Hondius had left the Netherlands in 1584 because of religious difficulties. The Moxon family went in the opposite direction, also because of religious difficulties. Joseph was born in Wakefield into an old Yorkshire family and educated at the Free Quenn Elizabeth Grammar School, where his uncle Peter Moxon was a governor.
Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source Welcome Collection via Wikimedia Commons
Joseph’s father, James Moxon, was a puritan, who was strongly opposed to the policies of William Laud (1573–1645), the Archbishop of Canterbury under Charles I from 1631–1645. In 1636, James left England for the Netherlands taking his sons James and Joseph with him. He set a printing shop, first in Delft then in Rotterdam, where he printed Puritan tracts. By 1638 he was printing English Bibles for the English Puritan community in Rotterdam. Laud was executed in 1645, followed by Charles I in 1649. The Moxons returned to London in 1646, where Joseph and his elder brother James continued to print and publish Puritan literature, with one exception, A Book of Drawing, Limning, Washing or Colouring of Mapps and Prints, printed for the engraver and publisher Thomas Jenner (died 1673), in 1647.
By 1650 Joseph had left the family busy, James carrying on alone. Joseph had taken up the study of globe and map making and developed a strong interest in practical mathematics. In the spring of 1652, he travelled to Amsterdam and acquired engraved copper globe-printing plates. Later in the same year in partnership with John Sugar, he began to sell 15 inch terrestrial and celestial globes. At the sign of the Atlas (shops didn’t have street numbers in those days) Joseph developed a business printing maps, charts, globes and paper mathematical instruments and publishing popular scientific books. Paper mathematical instruments is something that tend to get neglected by historians of mathematical instruments. Metal mathematical instruments were very expensive and there was a big trade in cheap printed paper instruments. These could be cut out and pasted onto wooden boards making a cheap functional alternative to the expensive metal instruments. Unfortunately, they are highly perishable and we only have very few examples that have survived the ravages of time.
Moxon’s original premises were in Cornhill and from 1665 to 1686 he was at Ludgate Hill except for six years when he was forced to move to Russell street following the Great Fire of London.
In 1654 he published his first book, A Tutor to Astronomy and Geography, an unacknowledged translation from the Latin of Institutio Astronomica by Willem Janzoon Blaeu (1571–1638) Jodocus Hondius’ greatest rival. Over the next thirty years Moxon published more than thirty popular scientific expositions and technical handbooks, many of which he wrote himself. The volumes, Vignola or The Complete Architect and A Tutor to Astronomy and Geography. Or an easie and speedy way to know the USE of both the GLOBES, Celestial and Terrestrial both of which he wrote himself went through several editions.
Moxon gained a reputation for printing mathematical texts (John Dansie’s Mathematical Manual, 1654, and Edward Wright’s Certain Errors in Navigation, (1657), and particularly of tabulated data (his tables of solar declination, Primum mobile, 1656, reprinted in John Newton’s A Help to Calculation, 1657, together with tables of logarithms); he also set the 230 pages of trigonometrical functions and logarithms in William Oughtred’s Trigonometria (1657).
Moxon sought to improve his status with a petition to Charles II, asking to be made Hydrographer to the King. By now Moxon was obviously well connected because his petition was supported by thirteen leading figures of the period–J. Newton D.D., L. Rooke, Walter Pope, John Collins, W. Chiffinch, E. Ashmole, G. Wharton , Henry Bonde, Jonas Moore, John Leeke, Thomas Harvie, Will Mar, Euclid Speidell–they stated that they were “Professors of Mathematics” meaning that the professed mathematics. Several of them had close connections at court.
Only Walter Pope and Lawrence Rooke were actually professors at Gresham College.
Moxon published Newton’s A Help to Calculation (1657), Leek’s Waterworks (1659), Moore’s Short Introduction Into the Art of Species (1660) and Bond’s Two Tables of Ranges, according to the Degree on Mounture (?)
On 10 January 1661/2 a warrant was issued by the King “To our Right Trusty and Right beloved Cousin and Councillor Edw: Earle of Manchester our Chamberlane of our household” as follows:
Our Will and Pleasure is that you give present order for the Swearing of Joseph Moxon our Servant in the quality of Hydrographer unto us for the making of Gloebes Mapps and Sea plats and he be admitted thereunto as out servant in ordinary and have and receive all Rights and Profitts Priviledges and advantages thereby in an ample manner as any our servants in that or like quality have doe or ought to enjoy and for do doeing this shall be your warrant.
Joseph Moxon had come up in the world, from Puritan refugee in the Netherlands to official servant to the King of England, whose father the Puritans had executed. The appointment led to a boom in Moxon’s activities. In the following period he was involved in the production of almost forty volumes, as printer, published, translator, or author.
Several of the supporters of Moxon’s petition were founding members of the Royal Society and over the next years he was in close contact with the society. He had close personal contact with Robert Hooke (1635–1703) the society’s demonstrator of experiments and the two men exchange information and undertook joint activities.
In 1678 Moxon’s status rose once more when he was elected to the Royal Society. In its early years the society resemble more a gentleman’s club that a scientific society. The fellows were either high ranking scholars or aristocrats. Moxon was the first tradesman elected to the society and remained the only one to receive this honour in the seventeenth century. That his election was unusual is reflected in the vote on his membership. When somebody was proposed for fellowship the vote by show of hands was almost always unanimous. By Moxon’s election, in a secret vote, there were four votes against.
Moxon was an active member for the first two years of his membership. In 1680, the possibility was raised of Moxon becoming the printer to the society. However, after a year of deliberation somebody else was appointed to this position. Following this Moxon took no further part in the activities of the society. It could have been the case that being a fellow of the society barred Moxon from receiving a paid position in the society. When Edmond Halley (1656–1742) was appointed secretary to the society he had to resign from his fellowship.
In his work as a printer, publisher, author Moxon was highly innovative. Moxon was the first to introduce pocket globes into England, sometime between 1659 and 1670.
A very rare Joseph Moxon 2 ¾-inch pocket globe, English, circa 1675 Source
As already noted he published a wide range of mathematical and technical literature but I will just highlight his three most significant publications.
In 1678, he published the first issue of what was effectively a monthly subscription magazine with the main title Mechanick Exercises or, The Doctrine of Handy Works…, the series was completed by 1680 after a total of fourteens parts had been issued. Published later, as it book The full title was: Mechanick exercises, or, The doctrine of handy-works : applied to the arts of smithing, joinery, carpentry, turning, bricklayery : to which is added Mechanick dyalling: shewing how to draw a true sun-dyal on any given plane …
Mechanick dyalling, or to give it its original full title, Mechanick dyalling teaching any man, though of an ordinary capacity and unlearned in the mathematicks, to draw a true sun-dyal on any given plane, however scituated : only with the help of a straight ruler and a pair of compasses, and without any arithmetical calculation had been published separately in 1668.
This was part of an interesting development, which Moxon didn’t start, in which the knowledge of the trades became increasingly public. Traditionally the hand-work trades were taught by a master to his apprentice(es), oft father and son, the knowledge imparted being kept secret, the classical “trade secrets.” In the early modern period as the barriers between practical knowledge and academic knowledge began to fall, one of the driving forces behind the so-called scientific revolution, various authors took to publishing those trade secrets to make them available to a wider public. Moxon took this to a new level.
The Mechanick Exercises might well have been instrumental in Moxon’s election to the Royal Society. In 1678, he had presented six issues of the work to the president of the society. He was much impressed, in particularly because the Royal Society had planned such a publication in 1660, which had never gotten off the ground.
Moxon’s Mechanick Exercises Volume II is regarded as his most important or significant publication. Originally published in twenty-four parts in 1683-84, the Mechanick Exercises: or the doctrine of handy-works applied to the art of printingwas the first comprehensive and detailed account of all aspects of printing written in English, or some sources say in any language.
Moxon scored another first, also in any language, with his Mathematicks made Easie: Or, a Mathematical Dictionary, Explaining The Terma of Art, and Difficult Phrases used in Arithmetick, Geometry, Astronomy, Astrology, and other Mathematical Sciences first published in 1679.
Note the presence of astrology in Moxon’s listing of the mathematical sciences. In 1682 he was heavily involved in an attempt to revive the London Society of Astrologers, originally created in 1649 by William Lilly and Elias Ashmole. Ashmole had been one of Moxon’s supporters in his petition to be appointed Hydrographer to the King. In general Moxon was deeply embedded in the scientific community in London in the second half of the seventeenth century. As well as those already mentioned at various point above, he is known to have made astronomical observations with Edmond Halley and he cut and cast the Irish characters commissioned by Robert Boyle (1627–1691) for the 1681-85 printing of the Bible in Irish.
Both volumes of the Mechanick Exercises and Mathematicks made Easie went through numerous editions right down to the present.
As an instrument maker, globe maker and printer Joseph Moxon was, like Elias Allen and Ralph Greatorex, part of the adhesive that turned a group of scientific researchers into scientific community but with the continued emphasis on big names and big discoveries in the history of science, people like Joseph Moxon don’t get the acknowledgement and recognition that they deserve.
1023 days ago, I posted the first episode of this series tracking the development of physics from Aristotle’s τὰ φυσικά to the point where the term physics began to be used. Now in the sixty-fourth episode we have finally reached our destination. In that first episode I took a look at the term physics its origins in Aristotle’s Greek and how it changed down the centuries until it first emerged with its modern meaning in 1715.
Although there is no link, the emergence of the term physics in its modern meaning is with certainty related to the publication of Newton’s Principia. Of course, Newton’s tome proudly contains the term Philosophiæ Naturalis (Natural Philosphy) in its title but it’s the other half of the title that is new Principia Mathematica (Mathematical Principals). For Aristotle ta physika, the description of nature, could never be mathematical. Numbers are not natural object so, cannot be used to describe nature. Mathematics was confined to the so called mixed or subordinate sciences–astronomy, optics, statics–these are not natural philosophy. Newton’s description of nature is purely mathematical and this was one of the main points of criticism made by both Huygens and Leibniz. Newton’s gravity had no physical explanation.
Despite these apparent failings Newton’s mechanics slowly but surely became dominant, the accepted norm. When we today refer to everyday physics, non-relativistic mechanics, the sort that’s taught in school we refer to it as classical of Newtonian mechanics or physics. However, the modern physics referred to as Newtonian physics is not Newton’s physics.
The first thing that changed was that mathematicians on the continent replaced Newton’s extra created analytical Euclidian geometry with Leibniz’s calculus and then later the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). Unfortunately, in England out of a sense of national pride, although the mathematicians replaced the analytical Euclidian geometry they did so with the much more unwieldly Newtonian analysis with its dot notation. This led to the infamous Analytical Society campaign in Cambridge, Newton’s own university, to promote “the principles of d-ism as opposed to the dot-age of the university” in Charles Babbage’s wonderful pun.
Turning to the physics, Newton had woven together the astronomy concepts of Johannes Kepler (1571–1630) and Giovanni Alfonso Borelli (1608–1679), with the advances in mechanics made by Simon Stevin (1548–1620), Isaac Beeckman !588–1637), Galileo Galilei (1564–1642), Giovanni Alfonso Borelli, René Descartes (1596–1650), Christiaan Huygens (1629–1695) and others to create a unified terrestrial-celestial mechanics that explained mathematically all movement on the earth and in the heavens. However, despite the fact that he had modified and improved his masterpiece in the second (1713) and third (1726) editions, it was still by no means perfect. There were still grey areas that needed improvement. One was the theory of comets that as we have seen was significantly improved by the work Edmond Halley (1656–1742) in his 1706 publication.
Throughout the eighteenth century, people worked on improving, correcting, expanding the foundations that Newton had laid down in his Principia. Unfortunately, very little of that work took place in Britain, which became moribund in its reverence for Newton’s great achievement. In Switzerland, the Bernoullis and Leonard Euler (1707–1783) made significant progress, whilst in France the native-born Italian Joseph-Louis Lagrange (1736–1813) and the Frenchmen Pierre Simon Laplace (1749–1827), Adrien-Marie Legendre (1752–1833), Jean le Rond d’Alembert (1717–1783), Pierre Louis Maupertuis (1698–1759), and Émilie du Châtelet (1706–1749). What follows are very brief sketches of some of the major developments.
Daniel Bernoulli (1700–1782) incorporated the beginnings of the kinetic theory of gasses and hydrostatics into the more general mechanics. Perhaps most spectacular in celestial mechanics was Pierre Simon Laplace’s solution of the problem of the orbit of the Moon (one that Newton had failed to bring convincingly into his general theory of gravity) in his Exposition du système du monde (1796) without details, and more fully in his monumental five volume Traité de mécanique céleste (1798–1825), a work that can be regarded as the crowning glory of Newton’s celestial mechanics.
Two aspects of mechanics which were only beginning to emerge in the late seventeenth and early eighteenth centuries were energy and work. Newton had argued that kinetic energy, the energy released by a moving object on impact, was mv, where m was the mass and v the velocity of a moving object. Johann Bernoulli (1667–1748) and Leibniz had hypothesised that it was mv2 but without any real foundation for their claim. Willem s’ Gravesande (1688–1742) carried out a series of experiments in which he dropped steel balls into clay and measured the impact craters. Émilie du Châtelet took the results of his experiments and deduced theoretically that Leibniz was in fact right and E ≈ mv2. Work on the concept of energy continued throughout the eighteen and nineteenth centuries.
