishing, and grinding of them, which only exists in manuscript and was never published. It was dedicated to William Cecil, 1st Baron Burghly, Lord High Treasurer, who had apparently questioned Bourne on the topic. Albert Van Helden in his Invention of the Telescope (American Philosophical Society, 1977 describes it as “a very useful review of the state of the art” and you can read the whole text in Van Helden’s book. In the final part of the text Bourne writes:
For that there ys dyvers in this Lande, that can say and dothe know muche more, in these causes, than I: and especially Mr. Dee and also Mr. Thomas Digges, for that by theyre Lerninge, they have read and seene moany moo [sic] auctors in these causes…
[…]
And so yt ys possible, that yt may bee hepped and furdered the one glasse with the other, as the concave looking glasse with the other gounde and polished glasse. That yt ys likely yt ys true to see a smalle thing, of a very greate distance. For that that the one glasse dothe rayse and enlarge, the beam of the other so wonderfully. So that those things that Mr. Thomas Digges hathe written that his father hathe done, may bee accomplished very well, withowte any dowbte of the matter : But that the greatest impediment ys, that yow can not beholde, and see, but smaller quantity at a tyme.
The text of Thomas Digges that Bourne is referring to is in his completion and publication of his father’s book Pantometria in 1571:
Source: Alfred Van Helden The Invention of the Telescope
The combination of the Digges’ text and Bourne’s elucidation of it has led some historian of science, most notably Colin Ronan (1920–1995), to claim that the Digges invented a reflecting telescope but both Watson and Van Helden dismiss this claim, arguing that they lacked to necessary technical ability to produce lenses and mirrors of the required quality.
Telescope aside, William Bourne is a truly fascinating figure, a self-educated man who contributed significantly to the development of the mathematical disciplines, most notably navigation, in England in the last quarter of the sixteenth century.
[1] For an excellent study of the birth of modern navigational instruction in the Iberian Peninsula and its gradual transfer to the other European seagoing nations see Margaret E. Schotte’s excellent Sailing School: NavigatingScience and Skill, 1550–1800, Johns Hopkins University Press, 2019, which I reviewed here.
[2] David Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 143. As we other posts in this series, the entire post is extensively but by no means exclusively informed by Waters’ excellen tome.t
The Renaissance is a period of intense mathematical activity, but it is not mathematics as somebody who has studied mathematics at school today would recognise it but rather practical mathematics, that is mathematics developed and utilised within a particular practical field of work or study. It should be emphasised that this is not what we now know as applied mathematics, which is, as its name suggests, the application of an area of pure mathematics to the solution of problems in other fields. Practical mathematics is, as already stated above, mathematics that evolves whilst working on problems in a variety of field, which are susceptible to mathematical solutions. This is, of course, the province of the Renaissance Mathematicus the eponym of this blog, and as I wrote in an earlier blog post, Why Mathematicus?
If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.
One major area of practical mathematics that bloomed and flourished in the Renaissance was surveying, as I described in detail in a post in my Renaissance science series. The root word survey has over the centuries acquired many different meanings, but it has a visual origin from the Medieval Latin supervidere “oversee, inspect,” from Latin super “over” plus videre “to see”. Renaissance land surveying is totally dependent on line-of-sight observations. The legendary straight Roman roads were so straight because the engineers laid them out from high point to high point by line of sight and then instead of going around obstacles cut through them, bridged them or whatever. Triangulation, the major advance in surveying that emerged during the Renaissance, also relies on direct line-of-sight observation from high point to high point to construct its triangles.
What, however, happens when you need to survey a territory were you literally can’t make direct line-of-sight observations? This is exactly the problem that had to be solved with the massive expansion in metal ore mining that took place during the Renaissance in eastern Europe. To solve it the miners developed their own form of practical mathematics that became known as Markscheiderkunst and its practitioners as Markscheider. Thomas Morel has written a fascinating and highly informative book, Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe[1] that investigates the origins and evolution of this branch of practical mathematics from its origins up to the beginning of the nineteenth century.
The terms Markscheider and Markscheidekunst are German and Morel’s book concentrates on the mining history of the mining regions in Eastern Germany because that is where the then modern mining industry developed and as Morel explains the knowledge that the German miners developed was then exported all over Europe. If you wanted to start your own mining endeavours, you imported German miners. As I explained in an earlier post this is why Nürnberg developed into a major centre for the manufacture of pencils. Miners in the service of Nürnberg companies were drafted into Borrowdale in Cumbria to exploit the recently, by accident, discovered graphite deposits in the sixteenth century and brought back the knowledge of this new writing material with them when they returned home to Nürnberg.
The Markscheidekunst, ‘the art of setting limits’, comes from the German words Mark, here with the meaning of boundary, and Scheiden meaning separate, so it means the setting of boundaries, originally between mining claims and the Markscheider is the surveyor, who determines those boundaries. On the surface, no different to other surveying but determining the same boundaries under ground becomes a whole different problem, which led to the Latin translation of Markscheidekunst, geometria subterranea.
The obvious difference between the German Markscheidekunst a term of the Bergmannsprache (the miners’ dialect) and the scholars’ Latin term geometria subterranean displays a divergence between the two worlds that illustrates one of the central theses of Morel’s narrative, which begins in the first chapter.
Morel starts there where somebody, like myself, with only a superficial knowledge of Renaissance metal ore mining would expect him to start with Agricola’s De Re Metallica. The first chapter covers both the publications on mining of Georgius Agricola (1494–1555) and of Erasmus Reinhold the Younger (1538–1592), the son of the famous astronomer, Erasmus Reinhold the Elder (1511–1553). Both authors were humanist Renaissance scholars writing in Latin and Morel shows that their presentations of underground surveying don’t match with the reality of what the Markscheider were actually doing. More generally the work of the Markscheider in the Bergmannsprache was largely incomprehensible to the educated scholars.
Morel’s second chapter goes into the detail of how the Markscheider actually went about their work. Firstly, how mining claims were staked out above ground and secondly how they measured and mapped the underground mine galleries, which followed the twist and turns of the veins of metal ore. Also, how they ensured that the underground galleries didn’t extend beyond the boundaries of the claim staked out on the surface. The Markscheider developed a practical mathematical culture that was substantially different from the learned mathematical culture of the university-trained scholars. In the early decades, the world of the Markscheider was, like other trades, one of an oral tradition with apprentices learning the trade orally from a master, who passed on the knowledge and secrets of the trade. Morel traces the evolution of this oral tradition and also the failure of university trained mathematicians to comprehend it
Despite their differences to their learned colleagues in the sixteenth century, because of the economic importance of the metal ore mines the Markscheider acquired a very high social status and achieved standing at the courts in the mining districts. They became advisers to the aristocratic rulers and their expertise was requested and applied in other areas of mathematical measurement such as forestry. All of this is dealt with in detail in Morel’s third chapter.
The seventeenth century saw the development of a scribal tradition with the appearance of the manuscript Geometria subterranea or New Subterranean Geometry, allegedly written by the mining official Balthasar Rösler (1605–1673). These manuscripts evolved over the century as did the methods of surveying and the instruments used by the mine surveyors. Surprisingly this literature remained in manuscript form for most of the century only appearing in print form with Nicolaus Voigtel’s Geometria subterranea in 1686. In his fourth chapter, Morel gives a detailed analysis of this manuscript tradition and offers and explanation as to why it remained unprinted, which has to do with the way these manuscripts were used to train the apprentice surveyors.
Chapter five takes into the late seventeenth early eighteenth centuries, following the publication of Nicolaus Voigtel’s Geometria subterranea and the life and work of Abraham von Schönberg (1640–1711), Captain-general of the Saxon mining administration, and his endeavours to revive the local mining districts in the aftermath of the Thirty Years War. Central to Schönberg’s efforts was the development of the mining map of which the most spectacular example in the Freiberga subterranea, a gigantic cartography of the Ore Mountains running continuously over several hundred sheets. Ordered by Schönberg and realised by the surveyor and mine inspector, Johann Berger (1649–1695).
First sheet of the Freiberga subterranea
Morel’s sixth chapter takes the reader into the eighteenth century and the attempts to raise the academic level of the mathematical knowledge of the mine surveyors and engineers leading up to the establishment of the Bergakademien (in English, mining academies). As Morel explains these were initially not as successfully as might be supposed. Morel takes his reader through the problems and evolution of these schools for mine surveyors. He also follows the significant developments made outside such institutions, particularly by Johann Andreas Scheidhauer (1718–1784). A recurring theme is still the inability of university educated mathematicians to truly comprehend the work of the practical mathematicians in the mining industry. As Morel writes at the beginning of his summary of this chapter, “Teaching a mathematics truly useful for the running of ore mines was a daunting task that underwent important transformations during the eighteenth century.”
Morel’s final chapter is dedicated to the story of the Deep-George Tunnel, a 10 km long drainage tunnel at a depth of 284 m, which connected up numerous mines in the Harz mining district. An extraordinary project for its times. Morel shows how the planning, for this massive undertaking, was based on data recording techniques for the run of the mine galleries developed in the preceding centuries rather than new surveying. The theoretical planning was on a level not previously seen in ore mine surveying. Morel also describes in detail an interesting encounter between the practical mining engineers and a theoretical scientist. The Swiss scholar Jean-André Deluc (1727–1817) visited the area in 1776, just before the start of the project, to test the calibration of his barometers to determine altitude by descending into the depths of the mine, having previously calibrated them by ascending mountains. Impressed by the undertakings of the mining engineers he returned several times over the years observing the progress of the tunnel and reporting what he observed to the Royal Society of London.
The story of the Deep-George Tunnel is a very fitting conclusion to Morel’s narrative of the evolution of the practical mathematical discipline of subterranean surveying in the ore mines of eastern Germany. The breadth and depth of Morel’s narrative is quite extraordinary and my very brief outlines of the chapters in no way does it justice, to do so I would have to write a review as long as his book. Morel is an excellent stylist, and his book is a real pleasure to read, a rare achievement for a highly technical historical text. There are extensive footnotes packed with sources and information for further reading. There is an almost thirty-page bibliography of manuscript, printed primary, and printed secondary sources, and the book closes with an excellent index. The book is nicely illustrated with grayscale reproductions of original diagrams.
This is truly a first-class text on an, until now, relatively neglected branch of practical mathematics, which should appeal to anyone interested in the history of mathematics or the history of mining. It will also appeal to anybody interested in a prime example of the narrative history of a technical disciple that combines mathematics, technology, politics and economics.
[1] Thomas Morel, Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe, Cambridge University Press, 2023.
The heading of today’s chapter is Brahe and Kepler, which immediately provokes a strange reaction in my brain. There is an unwritten convention in English that if one refers to Tycho Brahe by a single name then it is Tycho and not Brahe and by Johannes Kepler then it is Kepler not Johannes., so my brain says the chapter heading should be Tycho & Kepler. Why this is I have no idea and have often spent time wondering about it. Conventional use of names is a strange area that appears to defy logic. Galileo Galilei is almost always simply Galileo in English but in German he is Galilei, but I digress.
With this final chapter we are also scraping the barrel in terms of Strathern’s historical idiocies. It goes without saying that he pays far more attention to the long list of Tycho’s personal oddities than he does to his actual achievements in the history of astronomy. Quite often I couldn’t help getting the feeling that he actually just makes shit up. I have read an awful lot of literature on both of these astronomers, and I kept stumbling across statements that were not simply false but which I had never come across anywhere before. Let us begin. The opening paragraphs are pure purple prose of the worst sort and historically inaccurate:
Sometime during the 1590s, Richard Burbage and his players were invited by the King of Denmark to perform a lucrative summer season at the royal castle at Elsinore (Helsingør). Shakespeare was not amongst these players, but would later be regaled with tales of their foreign adventure. These would provide the background for the play he had in mind, whose full title would be Hamlet, Prince of Denmark.