Work according to the modern definition is the energy transferred to or from an object via the application of force along a displacement. The term work was first used in 1826 but already in a letter to Huygens in 1637 Descartes wrote:
Lifting 100 lb one foot twice over is the same as lifting 200 lb one foot, or 100 lb two feet. (Wikipedia)
In 1686 Leibniz wrote in his Brevis demonstratio:
The same force [“work” in modern terms] is necessary to raise body A of 1 pound (libra) to a height of 4 yards (ulnae), as is necessary to raise body B of 4 pounds to a height of 1 yard. (Wikipedia)
The English civil engineer John Smeaton (1724–1792), famous for building the third Eddystone Lighthouse (1755–59) did experiments relating power (his term for work) and kinetic energy, and supporting the conservation of energy, which he published in 1776 in the Philosophical Transactions of the Royal Society, of which he was a member. He supported Leibniz’s mv2, which made him unpopular with the other Royal Society members. His definition of power was “the weight raised is multiplied by the height to which it can be raised in a given time,” which was very close to the definition for work introduced in the late 1820s by the French mathematician Gaspard-Gustave de Coriolis (1792–1843), who first used the term travail, the French for work in his Calcul de l’Effet des Machines (“Calculation of the Effect of Machines”)in 1829. He established the correct expression for kinetic energy, 1/2mv2, and its relation to mechanical work. The French engineer Jean-Victor Poncelet (1788–1867) independently introduced the term mechanical work and its relation to kinetic energy at around the same time.
In 1773, the French chemist Antoine Lavoisier (1743–1794) stated the law of the conservation of mass based on his own experiment. By the beginning of the nineteenth century a large part of the body of classical physics erected on Newton’s foundations was in place. However, although Newton had written one of the most important books on optics, had discussed magnetism as another example of action at a distance and a series of electrical experiments were carried out at the Royal Society during his period as president, these three areas didn’t become integrated into the main body of physics until the discovery of the electromagnetic spectrum by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879) in the middle of the nineteenth century. James Clerk Maxwell’s work developed by Oliver Heaviside into the famous four Maxwell’s Equations announced the beginnings of the fall of Newtonian physics and would lead the way to Einstein’s relativistic physics.
People send me books. Sometimes it is a publisher or an author sending me a review copy of a recent publication that I have requested. I’m actually still somewhat in awe of the fact that leading publishers of history of science books are prepared to supply review copies for my humble blog, but am pleased that they do so. Sometimes its authors sending me copies of their latest tomes fresh off the press because I have helped them in some way with their emerging manuscripts; fact checking, providing feedback on a historical claim or whatever. Such volumes, always welcome, also tend to get thrown into the Renaissance Mathematicus review mill. Totally unexpected but always immensely pleasing is when someone sends me a book that they think I would appreciate simply because they like what I do.
One such was recently sent to me by Arjen Dijkstra, who is the director of Tresoar, Museum, Archive and Library Fryslân in Leeuwarden, and who specialises in the history of science. Arjen and I have never met but have been Internet friends for a number of years. The book he sent me is the English translation of a book he originally published in Dutch in 2021. It is the biography of an eighteenth-century, Friesian, amateur, mathematician and astronomer, who I had never heard of and the unbelievable planetarium that he built, which I had also never heard of; Builder of Heavens: How Eise Eisinga Created the Greatest Planetarium of his Time.[1]
Before I go into detail about this book a general comment. If I get asked what I do, if I’m answering in detail, I say, I’m a narrative historian of the contextual history of science or shorted, a contextual narrative historian. Dijkstra’s book is an absolutely first class example of contextual narrative history of science. One of the cover blubs sums it up perfectly, “It is best described as a scholarly novel.” Dijkstra’s book is fine quality but highly accessible literature, which is a pleasure to read, whilst at the same time it is obviously the product of high-level, detailed, accurate research without being obtrusively academic.
In the opening chapter we get introduced to Eisinga’s home town of Franeker in the province of Friesland and why it had a strong tradition of mathematics and astronomy in his time. We then get introduced to his family and their trade as wool combers and an explanation as to why wool combers have a down period every year where they can indulge their hobbies. Next we get Eise Esinga’s education and his introduction to mathematics. Having set the context, we get introduced to the star of the show, Eise Esinga’s planetarium. He quite literally, together with his father, turned the ceiling of his living room into the world’s biggest planetarium driven by clockwork in a period of just seven years.
In the succeeding chapters, Dijkstra takes us through the lives of the planetarium and its creator. This covers a wide spectrum of the contemporary Dutch academia and politics. The academics who became fascinated with Eisinga’s creation and their descriptions and promotions of it. The highly turbulent politics of the Netherlands during Eisinga’s life, which he became highly involved in both on a local and a national level. He became part of an attempted uprising, was forced to flee into exile and then tried and punished when he returned. Not the usual path through life of an amateur astronomy enthusiast. Along the way we get detailed descriptions of the planetarium, its inner life, and its functions.
Rehabilitated, his political movement now in power, Eisinga become even more politically involved, even sitting briefly in the national assembly. Parallel to his political rise, he and his planetarium become more and more popular reaching first national and then international fame. Eisinga dreams of building an even bigger, even more elaborate planetarium, drawing up detailed plans for its construction but which are never realised.
The planetarium was bought by the Dutch king for the nation, with Eisinga’s family given the right to continue living in the house for ever. In 2023, still a major tourist attraction the planetarium was declared a world cultural heritage by the United Nations.
The book is richly illustrated with grey tone prints, which includes many of Eising’s detailed plans for his planetarium. Following the acknowledgements, Dijkstra gives a detailed description of the sources he consulted to write his biography of Eise Eisinga. There is a Brief Biography, which is largely books in Dutch. The end notes are mostly the Dutch originals of quote given in English in the main text. The book closes with a competent index.
I have not gone into as much detail as I am wont to do in my book reviews because I didn’t want to spoil the joy for potential readers. I think this is a book of joy; I can’t remember when I last enjoyed reading a book as much as I did reading this one. If you are into the history of science, or history of astronomy, or history of technology, or eighteenth century Dutch history then this book is for you. If, however, you simply like to read well written, high quality, easy to read, non-fiction books that stimulate, entertain, and make curious this is a must read!
[1] Arjen Dijkstra, Builder of Heavens: How Eise Eisinga Created the Greatest Planetarium of his Time, Translated by Liz Waters, Noorboek, 2025
A caricature of my father done as a birthday card on his 71st birthday by my stepmother Rosemarie Simmons. He would die the following year of emphysema, hence the “Secretly indulges in oxygen” in the text. The original is approximately 3×2 feet.
It would be no exaggeration to say that the publication of Newton’s Principia was like a tidal wave swamping the European scientific community in the closing stages of the seventeenth century. Newton’s theories would dominate the discourse in both mechanics and astronomy till at least the middle of the following century.
Godfrey Kneller portrait of Isaac Newton 1689 Source: Wikimedia Commons
In his biography of Newton, Richard Westfall wrote:
Nevertheless, nothing had prepared the world of natural philosophy for the Principia. The growing astonishment of Edmond Hally as he read successive versions of the work repeated itself innumerable times in single instalments. Almost from the moment of its publication, even those who refused to accept its central concept of action at a distance recognised the Principia as an epoch-making book. A turning point for Newton, who, after twenty years of abandoned investigations, had finally followed an undertaking to completion, the Principia also became a turning point for natural philosophy.[1]
The advent of the book was not totally unexpected. Rumour had been ripe for much of 1687 and shortly before publication a long review appeared in the Philosophical Transactions of the Royal Society, who were after all the official publishers. The review was unsigned but it is known that Halley was the author. A fact that raises all sorts of ethical questions. The review, which summarises the Principia, begins:
The incomparable Author having at length been prevailed upon to appear in publick, has in this Treatise given a most notable instance of the extent of the powers of the Mind; and has at once shewn what are the Principles of Natural Philosophy, and so far derived from them their consequences, that he seems to have exhausted his Argument, and left little to be done by those who shall succeed him.[2]
Newton’s own copy of his Principia, with hand-written corrections for the second edition Source: Wikimedia Commons
The entire British mathematical community was eager to get its hands on a copy of this masterpiece and having done so rapidly discovered that it delivered an awful lot to chew on. John Locke (1632–1704), at the time of publication, a political refugee living on the European mainland, realised quickly that the mathematics was beyond him and so he asked Christiaan Huygens (1629–1695), whether the mathematics was sound. When Huygens answered in the affirmative, Locke proceeded to digest the propositions without the mathematical proofs.
Godfrey Kneller portrait of John Locke 1697 Source: Wikimedia Commons
Robert Hooke (1635–1703), who had loudly protested during the writing of the book that he should be acknowledged as the discoverer of the law of gravity, which almost drove Newton to abandon Book III, now seeing what he believed had been stolen from him protested even louder but simply got ignored.
Newtons book was greeted just as enthusiastically on the Continent as in Britain with lengthy reviews appearing in the spring and summer of 1688 in three of the leading journals: the Bibliothèque universelle in the Netherlands, the Journal des sçavans in France. And the Acta eruditorum in Germany.
The review in Bibliothèque universelle was purely a descriptive summary and was almost certainly written by John Locke. The Journal des sçavans stated that it presented “the most perfect mechanics that one can imagine” but fiercely rejected Newton’s physical concept–action at a distance. The Acta eruditorum devoted a total of eighteen pages to their review which warmly praised the book.
Halley had sent copies of the Principia to the leading natural philosophers on the Continent including Christiaan Huygens (1629–1695) and Gottfried Leibniz (1646–1716) both of whom were much impressed with Newton’s masterpiece but both of whom rejected the concept of action at a distance, Huygens called it absurd. However, he told his brother that he admired “the beautiful discoveries that I find in the work he sent me.”[3]
Huygens paid his respects to Newton when he visited London in 1689. From then on until his death in 1695 his correspondence with Newton was dominated by topics related to the theories presented in the Principia. The same is true of the correspondence between Newton and Leibniz. Their strong interest in all aspects of the Principia, which dominated their correspondence demonstrated that with its publication Newton had advanced to the highest rank of European natural philosophers.
Portrait of Christiaan Huygens by Bernard Vaillant (1686) Source: Wikimedia Commons
In his letters Leibniz insisted that gravity must have a physical cause in the form of an aethereal vortex ala Descartes, a concept that Newton firmly rejected.
Portrait of Gottfried Leibniz by Andreas Scheits Source: Wikimedia Commons
However, Newton was himself not at all happy with the concept of action at a distance as he wrote in a letter to Richard Bently (1662–1742) in 1692
That one body may act upon another at a distance through a vacuum without the mediation of any thing else…is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.
Newton played around with various concepts to account for gravity including a kind of aethereal explanation suggested by the Swiss mathematician, Nicolas Fatio de Duillier (1664–1753) and electricity. He finally adopted a kind of aethereal medium discussed in the Queries of the later editions of Opticks, which varies in density according to the matter of bodies located in it.[4]
Newton’s search for a physical cause for gravity was tied up with his aim to revise or even rewrite the Principia. The process that he had gone through in the three years between De motu and Principia of constantly rewriting, expanding and improving his ideas didn’t cease with the publication of the Principia. The book had only just left the printer when Newton began revising and improving it. He had two copies of the book, one of which even had blank leaves interspersed between the printed pages, in which he began to note changes, improvements, additions for a second edition. Although, it would be 1713 before this planned second edition would appear, edited by Roger Coates (1685–1716) the first Plumian Professor of Astronomy at Cambridge University of whom Newton said, “If he had lived we would have known something.”
I’m not going to list and/or analyse the various technical changes that Newton made to the second edition but I will address the General Scholium added to the end of Book III where Newton addresses the problem of the physical cause of gravity and delivers up one of his most famous quotes. The General Scholium opens with another explanation from Newton as to why the vortex theory is not necessary to explain the workings of the cosmos. This is followed by a defence of the fact that God created the cosmos; Newton’s system had come under criticism for its supposed religious implication. However, it is what comes next that interests us here:
Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centres of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances. Gravity toward the sun is compounded to the gravities towards the individual particles of the sun, and at increasing distances from the sun decreases exactly as the squares of the distances as far out as the orbit of Saturn, as is manifest from the fact that the aphelia of the planets are at rest, and even as the far as the farthest aphelia of the comets, providing that those aphelia are at rest. I have not as yet been able to deduce from phenomena the reason for these properties, and I do not feign hypotheses [ my emphasis]. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.
The emphasised phrase is, of course, the notorious Hypothese non fingo. What Newton is proposing here is a sort of provisional instrumentalism. He basically argues that I haven’t yet found the cause of gravity but it works mathematically so, I shall continue to accept and use it. He doesn’t exclude the possibility of eventually finding the cause. However, as is well known, or should be, a physical cause for Newton’s gravity has never been found and with time the successes of his theories led people to just ignore the fact that no cause had been found and to accept action at a distance as normal.
Another problem that readers of the Principia had was Newton’s mathematics. The widespread belief amongst those who have never read the book or even turned the pages is that Newton used analysis, of which he was, like Leibniz, one of those who produced a coherent system, to do his extensive mathematical work on motion. In fact, Newton had lost faith in the ability of analysis to provide undisputed mathematical proofs, so the whole Principia was composed and written in synthetic Euclidian geometry. However, traditional Euclidian geometry did not allow him to adequately model motion so, he devised a sort of analytical geometry, which he introduces as lemmas at the beginning of his work and then uses troughout the Principia. Even the leading mathematicians, such as Leibniz, had their problems with Newton’s innovations and both Leibniz and Jacob Hermann (1678–1733), a student of Jacob Bernoulli (1655–1705), translated Newton’s innovative geometry into Leibniz’s calculus.
Comets play a central role in Book III of the Principia the treatment of them taking up one third of the entire text. It was the demonstration that these apparently random visitors to the cosmos also obeyed Kepler’s laws of planetary motion and the law of gravity that sealed that claim that gravity was truly universal. Although, he had devoted so much time effort and space to the comets, Newton was still unsatisfied with his treatment of them. Following the publication of the Principia, he discussed this problem with Edmond Halley, who having already devoted time to the study of comets since the beginning of the 1680s offered to take on the task of further investigations. He did so, and the result of his investigations into the history of comet sighting led to his famous paper of 1705:
Portrait of Edmond Halley by Thomas Murray Source: Wikimedia Commons
Halley at first agreed with the longtime consensus that each comet was a different entity making a single visit to the Solar System. In 1705, he applied Newton’s method to 23 cometary apparitions that had occurred between 1337 and 1698. Halley noted that three of these, the comets of 1531, 1607, and 1682, had very similar orbital elements, and he was further able to account for the slight differences in their orbits in terms of gravitational perturbation by Jupiter and Saturn. Confident that these three apparitions had been three appearances of the same comet, he predicted that it would appear again in 1758–59
[…]
Halley’s predicted return date was later refined by a team of three French mathematicians: Alexis Clairaut (1713–1765),Joseph Lalande (1732–1807), and Nicole-Reine Lapaute (1723–1788), who predicted the date of the comet’s 1759 perihelion to within one month’s accuracy. (Wikipedia)
The successful prediction, based on Newton’s theories, of the return of what is now known as Comet Halley was a central factor in the victory of the Newtonian theories over the competing theories of the Cartesians. The other major victory concerned the debate over the shape of the Earth. Newton argued that the Earth was an oblate spheroid, flatted at the poles and bulging at the equator. Jean-Dominique Cassini and his son Jacques, both Cartesians, argued, based on measurements of a meridian, that the Earth was a prolate spheroid. Expeditions sent out by the French Academy of Science to Lapland and Peru to determine the length of one degree of longitude proved Newton right and the Cassini’s wrong. Both of these Newtonian victories in the middle of the eighteenth century led to a general acceptance that the cosmos was Newtonian.
As well these major scientific victories there was a second front working away to establish Newtonian mechanics against its Cartesian opponents that might be termed disciples spreading the Newtonian gospel. The Principia is for the normal human being impenetrable, a fact that is summed up by the, probably apocryphal, story about two students walking in Cambridge and spotting Newton on the street. “‘There goes a man,’ one of them said, ‘who writt a book that neither he nor anybody else understands.’” The following people made that impenetrable and the theories it contained accessible for a much wider range of people.
The first of those disciples were the Netherlander Willem ‘s Gravesande (1688–1742) and the French-born Englander John Theophilus Desagulier (1683–1744). ‘s Gravesande studied law at the University of Leiden whilst developing his interest in mathematics and astronomy, graduating with a doctorate in 1707. In 1715 he visited England with a Dutch delegation sent to welcome the Hanoverian succession in England. He met both George I and Isaac Newton and was elected a member of the Royal Society. In 1717, he was appointed professor of astronomy and mathematics in Leiden. In this position he began publicly to promote the Newtonian theories. In 1720, he published his Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam (Mathematical Elements of Natural Philosophy, Confirmed by Experiments; or an Introduction to Newtonian Philosophy). In that book, he laid the foundations for the teaching of Newtonian mechanics through experimental demonstrations. He presented his work before audiences that included Voltaire, and Émilie du Châtelet. His book was highly influential well beyond the borders of the Netherlands.
Portrait of Willem ‘s Gravesande by Hendrik van Limborch Source: Wikimedia Commons
John Theophilus Desagulier was born in La Rochelle. However, his parents, Huguenot refugees moved to London in 1692. In 1705, he entered Christ Church College, Oxford graduating BA in 1709. He had attended lectures by John Keill (1671–1721) an inner circle Newtonian, who promoted Newtons work in lectures and experimental demonstrations. When Keill left Oxford in 1709, Desagulier continued his program of lectures and demonstrations, obtaining his MA in 1712. Having graduated he moved to London and began to offer public lectures in experimental philosophy, offering them in English, French and Latin. He was very successful holding over 140 courses of about 20 lectures per course on mechanics, hydrostatics, pneumatics, optics, and astronomy. In 1714, Newton had Desagulier appointed as demonstrator at the Royal Society, as successor to Francis Hauksbee (1660–1713). In this role he continued to support an experimental Newtonian science after Newton died and Hans Sloane (1660–1753) became president of the society. In 1720, the year it was published, Desagulier produced an English translation of ‘sGravesande, Willem, Mathematical Elements of Natural Philosophy Confirmed by Experiment, or an Introduction to Sir Isaac Newton’s Philosophy (London, 1720).
Portrait of John Desagulier after Hans Hysing Source: Wikimedia Commons
France was, of course, solidly Cartesian and on both sides not a little nationalism played a role in which system of science people supported. However, there was one small centre of Newtonism in Cirey-sur-Blaise the country seat of Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (1706–1749), led by her lover François-Marie Arouet better known as Voltaire (1694–1778), writer, historian, philosopher, satirist. The two were actively supported in their Newtonism by the polymath Pierre Louis Moreau de Maupertuis (1698–1759), who led the expedition to Lapland to measure the length of a degree of arc of the meridian, which led to one of the major victories of Newton’s theories over those of Descartes, as already noted above. Also, by Alexis Clairaut (1713–1765) the mathematician and astronomer, who accompanied Maupertuis to Lapland and who played a central role in the recalculation of the return of Comet Halley, the other major victory of Newtonism.
Nicolas de Largillierre, portrait of Voltaire Source: Wikimedia Commons
Voltaire had spent the period from 1726 to 1729 exiled to England and in 1733 he published his Letters concerning the English Nation in English and in French the following year. The twenty-four letters were a wide-ranging account of various aspects of English culture, society and government. Four of them dealt with various aspects of Newton’s work:
Letter XIV: On Descartes and Sir Isaac Newton
Letter XV: On Attraction
Letter XVI: On Sir Isaac Newton’s Optics
Letter XVII: On Infinites in Geometry, and Sir Isaac Newton’s Chronology
In 1738, Voltaire published Éléments de la philosophie de Newton (Elements of the Philosophy of Newton) coauthored with Émilie du Châtelet, as noted above both had been introduced to Newton’s science by Willem ‘s Gravesande. This was an extensive, detailed exposition of Newton’s work written in simple language. A second edition in 1745, was prefaced by a section on Newton’s metaphysics which Voltaire had originally published separately in 1740. Historian of science, Charles Coulston Gillispie (1918–2015) wrote:
Voltaire explained Newtonian science to the educated public more successfully than any other writer, perhaps because he took more pains to understand it.
Émilie du Châtelet wrote and published her own original Institutions de physique (Lessons in Physics)(1st ed., 1740; 2nd ed., 1742) combining the work of both Newton and Leibniz. This was translated into both German and Italian. In 1749, she completed her translation with extensive commentary of Newton’s Principia into French. It was published in 1759.
Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet (1706-1749) Source: Wikimedia Commons
In Italy Francesco Algarotti (1712–1764) published his Neutonianismo per le dame (Newtonism for Ladies) dedicated to Bernard Le Bovier de Fontenelle (1657–1757) in 1737 – a work consisting of information on astronomy, physics, mathematics, women and science and education, which despite the title was actually addressed to the general reader. This was translated into English in 1739 also into French and German.
Francesco Algarotti portrait by Jean-Étienne Liotard Source: Wikimedia Commons
Portrait of Martin Folkes by John Vanderbank Source: Wikimedia Commons
Folkes went on a grand tour of Europe between 1732 and 1735 preaching the gospel of Newton to learned societies and individual savants, in particular demonstrating those of Newton’s optical experiments that others had had difficulty replicating.
From Anna Marie Roos, Martin Folkes (1690–1754): Newtonian, Antiquary, Connoisseur, OUP, Oxford, 2021
Thanks to the efforts of all of these people and other lesser lights by about 1750, Newtonian physics and astronomy had come to totally dominate Europe.
[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP, ppb. 1983, p. 469.
[4] Isaac Newton The Principia, Mathematical Principles of Natural Philosophy, A New Translation by I. Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia by I. Bernard Cohen p. 62
Henry Frederick Stuart eldest son of James VI of Scotland (1566–1625) and Anne of Denmark (1574–161), heir apparent to the throne of Scotland was born in Stirling Castle in 1594. Her was named after his grandfathers Henry Stuart (1564–1567), second husband of Mary Queen of Scots (1542–1587), and Frederick II of Denmark (1534–1588), patron of Tycho Brahe (1546–1601). When James and Anne married they paid a visit to Tycho’s observatory Uraniborg on the island of Hven in 1589.
Henry Prince of Wales c. 1610 after Isaac Oliver Source: Wikimedia Commons
Henry was kept separate from his mother and brought up by foster parents in Sterling Castle. Here his extensive and wide-ranging education began, which included various sports, music and dancing. In 1603, James acceded to the throne of England becoming James I of England and Henry soon followed him to England where he would become Duke of Cornwall and Prince of Wales and was now heir apparent to the thrones of England and Scotland.
His education continued, James directing that Henry’s household “should rather imitate a Collage than a Court.” Thomas Chaloner (1559–1615) was appointed governor of Prince Henry’s household which he described in 1607, “His Highness’s household […] was intended by the King for a courtly college or a collegiate court.” (Wikipedia) as already noted, his education was wide-ranging. As a teenager Henry developed a passion for geography, believing, as opposed to his father, in Elizabethan idea of the establishment of colonies and the creation of a British Empire, as first propounded by John Dee (1527–1609) and further promoted by Richard Hakluyt (1553–1616). In the same vein, Henry took a strong interest in naval and military affairs, which he studied from a young age.
Monument to Sir Thomas Chaloner in St Nicholas Church, Chiswick Source: Wikimedia Commons
In 1604, Charles Howard, Earl of Nottingham and Lord High Admiral (1536–1624) introduced Prince Henry to the shipwright Phineas Pett (1570–1647):
Phineas Pett artist unknown Source: Wikimedia Commons
Pett made a miniature ship for the Prince at Chatham. The keel was 28 feet and the breadth 12 feet, and was finished “battlement-wise” like the Ark Royal. On 22 March Pett presented the ship to Prince Henry, who named it the Disdain and “entertained it with great joy, being purposely made to disport himself withal.” On 26 April 1604, James I of England gave Phineas, described as a servant of Prince Henry, a grant of a shilling a day.
[…]
In 1607, Pett made and gave a model of a ship intended for Prince Henry to Howard. Howard thought the model good enough for the direct attention of King James and the Prince. He arranged for a presentation in the presence of both atRichmond Palace on 12 November 1607. The model was set up in a private room off the Long Gallery, in an arched frame curtained with crimson taffeta. King James being likewise impressed and “exceedingly delighted with the sight of the model” placed the task of constructing a full-size replica of the ship in Pett’s charge. (Wikipedia)
Henry’s introduction to the world of exploration, discovery, and colonisation began at an early age. His mother took him with her to visit Walter Raleigh (c. 1553–1618) during his incarceration in the Tower of London. Raleigh told the young prince tales of his voyages. Raleigh also wrote his most famous book, The Historie of the VVorld / In Five Bookes for the prince beginning in 1607. However, it was first published in 1614 two years after the prince’s death. It is thought that Raleigh’s Discourse on the Invention of Ships and his The Maxims of State were also written for Henry. Henry argued publicly against the wishes of his father James, who had imprisoned him, for the release of Raleigh.
Sir Walter Raleigh artist unknown Source: Wikimedia Commons
Raleigh’s cousin, the sea captain, poet, translator and courtier, Sir Arthur Gorges (c. 1569–1625) dedicated his A larger Relation of the … Ilsand Voyages, a detailed, firsthand account of the 1597 naval expedition against Spain, led by the Earl of Essex, to Prince Henry. Written in about 1607, it was first published as part of the Hakluytus Posthumus or Purchas his Pilgrimes by Samual Purchas (c. 1577–1626) in 1625 but without the dedication. Gorges also dedicated two poems to the prince.
Gorges was a friend of the mathematician and astronomer Thomas Harriot (c. 1560–1621), who was Raleigh’s navigational advisor and took part in the expedition to found the colony of Roanoke Island in Virginia in 1585. Harriott’s only publication during his lifetime was his A Briefe and True Report of the New Found Land of Virginia, published in 1588.
Harriot was part of a group of mathematicians that included, Sir Thomas Aylesbury (1576–1657), a patron of mathematical learning, who counted Walter Werner (1563–1643), like Harriot a part of the entourage of Henry Percy “The Wizard Earl” (1564–1632), and Thomas Allen (1542–-1632), teacher of mathematics at Trinity College Oxford amongst his beneficiaries. Harriot bequeathed his papers to Aylesbury, who with Warner was involved with the posthumous publication of Harriot’s Artis Analyticae Praxis in the 1620s. Also in this group were the astronomer Sir William Lower (1570–1615), Sir John Harrington (1592–1614), a courtier at Henry’s court and his friend, who was educated with him, and last but by no means least the mathematician, cartographer, and navigational expert Edward Wright (1561–1615). It is highly probable that members of this group would meet for discussions in Henry’s court.
Harriott and Wright were probably the two most accomplished mathematical practitioners in England at the beginning of the seventeenth century. As well as serving Henry Percy, 9th Earl of Northumberland at Syon House in Middlesex, he acted as a personal tutor in practical mathematics and geography to Henry at his court in Richmond.
Like his colleague Harriott, Edward Wright also acted as a personal tutor in practical mathematics and geography to Henry but for a much longer period and was obviously much more involved with the young prince. He dedicated the second edition of his important and highly influential Certaine Errors in Navigation, Detected and Corrected with Many Additions that were not in the Former Edition… to Prince Henry in 1610.
Cover of Wright’s Certaine Errors second edition 1610 Source
Earlier, when he had first taken up the post of tutor, Wright
caused a large sphere to be made for his Highness, by the help of some German workmen; which sphere by means of spring-work not only represented the motion of the whole celestial sphere, but shewed likewise the particular systems of the Sun and Moon, their circular motions, together with their places, and possibilities of eclipsing each other. In it was a work by wheel and pinion, for a motion of 171000years, if the sphere could be kept so long in motion.[1]
Henry also received tuition in other scientific disciplines. For example, Thomas Chaloner, the court’s governor was a naturalist and chemist. One of Henry’s tutors was John Lumley, 1st Baron Lumley (c. 1533–1609), who founded together with Richard Caldwell (1505?–1584) the Lumleian Lectures on anatomy and surgery at the College of Physicians in London. Lumley was a collector of art and books and was reputed to have possessed one of the largest libraries in England. When he died he bequeathed his library to Prince Henry, who appointed Edward Wright as librarian. Unfortunately, Henry died before Wright could take up the post.