It is at night on the battlements of Elsinore Castle that Hamlet encounters his father’s ghost, whose revelations sow the seeds of the ensuing tragedy. Coincidentally, some years earlier, while pacing these same battlements, the King of Denmark had suddenly seen the solution to a problem that was troubling him.
King Frederick II had taken under his wing an aristocratic young astronomer called Tycho Brahe, whose behaviour was as eccentric as his appearance: he wore a false metal nose and his awkward paranoid character inclined him to flamboyant cantankerous outbursts. [bullshit!] Brahe’s most recent astronomical observations had made him famous throughout Europe, and the king knew that Brahe was planning to leave Denmark. Brahe had received an offer to set up in Basel, one of the leading intellectual centres in Europe: home of the artistic Holbeins; where Paracelsus had briefly been professor; location of the skilled printer Oporinus to whom Vesalius had entrusted his masterwork. Looking out over the sea, Frederick II’s eye happened to alight on the remote island of Hven, in the middle of the Øresund (Sound) between Denmark and Sweden. Hven was royal territory, occupied only by a small village of fisherfolk and smallholders. If he offered Brahe this island, where the astronomer could build his own private residence, perhaps this would tempt him to remain in Denmark.
Although I studied English literature, amongst other things, at university I’m not a Shakespeare expert. There is a vast amount of literature about the possible sources of Hamlet. However, it is possible that Shakespeare did take Elsinore, as the setting for his play, from visiting actors but not from Richard Burbage and not from the 1590s. When Kronburg, the royal castle in Helsingør, was inaugurated in 1585, three English actors–William Kemp, Thomas Pope, George Bryan–performed there. Later the three, together with Shakespeare established the acting company, The Lord Chamberlain’s Men.
Kronborg Castle and the Øresund from the 1580s geography book Civitates Orbis Terrarum by Georg Braun (1541-1622) and Frans Hogenberg (1535-1590) Source: Wikimedia Commons
In 1575, when the scene Strathern is describing took place, Frederick II, would not have been pacing those same battlements, as the Kronburg was still being constructed. The suggestion that Tycho should be given his own observatory came from the astronomer Wilhelm IV Landgraf von Hessen-Kassel (1532–1592), whom Strather never mentions, but should have, Wilhelm was related by marriage to Frederick. His sister was married to one of Frederick’s uncles. The suggestion to let Tycho use Hven probably came from Tycho’s uncle Steen Bille. Frederick had already offered Tycho the choice of a traditional fiefs and honours as was his due as a high-ranking aristocrat, but Tycho had demurred. Steen Bille made Frederick aware that Tycho did not want the responsibilities and duties that went with a conventional fief, as they would interfere with his astronomical work, it was then that Frederick made his offer with a rhetorical flourish.
“…when he had been at Helsingør recently, checking on the construction of Kronborg Castle Frederick’s glance had happened to fall on the little island of Hven, on the southeast horizon. This he thought, was a perfect place for Tycho: isolated, unassociated with any administrative obligations, and unbound to any noble in fief. If the royal exchequer were tapped for the expenses of founding and maintaining a proper establishment, was there anything that Tycho hoped tom [sic] do abroad that he could not do here, where it would rebound to the credit of his country, his king and himself.”[1]
Strathern further:
Brahe had received an offer to set up in Basel, one of the leading intellectual centres in Europe: home of the artistic Holbeins; where Paracelsus had briefly been professor; location of the skilled printer Oporinus to whom Vesalius had entrusted his masterwork.
Although Tycho was planning on moving to Basel he had received no such offer to do so. One has to ask if Strathern thought that Tycho wanted to go ghost hunting in Basel? Remember we now have 1575, Hans Holbein the Younger was last in Basel in 1532 and had in fact died in 1543, his elder brother Ambrosius had already died in 1519. Oporinus was somewhat closer to Tycho’s times dying in 1563, as for Paracelsus, the city of Basel would prefer not to remember his brief stay there, less than a year, and he had departed the planet in 1541!
Strathern now heads off into his usual collection of fairy tales, avoiding facts in favour of sensation.
Tycho Brahe was amongst the more exotic characters to have contributed to the northern Renaissance. He came from a high-flying but dysfunctional noble family. His father, Otte, was the resident governor of a succession of royal castles (and may even have been a temporary governor of Elsinore). Tycho’s uncle Jørgen, who had inherited the considerable family fortune, was a royal counsellor, naval hero and hard-drinking pal of Frederick II.
Tycho Brahe surrounded by the shields of the families of his influential relatives
The Brahe family was anything but dysfunctional and I have no idea where Strathern got this idea from. Otte’s career was more successful than Jørgen’s, he held a series of important fiefdoms and was indeed governor of Helsingborg Castle. There was no law of primogeniture in Denmark, so Jørgen did no inherit the considerable family fortune. As the only two children of Tyge Brahe and Sophie Rud, Otte and Jørgen both inherited, receiving equal shares. Otte became a Rigsraad (royal counsellor), Jørgen didn’t.
When Jørgen discovered that he could not have children, he decided that he would select his own heir. In pursuance of this aim, he bullied his younger brother Otte into promising that he would present him with his firstborn son.
Otte’s disappointment with this arrangement was allayed when his wife gave birth to twin boys. Unfortunately, the other twin died in infancy, and Uncle Jørgen turned up to collect Tycho when he was just two years old. (Some reports claim that Tycho was kidnapped.) Tycho’s father threatened to murder his older brother, but nothing came of this.
Tycho’s own account:
His uncle Jørgen “without the knowledge of my parents (took) me away with him while I was in my earliest youth [and] brought me up and thereafter supported me generously during his lifetime … and always treated me as his own son.”[2]
There is no record of Otte Brahe threatening to kill Jørgen. Jørgen’s justification seems to have been that he and his wife Inger Oxe couldn’t have children. He seems to have waited till Tycho’s younger brother, Steen, had passed the greatest uncertainties of infancy, before abducting Tycho.
Tycho’s childhood was passed in a succession of cold draughty castles on the Baltic coast, dining at long wooden tables crammed with innumerable relatives. At the head of the table sat the intimidating figure of Uncle Jørgen; topics of mealtime conversation were ‘warfare, politics and court gossip’.
Tycho’s childhood was no different to that of any aristocratic child growing up in sixteenth-century Denmark. The only difference to his biological family is that he was, in his foster family, an only child. Fostering was, for various reasons, not unusual amongst the Danish aristocratic families, so Tycho’s situation was not so strange.
Otte wished his son to be educated in Latin, but Jørgen did not believe in such fripperies. Ten years before Tycho’s birth, in 1536, Denmark had broken definitively from the Roman Catholic Church and converted to Lutheranism. Despite this, Tycho received a traditional education in accord with the Aristotelian beliefs which still prevailed in Denmark.
The opening sentence of this paragraph is complete codswallop. Tycho’s education appears to have been managed by his foster mother Inger Oxe, an intelligent woman of intellectual interests and capabilities and above all her elder brother, Tycho’s foster uncle, Peder Oxe a man of great intellect, who spoke several languages fluently, and who, unusual for a Danish aristocrat, had spent five years studying at various European universities. From 1567, Tycho was just twenty-one, till his death in 1575, Peder Oxe was Lord High Steward of Denmark and the most powerful man in the country. He did much to facilitate Tycho’s career, pulling strings in the background to help his foster nephew. Peder Oxe does not feature at all in Strathern’s account of Tycho’s life, a serious omission.
Tycho attended grammar school, where he learnt Latin, from the age of seven to twelve when he then entered Copenhagen University as Strathern, for once, correctly notes. At grammar school he would have lived in the house of the bishop, and at university in the house of a professor. His interest in mathematics began at university.
The following year, the adolescent Tycho witnessed a partial eclipse of the sun. Although this eclipse arrived a day after it had been predicted, the very fact of its prediction was what most impressed Tycho. Here at last he had a glimpse of something certain in his life. He immediately began purchasing books on astronomy, including one by Regiomontanus, a map of the constellations drawn by Dürer and De Sphaera Mundi (The Sphere of the World) written by the thirteenth-century monastic scholar Johannes de Sacrobosco, which was regarded as the classic exposition of the Ptolemaic earth-centred astronomical system.
He bought the Sacrobosco, a very elementary text, in 1560. In 1561 he bought the much more advance Comographia of Peter Apian and Regiomontanus’ Trigonometry. He didn’t acquire the Dürer star map until 1562, when he was in Leipzig, where he also acquired several other astronomy and astrology texts.
Dürer’s star map of the Northern Hemisphere Source: Ian Ridpath’s Star Tales
Subsequently, Uncle Jørgen despatched the fifteen-year-old Tycho on a tour of German universities, accompanied by a nineteen-year-old tutor who was instructed to cure him of this astronomy nonsense and make sure he equipped himself with the type of education expected of a court counsellor. Within months the young Tycho’s enthusiasm had convinced his tutor to disobey his instructions, and together the two of them embarked upon the study of astronomy at the safe distance of the University of Leipzig.
Normally, at the age of fifteen, a young aristocrat would be sent to live on the court of another aristocrat to train as a page, the first step towards becoming part of the ruling classes. That Tycho instead was sent on a tour of European universities was certainly due to his foster mother and foster uncle and not his foster father. His tutor was Anders Sørensen Vedel. Although Tycho began to study astronomy seriously in Leipzig he was not joined in this endeavour by Vedel, who, did however, admit defeat in his attempts to get Tycho to concentrate on his university studies.
Here [University of Leipzig] Brahe gained a thorough knowledge of both the Ptolemaic and the Copernican systems. Together, he and his tutor observed a close conjunction of the planets Jupiter and Saturn. Brahe was perplexed to discover that the tables drawn up using both the Ptolemaic system and the Copernican system contained minor inaccuracies in their predictions of the conjunction. This led him to start making astronomical observations of his own.
Tycho had begun making his own observation well before he observed the great conjunction and had already discovered the discrepancies in both the Ptolemaic and the Copernican tables.
He decided that the only way to create correct tables was to make meticulous personal observations, night after night, using the most accurate astronomical instruments available. (The telescope had yet to be invented.)
The only instrument that Tycho had available, at that time, was a cross-staff, that he had purchased, and which proved to be not particularly accurate.
Tycho returned to Denmark in 1565 at the age of eighteen.
[…]
Jørgen heroically dived into the canal and rescued the king, but unfortunately died some days later of pneumonia.
The bit I left out is not particularly important, but Strathern now continues:
Using the inheritance he received from his stepfather, Brahe set off to study at the historic University of Rostock, on the north German coast of the Baltic.
Jørgen had been intending to draw up his will naming Tycho his heir, but he died before he could do so, as Tycho was not legally his son he, in fact, inherited nothing. He was now depended for money on his father, Otte, who following the death of Jørgen, had taken over the supervision of his son, who was still a minor.
Here Brahe became involved in an altercation with a Danish cousin who was also studying at the university. Their dispute originated over which of them was the finest mathematician. However, rather than settle this in the obvious mathematical manner, the two of them ended up having a duel. It was during the course of this that Brahe lost his nose, which was sliced off at the bridge by his opponent’s sword.
The duel was not about who was the finest mathematician; this is a myth that was created by Pierre Gassendi (1592–1655) in his biography of Tycho written long after Tycho’s death. At the time Denmark was still effectively a feudal state dominated by a warrior cast. All young aristocrats carried a sword and were trained in the use of them. Duels between them were common and often led to serious injury and even death.
Brahe would continue with his studies at various German universities until he was twenty-six years old, by which time he had accumulated a superb collection of observational instruments – including ‘a large quadrant of brass and oak, thirty-eight feet in diameter and turned by four handles’. This enabled him to measure with precision the angle of elevation of a star above the horizon.
Tycho returned to Denmark in December 1570, just twenty-four years old. At that point in his life, he had a very small collection of fairly inaccurate astronomical instruments. The large oak and brass quadrant that Strathern references was designed and built by Tycho on the estate of the astronomer Paul Hainzel (1527–1581) in Augsburg in March 1570, the arc of the quadrant was 78 feet long. Tycho made observation with it for about six weeks in April and May of that year. It required forty men to erect it, so he certainly didn’t take it home with him. Given its bulk and extreme weight, Thoren’s thinks it was very difficult to operate and therefore not particularly accurate.