Another leading figure in the practical mathematics scene was William Barlow (1544–1625), the author of The Navigators Supply(1597). He made important contributions to the study of magnetism and significant improvements to both the mariners compass and the dip circle. Barlow was actually a full time Church of England cleric, whose scientific work was his hobby. In 1605, he was appointed tutor and chaplain to Prince Henry a post that he held until Henry’s death in 1612. Like Edward Wright, Barlow had mathematical instruments made for the Prince. Barlow dedicated the original manuscript of his second book, an account of William Gilbert’s work in English as the original in Latin was not accessible for simple mariners, to Thomas Chaloner in 1609. Chaloner managed to loose both the original manuscript and a second one that he had agreed to get published. The book finally appeared in 1616 after Chaloner’s death as 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, as part of a dispute Barlow was having with Mark Ridley (1560–c. 1624) over, who was truly Gilbert’s disciple. Chaloner might well have been responsible for Barlow’s appointment to Henry’s court.
In his role as royal patron Prince Henry became directly involved in the English exploration and colonisation endeavours in various ways. He was a patron of the East India Company, which was founded in 1600. In 1609, he obtained a patent for the explorer Robert Harcourt (1574?–1631) to revive Walter Raleigh’s exploration of Guiana from 1594 and described in his book The Discovery of Guiana (1596).
Harcourts account of his voyage to Guiana
Like many others in this period, Henry was convinced of the importance of finding a North-West Passage and as “Supreme Protector” of the Company of Discoverers of the North-West Passage, he sponsored the expedition of Sir Thomas Button (c. 1575–1634) in 1612 to attempt to find Henry Hudson (c. 1565–1611), who had disappeared in 1611 after being set adrift in the Arctic in a small boat by mutineers. Button also hoped to discover the North-West Passage but was unsuccessful in both undertakings.
Portrait of Thomas Button artist unknown Source: Wikimedia Commons
Around 1610, the settlement of Jamestown in Virginia was in a fairly poor state. Henry arranged “that Captain Thomas Dale (destined by the King of Great Britain to be employed in Virginia in his Majesty’s service) may absent himself from his company for the space of three years, and that his said company shall remain meanwhile vacant, to be resumed by him if he think proper.” He was sent with three ships to Jamestown arriving 19 May 1611. He acted as Governor for three and a half months in 1611 and again for two years between 1614 and 1616. In the intervening period he served as Marshall. Put simply he ruled the colony for five years. Expanding the colony he established the village of Henricus, named after his patron. The village was destroyed in 1622 but the name survived first in the city of Henrico established in 1634, then later as a shire and finally as Henrico County, Virginia, which still exists today.
Sir Thomas Dale (c. 1615), attributed Marcus Geerearts. Source: Wikimedia Commons
Henry died of typhoid in 1612 and one should not forget that he was only eighteen years old at the time. His strong interest in exploration and colonisation and his patronage of many of the leading figures in the practical mathematical community of the period automatically lead to speculation as to what he might have done had he lived to become king.
[1] Quoted from Lesley B. Cormack, Twisting the Lions Tale: Practice and Theory at the Court of Henry Prince of Wales, in Bruce T. Moran ed. Patronage and Institutions: Science, Technology, and Medicine at the European Court 1500–1750, pp. 67–83, quote p. 75.
When Newton had his exchange with Robert Hooke in 1679 concerning Hooke’s hypothesis on planetary motion it rewoke his interest in the topic, which he had dabbled in around 1664 and led to him constructing a quick demonstration that forces vary inversely as the square of the distance at the two apsides of an ellipse and then the same relation holds for every point on an ellipse. However, in typical style he showed this demonstration to nobody. Hooke’s visit didn’t provoke any further action on the topic.
Godfrey Kneller portrait of Isaac Newton 1689 Source: Wikimedia Commons
However, when Edmond Halley visited him in 1684 asked, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it.” and he replied, “it would be an Ellipse.” Halley responded by asking how he knew this and Newton said, “I have calculated it” almost certainly referring to the calculation from 1680. He didn’t give Halley the earlier calculation but instead sat down an wrote the nine page manuscript De motu corporum in gyrum ( On the Motion of Bodies in an Orbit) which:
Not only did it demonstrate that an elliptical orbit entails an inverse-squared force to one focus, but it also sketched a demonstration of the original problem: An inverse-square force entails a conic orbit, which is an ellipse for velocities below a certain limit. Starting from postulated principles of dynamics, the treatise demonstrated Kepler’s second and third laws as well. It hinted at a general science of dynamics of a projectile through a resisting medium.[1]
Having brought this manuscript to the attention of the Royal Society, Halley was naturally eager to see it published but Newton insisted on improving his initial effort and set about doing so, a process on very intensive work that would take him well into 1686 and would end with the publication of the first edition of his Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), which finally appeared in July 1687, a monumental work of several hundred pages that would fundamentally change the course of physics. This was not a straight expansion of the original nine page manuscript or the bringing together of preexisting material but the creation of completely new concepts in a process of increasing awareness of what was needed, and the writing of a work then abandoning it to start again not just once but several times. During the period from the autumn of 1684 until the spring of 1686, Newton abandoned all other activities in his life.
Newton started out by redrafting and expanding De motu. We know this because there are three surviving manuscripts of this work. One is the original that Halley took to the Royal Society and is archived there. The second is an exact copy of this made by Halley. The third manuscript is amongst Newton’s papers and is substantially different to the other two.
Like the original this starts with the definition of centripetal force which impels or attracts a body to some point regarded as a centre. So, the opposite of Huygens centrifugal force, which Newton acknowledges inspired the name that he chose for this new force. This is the first innovation that Newton brought into the discussion of motion and forces but was by no means the last.
We have become so used to Newton’s three laws of motion, which we get introduced to beginning in school physics lessons–although the modern versions that we get taught differ substantially from what’s presented in Principia–that we somehow think that they are obvious, natural or god given. However, if one follows Newton’s work in the 1680s one can see how he searched for and found them over various revisions. Following two definitions, the original De motu has four hypotheses of which the first would eventually become Newton’s first law, the principle of inertia. In his reworking of De motu, Newton demoted hypotheses three and four to lemmas, changed the name from hypothesis to law and added three new ones, making now a total of five laws. Only over time and various revisions did he whittle them done to the three laws for which he is famous.
As he worked, Newton became aware of two omissions from his original work the correction of which lays at the heart of the innovation presented in Principia. Up till Newtons time all of the theories of motion were what we now term kinematics, that is the study of motion without reference to mass or force. Newton turned kinematics into dynamics by introducing the concept of mass. As Wikipedia puts it: The fundamental principle of dynamics is linked to Newton’s second law. Which we now famously render as F= ma but in the original reads: A change in motion is proportional to the motive force impressed and takes place along the straight line in which the force is impressed. Mass, which Newton calls quantity of matter is defined in the very first definition in Principia: Quantity of matter is a measure that arises from its density and volume jointly.
As we all learned in school mass is constant whereas weight varies according to the force acting on the mass so, you have the same mass but weigh less on the Moon, with its lower gravity, than you do on Earth. It is thought that Newton was led to the necessity of a definition of mass by the experiments of Jean Richer (1630–1696), during his time in Cayenne, French Guiana (1671–1673), in which he determined, using a second pendulum, that the force of gravity on the equator differs from the force of gravity in Paris and consequently the weight of objects also varies.
Astronomical and gravimetric observations made on the island of Cayenne by Jean Richer, after an engraving by Sébastien Leclerc. Source: Wikimedia Commons
Newton’s other omission in the original manuscript of De motu is a complete lack of a concept of universal gravity. Over the months that he worked on his revision he began to examine the whole concept of attraction within the cosmos. To do so he asked the Astronomer Royal, John Flamsteed (1646–1719), for the observational data on the planets Jupiter and Saturn that were approaching a major conjunctions to determine how much they deviated from the ideal orbit predicted by Kepler’s laws due to mutual attraction, or perturbation. From Flamsteed he also acquired data on the great comet of 1680. Analysing the data, Newton now became convinced that all bodies attract each other with a force for which he continued to use the term gravity. For terrestrial motion he stopped using the term gravity and consistently used he own freshly coined term centripetal force.
Portrait of John Flamsteed by Thomas Gibson 1712
For his two innovations, Newton had turned to data from Richer and Flamsteed. This is an important aspect of the evolution of Principia out of the original De motu. Although he cut himself off from his everyday world to concentrate on his writing, he reached out by letter to Flamsteed and others to get data and other information that he required. In particular Edmond Halley became his errand boy, finding and supplying information that Newton would demand at regular intervals. Although Newton did most of the heavy lifting, Principia was anything but a solo effort.
Portrait of Edmond Halley by Thomas Murray c. 1690 Source: Wikimedia Commons
By November 1685, Newton had expanded the original nine page manuscript into two books with a total of around one hundred pages. This he named De motu corporum (On the Motion of Bodies). Book I frequently called Lectiones de motu (Lessons on Motion) covers his terrestrial dynamics and he actually submitted it to the university as his professorial lectures for 1684 and 1685. Book II dealt with celestial mechanics applying the physics developed in Book I to the cosmos. This was submitted as his professorial lectures in 1687 and published shortly after his death as De mundi systemate (The System of the World) in 1728. What we now have are the drafts of Books I and III of the Principia.
Newton went back to the grind stone and began revising and expanding the two books of this De motu corporum. Book I was developed into Book I and Book II was expanded into Book III of Principia. At the end of the original nine page De motu, Newton had included a brief section on motion in a resisting medium, a novum in the seventeenth century literature on motion. He now developed this giving the subject a full expansion and this became Book II of Principia.
As this final version began to take shape, Edmond Halley took on the role of editor and publisher on behalf of the Royal Society. Newton would send sections of the book to Halley, who would correct them then send them back to Newton. When they were both satisfied with the section, Halley would then take it to the printers, now correcting the galley proofs. As is well known, Halley also took on another responsibility. The Society had spent all the money available for book publications on De Historia Piscium (Of the History of Fishes) by Francis Willughby (1635-1672) and John Ray (1627–1705) in 1686, which failed to sell, leaving the Society unable to fund the publication of Principia. Halley ended up paying the cost of publication of Principia out of his own pocket.
Halley formally presented the finished first volume to Samual Pepys (1633–1703), the then president of the Royal Society, who gave his imprimatur on 30 June 1686, licensing the book for publication. The book finally appeared in summer 1687. Between November 1684 and the summer of 1687 Newton’s epoch-making work had grown through a series of transformations from a nine page manuscript into a five hundred page, three volume, printed and published book.
Newton’s masterpiece was intentionally anti-Cartesian. The prominent inclusion of mathematical as a qualifier for principles was a direct challenge to Descartes own Principia Philosophiae (Principles of Philosophy) from 1644 in which he outlined his own theory of the cosmos with its mechanical particle filled space and vortex theory. Book II of the Principia with its motion in a resistant medium, is the least read and least impactful part of Newton’s work but it closes with a proof that Descartes’ vortex theory doesn’t work.
It is important to note that there is a certain amount of irony attached to the fact that Principia was written for and published by the Royal Society. The Royal Society was solidly Baconian in its outlook. Natural philosophy should be utilitarian, developed for the good of mankind. There was nothing of this in the Principia a solidly abstract mathematical work. Bacon didn’t approve of mathematics either. Even worse, Bacon preached that natural philosophy should proceed inductively, the researcher collecting observed facts from which the hypothesis would eventually naturally emerge. Principia was instead strictly Aristotelian, a set of axioms from which the philosophy is developed deductively.
The initial reception of Newton’s monumental masterpiece was very mixed and very complex and will be the subject of the next episode in this series.
[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP, ppb. 1983, p. 404
I acquired the book under review here back in 2024 shortly after it was first published and having read it was astounded at how bad it actually was. I started to write a review but after much effort and more than 8000 words, I was about half way through and couldn’t take anymore. I put it to one side aiming to take it up again later, I never did. Recently on an Internet forum somebody asked if anybody knew the book and what they thought of it? I replied with my honest opinion that I thought it was crap and was asked if I had written a review of it. I replied with the explanation given above and the enquirer asked if he could read my unfinished review, as did several others. Having dug it out and reread it, I sent it to those who wished to read it. I have now posted it here to warn any other potential readers of those subpar tome. I will only point out that the chapters I haven’t reviewed here are just as bad as the ones I have reviewed.
Back in 2019, I decided to buy the highly praised debut book by Violet Moller, The Map ofKnowledge: How Classical Ideas Were Lost and Found: A History in Seven Cities (Picador, 2019). Typical of the promotion for this volumes was Peter Frankopan’s cover blurb:
A lovely debut from a gifted young author. Violet Moller brings to life the ways in which knowledge reached us from antiquity to the present day in a book that is as delightful as it is readable.
I have a lot of respect for Peter Frankopan so, I took the plunge. When I tried to read this highly praised volume, Frankopan was not alone in his gushing praise, I found it factually inaccurate and shoddy so I gave up. More recently an internet acquaintance asked me my opinion of the book and I said I wouldn’t recommend it. He then asked me why and I said, to be honest I have a negative view of the book but I can’t remember why! One evening I took it down from the shelf and reread parts of it and came to the conclusion that it was even worse than I remembered.
Given these facts, it might seem surprising that, when Violet Moller’s new book was launched, with similar fanfares, although nothing from prominent historians, I bought a copy. Given the title, I simply couldn’t resist, Inside The Stargazers Palace: The Transformation of Science in 16th-Century Northern Europe (One World, 2024). If I claim to have even a modicum of expertise in the history of science it is in The Transformation of Science in 16th-Century Northern Europe a topic to which a substantial percentage of this blog has been devoted over the last sixteen years. I wish I had resisted!
Moller sets out her intentions in a nineteen page Prologue: Before in which she explains, quite correctly, that substantial progress was made in advancing science in Europe in the sixteenth century before the seventeenth-century Scientific Revolution. She also correctly notes that these advances were still mixed up with the so-called occult sciences, astrology and alchemy. She writes:
The stars, or rather astronomy, will be our guide. This was the most prestigious of the mathematical disciplines, one that long played a leading role in the development of science in part because it was often the starting point for investigation of the natural world. People have always built places to observe, to enhance their understanding of the night sky.