Thoren’s Lord of Uraniborg p. 34
Next up:
Brahe was the first to insist upon the central importance of precise astronomical observation.* As recognized by the twentieth-century American philosopher of science E. A. Burtt, Brahe was ‘the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts’. It was this empiricism, and his reliance upon mathematical calculation, which makes him a truly modern scientist – one of the first to emerge in the Renaissance era. Not until the third decade of the ensuing century would Galileo famously proclaim: ‘The book of nature is written in the language of mathematics.’ Brahe may not have said this, and he certainly would not have fully realized its implications, but his practice undeniably chimed with Galileo’s later remark.
I feel that both Regiomontanus and Wilhelm IV of Hessen-Kassel would feel deeply insulted by this paragraph. In 1471, Regiomontanus moved to Nürnberg explicitly to carry out a major programme of accurate astronomical observations to replace the data from the ancient Greeks that had become corrupted through multiple copying over the centuries. Sadly, he died before he could really get his programme started. Wilhelm IV set up an observatory in his castle beginning in 1560, so well before Tycho, with the same aim. He was instrumental in helping Tycho along his path and, as noted about, recommended to Frederick that he should give Tycho an observatory. Wilhelm and Tycho cooperated over the decades and Wilhelm’s observations were as accurate as Tycho’s. In terms of Galileo’s ‘The book of nature is written in the language of mathematics,’ I have pointed out often in the past this was old hat when Galileo wrote it, for example Robert Grosseteste said almost the same in the thirteenth century.
Wilhelm IV. Landgraf von Hessen-Kassel Portrait by Casper van der Borcht 1577
The footnote attached to this paragraph is hilarious:
* As Arthur Koestler pointed out, during the course of his life Copernicus would just make twenty-seven astronomical observations. The remainder of his astronomical data was reliant upon observations made by the likes of Ptolemy and Hipparchus in the second century AD. [my emphasis]
Ptolemy did indeed live in the second century AD, but Hipparchus lived in the second century BC!
Strathern now covers Tycho’s move, in 1570, to Herrevad Abbey with his Uncle Steen Bille, where they set up a laboratory, a glass works and a paper mill. He then writes:
Herrevad Abbey A depiction of the estate in 1680 Burman, Gerhard von, 1653-1701 (author) Fischer, Abraham, 1724-1775 (publisher) Source: Wikimedia Commons
Despite such distractions, Brahe was able to continue with his unrelenting schedule of nightly observations.
What Strathern neglects to mention is that the chief attraction of Herrevad Abbey, for Tycho, was that he and his uncle had also set up an observatory, so astronomical observations were his principal activity.
We then get the story of the 1572 nova and Tycho’s book De Stella Nova (About the New Star), which did indeed establish his reputation as an astronomer. However, Strathern goes over the top with his purple prose:
The publication of this work would make Brahe’s name known in universities throughout Europe. He had done for the universe something similar to what Copernicus had done for the Ptolemaic geocentric solar system. Astronomy was now a new science, released from the constrictions of a false Aristotelian orthodoxy [my emphasis]. Brahe was invited on a tour of European universities, and the metal-nosed Danish wonder with the huge, drooping, sausage-like moustache delivered lectures in halls from Heidelberg to Basel, and even as far afield as Venice, where he prolonged his stay for some weeks.
The sentence in bold is complete and utter twaddle. Although the observation of the nova, and Tycho was not the only astronomer to determine that it was supralunar, had an impact on Aristotelian cosmology, it is in no way comparable to Copernicus’ introduction of heliocentric astronomy. Note I use the word cosmology, whereas Strathern writes incorrectly astronomy. There is a major difference between astronomy and cosmology and I’m not even sure that Strathern knows the difference. The Aristotelian cosmological postulate that the heavens were incorruptible had already been seriously question in the sixteenth century by those observing the comets of the 1530s. This was why every astronomer in Europe, and not just Tycho, very actively observed the comet of 1577, to determine whether it was sub- or supralunar. The scientific status of astronomy was in no way changed by the nova of 1572.
Tycho was not invited on a tour of the European universities, another one of Strathern’s fantasies. His father having died in 1571 and his testament finally having been settled in 1574 with Tycho receiving his share, he was now a wealthy man. In March 1575, he went on a full-blown aristocratic peregrination during which he visited friends and fellow astronomers, it was on this journey that he met Wilhelm IV of Hessen-Kassel for the first time, which led to Wilhelm suggesting that Frederick give Tycho an observatory. He visited many towns in Germany but also Basel and Venice, where he did stay for a couple of weeks chatting to the local intelligentsia.
Brahe took up the king’s offer, and was soon at work constructing a large castle on Hven. In this he was inspired by the Italian Renaissance architect Andrea Palladio, with whose work he had been favourably impressed during his stay in Venice. Palladio’s villas sought to emulate the work of Ancient Greek and Roman architects, notably Vitruvius.
Uraniborg main building from Blaeu’s Atlas Maior (1663) Source: Wikimedia Commons
Brahe’s castle was named Uraniborg after Urania, the ancient classical muse of astronomy, mathematics and the exact sciences. The islanders were conscripted as building labourers, and 100 students were brought on board – to learn from the master, as well as assist him in his building project. Uraniborg was soon envisaged as far more than a castle, or even a scientific laboratory (though it would fulfil both these purposes); it was to be a Renaissance palace, fit for entertaining visiting scholars from all over Europe.
Urania was in Greek mythology the muse of astronomy. Urania is the goddess of astronomy and stars and has nothing to do with mathematics and the exact sciences, both terms being completely alien to Greek mythology. When I read about the 100 students drafted in to assist in building Uraniborg, I thought WHAT! Where did Strathern dredge that one up? Approximately one hundred was the number of students and assistant who worked on Hven, in the twenty-one years that it was in operation. Next paragraph, next blunder:
But this was not all. Quite apart from the castle, Brahe was determined to build himself the finest observatory in Europe [my emphasis]. This Stjerneborg (City of the Stars) would be constructed in the grounds of the castle, and would consist of no less than six chambers, placed underground so as ‘not to be exposed to the disturbing influence of the wind’.
Uraniborg was built primarily and principally as an observatory. The towers on either side of the building were observation platforms and the large mural quadrant that features in so many articles about Tycho ran through the very centre of the building.
Tycho Brahe’s large mural quadrant at Uraniborg Engraving from the book: Tycho Brahe (1598), Astronomiae instauratae mechanica Source: Wikimedia Commons
Stjerneborg was a secondary observatory built after the fact for a number of reasons. Later, when both observatories were in operation, they would observe fully independently of each other and then Tycho would compare the results obtained. The “no less than six chambers” makes it sound enormous, but they were in fact all very small.
Observatory Stjerneborg from Blaeu’s Atlas Maior (1663) Source: Wikimedia Commons
Strathern continues:
Such was the cost of Brahe’s project on Hven that Frederick II was soon diverting no less than 1 per cent of the entire national budget in order to keep it going, while many of the students and all of the locals were declared ‘indentured’ labour, i.e. unpaid.
The often repeated “1 percent” of crown revenues that flowed to Hven is misleading. Denmark was an oligarchy. Through his father and his foster father’s family, his mother’s family, and his foster mother’s family, Tycho belong to the upper one percent of the population. If he, as would have been expected of him, with his obvious intelligence and organisational talents, had taken up a political role, his share of the crown revenues would certainly have been more than one percent.
Nobody was declared ‘indentured’ labour. Hven was Tycho’s fiefdom and under Danish law, each farm on Hven was required to provide him with two man-day-labour a week, irrespective of the type of labour. The students who came to Hven over the years, did not work on the construction site but in the observatories. In exchange for their labour, they received free board and lodging as well as an on hands education in observational astronomy.
We then get the usual stories of royal visits, banquets at Uraniborg, and Tycho’s dwarf, Jepp. Strathern then delivers his usual presentist disapproval:
As we have already seen, Brahe remained susceptible to the scientific misapprehensions of his age. (The basement of Uraniborg also contained a number of furnaces, which were used for alchemy.)
The basement of Uraniborg was a purpose-built alchemical laboratory that was principally used to produce Paracelsian medicine, with which Tycho treated the inhabitants of his astronomical kingdom. Tycho was a close friend of Peder Sørensen (1542–1602), widely known by his Latinized name, Petrus Severinus, one of Europe’s leading Paracelsian physicians and personal physician to the king.
We finally get some more astronomy:
It was during these years that Brahe observed the Great Comet which was visible throughout Europe from November 1577 to January 1578. Brahe managed to calculate the distance of this comet from earth, and also its direction of flight. He was thus able to show that its orbit lay far beyond that of the moon. This disproved once and for all the Aristotelian contention that all stars beyond the moon were ‘immutable and eternal’.
The Great Comet of 1577, seen over Prague on November 12. Engraving made by Jiri Daschitzky. Source: Wikimedia Commons
As already mentioned above the central debate as to whether comets were sub- or supralunar had been raging in astronomical circles in the comets of the 1530s and that is why astronomers throughout Europe, and not just Tycho, very carefully observed the comet of 1577. Brahe did not calculate its distance from the Earth, but did, like several others, determine that it displayed no parallax and was therefore supralunar.
Tycho’s elk, which Strathern calls a Moose, falls down the stairs and Tycho’s sister, Sophie Brahe, gets an inaccurate nod:
Yet amidst all this, Brahe continued with his dogged research into what was indisputably genuine science. His meticulous map of the night sky had now progressed well beyond 500 stars. In this he was aided by his students, as well as his long-time assistant Sophie, his younger sister, who since the age of fourteen had clocked up a series of remarkable triumphs. These included a precise observation of the eclipse of the moon, as well as many adjustments to the Copernican tables.
There is no indication in Strathern’s narrative when exactly Tycho had succeeded in mapping 500 stars, but it would have been well into the 1580s. However, he places this next to his brief comment about Sophie Brahe. Sophie assisted Tyco in his observations of the lunar eclipse of 1573. This, observation, took place in Knutstorp Castle, the Brahe family seat, and not Uraniborg, which was not even a distant dream then. In Uraniborg, Sophie’s principal functions, on her visits, were acting as a host for aristocratic and royal visitors, a role Tycho’s common law wife could not fulfil and she was probably also, as a horticulturalist, responsible for the extensive herb garden and involved in the production of medicine, being like her brother a Paracelsian alchemist.
Up next is a long paragraph on the legendary accuracy of Tycho’s observations This contains the following gem:
Nothing before, or since, matched the accuracy of his observations reliant upon the naked eye, using early theodolites and such, unaided by lenses or telescopes.
The invention of the theodolite is attributed to Leonard Digges (c. 1519–c. 1559) in a book first published posthumously in 1579 and I doubt that its existence had been noted on Hven, also it is of course a surveying instrument and not an astronomical one:
The section on Tycho’s accuracy end thus:
Such was the accuracy of Brahe’s observations of the motion of the sun that he was able to calculate the length of a year to within less than a second. As a result, Brahe’s readings would play a decisive role in the reformation of the calendar which took place under Pope Gregory XIII in 1582.
The Papal bull, Inter gravissimas, announcing the advent of the Gregorian calendar was issued on 24 February 1582. Tycho started building Uraniborg in 1579 and it only became operational as an observatory in 1583. Even if the very first thing that Tycho had done was to determine the length of the year, it wasn’t, I see a “slight problem” here. The length of year based on Tycho’s observations, 365 solar days, 5 hours, 48 minutes, 45 seconds (365.24219 days), was first published by Johannes Kepler in the Rudolphine Tables in 1627! The mathematical model used for the Gregorian calendar was produced by Aloysius Lilius (c. 1510–1576), who used the length of the year from the Alfonsine Tables, 365 solar days 5 hours 49 minutes 16 seconds (≈ 365.24255 days). In fact, he only used the value to two sexagesimal fractions (that’s base sixty), as was general astronomical practice at the time, 365; 14, 33 days.
The first page of the papal bull Inter Gravissimas Source: Wikimedia Commons
Next up more garbage:
On the other hand, Brahe’s observations did not prevent him from making certain mistakes. For instance, he concluded that the distance from the earth of the planet Saturn (the furthest known planet at the time) was 48 million miles. As Asimov observed, this ‘seemed an enormous distance for the astronomers of the age but was only one-eighteenth of the real figure’.
Determining the actual sizes of the known cosmos and the orbits of the planets was in fact extremely difficult. The problem was only solved with the first approximately accurate determination of the astronomical unit, the mean distance between the Earth and the Sun, in the 1770s.
Strathern displays his ignorance of the history of astronomy in his brief presentation of the Tychonic system:
Another oddity in Brahe’s thinking was his overall conception of the universe – the so-called Tychonic system. Although Brahe was well aware of the Copernican heliocentric system, he refused to jettison all the workings of the Ptolemaic geocentric system. His view of the universe was essentially a compromise between the two. For Brahe the earth remained at the centre of the universe. The sun and the moon circled the earth. However, all other planetary bodies revolved around the sun. This lopsided picture found little favour with either camp in the growing Copernican–Ptolemaic debate [my emphasis].
We then get the death of Frederick and Tycho’s abandonment of Hven and his eventual invitation from Rudolf II to settle in Prague:
In 1599 Brahe accepted the invitation of the Holy Roman Emperor Rudolf II, and moved to Prague to take up the post of Imperial Court Astronomer. He was given a castle in which to set up an observatory, and a young German assistant named Johannes Kepler. Brahe gave Kepler access to his star catalogue, and together they began working on the planetary motions, with the aim of drawing up a complete chart of these.
Rudolf II did not give Tycho a young German assistant named Johannes Kepler! The very idea is totally absurd. Kepler came to Prague on his own volition in 1600 hoping to find employment with Tycho and to gain access to Tycho’s data to fine tune his Platonic solids model of the cosmos. Tycho did not give Kepler access to his star catalogue, believing that Nicolaus Reimers Baer (Ursus) (1551–1600) had plagiarised him, he feared that Kepler would do the same. In fact, the first task that Tycho gave Kepler was to write an essay proving that Ursus had plagiarised him. Kepler wrote his Apologia Tychonis contra ursum (A Defenceof Tycho against Ursus), which, however, was first published in the nineteenth century, but is now regarded as an important contribution to the history and philosophy of science.[3] Following this, Tycho gave Kepler limited access to his data with the task of determining the orbit of Mars.
The misinformation continues:
Brahe was fifty-four years old and feared that he had not fully accomplished his life’s mission. His last words to Kepler were: ‘Let me not seem to have lived in vain.’ But already Brahe had justified himself. In the eyes of Asimov, and other historians, ‘the crowning act of [Brahe’s] life’ was placing his star catalogue into the hands of his young assistant Kepler [my emphasis]. By now this did indeed record the verified position of almost 1,000 stars. Using Brahe’s work, Kepler would lay the foundations for the seventeenth-century Scientific Revolution, which culminated in Newton’s law of universal gravitation.
Portrait of Johannes Kepler 1620 artist unknown Source: Wikimedia Commons
We then get a potted biography of Kepler’s childhood. Followed by Strathern’s antipathy towards everything that he doesn’t consider to be science, which culminates with the following description of Harmonice Mundi:
Not for nothing would his most characteristic work be entitled Harmonice Mundi (The Harmony of the World), which sought to bridge what we – with hindsight – see as the chasm between his scientific and pseudo-scientific thought. Here Kepler referenced musical harmony – his ideas harking back to Pythagorean mysticism. According to these ancient ideas, the individual soul is attuned to the movements of the heavens, reacting to the light emanating from the planets ‘according to the angles they form with each other, and the geometrical harmonies or disharmonies that result’. This is compared with the way the ear hears harmonies in music, and the eye sees harmonies in colour: ‘The capacity of the soul to act as a cosmic resonator has a mystic and a causal aspect: on the one hand it affirms the soul’s affinity with the anima mundi [world spirit], on the other, it makes it subject to strictly mathematical laws.’
After excelling at school, Kepler gained a scholarship to attend the nearby University of Tübingen. Kepler had been a sickly child, and it was expected that he would enter the Church, as his physique was thought incapable of surviving a more strenuous occupation. At university, Kepler studied theology.
Kepler did not study theology, as I explained in another blog post. Briefly, his scholarship was for a course of studies created to train new teachers and parish priests in Protestant Württemberg to replace the previous Catholic ones. Württemberg had only converted to Lutheran Protestantism thirty-six years before Kepler was born.
Strathern:
Fortunately, during this period theology was so all-pervasive that it included what we would call philosophy. And in doing so, it also included natural philosophy or science. All this was comprehended in the study of Aristotle – the most wide-ranging of the ancient philosophers. Aristotle’s theology predated Christianity; but as we have seen, over time this had been skilfully elided to enable his natural philosophy to become that most unscientific of entities – namely, the Holy Writ.
This is a constantly repeated claim of Strathern’s but no matter how oft he repeats it Aristotelian natural philosophy was never Holy writ. I’m still trying to imagine what Strathern thinks Aristotle’s theology was.
One step backwards, one step forwards: at Tübingen Kepler also embraced the Copernican view of the universe, yet with an unusual mystical twist. In student debate, ‘he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe’.
Strathern very obviously doesn’t realise that Kepler’s “the Sun was the principal source of motive power in the universe”, was in the context of the times a major step towards a theory of gravity.
Kepler would not finish his studies at Tübingen.
Yes, he did, see my blog post.
Possibly due to financial constraints, during his last year he accepted a post as a teacher of mathematics and astronomy at the Protestant school in Graz (in modern-day Austria). Here he continued to develop his mystic-scientific ideas along Aristotelian lines of teleology: the idea that everything in the universe has been created according to a divine purpose.
Kepler was sent to Graz as maths teacher at the Protestant school, and district mathematicus, as a condition of his scholarship, he would have preferred a position as a parish priest and only took up the post under protest. Kepler’s God was a mathematician and his philosophy of science was very definitely Platonic and not Aristotelian. Strathern obviously thinks that Aristotle’s philosophy was the only other thing around apart from modern science at the end of the sixteenth beginning of the seventeenth centuries. He apparently knows nothing about the revivals of Platonic, Stoic, and Archimedean philosophies, to say nothing of hermeticism, which are an important element of what we call the Renaissance.
One day while teaching at Graz, Kepler experienced a sudden insight into his understanding of the cosmos. He saw the sun as the centre of the solar system, with each of the planets orbiting about it according to a complex mathematical system. This involved an ingenious nesting of the five platonic solids, one within the other. Each of these solids was encased within a sphere, and these expanding spheres described the circular orbits of the planets about the sun. Though based on Greek mathematics, this shows a medieval ingenuity in its abstraction and symbolism. However, empirical science it is not.
This is a truly terrible description of how Kepler came to develop his geometrical model of the cosmos and I can’t be bothered to write the two-thousand-word essay needed to disentangle it; just accept it’s crap. I have a more accurate account here.
Kepler would publish these ideas in his first work, which he characteristically entitled Mysterium Cosmographicum (loosely, The Mystery of the Cosmos). This again has a distinctly medieval resonance: the Renaissance was very much an age of de-mystifying [my emphasis].
On the other hand, Kepler’s work was undoubtedly revolutionary – making, as it did, a strong contribution to the advancement of science. This was indeed the first work which publicly endorsed the Copernican heliocentric system [my emphasis].
No, it wasn’t! Rheticus, Gemma Frisius, Thomas Harriot, Giordano Bruno, …
Despite his otherworldly views, Kepler was ambitious and determined that his work should be recognized. With this in mind he sent copies of his Mysterium to the finest astronomers he knew – including Galileo and Brahe.
Brahe, on the other hand, recognized a kindred spirit. Although he dismissed Kepler’s Copernican view in favour of his own, he was sufficiently impressed to enter into a correspondence with Kepler. As a result, when Brahe arrived in Prague in 1599 he invited Kepler to visit him. By now Kepler’s Copernican views were beginning to attract the attention of the Catholic authorities of the Counter-Reformation, which was becoming a force to be reckoned with in Graz [my emphasis].Kepler travelled to Prague and was more than pleased when Brahe offered him the post of his assistant, under the auspices of the Holy Roman Emperor Rudolf II.
In the 1590s Kepler’s Copernican views did not interest the authorities in any way. Ferdinand the Archduke of Austria decided to banish all the Protestants from Styria. They were offered the choice of conversion or banishment. In the first wave of bans Kepler, a Lutheran Protestant, was granted an exception because in his role as district mathematicus he had produced very impressive astrological prognostications. Later the Protestant school was closed, and it was obvious that Kepler wouldn’t get a new exception, so he was desperately looking for alternative employment. After Mästlin and Tübingen refused to help, he set off to Prague to ask Tycho for work. Tycho had indeed invited him to Prague, but he never saw the invitation as he was already on his way to Prague before it arrived in Graz.
We get a garbled and inaccurate account of the initial dispute between Tycho and Kepler and then we move onto Tycho’s death:
When Brahe died in 1601, Kepler was left to fulfil Brahe’s injunction that he had not ‘lived in vain’. Kepler would more than fulfil this. Brahe had specifically set him the task of calculating the orbit of Mars, using his observations. Kepler had bragged that he would complete this within a week. In the end it took him eight years of ceaseless calculation [my emphasis].
Kepler continued in the employ of Rudolf II, painstakingly seeking to complete Brahe’s map of the stars.
No, he didn’t! He was a theoretical astronomer and not an observational astronomer. His eyesight had been damaged by a case of smallpox when he was four years old, so he didn’t seek to complete Brahe’s map of the stars, painstakingly or in any other way.
In 1611 Bohemian Protestants rose against Rudolf II, and he was forced to abdicate in favour of his brother Matthias. Both parties in the dispute turned to Kepler for astrological advice. He did his best to produce conciliatory interpretations of the movements of the heavens, but to no avail. Amidst the deteriorating situation Kepler and his family fled Prague. While travelling, his wife Barbara and three sons contracted smallpox. In the year that followed, Barbara and one of his sons died. Eventually Kepler returned to Austria, this time settling in Linz, where he would later remarry.
It was Rudolf’s brothers, Ernst, Maximillian and Matthias, all staunch Catholics, who led the rebellion against him. Barbara Kepler contracted Hungarian spotted fever, and their three sons’ smallpox whilst they were still in Prague, and one son, Friedrich 6, died there. Kepler travelled alone to Linz to secure a position as teacher and district mathematicus. On his return to Prague, Barbara died, and he remained in the city until Rudolf died in early 1612 and Matthias became Holy Roman Emperor. Matthias re-affirmed Kepler’s position (and salary) as imperial mathematicus but allowed him to move to Linz.
Despite his troubles, Kepler persisted with his astronomical work, completing Brahe’s catalogue of the stars, along with his own additions, in 1617. Owing to the political situation it would be another ten years before it was published as the Rudolphine Tables, named after his former benefactor Rudolf II.
Kepler added nothing to Tycho’s star catalogue. He completed the Rudolphine Tables in 1623 and they were printed in 1627.
Frontispiece of the Rudolphine Tables Source: Wikimedia Commons
Despite the advent of the telescope, these would become the standard work of reference for many decades to come. Despite their differences, Kepler and Galileo would continue to correspond on surprisingly amicable terms. Galileo even sent Kepler one of his telescopes. This enabled Kepler to see for himself the moons of Jupiter, whose existence he had previously dismissed.
We unpack this backwards. Kepler never dismissed the existence of the Moons of Jupiter, rather he sat down and wrote an enthusiastic book praising Galileo’s telescopic discoveries, sight unseen, his Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610). He sent a copy to Galileo in Padua, who had a new edition printed and published there, without asking Kepler’s permission or even informing him of what he had done.