And then:
In my last book, The Map of Knowledge, I followed three major scientific texts as they were transmitted and transformed in the Middle Ages , following them on a thousand-year journey through seven cities that ended in 1500. This is where we will begin, taking up where we left off and travelling to seven places north of the Alps where people studied the stars and made instruments in their quest to deepen their understanding of the world around them.
If Moller had actually delivered that which she outlines in this prologue in an accurate factual manner then this would have been a good book, unfortunately, she doesn’t. The book is littered with errors inaccuracies and an incredible amount of waffle. A couple of inaccuracies from this prologue to give a taste before we dive into the morass.
A central theme of the book is instruments and she writes:
By the second century CE, Ptolemy had an array of instruments at his fingertips, simple ones for measurement like quadrants but also more complex astrolabes and armillary spheres which could calculate and predict celestial activity.
Ptolemy did not have astrolabes. He uses the name for what we now call armillary spheres. Ptolemy’s armillary sphere was a large observational instrument, which was used to measure the positions of celestial object, as described in Book V of the Almagest, and was not used for calculations.
Throughout her book Moller seems to be obsessed with clocks and it starts in the prologue with the following:
Of all the astronomical instruments developed before the telescope, clocks were the most significant. Being able to accurately measure time had a profound influence on so many aspects of life, and a singular effect on the accuracy and potential use of astronomical observations. There had been clocks of various kinds for centuries; water clocks were popular in the Arab world and famously reached Europe when the caliph Harun al-Rashid sent one to the emperor Charlemagne – a classic example of one-upmanship masquerading as generosity.
Let’s quote Wikipedia:
Water clocks are some of the oldest time-measuring instruments. The simplest form of water clock, with a bowl-shaped outflow, existed in Babylon, Egypt, and Persia around the 16th century BC. Other regions of the world, including Indiaand China, also provide early evidence of water clocks, but the earliest dates are less certain. Water clocks were used inancient Greece and in ancient Rome, as described by technical writers such as Ctesibius (died 222 BC) andVitruvius (died after 15 BC).
[…]
Some water clock designs were developed independently, and some knowledge was transferred through the spread of trade. These early water clocks were calibrated with a sundial. While never reaching a level of accuracy comparable to today’s standards of timekeeping, the water clock was a commonly used timekeeping device for millennia, until it was replaced by more accurate verge escapement mechanical clocks in Europe around 1300.
Put simple medieval Europeans didn’t need to be told by Harun al-Rashid what a water clock was.
We move to the first of Moller’s ‘seven places,’ Nuremberg! If only I knew an expert on the history of science in sixteenth century Nuremberg, who could point out Moller’s errors. Moller doesn’t actually engage with the extensive and varied mathematical and astronomical culture of sixteenth-century Nuremberg but only presents potted biographies of Regiomontanus, who lived and died in the fifteenth century, Albrecht Dürer, Wenzel Jamnitzer and a purple prose section on Augsburg and the Fugger.
The chapter opens with a general account, which is OK, briefly discusses Hans Sachs’ The Book of Trades noting that it doesn’t contain an instrument maker, not surprising as it wasn’t a recognised trade, which she doesn’t mention. She then indulges her spleen for clocks by introducing Peter Henlein (1485–1542), she delivers a typical Moller nonsense:
In the early years of the sixteenth century Peter Henlein, a local artisan, made a small portable clock designed to be worn around the neck or fastened onto clothing—the first known watch, called a ‘living egg’ because of its shape and the miniscule steel cogs that turned inside it. Henlien’s workshop produced hundreds of these…
Henlein was indeed one of the first craftsmen to make small ornamental portable clocks which were often worn as pendants or attached to clothing and is credited with inventing the watch. He did not produce hundreds of these and he did not produce the egg shaped watches that became popular around 1580 twenty years after his death.
Enter Regiomontanus who also featured in her earlier book and it is interesting to note that her account of his wanderings between leaving Vienna in 1461 and arriving in Nuremberg in 1471 is highly inaccurate in both books but the two accounts also contradict each other! I’ll just stick to the new book.
Moller quotes Regiomontanus’ letter in which he explains his move to Nuremberg in 1471 “on account of the availability of instruments, particularly the astronomical instruments on which the entire science of the heavens is based, but also on account of the very great ease of all sorts of communication with learned men everywhere.”
She complains that Regiomontanus doesn’t receive the attention he deserves, “There is only one biography of him in English (translated from the German) and his presence in Nuremberg today is slight, although there is a small observatory named after him. I don’t quite know what Moller expects, although my friends at the highly active observatory will be pleased to have got a mention. I recently had a discussion on social media with other experts on the history of astronomy about producing a new Regiomontanus biography, which given his very broad pallet of activities would be a horrendous task. There are however numerous scientific papers on the various aspects of his life and work.
We get a brief sketch of his life up to his work with Peuerbach in which Moller calls Regiomontanus a Latinized ‘nickname’–it’s a toponym! She also fails to note that he was never called that, the name was first used by Melanchthon sixty years after his death. We then get the following:
Then in 1461, disaster struck – Peuerbach died suddenly, aged just thirty-eight. Regiomontanus had lost his collaborator and friend, at a time when astronomers were thin on the ground. Fortunately, he had met someone the year before who could help. Cardinal Johannes Bessarion … Regiomontanus must have felt he had entered the very gates of heaven when he entered when he arrived at Bessarion’s elegant house and saw the library.
Firstly, Bessarion’s name was not Johannes, it was Basilios. We get no mention of the fact that Bessarion had sought out Peuerbach to make new translation from the Greek of the Almagest, which he couldn’t do as he didn’t speak Greek but agreed to write an undated Epitome of the Almagest. Bessarion then invited him to return to Italy with him, Peuerbach accepted but only on the condition that Regiomontanus also went. So, Bessarion’s adoption of Regiomontanus into his familia was agreed before Peuerbach’s death. Moller tells us:
Regiomontanus taught Bessarion astronomy and mathematics , receiving tuition in Greek in return…
Bessarion did indeed teach Regiomontanus Greek but I know of no lessons in astronomy and maths for Bessarion. We get told:
He and Bessarion spent the next four years travelling around Italy together … In 1467 Regiomontanus was tempted back over the Alps by an offer from Matthias Corvinus, King of Hungary, whose recent victory against the Turks had left him in possession of several rare manuscripts. Unable to resist the prospect of new texts, Regiomontanus set off northwards to the Hungarian court in Buda, a rare beacon of humanism outside Italy.
Regiomontanus left Italy in 1465 and it is not known where he was for the next two years, so if he headed northwards when he went to Hungary is not known. He received no offer from Matthias Corvinus but travelled to Esztergom (German Gran) to the court of the Archbishop János Vitéz (c. 1408–1472) as a potential member of staff for the newly established University of Bratislava. Vitéz had earlier been a patron of Peuerbach’s and most probably wanted to engage Regiomontanus for his skills as an astrologer. Regiomontanus later transferred to Matthias Corvinus’ court in Buda. Corvinus did not have ‘several rare manuscripts’ but had established a royal library, the Bibliotheca Corviniana in 1465, one of the most renowned libraries in the Renaissance world, which had grown to about 3,000 codices, which included about four to five thousand various works, many of classical Greek and Latin authors. That is four times as large as the library of Bessarion that Moller waxes lyrical about over several pages.
Moller now tells us:
A few years later still in Matthias’ service, Regiomontanus wrote a letter to a fellow scholar at the University of Erfurt … This letter written in July 1471 is an invaluable source of information on his plans, … One of his priorities was to calculate new planetary tables based on his own improved observations; another was to set up a printing press to publish a selection of scientific works.
Moller then tells how valuable Regiomontanus’ time in Italy was and can’t resist, “Italy was the main beneficiary of manuscripts brought from Constantinople after it was taken by the Ottomans in 1453…” the flood of manuscripts out of Constantinople in 1453 is a myth. She adds, Occasionally he discovered manuscripts for himself…” Regiomontanus’ main occupation was to seek out and make copies of manuscripts for Bessarion.
We return to Matthias, “In 1471, King Matthias sent Regiomontanus to Nuremberg to work on a new set of astronomical tables based on new, improved observations.”
Actually, according to legend Regiomontanus was asked in Buda why astrological prognostication were so inaccurate, to which he replied because the astronomical data on which they are based is too inaccurate. He then requested permission from Matthias to leave Buda and travel to Nuremberg to carry out his programme of observations. The letter from July 1471, which Moller had actually quoted earlier in her narrative was actually written from Nuremberg, a fact that she quotes, where he had been living since 2 June at the latest.
Moller now rambles on extensively about Regiomontanus’ workshop, his famous Tradelist (1474), in which he announced the books he intended to publish, and his intention also to manufacture scientific instruments. In the early history of printing Regiomontanus’ Tradelist is a fascinating and interesting document and it is right to draw attention to it but Moller’s comments on his workshop are totally speculative as we know absolutely nothing about it. Although here Moller allows herself another blunder, she writes:
The list contains several works by Ptolemy, including his masterpiece on astronomy the Almagest, and Euclid’s foundational text on mathematics, the Elements (neither had been printed with their diagramsbefore [my emphasis])…
Neither had even been printed! The first Latin edition of the Almagest printed in 1515 and the first Greek edition in 1538. The first edition of the Elements was that of Ratdolt in 1482.
Moller quotes from the Tradelist, “There shall be made also astronomical instruments for celestial observations,” leaving out the next sentence, “And also other things for common daily use, the names of which it would be tedious to relate.” She then goes on to say:
“In this period, if you wanted an astrolabe, you either had to make on yourself using a manual, or specifically commission one from a goldsmith. There were no dedicated instrument shops, but as scholarship spread in Europe, more and more people became interested in measuring the stars, transmuting metals, and distilling tinctures. As the demand for astrolabes, glass vessels and other specialist equipment rose, people started making them to sell, setting up centres of production to cater for the new market. … Regiomontanus was a pioneer in this field…
Unfortunately for Moller, and her glorification of Regiomontanus the instrument maker, when he moved to Nuremberg there were already many workshop producing astronomical instruments, which is one of the two reasons he moved there, as he wrote in that letter from July 1471, which she quotes six pages earlier:
Quite recently I have made [observations] in the city of Nuremberg…for I have chosen it as my permanent home, not only on account of the availability of instrument, particularly the astronomical instrument on which the entire science of the heavens is based…
Apparently she doesn’t actually read what she writes! Nuremberg would continue to be the major centre for the production of scientific instruments until at least the middle of the sixteenth century.
Moller tries to present the printer publisher, Regiomontanus, as some sort of highly influential role model in the history of scientific publishing but, although he was the first scientific publisher, there is little or no evidence that he influenced anybody apart from Erhard Ratdolt. Moller, of course, tries to push the story that Ratdolt learnt printing working for Regiomontanus in Nuremberg but there is absolutely no factual evidence for this theory. I argue that given the impact of Regiomontanus’ Ephemerides and Calendaria, and his reputation as an astrologer, that if Ratdolt had learnt his trade from him he would have loudly announced the fact, when he set up his own publishing house in Venice.
Moller’s obsession with clocks come out with another quote from the Tradelist, “The Tradelist mentions of a planetarium or astronomical clock being made in the workshop, ‘a work clearly to be gazed upon as a marvel’… The actual quote, “In the workshop of the artisan a planetarium is under continuous development. A work clearly to be gazed upon as a marvel” makes no mention of an astronomical clock and a planetarium is not an astronomical clock.
Following Regiomontanus’ death, Moller gives out another piece of ahistorical garbage, she writes:
Mathematical printing continued, and in the following decades the city became a flourishing centre with Regiomontanus’ own De Triangulis (1533), Copernicus’ DeRevolutionibus (1543) and Cardano’s Ars Magna testament to ‘Regiomontanus’ importance, not only as a mathematician and astronomer, but also as a publicist a publicist and architect of the renaissance of mathematics.’ (The quote is from Paul Rose’s The Italian Renaissance of Mathematics p. 109).
All three books were published by Johannes Petreius, who had nothing to do with Regiomontanus’ efforts as a printer/publisher, but who had learnt the printing trade from his uncle Adam Petri in Basel before moving to Nuremberg in 1523 almost certainly to try and fill the gap left by the death of Anton Koberger. Moller never mentions Petreius the most important scientific publisher in Europe in the first half of the sixteenth century or Koberger, who started printing in Nuremberg a year before Regiomontanus and was in the last decades of the fifteenth century and the first decades of the sixteenth, the biggest printer publisher in the whole of Europe.
Moller now moves on to Regiomontanus’s partner in Nuremberg, Bernhard Walther and the house he purchased, when he retired in 1501. When I read what she now wrote I didn’t know whether to laugh or cry:
He had two windows and a balcony built onto the top floor of the southern gable and installed his instruments there, creating a modest, yet ground-breaking observatory – the first identifiable one in northern Europe.
Actually, Walther added the entire third floor to the building. I will show you a picture of his balcony to explain my reaction!
Walther House with Observatory Window in the south gable Photo: Nora Reim Source: Astronomie in Nürnberg
As you can see it is actually a stone window sill on which he supported his instruments when making observations. It is probably less that a metre long and maybe thirty centimetres wide at its widest point. Moller, who obviously not done the necessary research seriously thinks Walther built a balcony because later when discussing the observatory of Wilhelm IV of Hesse-Kassell, she wonders whether Walther’s balcony served as a role model for Wilhelm’s observing balcony.
She uses Walther’s house to introduce Albrecht Dürer, who bought the house in 1509, because it had been Walther’s house, and it is today a museum dedicated to Dürer. After a couple of introductory lines of biography Moller send Dürer off on his traditional journeyman years of travel and then writes:
When he returned to marry Agnes Frey, the daughter of a wealthy brass maker, he was a master of copperplate engraving, an almost unknown art in Nuremberg.
Copperplate engraving was an almost unknown art everywhere. Also, when Dürer returned to Nuremberg in 1494 he was anything but a master in the art but a shaky beginner. There are three small copperplate prints from that year that are very obviously the work of a beginner. Also, he didn’t learn the art during his journeyman years of travel. Copper plate engraving was invented by gold smiths and Dürer certainly learnt the art in his father’s workshop. Moller now tackles his first journey to the south, which she following the tradition went to Venice. Modern research doubts that on that first journey Dürer ever left Germany. However, Moller writes:
There were many reasons for him to visit the magical city on the lagoon, but high on the list must have been visiting its printing presses and gathering expertise and contacts for the venture he was about to launch in Nuremberg.
The knowledgeable reader must ask himself at this point, why would Dürer visit Venice to look at printing presses, when by 1595 his godfather Anton Koberger was the biggest printer publisher in Europe. Koberger had printed the Nuremberg Chronicle in 1593, which is full of woodblock prints from the workshop of Michael Wolgemut, Dürer’s master! From Koberger and Wolgemut, Dürer could and did learn everything he needed to know about setting up a print workshop.
We now get a piece of arrant bullshit:
The workshop gave Dürer control, just as it had Regiomontanus. Here he was able to oversee every stage of his cultural output, from initial design to finished painting or print. Dürer’s success in this endeavour, along with the house’s preservation, give us unprecedented access [my emphasis] to one of the most important and innovative workshops, there has ever been. It is a portal into the sixteenth century and the life of Albrecht Dürer.
All leading Renaissance artists set up their own workshops giving them control. Whilst in detail different, Dürer’s workshop was no more innovative that those of Lorenzo Ghiberti (1378–1455), Andrea del Verrocchio (c. 1435–1488), Leonardo’s master, or Dürer’s own master, Michael Wolgemut (1434–1519), who taught Dürer the art of woodblock printing and introduced him to the concept of selling prints individually, which Moller seems to think Dürer invented. He turned the concept into big business but he didn’t invent it.
After a passage of purple prose about the workshop Moller delivers her next metaphorical history of art, pratfall:
Dürer was awestruck by the natural world, obsessed with studying and capturing it. In 1503, he turned his forensic gaze upon a patch of weeds, dug from the surrounding countryside and carried back to the studio where, using pen, ink and watercolour he produced an image of ground-breaking naturalism and beauty. Every plant in the Great Piece of Turf is identifiable, each blade of grass perfectly rendered. This study of nature is scientific in detail and accuracy. Even the roots and soil are shown; it is the first image of its kind.
The Great Piece of Turf is not a parch of weeds, dug from the surrounding countryside and carried back to the studio, it is an artificial construct carefully put together to create an illusion of realism, which is in fact hyper-realistic.
Moller keeps trying to forge a link between Dürer and Regiomontanus that simply didn’t exist. For example, she write:
Inspired by what he had seen in Italy and by Regiomontanus’ enterprise in Nuremberg…
She seems to think that because Regiomontanus set up a printing works in Nuremberg to print books in 1471 that Dürer was copying him when he set up an artist’s workshop in 1495 specialising in woodcut prints. Dürer had served his apprenticeship in the workshop of Michael Wolgemut, who specialised in woodcut prints!
The quote above has a bizarre footnote:
Dürer was a leading member of a circle of intellectuals who saw themselves as Regiomontanus’ successors, men like Walther, Willibald Pirckheimer, Johannes Werner and Johannes Schöner.
Apart from Walther, these men did not see themselves as Regiomontanus’ successors but had varied and complex backgrounds. Although Pirckheimer, Werner, and Schöner were all major scientific figures in Nuremberg during the period Moller covers , she makes no other mention of them or any attempt to describe their significant contributions to Renaissance science. Any non-expert reading her footnote would probably think, “who the fuck are they?”
After a couple of paragraphs of waffle about the importance of patronage, Moller now drifts off to write a five page gloss on the banking family the Fuggers of Augsburg in a chapter about Nuremberg. This ends in Antwerp where we then get the following:
Dürer, visiting in 1520 on his ill-fated mission to find a whale, noted that it was ‘constructed altogether new and at great expense, with a particular tower, wide and large, and with a beautiful garden’.
It would appear that Moller expects her readers to be fully informed about Dürer’s expedition to Zeeland to view a whale beached by a storm, because she gives no further explanation of this statement, except:
Dürer returned home to Nuremberg, weakened from an illness he had caught on his travels and disappointed he had neither secured Charles V’s patronage nor encountered a whale.
Dürer didn’t travel to the Netherlands to see a whale, that was simply an accidental opportunity that occurred whilst he was there. He travelled because the Holy Roman Emperor Maximillian I had died in 1519 and with his death Dürer had lost his Imperial Pension. He travelled to the crowing of Charles V as emperor in Aachen to get his Imperial pension renewed , an endeavour in which he was successful. Apparently that news never reached Moller.
Before leaving Dürer, it is interesting to note that in a book with the subtitle, The Transformation of Science in 16th-Century Northern Europe Moller completely ignores the three maths book Dürer authored, Various Lessons on the Fortification of Cities, Castles, and Localities (Etliche Underricht zu Befestigung der Stett, Schloss und Flecken) (1527), Four Books on Human Proportion (Vier Bücher von menschlicher Proportion) (1528) and Four Books on Measurement (Underweysung der Messung mitdem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler) (1525). The latter was the first mathematics book printed in German and was translated into Latin and several major European languages. He also, together with Johann Stabius produced a world map. Most telling in a book which the author says, The stars, or rather astronomy, will be our guide, she completely ignore the fact that Dürer provided the images for the first ever in Europe printed star maps produced by Johann Stabius and Conrad Heinfogel.
We now get a page and a half devoted to the goldsmith Wenzel Jamnitzer, who moved to Nuremberg in 1534, who as Moller points out was famous for his delicate gold flower but also for his book on the theory of perspective Perspectiva corporum regularium (Perspective of the Regular Solids), which was illustrated by Jost Amman (1539–1591). He was also an instrument maker. Moller tells us:
In 1562, Jamnitzer commissioned a portrait of himself. However, unlike Amman’s goldsmith in the Book of Trades, he is not painted holding the tools of his trade. In his left hand is a silver conversion rule he made himself, designed to compare the weights of different metals; in his right a variable proportional compass – precise mathematical instruments rather than pliers of hammers.
What Jamnitzer is holding in his hands are the tools of his trade! She then goes onto give other examples of Jamnitzer presented with mathematical instruments. Then she writes:
In presenting himself as more than a craftsman, Wenzel was taking the mantle directly from Dürer, continuing his crusade to elevate the status of artists, scholars and artisans. His emphasis on the scientific aspects of his career shows how it was developing during the century, and with it, those who practiced it.
Jamnitzer was possibly the best goldsmith who worked in Nuremberg during the Early Modern Period but he was by no means the only one who designed and made scientific or mathematical instruments and not even the first to do so. Moller is here trying to claim some sort of special status for Jamnitzer that he simply didn’t have.
Moller closes this train wreck of a chapter with a quite frankly ludicrous claim.
Thanks to Regiomontanus, Dürer, and Jamnitzer, Nuremberg was the first place in northern Europe where the combination of commercial success and technological ambition came together to create a new world of knowledge, an inspiring example to others; the city remained a thriving centre of instrument making, but this example too was beginning to spread to other places.
Nuremberg was a major centre for the production of scientific instruments before Regiomontanus moved there; in fact, that’s one of the principle reasons he moved there. It is not known if Regiomontanus actually produced any instruments in Nuremberg. In terms of instrument made in Nuremberg, Jamnitzer was very much a late comer. Whilst Regiomontanus set standards for the quality of his scientific publishing, he general impact as a printer/publisher was minimal compared to the contemporary publishing house of Anton Koberger or in scientific publishing compared to the slightly later Johannes Petreius. Although commercially more successful, Dürer’s workshop was no different to that of his master Michael Wolgemut, from whom he learnt the art of making and marketing woodcut prints. In general Moller completely ignores the people who actually made Nuremberg the centre of a new world of knowledge, Erhard Etzlaub, Willibald Pirckheimer, Johannes Werner and Johannes Schöner, Georg Hartman, Johannes Stabius (not a resident but a frequent visitor), Johannes Neudörffer and, Thomas Venatorius, and many other minor figures.
Having right royally screwed the history of science of sixteenth century Nuremberg, Moller now takes us to the University of Louvain in the Spanish Netherlands. She opens with the arrival of a young John Dee in 1547 and tells us:
It’s hard to believe Dee would not have passed through Antwerp on his way to Louvain, which lies a few hours’ walk through the gently undulating countryside to the south-east.
Antwerp to Louvain is 43.5 kilometres as the crow flies so allowing for normal roads about fifty kilometres by road, it’s not exactly what I would describe as a few hours walk. After a lot of waffle about Antwerp, Louvain and the Spanish Netherlands we arrive at the University of Louvain, and Moller informs us:
When Dee arrived, Louvain University had been educating young men for a little over a century. Known as the ‘Athens of Belgium,’ [Really? Belgium didn’t exist then!] it had grown quickly and was now only second to Paris in reputation.
“…now only second to Paris in reputation?” I known an awful lot of European universities who would seriously dispute that claim. Apart from anything else Louvain only acquired a university library in 1636.
She continues:
Having completed the traditional BA degree, the three main MA subjects on offer were theology, philosophy and medicine.
On the medieval university the MA was a teaching qualification, qualifying the holder to teach undergraduates. The advanced study was for a doctorate and the three subjects were theology, law and medicine.
We get a lot of background detail about the history of the university till we arrive at Andreas Vesalius, who we are told studied in the arts faculty as an undergraduate without a date, it was from 1528 to 1532. “Before long he became he became interested in the family business,” which was medicine. Moller then delivers up the story about Vesalius and Gemma Frisius stealing bits of a skeleton from a gibbet in 1536. Somehow she neglects to mention that Vesalius left Louvain to study medicine in Paris between 1533 and 1536, only returning to Louvain because of armed hostilities.
We now get brief sketches of the life stories of Gemma Frisius and Gerhard Mercator. We are already eight pages into the chapter when finally on page nine we finally get something from the history of science:
In 1529, aged twenty-one and just one year after graduating his BA, he published a new edition of Peter Apian’s astronomical manual of 1524, Cosmographia, ‘carefully corrected and with all errors set to right, by Gemma Frisius’.
So far so good but the title is Cosmographicus liber not Cosmographia and it is not an astronomical manual, it’s a cosmography manual as the title says, which means it covers astronomy, astrology, geography, cartography, navigation, surveying, instrument making etc. Moller continues:
Gemma Frisius had arrived, and from that moment on, the eyes of Europe looked to the Low Countries for progress in geography, cartography, and astronomy.
Correct would be, with the publication of the second edition of Apian’s Cosmographicus liber by Gemma Frisius, Louvain became a new additional centre for progress in geography, cartography, and astronomy, in northern Europe alongside Nuremberg, Ingolstadt, Vienna, Tübingen, Basel and Paris. Moller sinks deeper in the mire:
Apian’s text is a layman’s introduction to astronomy, geography and mathematical instruments, which Frisius adapted to make it more even more [sic] accessible.
Written in Latin and highly technical, the Cosmographicus liber is hardly a layman’s introduction but a serious textbook forcosmography. Also, although Frisius expanded it, and would continue to do so over many new editions, he didn’t, in any real sense make it mor accessible.
Moller continues:
In a canny commercial move, he also began making instruments to sell alongside the text. There were very few workshops producing items like astrolabes and astronomer’s rings, while books like Cosmographia were introducing them to a wider audience, creating a new market.
Nuremberg had a large number of workshops producing mathematical and astronomical instruments, which Moller simply chose to ignore in her highly inadequate account of the city. Georg Hartmann (1489–1564) for example produced sundials, astrolabes, armillary spheres and globes. He was probably the most prolific astrolabe maker in Europe, as he was the first to introduce the serial production of the instrument. We return to Moller:
His next move was to design ‘a geographical globe with the most important stars of the celestial sphere’ – a combined terrestrial and celestial globe. He worked in collaboration with his friend Gaspar van der Heyden, a local goldsmith who did the engraving work.
[…]
He [Gaspar van der Heyden] had already made a globe in 1527 with the monk from Mechelen, Franciscus Monachus. The ‘gores’ (the petal-shaped segments on which the maps were printed before being pasted onto the globes) would have been printed at the publishers in Antwerp, but pasted and finished in the workshop where the spheres were made and inscribed, ‘Gaspar van der Heyden, from whom this work which cost much money and no less labour, may be acquire’.
Gemma published On the Principles of Astronomy and Cosmography, with Instructions for the Use of Globes, and information on the world and on Islands and Other Places Recently Discovered (like his first book printed in Antwerp) to go with the globe.
[…]
In the early sixteenth century, only a small number of workshops produced these marvellous objects [globes], usually engraved sphere of wood or metal made in commission for wealthy clients. The printing press made a new kind of globe possible, one that was made of two hollow hemispheres, usually of wood but sometimes papier mâché and plaster, glued together with the maps printed on gores and then pasted onto the surface. This type of globe was cheaper and easier to produce, enabling workshops to make theme in larger numbers for general sale rather than on commission, reducing the price and increasing their availability. Gemma saw the potential of this and ran with it. His combined globe, which was being produced in Louvain workshops by 1530, was the first of several that he designed, each one with improved geographical information which was constantly being updated by sailors and merchant returning to Antwerp from voyages.
There is an awful lot to unpack here. As far as we know the first cartographer to produce printed gores for a globe was Martin Waldseemüller (c.1470–1520), who made a very small globe, 12cm, of his famous world wall map, the first to use the name America, both in 1507. None of the globes have survived but four sets of gores are still extant.
Unlike his map, Waldseemüller’s globe had little impact and it was Johannes Schöner (1477–1547), one of those mathematical practitioners from Nuremberg, who Moller ignored, who is credited with the first serial production of printed globes. Schöner produced a 27 cm terrestrial printed globe in 1515. This was followed by a matching celestial globe in 1517. He established the concept of matching pairs of terrestrial and celestial globes and the way that they were mounted that remained a standard down to the end of the nineteenth century. Standards also adopted by Gemma Frisius and his pupil Mercator. The cartography of the terrestrial globe was clearly based on the Waldseemüller wall map and the only surviving copy of the wall map, now in the Library of Congress, was that owned by Schöner. In 1533, Schöner produced a new pair of terrestrial and celestial globes with updated cartography.