Dissertatio cum Nuncio Sidereo Kepler original publicationDissertatio cum Nuncio Sidereo Galileo’s pirate copy
Their very limited correspondence was seldom amicable. Galileo never sent Kepler a telescope, he regarded him as far too lowly and lacking in influence to be worth one of his telescopes, but he sent one to the Venetian ambassador in Prague with a request that Kepler be allowed to use it. The RudolphineTables remained the standard work of reference for decades because even with telescopes it would take decades before astronomers could make the necessary new observation needed to replace them. It took John Flamsteed (1646–1719) more than forty years to produce the next star catalogue and tables that replaced the Rudolphine Tables.
His knowledge of optics even enabled him to make considerable improvements to Galileo’s telescope, introducing two convex lenses, which were capable of higher magnification than Galileo’s combination of convex and concave lenses.
Strathern makes it seem that Kepler was a telescope builder, he wasn’t. In 1611, he published his Dioptrice, building on his Astronomiae Pars Optica from 1604, in which he explained the optics of the Dutch or Galilean telescope, a necessary step to the acceptance of the validity of the telescopic observations and discovery being made by Galileo and others. The book goes on to explain the optics of the astronomical telescope, two convex lenses, which took a long time to become accepted because it produced an inverted image and also because Galileo dismissed it. He also described the optics of the terrestrial telescope, like the astronomical telescope but with a third lens to invert the image and, last but not least, the telephoto lens. Galileo dismissed this milestone in the history of optics, as unreadable.
Kepler continued with his observations of the planets, and his calculations enabled him to predict that the planets Venus and Mercury would pass across the sun and be visible from earth as they made this ‘transit’. Kepler died in 1630 at the age of fifty-eight, while travelling back through Germany. The following year the first ‘transit’ of Mercury across the face of the sun was observed, just as Kepler had predicted.
Kepler’s legacy is difficult to underestimate. Despite his mystical inclinations, his mathematical descriptions of the solar system were novel, revolutionary in scope, and precise. Such innovations proved so difficult to accept, let alone understand, that many astronomers refused to accept his elliptical-orbit version of the Copernican solar system, with the planets altering speed as they swept through their orbits. But the confirmation in 1631 of his prediction of the transit of Mercury would prove a tipping point. Kepler’s laws of planetary motion would lead directly to Newton’s law of universal gravitation, which he formulated just thirty-five years after Kepler’s death.
Kepler’s first law was accepted relatively quickly, as was the third law, which however remained largely ignored for several decades. There was much discussion of his second law, his own proof of which was to say the least suspect, with various astronomers trying to find a better one. This debate played a significant role in the final acceptance of Kepler’s model of the solar system. What also played a significant role was his work on comets De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero … published in 1619,and which was much consulted during the wave of comets in the 1660s. Strathern doesn’t mention this work at all. The confirmation in 1631 of his prediction of the transit of Mercury was not a tipping point for the Keplerian system. It was a confirmation of the accuracy of the Rudolphine Tables and of the fact that Mercury orbited the Sun, which had been tacitly assumed since the first telescopic observations of the phases of Venus. But, as I get tired of repeating, this fitted into any Tychonic or semi-Tychonic geo-heliocentric model; the most widely accepted solution at the time, which, as we saw above, Strathern dismisses out of hand. The statement that ‘Kepler’s laws of planetary motion would lead directly to Newton’s law of universal gravitation,’ is simply factually false. Newton would go on to prove the law of universal gravitation using Kepler’s laws, but they didn’t lead him to it. Also, Newton didn’t form the law of universal gravitation, which wasn’t ‘his’, thirty-five years after Kepler’s death, i.e., in 1665, Strathern is obviously here buying into the myth of the Annus mirabilis. As a last comment, Strathern also completely ignores Kepler’s role in the founding of modern optics, at least as important as his work in astronomy.
Like all the preceding chapters that I have reviewed from this book, this final chapter on Tycho and Kepler maintains a standard of scholarship that is so low that to use the word scholarship at all is to misuse it. The history of science chapters of Strathern book are a badly thrown together collection of factual errors, misinformation, myths, straight forward falsehoods, and indescribable garbage. That a serious publisher brought this rubbish onto the book market in a thought crime, and it should be removed and pulped immediately.
[1] Victor E. Thoren with contributions by John R. Christianson, The Lord of Uraniborg: A Biography of TychoBrahe, CUP, 1990, p. 103 The Thoren’s Tycho biography is a masterpiece but of course Stratern didn’t consult it!
Discover has an article titled Galileo Galilei’s Legacy Went Beyond Science, which is about his artistic talents. Although, in style, totally over the top purple prose, the main content of the article is correct but nothing new. It is well known that Galileo was an excellent lutist and that he was a fully trained artist. In fact, his ability to recognise that what he was seeing on the Moon were the shadows of mountains and valleys was due to his artistic training. However, there are some points in the article that require comment.
The article opens thus:
In the first book of his epic poem Paradise Lost, John Milton mentions a “Tuscan Artist” who views the moon’s orb through optic glass. He is referring, somewhat perplexingly, to Galileo Galilei, the Italian scientist famed for his telescopic observations and study of fundamental physical laws.
Today, it might seem odd that Milton’s description of the so-called “father of modern science” was first and foremost an artist. In their context, however, it makes perfect sense — both men lived during the Renaissance, a period of fervent innovation in politics, culture, art and science. To them, it seemed far more natural to blend the many fields of inquiry than to compartmentalize them.
In short, if there is a border between Galileo’s intellectual endeavors, it is often too fine to distinguish.
The authors interpretation of Milton’s use of the term artist is rubbish. In the first half of the seventeenth century the word artist would generally mean “one skilled in any art or craft” and not artist as we understand the word today and this is certainly the sense in which Milton used the term. Artist and artisan are still synonyms at the time.
We pass on:
We remember Galileo today mainly for his pivotal contributions to astronomy, physics and mathematics.
Galileo made almost no contributions to mathematics.
The Italian thinker emphasized a methodical approach to the study of the universe, and inspired the modern scientific method that remains a bedrock of scientific inquiry even 380 years after his death.
Beyond that, his astronomical observations completely upended the way we think about the cosmos. In short, we mostly think of Galileo as one of the greatest scientists of all time.
In reality, however, his accomplishments and expertise — including music, literature and visual arts — ranged as widely as those of other quintessential Renaissance figures, like Leonardo da Vinci and Leon Battisa Alberti, the latter of whom proclaimed the ideal of the era: “A man can do all things if he will.”
As already acknowledged above, it is well known that Galileo possessed talent as a musician, writer, and artist (in the modern sense). However, whether it is wise to compare him with Leonardo da Vinci is debateable. There is, however, an excellent book by Matteo Valleriani, Galileo Engineer (Springer, 2012) that argues persuasively for a general assessment of Galileo as a Renaissance engineer rather than as a scientist.
The description of his up bringing and musical education from his father is OK if somewhat overblown but the closing paragraph to that section is to say the least very questionable.
After the Inquisition forced Galileo to recant his views on heliocentrism (the then-heretical theory that Earth revolves around the sun), he spent much of his final decade under house arrest, blind and ailing.
The heliocentric theory was never declared heretical! The second half of the sentence is unnecessarily plaintive. It implies, whether intended or not, that Galileo’s ill-health in the last decade of his life were somehow a result of his house arrest. Let us first clear up what Galileo’s house arrest consisted of. He lived in his villa in Tuscany cared for by servants and served by an amanuensis, working in comfort on his real scientific legacy, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences, 1638).
The villa in Tuscany where Galileo lived between 1631 and his death in 1642
He was also allowed to have visitors, John Milton for example. Although not allowed to travel, which given his age and his state of health he probably wouldn’t have done anyway, he led a life that was in quality considerable better than a large part of the general Tuscan population of the time. In 1633, when his house arrest began, he was already sixty-nine years old and had been suffering from ill-health for several years that was not unrelated to his bacchanalian lifestyle, he always loved his food and wine. He first went blind in 1638 and, despite his house arrest, he was allowed to travel the Florence for medical treatment.
To close:
And once again, Galileo’s aesthetic education can be detected in his scientific discourse. Years of reading these poets taught him to write clearly and believably about even the most foreign concepts, as he did in defending the heliocentric model of the universe against deeply entrenched beliefs, not to mention commonsense.
In fact, Galileo’s undeniable talents as a writer and polemicist, which make his writings so very readable, lead to the fact that people very easily oversee the large chunks of those writings that are in fact wrong and were wrong when he wrote them. For example, his Il Saggiatore (The Assayer, 1623) is undoubtably a polemic masterpiece but almost nobody realises that in the central argument of the debate on the nature of comets, of which the book in part, Galileo is simply and totally wrong and that the empirical evidence of the period clearly showed him to be wrong. The greatest scientists of all time‽
Regular readers of my series of posts on English mathematical practitioners in the late sixteenth and early seventeenth centuries might have noticed the name John Davis popping up from time to time. Unlike most of the other mathematical practitioners featured here in the early modern history of cartography, navigation, and scientific instrument design, who were basically mathematicians who never or seldom went to sea, John Davis (c. 1550–1605) was a mariner and explorer, who was also a mathematician, who wrote an important and widely read book on the principles of navigation, which included the description of an important new instrument that he had designed.
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
John Davis was born and grew up in Sandridge Barton, the manor farm on the Sandrige Estate of Stoke Gabriel in Devon, a small village on the river Dart about six kilometres up-river from Dartmouth, which was an important port in the early modern period, so it seems that Davis was destined to go to sea. Amongst his neighbours, on the Sandrige Estate, were the five sons of the Gilbert-Raleigh family, Humphrey, John and Adrian Gilbert and their half brothers Carew and Walter Raleigh. Both Humphrey Gilbert (c. 1539–1583) and Walter Raleigh (c. 1552–1618) were important Elizabethan explorers and Carew Raleigh (c. 1550–c. 1625) was a naval commander. Adrian Gilbert (c. 1541–1628), who became an MP was an intimate friend of the young John Davis as was Walter Raleigh. Little is known of his childhood and youth, but we do know that he early became a friend and pupil of the leading Elizabethan mathematical practitioner, John Dee (1527–c. 1608). Davis’ friendship with the Gilbert-Raleigh brothers and John Dee would prove helpful in his first major exploration endeavour, the search for the Northwest Passage.
Stoke Gabriel SourceThe Dartmouth Town Council blue plaque erected in memory of Davis Source: Wikimedia Commons
Throughout the Middle Ages, Europe had imported good, in particular spices, from Asia via a complex, largely overland route that ended in Northern Italy, from whence the city of Nürnberg distributed them all over Europe. As the European began to venture out onto the high seas in the fifteenth century, the question arose, whether it was possible to reach Asia directly by sea? The Portuguese began to edge their way down the West African coast and in 1487/88 Bartolomeu Dias (c. 1450–1500) succeeded in rounding the southern end of Africa.
Source: Wikimedia Commons
Between 1479 and 1499 Vasco da Gama (c. 1460–1524) succeeded, with the help of an Arabic pilot, in crossing the Indian Ocean and bringing back a cargo of spices from India to Portugal. This established an initial Portuguese dominance over the oceanic route sailing eastwards to Asia, which with time they extended to the so-called Spice Islands.
Vasco da Gama Source: Wikimedia Commons
As every school kid knows, Christopher Columbus (1451–1506) believed that there was open water between the west coast of Europe and east coast of China, and that he could reach Asia faster and easier sailing west across the ocean rather the east around Africa. In 1492, he put his theory to the test and, having vastly underestimated the distance involved, just as he was running out of food, his small fleet fortuitously ran into the Americas, although they weren’t called that yet. In 1519, the Spanish seaman Ferdinand Magellan (1480–1521) proved it was possible to get past the southern tip of America and into the Pacific Ocean. The last remnants of his very battered fleet returning to Spain, without Magellan, who was killed on the way, in 1522, becoming the first people to circumnavigate the globe.