Although very few of Schöner’s globes have survived, they were made of papier mâché and plaster, we now from correspondence that they were very much in demand and that he sold comparatively many of them, throughout Europe. The celestial globe in Hans Holbein’s painting The Ambassadors, painted in London in 1533, is one of Schöner’s and the small terrestrial globe is at least based on Schöner’s work. Schöner also printed books on how to use his globes, Luculentissima quaedam terrae tortius descriptio (A Very Clear Description of the Whole Earth) for his terrestrial globe and Solidi et sphaerici corporis sive globi astronomici canones usum (Manual for the Use ofthe Solid Spherical body and Astronomical Globe) for his celestial globe.
The demand for Schöner’s globes was very high and he could not fulfil it. In the 1520’s the Antwerp printer publisher, Roeland Bollaert had Schöner’s books but couldn’t get any of his globes. It was he who commissioned Franciscus Monachus (c. 1490–1565) together with Gaspar van der Heyden (c. 1496–c. 1549) to produce a terrestrial globe together with a descriptive book De Orbis Situ ac descriptione ad Reverendiss. D. archiepiscopum Panormitanum, Francisci, Monachi ordinis Franciscani, epistola sane qua luculenta. (A very exquisite letter from Francis, a monk of the Franciscan order, to the most reverend Archbishop of Palermo, touching the site and description of the globe), which he printed in Antwerp, in 1524. None of the Monachus globes have survived.
In 1529, as Moller correctly pointed out Roeland Bollaert printed the second edition of Peter Apian’s Cosmographia as edited by the young Gemma Frisius. A year later he commissioned Frisius together with Gaspar van der Heyden to produce a new terrestrial globe and this is the globe that Moller describes as a combined terrestrial and celestial globe. For this Frisius wrote his De principiis astronomiae et cosmograpiae deque usu globi (Principles of Astronomy and Cosmography and the Use of the Globe), which was published by the Antwerp publisher Johannes Graheus. It is probably that Roeland Bollaert had died in the meantime. Monarchus had also acknowledged his debt to both Schöner and Peter Apian in his De Orbis Situ. None of these globes have survived.
This globe “the first of several that he designed”! In 1536, Frisius produced, in imitation of Schöner, a matched pair of terrestrial and celestial globes. One of each has survived but the terrestrial globe has lost its stand. Interestingly, Frisius’ celestial globe uses for the constellations the images created by Dürer for the Stabius/Dürer/Heinfogel printed star maps that Moller didn’t think worth mentioning. The globe from 1530 and the globe pair from 1536 were the only globes that Gemma Frisius produced. Moller claims the 1536 globe pair was commissioned by the Emperor Charles V, it wasn’t. Charles V granted him a patent which is something else altogether.
Gerard Mercator, who was a pupil of Gemma Frisius, provided the italic inscriptions on the globe pair from 1536, Moller informs us:
Mercator had already made several maps by this point and had begun to use an Italian cursive script called cancellerescato mark up place names.
Mercator’s earliest map, a wall map of the Holy land was produced in 1537 after he had finished work on Frisius’ globes.
Having dealt with the history of Frisius’ globe production I’ll go back to Moller’s description of his publication in 1533 of the appendix to the third edition of the Cosmographia explaining triangulation. This she manages reasonably well although her explanation of triangulation is a bit terse. She then ruins it with the following:
Triangulation made it possible, for the first time, to correctly locate places on a map, to capture the vast tracts of the planet and plot them onto the page to scale. The whimsical maps of the Middle Ages like the Mappa Mundi in Hereford cathedral, which its absence of geographical knowledge, presented a vision of the cosmos based on imagination and faith, were gradually replaced by accurate charts and surveys.
I politely suggest that Moller takes a course of study in the histories of surveying and cartography. Whilst triangulation, as described by Frisius, improved the accuracy of surveying, map makers had been producing reasonably accurate maps long before Frisius was born, using other methods of surveying. Some of those methods were actually described in Peter Apian’s Cosmographia that Frisius took over. The Mappa Mundi in Hereford cathedral is one is termed a philosophical map and serves a different function, namely that of presenting a philosophical, in this case Christian, world view. She then goes off the rails with:
Maps enabled geography (the description of the world based on observation and measurement) to gradually eclipse cosmography (the conception of the universe based on philosophy and conjecture), changing the way humanity saw the world and how to approach it as an area of study.
I really don’t know where to begin in dismantling this wonderfully wrong pair of definitions. Perhaps we could start with the book that Ptolemy wrote in the second century CE, his Geōgraphikḕ Hyphḗgēsis, lit. Geographical Guidance, which was titled in Latin in different edition both Geographia and Cosmographia. This was a collection of maps based as far as possible on observation and measurement, although it presupposed the philosophical assumption that the oecumene, i.e. Europe, Asia, Africa, constituted the entire world. Later the two words became distinguished, geography referring to what we now understand under the term, and cosmography referring to a description of the entire cosmos, which included geography as one of its constituents along with astronomy etc. Exactly that which Apian’s Cosmographia delivered.
There are lots and lots of examples of maps based on observation and measurement, as far as it went, between Ptolemy’s Geographia and the invention of triangulation.
We now get a lot of filler about how the workshops in Louvain might have appeared, we don’t actually know, then Moller makes the following categorical claim:
By the mid-1540s the workshops of Louvain were famous for producing the most accurate and most beautiful tools for studying astronomy that money could buy, eclipsing even the masters of Nuremberg.
This is hyperbolic hogwash. The instruments coming out of Louvain were indeed excellent quality but they did not eclipse the masters of Nuremberg.
We get nothing almost nothing from Moller about Mercator’s cartographical work, although he is without doubt the most significant cartographer of the sixteenth century. We do get a longish account of his imprisonment on religious ground and then on his friendship with John Dee. Moller tells us that they spent their time discussing astrology. In this context she also claims:
“Astrology had been under attack for several decades; Mercator and Dee were keen to ground it on a more scientific basis and place it within Copernicus’ new cosmographical framework.”
Astrology was always under attack from somebody or other but I know of no special state of attack in the first half of the sixteenth century: Steven Vanden Broecke has this to say about those discussions as related by John Dee:
Except for the present disc, Mercator has left no explicit record of his attitude towards astrology prior to his departure from Louvain to Duisburg in 1552. An important indirect source, however, is John Dee’s Propaedeumata Aphoristica (1558), which is dedicated to Mercator. After graduating from the University of Cambridge, the English polymath, John Dee (1527±1608) made two study tours to Louvain, one in the summer of 1547 and a second from June 1548 until at least July 1550. Apparently Dee spent much of his second stay at Louvain `learning and philosophizing ’ with Mercator. The precise content of these discussions is clarified in the preface: `Your next to last letter, in which you seemed to wish to refresh my memory of that noble debate formerly carried on between us, has given me an occasion to choose, in preference to all others, that subject which I am now to treat.’
In other words, the topic of the Propaedeumata Aphoristica is the same as that of parts of Dee and Mercator’s debates at Louvain. Nicholas Clulee’s studies have established the Propaedeumata as Dee’s attempt to provide astrology with a firm physical and epistemological basis. In the common vein of Aristotelian natural philosophy, Dee explains that natural change is ultimately caused by celestial influence, adding the no less unexceptional conviction that such change is subject to a natural and predictable causality[1].
Traditionally Aristotelian, no mention of Copernicus!
Towards the end of the chapter Moller tells us:
Gemma died in 1555, and Mercator had left Louvain for the peace of Protestant Duisburg over the German border three years earlier, but the workshop continued to thrive under Gemma’s son Cornelius and his colleague Walter Arsenius. The number of instruments that survive suggest impressive production levels, and makers across the continent were influenced by the design and quality the city stood for, just as astronomers were enabled to make better, more accurate observations than ever before.
So much hogwash in one brief paragraph. Cornelius Gemma didn’t make instruments and in terms of the earlier comments on astrology in Louvain it is interesting to note that he shared in his father’s efforts to restore ancient Ptolemaic practice to astrology, drawing on the Tetrabiblos. What was that about Copernicus? Gualterus Arsenius, Gemma Frisius’ nephew, was the head of the family that actually produced the largest number of astronomical instruments in the Louvain workshop. The workshop was productive but no more or less so than other major European instrument workshops. The instruments from Louvain were no more accurate than those from earlier European workshops.
Moller ramps up the stupidity a couple of lines further on:
The expertise in designing evermore accurate instruments enhanced the quality of observational data, its usefulness and status. This strengthened the role of instruments in the scientific enterprise; today, technology is so integral it is no longer possible to draw a line between the two. Modern astronomy is cutting-edge technology, and the complex telescopes that empower us to see into the darkest corners of the universe have their roots in the workshops of Louvain, and the standards and ideals that were generated there.
This is in the favourite expression of my friend the HISTSCI_HULK pure hyperbolics. The instruments makers in Louvain did not create any new or novel instruments and although their quality was high, their accuracy was not greater than other astronomical instrument makers in the sixteenth century. Lastly astronomy had been the cutting-edge technology for its time since at the latest Ptolemy. To suggest that modern astronomy has its roots in the workshops of Louvain any more than in the workshops of Nuremberg, of medieval Baghdad, ancient Alexandria or first millennium BCE Mesopotamia is quite simply bullshit.
Having entered Louvain with the young John Dee, Moller now takes us back with him to his house in Mortlake, in those days a small parish on the Thames about ten miles to the west of the City of London. Moller wishes to present Dee’s house and its library as one of her “Stargazer’s Palaces”. As with so many people who write about Dee she emphasises his occult activities whilst almost totally ignoring his scientific activities. She mentions, quoting Dee, that when he returned from Louvain he brought globes and scientific instruments with him, pointing out their scarcity in England at the time. Then she tells us:
Globes were not produced domestically until the 1590s, so the only way to get one, or two (from 1551 onwards the publication of Mercator’s celestial globe to go with the terrestrial one of 1541 set the fashion for them almost always being sold in pairs [my emphasis]), was to import them from abroad.
Both Gemma Frisius and Mercator made matching pairs of terrestrial and celestial globes in imitation of Johannes Schöner, who “set the fashion for them almost always being sold in pairs.”
She mentions several times his financial problems and his difficulties in finding patrons/employment, whilst hardly mentioning his extensive, and historically very important, employment as an advisor and teacher of navigation, cartography etc. for the Muscovy Company amongst others. This is made even more bizarre, as she explains that Dee owned instruments designed by Richard Chancellor (c. 1521–1556). She writes:
Chancellor was a navigator who had been introduced to Dee by their mutual patron Sir Henry Sidney. He led voyages for the Muscovy Company which failed to find the Northeast Passage, but opened trade with Russia and took Chancellor to Ivan the Terrible’s court in Moscow.
She fails to mention that Dee, who worked as an advisor, teacher, and supplier of charts and instruments for ships masters and pilots of the Muscovy Company, was actually Chancellor teacher. He also wrote his The Astronomicall and Logisticall Rulesand Canons to calculate the Ephemerides to be used on the first Northeast Passage voyage, by Willoughby and Chancellor.
We now get a classic, Moller writes:
Sailors needed instruments, especially astrolabes to help them navigate…
To quote David King, leading historian of scientific instruments and one of the greatest living experts on astrolabes, “astrolabes were never used for navigation.” In case you think she was referring to mariner’s astrolabe, she continues:
…and one of these, now in a museum in Belgium, is engraved with Edward VI the Duke of Northumberland’s coats of arms. It was made in 1552 by Thomas Gemini, a founder of the instrument making trade in England, who was affected by the same religious persecution that pushed Mercator to flee Louvain and settle in the Protestant backwater of Duisburg.
We then get the “life stories” of Thomas Gemini, Leonard Digges, and Thomas Digges all in one page of the book. …
At this point, as noted above I broke off in frustration!
[1] Steven Vanden Broecke, Dee, Mercator, and Louvain Instrument Making: An Undescribed Astrological Disc by Gerard Mercator (1551), Annals of Science, 58, 2001, 219-240 p. 226
More than twenty years would pass between Newton’s awakening and his extraordinary period of learning in the mid 1660s and his finally putting pen to paper and writing the Principia. That period of his life is one that in popular history is full of myths and legends.
Godfrey Kneller portrait of Isaac Newton 1689 Source Wikimedia Commons
The whole period starts with a tangle of myths. There is a myth that Newton already had the concept of universal gravitation, the central element of his Principia, in the middle of the 1660s. Central elements of this are the apple story, both myth and legend, and the Annus mirabilis myth. I have dealt with the apple story in great detail here and am not going to repat myself. As I explained, also in great detail, the Annus mirabilis, in which it is claimed that in one year during the plague in 1665, the young Newton, he turned twenty-three in that year, basically discovered everything–calculus, optics, universal gravity–for which he later became famous. As I point out in my analysis this is total rubbish but the myth persists. In all of this, Newton himself is to blame because of claims that he made fifty years later:
In the beginning of the year 1665 … [claims about mathematics and optics]
And in the same year I began to think of gravity extending to ye orb of the Moon ] (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the centre of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of the distances from the centres about wchthe revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly.[1]
In his Waste Book, a large notebook inherited from his stepfather, during this period Newton, inspired by Descartes, made three geometrical determination of circular motion none of which is of particular importance. Of interest is that at this time he didn’t accept the law of inertia. However, these determinations led on to his comparison of the “endeavour of the Moon to recede from the centre of Earth” with the force of gravity at the surface of the earth. He found that gravity if somewhat more that 4,000 times as great. He also substituted Kepler’s third law (that the cubes of the mean radii of the planets vary as the squares of the periods) into his formular for centrifugal force [taken from Huygens]: “the endeavours of receding from the Sun [he discovered] will be reciprocally as the squares as their distances from the Sun.” Here was the inverse-square relation resting squarely on Kepler’s third law and the mechanics of circular motion.[2]
Newton’s elaboration, in old age, on what he had actually achieved in the 1660s was designed to silence his critics and to establish his priority for everything, at the time motivated by his dispute with Leibniz over the calculus. The comments on gravity were posthumously aimed at Robert Hooke (1635–1703) and Hooke’s claim that Newton had the concept of universal gravity from him. This goes back to an exchange from 1679, Newton in he meantime being occupied with teaching, mathematics, alchemy, and theology, having done nothing more on the question of gravity.