In 1577, Francis Drake (c. 1540–1596) set out to attack the Spanish on the west coast of the America, decided to return via the Pacific Ocean arriving back in England in 1580, becoming the second to circumnavigate the globe, and the first commander to survive the journey. Between 1586 and 1588, Thomas Cavendish (1560-1592), a protégé of Walter Raileigh, became the third man to circumnavigate the globe, on what was the first planned voyage to do so.
Thomas Cavendish An engraving from Henry Holland’s Herōologia Anglica (1620). Source: Wikimedia Commons
The successful circumnavigations via the southern tip of the Americas led to speculation whether it was possible to reach the Pacific Ocean by rounding the northern end of the Americas. These speculations led to the search for the so-called Northwest Passage, an endeavour in which English mariners would dominate.
Already in 1497, Henry VII sent the Italian mariner, John Cabot (C. 1450–c. 1500) to attempt to find the Northwest Passage. He is thought to have landed once somewhere on the coast of what is now Canada before returning to Bristol. In 1508, Cabot’s son Sebastian (c. 1474–1557) followed his father in trying to find the Northwest Passage. He is thought to have sailed as far north as Hudson Bay. In 1524, the Portuguese mariner, Estêvão Gomes (c. 1483–1538), who had mutinied on the Magellan circumnavigation, bringing his ship back to Spain in 1521, was commissioned by the Spanish Crown to seek a northern route through the Americas, reaching Nova Scotia before returning to Spain.
In 1551, the Muscovy Trading Company was founded in London with the specific intention of finding a Northeast Passage to China by sailing around the northern coast of Russia. A project for which they were granted exclusive rights by the English Crown. The Muscovy Company employed John Dee to teach cartography and navigation to its ships’ officers. They failed in their endeavour to find the Northeast Passage but did establish successful trading deals with Russia.
According to Charlotte Fell Smith, this portrait was painted when Dee was 67. It belonged to his grandson Rowland Dee and later to Elias Ashmole, who left it to Oxford University. Source: Wikimedia Commons
In the 1560s Humphrey Gilbert wrote a detailed treatise supporting the idea of a government supported endeavour to search for the Northwest Passage. In 1574, the privateer Martin Frobisher (c. 1535–1594) petitioned the Privy Council for permission and financial support for an expedition to find the Northwest Passage. They referred him to the Muscovy Company, who eventually agreed to licence his voyage. Altogether Frobisher undertook three attempts, in 1596 with three ships, in 1597 with a much larger fleet and finally in 1578 with a total of fifteen ships. Although he explored much of the coast and islands of Northern Canada the undertaking was basically an expensive flop. On the second expedition Frobisher’s master was Christopher Hall. Frobisher and Hall were coached by Dr John Dee in geometry and cosmography in order to improve their use of the instruments for navigation in their voyage.
Full-length life-size oil painting portrait of English explorer Martin Frobisher commissioned by the Company of Cathay to commemorate his 1576 Northwest Passage voyage and promote the planned follow-up expedition of 1577 painted by Cornelius Ketel Source:Wikimedia Commons
In 1583, Humphrey Gilbert launched an attempt, based on letters patent, that he had acquired from the crown in 1578, to establish an English colony in North America. His half-brother Walter Raleigh sailed with him but had to turn back due to lack of food on his ship. Having taken possession of Newfoundland by force, he then left again without establishing a colony due to lack of supplies. The return journey was a disaster with the loss of the biggest vessel with most of there stores and Gilbert died of blood poisoning, having stepped on a nail.
Portrait Sir Humphrey Gilbert artist unknown Source: Wikimedia Commons
The only halfway positive outcome was that Walter Raleigh received a royal charter based on Gilbert’s letters patent and would in turn go on to found, with Thomas Harriot (c. 1560–1621), as his cartography and navigation advisor, the first English colony in North America on Roanoke Island in 1584. Only halfway positive because the Roanoke colony was also a failure.
It was against this background of one hundred years of failure, from John Cabot to Martin Frobisher, to find a northwest passage that John Davis became involved in the launching of yet another expedition to find one, initiated by his childhood friend Adrian Gilbert and John Dee. Gilbert and Dee, appealed to Sir Francis Walsingham (1573–1590) Secretary of State for funding in 1583. Whilst Walsingham favoured the idea politically, no money from the state was forthcoming. Instead, the planned expedition was financed privately by the London merchant, William Sanderson (c.1548–1638).
Sanderson was trained by Thomas Allen, an assistant to the Muscovy Company, who supplied the Queen’s Navy with hemp, rope, flax, and tallow, which he imported from the Baltic countries. As a young man, Sanderson travelled with Allen throughout the Baltic, France, Germany, and the Netherlands. According to his son, he became wealthy when he inherited the family estates following the death of his elder brother. In either 1584 or 1585 he married Margaret Snedall, daughter of Hugh Snedall, Commander of the Queen’s Navy Royal, and Mary Raleigh sister to Walter Raleigh. Sanderson would go on to become Walter Raleigh’s financial manager.
Here we have once again a merchant financing exploration in the early stumbling phase of the British Empire, a concept that was first floated by John Dee and was propagated by the various members of the Gilbert-Raleigh clan. As we saw in an earlier post, it was the merchants Thomas Smith and John Wolstenholme, who later founded the East India Trading Company, who financed the mathematical lectures of Thomas Hood (1556–1620). Above, we saw that the Muscovy Trading Company financed Frobisher’s efforts to find the Northwest Passage. The founding of the British Empire was driven by trade, and it remained a trading empire throughout its existence. Trade in spices, gold, opium, tea, slaves and other commodities drove and financed the existence of the Empire.
Davis led three expeditions in search of the Northwest Passage in 1585, 1586, and 1587. He failed to find the passage but carried out explorations and surveys of much territory between Greenland and Northern Canada liberally spraying the map with the names of Sanderson, Raleigh, and Gilbert. On these voyages Davis proved his skill as a navigator and marine commander, his logbooks being a model for future mariners and although the expeditions failed in their main aim, they can certainly be counted as successful.
Map showing Davis’s northern voyages. From A life of John Davis, the navigator by Clements R. Markham, (1889) Source: Wikimedia Commons
George Clifford, 3rd Earl of Cumberland after Nicholas Hilliard Source: Wikimedia Commons
In 1591, he was part of Thomas Cavendish’s voyage to attempt to find the Northwest Passage from the western end in the Pacific. The voyage was a disaster, Cavendish losing most of his crew in a battle with the Portuguese and setting sail for home. Davis carried on to the Straits of Magellan but was driven back by bad weather, also turning for home. He too lost most of his crew on the return journey but is purported in 1592 to be the first English man to discover the Falkland Islands, a claim that is disputed.
Davis sailed as master with Walter Raleigh on his voyages to Cádiz and the Azores in 1596 and 1597. He sailed as pilot with a Dutch expedition to the East Indies between 1598 and 1600. From 1601 to 1603 he was pilot-major on the first English East India Company voyage led by Sir James Lancaster (c. 1554–1618), a privateer and trader.
James Lancaster in 1596 artist unknown Source: Wikimedia CommonsLancaster’s Ship the Red Dragon
Although a success, the voyage led to a dispute between Davis and Lancaster, the later accusing the pilot of having supplied false information on details of trading. Annoyed, Davis sailed in 1604 once again to the East Indies as pilot to Sir Edward Michelbourne (c. 1562–1609) an interloper who had been granted a charter by James I & VI despite the East India Company’s crown monopoly on trade with the East. On this voyage he was killed off Singapore by a Japanese pirate whose ship he had seized. Thus, ending the eventful life of one of Elizabethan England’s greatest navigators.
All the above is merely an introduction to the real content of this post, Davis’ book on navigation and his contribution to the development of navigation instruments. However, this introduction should serve to show two things. Firstly, that when Davis wrote about navigation and hydrography, he did so as a highly experienced mariner and secondly just how incestuous the exploration and navigation activities in late sixteenth century England were.
In 1594, Davis published his guide to navigation for seamen, which could with some justification be called Navigation for Dummies. It was the first book on navigation actually written by a professional navigator. To give it its correct title:
THE SEAMAN’S SECRETS; Deuided into 2, partes, wherein is taught the three kindes of Sayling, Horizontall, Peradoxal, and sayling vpon a great Circle: also an Horizontall Tyde Table for the easie finding of the ebbing and flowing of the Tydes, with a Regiment newly calculated for the finding of the Declination of the Sunne, and many other necessary rules and Instruments, not heretofore set foorth by any.
Newly published by Iohn Dauis of Sandrudge, neere Dartmouth, in the County of Deuon. Gent.
Imprinted at London by Thomas Dawson, dwelling at the three Cranes in the Vinetree, and are these to be solde. 1595
David Waters write, “his work gives in the briefest compass the clearest picture of the art of navigation at this time.”[1]
Davis defines his three kinds of sailing thus:
Horizontal [plane] Navigation manifesteth all the varieties [changes] of the ship’s motion within the Horizontal plain superfices [on a plane chart], where every line [meridian] is supposed parallel.
This was the traditional and most common form of navigation at the time Davis wrote his book and he devotes the whole of the first part of the book to it.
Paradoxal Navigation demonstrateth [on circumpolar charts] the true motion of the ship upon any corse assigned … neither circular nor strait, but concurred or winding … therefore called paradoxal, because it is beyond opinion that such lines should be described by plain horizontal motion.
What Davis is defining here is rhumb line or Mercator sailing.
Great circle navigation he considered as the ‘chiefest of all the three kinds of sayling’, and defined it as one ‘in whom all the others are contained … continuing a corse by the shortest distance between places not limited to any one corse.’
He lists the instruments necessary for a skilful seaman:
A sea compass, a cross staff, a quadrant, an Astrolaby, a chart, an instrument magnetical for finding the variations of the compass, an Horizontal plain sphere, a globe and a Paradoxal compass.
He then qualifies the list:
But the sea Compass, Chart and Cross Staff are instruments sufficient for the Seaman’s use … for the Cross Staffe, Compass and the chart are so necessarily joined together as that the one say not well be without the other … for as the Chart sheweth the courses, so doth the compasse direct the same, and the cross-staffe by every particular observed latitude doth informe the truth of such course, and also give the certaine distance that the ship hath sayled upon the same.
Davis describes the technique of plane (horizontal) sailing as–’the god observation of latitude, careful reckoning of the mean course steered (corrected for variation), and careful estimation of the distance run’. Of these ‘the pilot has only his height [latitude] in certain.’[2]
Davis gives clear definition of special terms such as course and traverses and delivers an example of how he wrote up his ship’s journal. His was the first book published to give such things.
Source: Waters’ The Art of NavigationSource: Waters’ The Art of Navigation
He gave much space to how to calculate the tides, including the use of ‘An Horizontal Tyde-Table,’ an instrument for calculating tide times.
Davis goes into a lot of details on how to calibrate the cross-staff, he paid particular attention to the problem of parallax produced by placing the end of the cross-staff in the wrong position on the face. This is interesting given his development of the back-staff.
In order to determine one’s latitude, it was necessary to determine the altitude of the sun at noon. This was usually done using a cross-staff, also known as a Jacob’s staff, but could also be done with a quadrant or a mariner’s astrolabe.
Source: Waters’ The Art of Navigation
The cross-staff suffered from a couple of problems. As well as the eye parallax problem, already discussed, the user had to hold the staff so that the lower tip of the traverse rested on the horizon, whilst the upper tip was on the sun, then the angle of altitude could be read off on the calibrated scale on the staff. There were different sized traverses for different latitudes and there were scales on the staff for each traverse, a topic that Davis delt with in great detail. It was difficult for the user to view both tips at the same time. Added to this the user was basically staring directly into the sun.
The cross-staff Wikimedia Commons
To get round these problems Davis invented the backstaff. At the end of the staff was a horizon vane through which the user viewed the horizon with his back to the sun. An arc, ewith a shadow vane, was attached to the staff which could slide back and forth until its shadow fell on the horizon vane the angle of altitude could be read off on the calibrated staff. This staff did not suffer from the eye parallax problem, the user only had to observe the horizon and not the sun at the same time, and the user did not have to look directly into the sun.
Source: Waters’ The Art of NavigationFigure 1 – A simple precursor to the Davis Quadrant after an illustration in his book, Seaman’s Secrets. The arc was limited to measuring angles to 45°. Source: Wikimedia Commons
Davis’ original back staff could only measure a maximum angle of altitude of 45°, which was OK as long as he was sailing in the north but was too small when he started sailing further south, so he developed a more advanced model that could measure angles up to 90°.
Source: Waters’ The Art of NavigationFigure 2 – The second Davis Quadrant after an illustration in his book, Seaman’s Secrets. The arc above is replaced with an arc below and a shadow-casting transom above. This instrument can now measure up to 90°. Source: Wikimedia Commons
This evolved over time into the so-called Davis quadrant.
Source: Waters’ The Art of NavigationFigure 3 – The Davis Quadrant as it evolved by the mid-17th century. The upper transom has been replaced with a 60° arc. Source: Wikimedia CommonsLate 17th-century engraving of Davis holding his double quadrant Source: Wikimedia Commons
Better than the cross-staff for measuring the sun’s altitude, the back-staff became the instrument of choice, particularly for English mariners for more than a century, but it was not perfect. Unlike the cross-staff, it could not be used at night to determine latitude by measuring stellar altitudes, also its use was limited by overcast weather when the sun was not strong enough to cast a shadow. To help with the latter problem, John Flamsteed replaced the shadow vane with a lens that focused the sunlight on the horizon vane instead of a shadow. The weak sunlight focused by the lens could be better seen that the faint shadow. The backstaff with lens evolved into the Hadley quadrant, which in turn evolved into the sextant still in use today.
Davis also gives an extensive description of how to navigate using a terrestrial globe. This was very innovative because mass produced printed globes were a fairly recent invention, Johannes Schöner (1477–1547) produced the first serial printed terrestrial globe in 1515, and were not easy to come by. It was Davis, who persuaded his own patron, William Sanderson, to finance Emery Molyneux’s creation of the first printed terrestrial and celestial globes in England in 1592.
Source: Waters’ The Art of Navigation
Davis emphasised that the terrestrial globe was particularly good for instruction in navigation because all three forms of sailing–plane, rhumb line, great circle–could be demonstrated on it.
In his original list of instruments for the seaman, Davis included the Paradoxal compass but he doesn’t actually explain anywhere what this instrument is. John Dee, who remember was John Davis’ teacher, also mentions the Paradoxal compass in his writings without explanation. There is talk of how he created a Paradoxal chart for Humphrey Gilbert for his fatal 1583 expedition. It turns out that the Paradoxal compass and Paradoxal chart are one and the same and that it is an azimuthal equidistant circumpolar chart, with the north pole at its centre and the lines of latitude at 10° interval as concentric circles. The azimuthal equidistant projection goes back at least to al-Bīrūnī (973–after 1050) in the eleventh century.
An azimuthal projection showing the Arctic Ocean and the North Pole. The map also shows the 75thparallel north and 60th parallel north. Source: Wikimedia Commons Davis Paradoxal compass would have covered a similar area.
In his book on plane sailing, Davis discusses the drawbacks of the plane chart or equirectangular projection, which assumes that the world is flat and on which both lines of longitude and latitude are straight equidistant parallel line which cross at right angles, which according to Ptolemaeus was invented by Marinus of Tyre (c. 70–130 CE) in about 100 CE. A plane chart is OK for comparatively small areas, the Mediterranean for example, and Davis praises its usefulness for coastal regions. However, it distorts badly the further you move away from its standard parallel.
Equirectangular projection with Tissot’s indicatrix of deformation and with the standard parallels lying on the equator Source: Wikimedia Commons
As a result, it is useless for exploration in the far north and hence the use of the Paradoxal compass. The use of such circumpolar maps became standard for polar exploration in the following centuries.
Straight forward, clear and direct The Seaman’s Secret was very popular and went through several new editions in the decades following Davis’ death. A year after it was published Davis published a second book, his The World’s Hydrographical Description or to give it its full title:
THE
WORLDES HYDROGRAPHI-
CAL DISCRIPTION.
Wherein is proved not only by Aucthoritie of Writers, but also by late experience of Travellers and Reasons of Substantial Probabilitie, that the Worlde in all his Zones, Clymats, and places, is habitable and inhabited, and the Seas likewise universally navigable without any naturall anoyance to hinder the same,
Whereby appears that from England there is a short and
speedie passage into the South Seas, to China,
Molucca, Philippina, and India, by Northerly
Navigation.
To the Renowne, Honour, and Benifit of Her Majesties State and
Communality
Published by J. DAVIS OF SANDRUG BY DARTMOUTH
In the Countie of Devon, Gentleman. ANNO 1595, May 27.
Imprinted at London
BY THOMAS DAWSON Dwelling at the Three Cranes in the Vinetree, and there to be sold.
1595.
The ‘by Northerly Navigation’ reveals that it is in fact a long plea for a return to exploration to find the Northwest Passage.
With his The Seaman’s Secrets based on his own extensive experience as an active navigator and his invention of the backstaff, John Davis made a substantial contribution to the development of mathematical navigation in the Early Modern Period.
[1] David Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, New Heaven, 1958, p.201
[2] All the above is distilled from Water’s page 202.
Today, I’m looking at Strathern’s chapter on Vesalius. It goes without saying that Strathern evokes the mythical religious taboo on dissection of the human body.
The dissection of human bodies had been a religious taboo in the western world since well before the birth of Christ. This taboo extended through all Abrahamic religions – i.e. Judaism, Christianity and Islam – as well as most of the heterodox sects and cults which pervaded the Mediterranean region and the rest of Europe.
Despite such mistakes, Galen’s ‘authority’ on medical matters reigned supreme throughout the medieval era, alongside that of Aristotle. Not until the Renaissance would his errors come to light.
Galen was just one of several medical authors whose texts were used on the medieval universities and despite challenges continued to be used throughout the Renaissance. In fact, there was during the Renaissance a strong neo-Galenic movement that challenged Vesalius.
It’s almost unavoidable that Strathern, like everybody else, includes Leonardo, he writes:
A century prior to Vesalius, Leonardo da Vinci’s obsessive curiosity led him to carry out dissections of human cadavers, which he recorded in his notebooks. By now the prohibition of such activities had become somewhat more relaxed, though they remained frowned upon.
As already noted, there was no prohibitions and Leonardo, like all the apprentices of Andrea del Verrochio (1435–1488), who insisted that his apprentices gain a thorough grounding in anatomy, would have attended dissections as an apprentice.
Leonardo carried out systematics anatomical investigations together with Marcantonio della Torre (1481–1511), lecturer on anatomy at the universities of Pavia and Padua, between 1510 and 1511. Vesalius’ principle anatomical work, his De fabrica, of which more later, was published in 1543. According to my arithmetic that is a span of thirty-one years and not a century. Maybe Strathern uses a different number system?
We get no account of Leonardo’s systematic work with Andrea del Verrochio this would spoil the image that Strathern creates of the chaotic nature of Leonardo’s work and notes. We do, however get a lengthy anecdote about his dissection of a man who claimed to be one hundred years old. Then Strathern drops the following gem:
But why this diversion? What possible relevance does such work by Leonardo have to the northern Renaissance? In fact, none. And that is the point. By recounting these pioneering anatomical experiments – unique in their breadth, depth and explication – we gain an insight into the immense difficulties involved in human dissection during this period. We can also witness the birth of a new, forbidden science coming into being. Or apparently so. For this infant body of learning would not survive its premature birth – stillborn before it could draw breath – largely through the procrastination of Leonardo himself.
As already stated, we do not have “the birth of a new, forbidden science”, dissection of human cadavers was routine by the time that Leonardo was active. Also, if he poses the question, “What possible relevance does such work by Leonardo have to the northern Renaissance?” then he must also pose it for Vesalius, who although he came from the Netherlands did all his anatomical work in Padua and was very much an integral part of the Italian Renaissance.
We then get a brief description of the fate of Leonardo’s papers and drawings which closes with the repeat of the arithmetical error:
Working a century later, Vesalius would remain unaware of Leonardo’s pioneering work, which remained lost to history.
Leonardo lived from 1452 to 1519, Vesalius was born in 1514 and carried out his anatomical work in Padua beginning in 1537, publishing the De fabrica in 1543. No matter how I try I can’t make a century out of these dates! The century is merely a lead into a piece of pseudo historical pathos:
Such a lacuna leads one to speculate on how much more, of genuine worth, was lost during this period. Such discovery and progress had little place in the medieval era. The Renaissance would have to find its own way of accommodating and preserving the innovations it produced. All we know are the successes which eluded loss or destruction: Copernicus’s revolutionary work published by his friends and gifted to him on his deathbed; Paracelsus’s haphazard discoveries, and superstitious lapses, disseminated by means of Gutenberg’s invention, which was itself wrested from the hands of its creator. In this aspect, more than most, no history can be any more than an incomplete account. Fortunately for history, Vesalius would do his utmost to gainsay this fact, his work being both painstaking and thorough from the outset. And his motives throughout his long and arduous task would be single-mindedly focused on public recognition and public reward.
In the history of science many new ideas, theories and discoveries have been lost, forgotten, or suffered a delayed reception. The reasons are numerous but, and it’s a very big but, they were not somehow actively repressed during the Middle Ages as Strathern would have us believe. I have already pointed out in my review of the chapter on Copernicus, his work was not published by his friends in an act of deception as Strathern claims, but he sent his book to Petreius in Nürnberg to be published himself. Paracelsus’ work was mostly posthumously printed and published by his disciples, a case of late reception and in Gutenberg’s case, if you build up your business with large sums of borrowed cash and then get into a dispute with your financier, then you tend to lose your business. However, the invention of printing with moveable type was in no way effected by Gutenberg’s financial problems. Strathern’s examples don’t illustrate his argument at all.
We now arrive at Vesalius and the usual brief biography. Strathern tries to paint his father as somehow inferior and suffering from an inferiority complex. Claiming that it was his mother who raised him and set him on his way entering him, like Mercator and Gemma Frisius before him, in a school of the Brotherhood of the Common life, in his case in Brussels. It was actually his father who entered him in the school. Like Mercator and Gemma Frisius, Vesalius now entered the University of Leuven, and Strathern displays his total ignorance of the medieval university system:
Surprisingly, Vesalius did not register at the school of medicine, but instead chose to study the arts and humanities, which included learning Latin and Greek, at which he thrived. (The books in his grandfather’s library would mostly have been written in Latin, and Vesalius almost certainly had extended his schoolboy Latin by reading these works.) After young Vesalius graduated with a good arts degree in 1532, he was accepted to study at the prestigious University of Paris, where he entered the school of medicine. Only now did he begin the formal study of this subject.
Despite its reputation, the University of Paris remained firmly committed to the teachings of Aristotle, and its school of medicine was still dominated by the 1,300-year-old ideas of Galen. Lectures in practical anatomy were a comparatively rare novelty, having only recently received limited Church dispensation [my emphasis].
Lectures in practical anatomy were a standard part of the medical curriculum in Paris, there being no Church restriction on them as I’ve already explained above. Strathern contradicts himself by explaining that anatomical lectures, with public dissections, were a standard part of the curriculum, although he correctly observes that the student were only allowed to observe but not to dissect themselves. He notes correctly that the one professor of anatomy, Jacobus Sylvius (1478–1555) was a strict adherent of Galen but that another, Johann Winter von Andernach (1505–1574) was more open minded and even allowed students to participate in dissections. Winter became Vesalius’ mentor and even employed Vesalius as an assistant in the preparation of his four volume Institutiones anatomicae (Paris, 1536) for the press, praising him in the preface; it would become a standard work, of which Vesalius published a second updated edition in 1539. It should, however, be pointed out that Winter was one of those who triggered to renaissance in Galenic anatomy when he produced and published a Latin translation of Galen’s newly discovered and most important De Anatomicis Administrationibus (On Anatomical Procedures) 9 vols. Paris in 1531, which Strathern doesn’t mention at all.