Following their bitter dispute over optics, Hooke having rudely dismissed Newton’s first paper from 1672, the two had had no contact. However, in 1679, Hooke now secretary of the Royal Society wrote to Newton to reestablish contact. He asked Newton if he was aware of his hypothesis on planetary motions as compounded of a tangential motion and “ an attractive motion towards the centrall body…”
Hooke was referring to a remarkable paragraph that had concluded his Attempt to prove the Motion of the Earth (1647, republished in 1679 in his Lectiones Cutlerianae). There he had mentioned a system of the world he intended to describe.
This depends upon three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the earth to do, but that they also attract all other Coeletial Bodies that are within the sphere of their activity … The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into Motion. Describing a Circle, Ellipsis, or some other compounded Curve Line. The third supposition is, That these attractive powers are so much more powerful in operating, by much how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified …[3]
Hooke is on the way to the concept of universal gravity but hasn’t arrived there yet. He is, however, obviously progressing past the concept that each planet has its own gravity, as expressed, for example, by Copernicus in De revolutionibus. His second supposition is obviously the principle of inertia and he correctly defines the dynamic elements of orbital motion. It is, however, important to note that whilst Hooke gives a good verbal account of his hypothesis on planetary motions he doesn’t provide a rigorous mathematical demonstration of it, and in fact never did. The difference between what Hooke achieved and what Newton would go on to do was summed up very neatly by Alexis Clairaut (1713–1765), after reviewing Hooke’s work, he wrote:
“what a distance there is between a truth that is glimpsed and a truth that is demonstrated”[4]
On the basis of this letter Hooke later claimed that he had given Newton the concept of universal gravitation. Newton countered by saying that Hooke’s letter had merely returned his thoughts to a topic that he had already thought through earlier. The exchange between the two disputatious scholars continued on the subject of how an object would fall from a high tower if the earth was moving. Newton made a mistake in his analysis of the case, which Hooke corrected, surprisingly mildly, and the exchange petered out.
We now arrive at the legend that supposedly led to Newton putting pen to paper and writing the Principia. This is the infamous coffee house meeting in London between Hooke, Christopher Wren (1632–1723) and Edmond Halley (1656–1742) following a meeting of the Royal Society in January 1684. I’ve described this in detail in an earlier post but I will give a brief summary here. The question raised during the conversation is, given an inversed squared law of gravity would this lead to Kepler’s elliptical planetary orbits and his three laws. Wren offered a prize of a book worth forty shillings–that’s two pounds and one should remember that ten pounds p.a. was a labourer’s wage–to the first to provide a demonstration that this was indeed the case. Hooke claimed that he already had the solution but would only reveal it when the other two had failed to find one.
In August, Edmond Halley travelled to Cambridge and visited Newton in his chambers. Whether he had gone there to specifically put the question to Newton or he was there on other business and took the opportunity to do so, is not known.
According the Newton’s account as told to Abraham DeMoivre many years later, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…”
Newton searched for this calculation but failed to find it but then promised Halley that he would send him the solution. Although Newton’s search seems like a charade, the claimed earlier solution really did exist:
Recently a copy of the demonstration has been identified. In it, began (as he later asserted) by demonstrating Kepler’s law of areas. Using the law of areas and accepting Hook’s definition of the dynamic elements of orbital motion, he showed first that the forces vary inversely as the square of the distance at the two apsides of an ellipse and then the same relation holds for every point on an ellipse. If the inverse-square relation initially flowed from the substitution of Kepler’s third law into the formula for centrifugal force under the simplifying assumption of circular orbits, the demonstration of its necessity in elliptical orbits far excelled in difficulty what had been a simple substitution. In fact, the demonstration, which probably dated from early 1680, was one of the two foundation stones on which the concept of universal gravity rested.[5]
In November of 1684, Halley received his solution in the form of the nine page manuscript De motu corporum in gyrum ( On the Motion of Bodies in an Orbit) brought to him by Edward Paget, a young fellow of Trinity College.
Not only did it demonstrate that an elliptical orbit entails an inverse-squared force to one focus, but it also sketched a demonstration of the original problem: An inverse-square force entails a conic orbit, which is an ellipse for velocities below a certain limit. Starting from postulated principles of dynamics, the treatise demonstrated Kepler’s second and third laws as well. It hinted at a general science of dynamics of a projectile through a resisting medium.[6]
Halley realised that he was in possession of a potential revolution in celestial mechanics. He immediately returned to Cambridge to talk to Newton about this treatise and on 10 December made a report to the Royal Society:
Mr. Halley gave an account, that he had lately seen Mr. Newton at Cambridge. Who had shewed him a curious treatise, De motu; which, upon Mr Halley’s desire, was, he said, promised to be sent to the Society to be entered upon their register.
Mr Halley was desired to put Mr. Newton in mind of his promise for the securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.[7]
Newton now set about revising his manuscript for publication with the same intensity and single mindedness that he had devoted to the study of the modern mathematics and sciences in the period between 1664 and 1670. The revision took the best part of three years and the final product the three volumes of his Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) finally appeared in July 1687.
Newton’s own copy of Principia with Newton’s hand-written corrections for the second edition, now housed in the Wren Library at Trinity College, Cambridge Source: Wikimedia Commons
[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP, ppb. 1983, p. 143
This is one of my occasional autobiographical posts and has nothing to do with the history of science so, if you come here just for that you can skip this post. I also chronicles the heavy use of psychedelic drugs so, if you have problems with that, once again you can skip this post.
On Saturday 7 March, the singer, songwriter, musician, and political activist, Joseph Allen McDonald, better known as Country Joe, died of complications from Parkinson’s in Berkeley California. Country Joe and his music wove their way through my life over many years and left strong traces in my development.
As I have documented elsewhere, my mother died under tragic circumstances of a heart attack at Christmas in 1966. My brother had already left home and was in fact already married and father of my eldest nephew. My two sisters, both older than me, left home in the summer of 1967 to begin their careers, leaving just me and my father in the family home. We left the village in northeast Essex, where I grew up, and moved to London where my father worked. He decided it would be better if my education was not interrupted and so I entered the boarding house of the grammar school in Colchester, where I had spent the first four years of my secondary education, in the autumn of 1967. To say that I was not a happy bunny would be an understatement and I slowly drifted ever more into a malaise, which ended with me getting expelled at the end of the academic year 68/69.
My father now got me admitted to Holland Park Comprehensive School the flag ship of the Labour Government’s comprehensive education policy. It counted both Stephen and Hilary Benn, the sons of Anthony Benn the notorious Labour politician, and the step children of Roy Jenkins, the future President of the European Commission, amongst its pupils. Also attending were Damien and Nico Korner the sons of blues musician Alexis Korner, who served as chairman of the PTA. The school was huge but had a comparatively small sixth form, of which I was now a member. Like myself many of the sixth formers had been expelled from other schools, many of them from notable public schools.
At this point in my life, I was living with my father and first step mother in Colville Place, which is just off Tottenham Court Road in the West End. Not long after I started at Holand Park one of my fellow students introduced me to DSK a crazy white Rhodesian Jew, his description, who had been expelled from both Westminster Public School and Holland Park, who lived not far away from where I lived, in Grape Stret, which is behind the Shaftsbury Theatre, long time home of the musical Hair. I had already started smoking dope shortly before getting expelled in Colchester and DSK introduced me to LSD, or as we called it Acid.
We became best friends and I spent most of my free time together with him, smoking vast quantities of dope and dropping acid about once a week. DSK was a minor dealer so my drug consume didn’t cost me anything. We would wander around the streets of Soho at night tripping out of our heads, stopping at the all night Whimpey Bar for sustenance. We attended concerts, I saw Sly and the Family Stone high as a kite at the Lyceum Theatre, a truly mind blowing experience but very often we just stayed in DSK’s room listening to albums whilst exploring the psychedelic stratosphere. Much Pink Floyd and Sid Barrett’s The Madcap Laughs found their way regularly onto the turntable but two albums had the biggest impact on me and my future development. Firstly, the Grateful Dead’s Live Dead, which made me a lifelong Dead Head and which remains my all time favourite album and secondly Country Joe and the Fish, Electric Music for the Mind and Body, the start of a lifelong love affair with the music of Country Joe.
Source: WikimediaCommons
This was the age of the big rock festivals and in the summer of 1970, the Bath Festival of Blues and Progressive Music was announced with a stellar line up including Led Zeppelin, Pink Floyd, Flock, It’s a Beautiful Day, Jefferson Airplane, Santana, Frank Zappa and the Mothers of Invention, and many others but I wanted to go because Country Joe was on the bill. To earn the money for a ticket and the coach fare to Bath I worked for a time in the Fitzroy Taverne legendary watering hole of the Bloomsbury Set, Dylan Thomas, Augustus John and many others. At the appointed time I duly took a coach to Bath and then a bus out to the festival site in Shepton Mallet.
From the beginning the festival fulfilled all expectations, with one superb set following another. On Saturday evening, Led Zeppelin took to the stage and delivered up three hours of pure dynamite. The people who care about such things rate it as possibly their best ever live performance. I grew increasingly worried because I knew that Country Joe was due to follow them onto the stage with just an acoustic guitar and I feared he would die a death.
To add to my fears, by the time Country Joe finally took to the stage after midnight it was raining quite heavily. With his acoustic guitar strapped to his chest Country Joe walked up to the solitary microphone in the middle of the stage. “Is this microphone working?” It obviously was. “Sorry about the rain.” “GIVE US AN F!” 150, 000 people gave him an F and we were off with Fixin’ to Die Rag. In a masterful demonstration of charisma Country Joe captured the audience completely and delivered up a wonderful set of his songs finishing up with Fixin’ to Die Rag twice as encores. The audience wanted more. Country Joe explained that he was currently recording an album of poems about WWI and he would now play one of them but it was a long, quiet song and the audience would have to be very still. He then played Jean Desprez a ballad about a young boy who tried to save a wounded French soldier, its almost ten minutes long. It was still pissing down but you could have heard a pin drop. As he finished I think more than half the audience had tears in their eyes. The album War War War is superb.
After the festival was over I travelled down to South Wales and my second summer season working on the archaeological excavation of a Roman fort in Usk, run by University College Cardiff. Whilst there I got presented with an end of first year Cardiff student, who had absolutely no digging experience, and told to teach him how to dig. We soon discovered that we had both just come from the Bath Festival and went on to become best friends and are still in contact fifty five years later.
In autumn 1970, I went up to University College Cardiff to study archaeology despite having royally screwed up my A-levels, too much dope and acid! Through the people I had already got to know at Usk I immediately became a Student’s Union insider and, amongst other things began to work for the Union Events, the group that ran the concerts, as a stagehand, on the door, fly poster and whatever. I continued to do so long after I dropped out in 1971 at the end of my first year.
In 1973, Country Joe released his excellent Paris Sessions album of largely feminist songs recorded with a largely female band. He took this on the road and they played a gig at Cardiff Students Union. A friend of mine was Events secretary in that year and I asked him if I could manage to concert on that evening, he said yes. So, I came to meet Country Joe in person. As they were setting up I got into conversation with Pete Albin, the bass player from Big Brother and the Holding Company, who played base in the Paris Sessions band. And he told me a lot about the history of Country Joe’s music and political career. Later I found myself with the man himself and his road manager in the artists dressing room. We were smoking dope and drinking Newcastle Brown Ale. I told him that I had seen him at Bath and he responded, “ Hundred thousand of you fuckers sitting in the pouring rain and you could have heard a pin drop!” I then asked him if he would perform a solo set before the band set for me and sing Jean Desprez. He said he would and then turned to his road manager, “Do you know why I stopped doing solo concerts?” “No.” “I’m scared shitless of the audience!” This is a man who berated 300,000 at Woodstock for not singing loud enough!
Later I was stood out in the concert hall with his very cute lady drummer wrapped up in my arms, don’t ask, listening to him sing Jean Desprez for me. The lady turned to me and said, “I sit behind him every evening but you know I’ve never seen him perform. He’s good isn’t he?”
Sometime later, I can’t remember the exact year, I attended a superb duo concert of Country Joe and Barry Melton, the original fish guitarist, in the then new students union building in Cardiff.
The next highpoint came in 1976, when I finally got to hear the original Country Joe and the Fish lineup live. There was a Bob Marley and the Wailers open air in the football stadium in Cardiff. Country Joe and the Fish were one of the support acts on their reunion tour. I would have attended for Bob Marley but Country Joe and the Fish sealed to deal. On the day of the concert it was pissing down but we had tickets so we went in anyway. We spent the day in the roofed over stands , whilst the field, which was slowly turning into a swamp, where the audience would usually have stood remained empty. Because of the downpour les than 2000 people attended and the promoter went bankrupt. Despite the weather the concert was great and Country Joe and the Fish were the final act on before Marley. The local Rastas, who had come for the Wailers and didn’t want to hear some sixties San Fran hippie band, were restless and basically jeered when they took the stage. Barry Melton looked out into the rain and said, “In California we call this liquid sunshine,” and they took off. It was pure magic and by the end the Rastas were loudly calling for encores. Ironically it was the last day that it rained before the drought of 76!
There is one final strange episode to my Country Joe odessey. In 2015, I got invited to participate in SciFoo the major unconference, which took place at Google in Mountain View. I flew in in advance to San Francisco and went to Oakland to visit the National Council for Science Education because I knew one of the prominent workers from the Internet. At some point I got introduced to the then Executive Director Eugenie Scott. She lives in Berkley and I can’t remember how the conversation took the turn but it turned out that her next door neighbour was Country Joe!
I still own Electric Music for Mind and Body. In fact, I own four copies the original mono album from 1967 that I bought in 1969, the stereo remix from 1969 that I acquired sometime later and the double CD, one disc is the original mono mix and the other is the stereo mix. Now Country Joe has departed from us, which has stirred up a lot of memories leading to this very personal post.
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