Strathern delivers up some waffle about what happened next when Vesalius was forced by war to leave Paris and return to the Netherlands, where he re-entered the University of Leuven to complete his medicine degree. Here he wrote his doctoral thesis and Strathern once again displays his ignorance:
At the same time, Vesalius began composing his graduation thesis. Interestingly, he chose for his subject the tenth-century Persian physician and alchemist known in the west as Rhazes. (In the Arabic world his full name was Abu Bakr Muhammad ibn Zakariya al-Razi.) The important fact about Rhazes was that he not only based his science upon the experiments he conducted himself, but he also wrote these out in detail, step by step. This meant that they could be precisely repeated by other scientists. Here, reliance upon the word of a universal and unchanging ‘authority’ was skilfully circumvented.
This important lesson would soon begin to permeate the world of science in both the northern and the Italian Renaissance. The days when scientists – from mathematicians to alchemists – kept their discoveries secret in order to gain advantage over their rivals were coming to an end. Science was entering the public domain. Experimenters would publish their work in books, and their results could be verified (or shown to be faulty) by their peers.
Vesalius’ doctoral thesis was actually Paraphrasis in nonum librum Rhazae medici Arabis clarissimi ad regem Almansorem, de affectuum singularum corporis partium curatione, a commentary on the ninth book of Rhazes.
Strathern tries to make it seem as if Vesalius’ thesis was in somehow exceptional in its choice of topic and in some way ground-breaking, whereas it was perfectly normal. The book of Rhazes referred to here is his The Virtuous Life (al-Hawi), a nine-volume posthumous collection of his medical notebooks, which was translated into Latin in the late thirteenth century and was a standard textbook in the medical faculties of the European medieval universities, so there was nothing exception about Vesalius writing his doctoral thesis on part of it. Strathern continues:
Vesalius’s reputation as a talent of great promise seems to have spread far and wide, almost certainly aided by Andernach’s description of him in Institutiones Anatomicae. Immediately upon his graduation from Leuven, Vesalius received an invitation to become a professor of anatomy and surgery at the University of Padua, one of the finest centres of scientific research in Italy.
This proving that Vesalius was very much part of the Italian Renaissance and not the Northern Renaissance! Now Strathern starts off on a path where he will begin to mix fact with fiction:
More importantly for Vesalius, Padua was just twenty miles from Venice, the commercial and cultural capital of the region, and it was here that he met the German-born artist Jan von Calcar, who had served his apprenticeship under Titian. Calcar’s particular talents were his ability to imitate the works of others and his supreme skill with woodcuts.
In 1538 Vesalius collaborated with Calcar on the production of his first anatomical text, Tabulae Anatomicae Sex (Six Anatomical Charts.) Three of these charts were produced by Calcar, taken from a full-scale skeleton of the human body which Vesalius had put together. The other three made use of charts which Vesalius himself had drawn for lectures to his students.
Although the story is well document, Strathern can’t get the facts right. The Tabulae Anatomicae Sex were originally six large, woodcut, wall posters that Vesalius had created for his lecture theatre. He discovered that students were copying them, so he decided to make a professional printed edition of them. Of the printed edition the first three were entirely his own work but for the second set of three he employed Jan van Calcar. Strathern notes correctly that here Vesalius corrects some of Galen’s anatomical errors but repeats some others.
Tabulae Anatomicae Sex the first three illustrations are by Vesalius the three skeletons by Calcar Source: Welcome Collection
Strathern now delivers up a classic historical myth in a footnote:
From now on, the more Vesalius continued with his investigations of the human body, the bolder he became. By this stage he had reached an agreement with the Paduan authorities, who allowed him to dissect the regular supply of cadavers of prisoners executed on the gallows. Vesalius’s retelling of how he carried out his researches paints a vivid, if lurid, picture. He described how he ‘would keep in my bedroom for several weeks bodies from graves or given me after public executions’. How did his neighbours put up with the appalling stench? To say nothing of their suspicions that he might be indulging in necromancy or demonology? The answer is that they may well have been unable to distinguish the stench from the general pervasive malodorousness.*
* During this era the waterways of Padua, like the canals of Venice and its nearby lagoon, emitted powerful smells, especially in the summer. This was hardly helped by the customary lack of bathing and personal hygiene which pervaded all classes throughout Europe. [my emphasis] Indeed, such habits accounted for the constant use of sweet- smelling nosegays in genteel society. These consisted of flowers or herbs intended to mask the sense of smell. It is said that in Venice a certain type of nosegay evolved which went further, using citrus oil or extracts of resin intended to numb the olfactory sense altogether, rather than simply distracting it.
The sentence that I have emphasised is, unfortunately, a widespread myth and total piffle! Europeans in the Renaissance bathed regularly and took great care of their personal hygiene. Nobody claiming to be an academic historian, as Strathern does, should be repeating this garbage in 2023! On the subject of demonology Strathern drops the following gem:
As for the suspicion that Vesalius might have been involved in occult practices – presumably he remained under the protection and good name of the university. This was still an era when a large majority of the population believed in demonology, witchcraft and the like – general superstition was rife. Here was one area where the power of the Church and its insistence on orthodoxy was beneficial: in its suppression of heretical practices and beliefs, it undoubtedly reduced the credulity [my emphasis] which led to the outbreaks of mass hysteria that were prevalent during this period.
It was the Church with its insistence on the real existence of the Devil, demons, black magic, witches, and all the rest that was the main driving force fuelling the credulity.
It is now that Strathern begins mixing fact with fiction or maybe fantasy.
Vesalius now began assembling, together with Calcar, the large, precisely delineated drawings that would become the body of the master- piece which assured his lasting place in medical history. Apart from Leonardo’s, previous books containing anatomical illustrations had tended to be schematic, or cartoon-like, mostly drawn by their medical author – whose talent would often be amateurish at best. By contrast, Vesalius’s De Humani Corporis Fabrica (The Apparatus of the Human Body) would not only be comprehensive and encyclopedic in its knowledge, but its precise illustrations would also be works of art as much as science. Calcar’s large exact drawings, made under Vesalius’s painstaking direction, would in their own distinctly different style be a match for the as-yet-unseen drawings of Leonardo.* Meanwhile Vesalius’s text would set medicine free from the stranglehold of Galen.
That Calcar was the artist, who created the illustration in De fabrica is an unsubstantiated claim made by Giorgio Vasari (1511–1574) in his Le Vite de’ più eccellenti pittori, scultori, ed architettori (Lives of the Most Excellent Painters, Sculptors, and Architects), 1st edition 1550, 2nd expanded edition 1558, a book not exactly renowned for its historical accuracy. There is no mention in the De fabrica, who the artist actually was. In a footnote in her The ScientificRenaissance 1450–1630 (ppb. Dover, 1994) Marie Boas Hall writes about the illustrations:
These are attributed to Jan Stephen van Calcar (1499–c. 1550) by the sixteenth-century art historian, Vasari. Modern students have doubted this, because the figures are as superior to those of the Tabulae Sex as the text of the Fabrica is to that of the earlier work–though it is possible that the artist had learned as rapidly as the author. In place of Jan Stephen van Calcar, the only candidate is an unknown, also a member of Titian’s studio. It seems difficult to believe that so spirited a draughtsman as the artist who drew the pictures for the Fabrica should be otherwise unknown; though it is odd that Vesalius, who had given Jan Stephen credit for his work on the Tabulae Sex, did not mention the name of the artist of the Fabrica.
It has also been speculated that is unlikely that a single artist created all 273 illustrations in such a short period of time. So, Jan van Calcar as the author of the medical illustrations in De fabrica is anything but an established fact but this doesn’t stop Strathern writing the following in a footnote to the paragraph quoted above:
* Such artistry did not come cheap. Indeed, Vesalius was unable to pay Calcar, and in lieu of a fee he signed over to the artist any future profits the Fabrica would make.
Either Strathern is making things up or he is quoting a source, which he doesn’t name, that is making things up without checking on the accuracy of the claim made. It doesn’t stop here. Later in his lengthy description of the book itself he writes:
Alas, Vesalius’s perfectionism would result in an increasing number of quarrels with Calcar. Breaks in their collaboration now followed, and Vesalius began drawing a number of the anatomical illustrations in the Fabrica himself.
A couple of paragraphs further on:
By now, it appears, Calcar had quit the project altogether. We must imagine him storming off in some indignation at Vesalius’s tenacious insistence upon the minutest detail. (This was woodcut, remember, not drawing; erasure was no simple matter with a gouged wooden surface.)
Here also Strathern appears to not know the difference between the artist and the woodblock cutter. Calcar or whoever was the artist, would draw the images onto the surface of the woodblock, but the actual cutting would be done by a professional woodblock cutter and not the artist.
I’m not going to do a blow-by-blow analysis of Strathern’s long account of De fabrica, as this review is already over long, but just mention a couple of salient points. To start with Strathern makes no mention of the fact that just as Copernicus modelled De revolutionibus on the Epytoma…in Almagestum Ptolomei of Peuerbach and Regiomontanus, so Vesalius modelled his De fabrica on Galen’s De Anatomicis Administrationibus (On Anatomical Procedures), which as I mentioned above was first translated into Latin and published by his mentor Johann Winter von Andernach.
At one point Strathern tells us, “As the work continues, the illustrations become less precise and their interpretation less exact.” The final chapter of De fabrica, Book VII, deals with the brain and Strathern writes, apparently contradicting himself, “Ensuing books of the Fabrica would prove similarly perceptive – especially Vesalius’s investigations of the human brain.” Do these images appear imprecise to you?
Fabrica Book VII Source: Wikimedia CommonsFabrica Book VII Source: Wikimedia Commons
Strathern also writes, And the illustration of the pregnant uterus containing a foetus is undeniably medieval in its crudity…” Vesalius has no illustration of the pregnant uterus containing a foetus;maybe he was confusing it with the illustration of the placenta with its attached foetus?
Fabric Book VII Source: Wikimedia Commons
Having completed his tour of De fabrica, Strathern now jumps the shark!
When he had completed the manuscript of Fabrica, he sent the text and illustrations north to Basel in Switzerland. This was the home of Johannes Oporinus, who sixteen years previously had worked as Paracelsus’s long-suffering assistant. Oporinus had now succeeded Paracelsus as a rather more orthodox professor of medicine in Basel. He also happened to come from a family renowned for their printing and engraving skills, and combined his medical knowledge with an expert understanding of the entire printing process. This was the only man in Europe whom Vesalius could trust with the production of his masterwork.
Johannes Oporinus (1507–1568) had very little to do with Paracelsus, he was merely for a brief period in 1527 his famulus. The son of a painter he studied law and Hebrew at Basel University, whilst working as a proofer in the print workshop of Johann Froben (c. 1460–1527). He also worked as a schoolteacher for Latin. From 1538 to 1542, he was professor for Greek at the University of Basel, resigning to devote himself fulltime to his own print workshop.
Portrait of Johannes Oporinus by Hans Bock Source: Wikimedia Commons
Strathern closes his chapter on Vesalius with a long-winded account of further biography as Imperial physician to Charles V and later Philip II. Strathern of course cannot resist including the unsubstantiated anecdote that in Spain Vesalius started to carry out an autopsy on a corpse only to discover that the man wasn’t actually dead. There are numerous cases of this happening throughout history, and it even still occasionally occurs today, but whether it actually happened to Vesalius is, as I said, unsubstantiated.
In his chapter on Vesalius, as usual Strathern delivers up a collection of inaccuracies, myths, and in the case of the relationship between Vesalius and Calcar some pure fantasy. Once more I am forced to ask how did this book ever get published?
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 
