The emergence of modern astronomy – a complex mosaic: Part XLVII

One aspect central to the astronomical-cosmological discourse since antiquity was the actual size of the cosmos. This became particularly relevant to the astronomical system debate following Tycho’s star size argument. He argued given his failure to detect the stellar parallax, which should be observable in a heliocentric system, the stars must be so far away that the apparent size of the star discs would mean they must be quite literally unimaginably large and thus the system was not heliocentric. He also argued that under these circumstances there must also be an unimaginably vast distance between the orbit of Saturn and the sphere of the fixed stars. He thought it was ridiculous to suppose that there exists so much empty space, which for him also spoke against heliocentricity.

The earliest known serious attempt to determine the dimensions of the solar system was made by Aristarchus of Samos (c. 310–c. 230 BCE) infamous for proposing a heliocentric theory of the cosmos. We only have second-hand accounts of that system from Archimedes and Plutarch. However, the only manuscript attributed to him is Peri megethon kai apostematon (On the Sizes and Distances (of the Sun and Moon)). Aristarchus assumed that at half-moon the Earth, Moon and Sun form a right-angle triangle and that the angle between the Earth and the Moon is 87°.


From these assumptions he calculated that the ratio of the Earth/Sun distance to the Earth/Moon distance is approximately 1:19. In reality the ratio is approximately 1:400 because the angle is closer to 89.5° and is not differentiable by the human eye. Also, it is almost impossible to say exactly when half-moon is.

Aristarchus used a different geometrical construction based on the lunar eclipse to determine the actual sizes of the Earth, Moon and Sun.



Aristarchus’ 3rd century BCE calculations on the actual sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy Source: Wikimedia Commons

It is possible to reconstruct Aristarchus’ values (Source: Wikimedia Commons



Actual Values

Sun’s radius in Earth radii (e.r.)



Earth’s radius in Moon radii



Earth/Moon distance in e.r.)



Earth/Sun distance in e.r.)



Hipparchus (c. 190 – c. 120 BCE) used a modified version of Aristarchus’ eclipse diagram, using a solar rather than a lunar eclipse, to make the same calculations arriving at a value of between 59 and c. 67 e.r. for the Moon’s distance and 490 e.r. for the Sun.


As with almost all of Hipparchus’ other writings, his work on this topic has been lost but we have his method and results from Ptolemaeus, who also used a modified version of the solar eclipse diagram to make the same calculations. Ptolemaeus got widely different values for the furthest c. 64 e.r. and nearest c. 34 e.r. distance of the Moon from the Earth. The first is almost the correct value the second wildly off. He determined the Sun to be 1,210 e.r. distant.

In the history of astronomy literature, particularly the older literature, it is often claimed that Copernicus’ heliocentric model leads automatically to a set of relative distances for all the known planets from the Sun, which is true, but there is no equivalent set of measures for a Ptolemaic geocentric system, which is false. It is the case that in his great astronomical work, the Mathēmatikē Syntaxis (Almagest), he gives detailed epicycle-deferent models for each of the then known seven planets–Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn–but does not deal with their distances from each other or from the Earth. However, he wrote another smaller work, his Planetary Hypotheses, and here he delivers those missing dimensions. For Ptolemaeus each planetary orbit is embedded in a crystalline sphere the dimensions of which are determined by the ecliptic-deferent model for the planet. How this works is nicely illustrated in Georg von Peuerbach’s (1423–1461) Theoricae Novae Planetarum (New Planetary Theory) published by Regiomontanus in Nürnberg in 1472.


Diagram from Peuerbach’s Theoricae novae planetarum showing the orbit embedded in its crystalline sphere (green) Source: Wikimedia Commons

It was long thought that Peuerbach’s was an original work but when in 1964 the first ever know manuscript in Arabic, and till today the only one, of Ptolemaeus Planetary Hypotheses was found it was realised that it was merely a modernised version of Ptolemaeus’ work.

Ptolemaeus’ model of the cosmos was quite literally spheres within spheres, a sort of babushka doll model of the solar system. The Moon’s sphere enclosed the Earth. Mercury’s sphere began where the Moon’s sphere stopped, Venus’ sphere began where Mercury’s stopped, the Sun’s sphere began where Venus’ stopped and so on till the outer surface of Saturn’s sphere. Using this model Ptolemaeus calculated the following values and a value of 20,000 e.r. for the distance from the Earth to the sphere of fixed star and c. 1,200 e.r. for the Earth/sun distance.


Ptolemaeus’ model and at least his basic dimensions–Earth/Moon, Earth/Sun and fixed star sphere distances–remained the astronomical/cosmological norm for nearly all astronomers in the Islamic and European Middle Ages and we first begin to see new developments in the sixteenth century and the so-called astronomical revolution.

In the geocentric model the order of the orbits of Mercury, Venus and the Sun moving away from the Earth and the Moon is purely arbitrary as they all have an orbital period of one year relative the Earth. Ptolemaeus’ order was, in antiquity, only one of several; in fact, he played with different possible orders himself. In a heliocentric system the correct order of the planets moving away from the Sun is given automatically by the length of their orbits. This is, of course, the basis of Kepler’s third law of planetary motion. The relative size of those orbits is also given with respect to the distance between the Earth and the Sun, the so-called astronomical unit. This gives a new incentive to trying to find the correct value for this distance, determine the one and you have determined them all.

Copernicus determined the distances between the Earth and the other planets using his epicycle models and Ptolemaeus’ data, which produced much smaller values for those distances that by Ptolemaeus. Although he appeared to calculate the astronomical unit for himself, however, he chose parameters that gave him approximately Ptolemaeus’ value of 1,200 e.r.


Tycho Brahe’s values were also smaller than those of Ptolemaeus, but he also chose a value for the astronomical unit that was in the same area of those of Ptolemaeus and Copernicus. Tycho’s failure to detect stellar parallax led him to argue that the parallax value for the fixed stars, if it exists, must have a maximum of one minute, i.e. one sixtieth of a degree, meaning that in a Copernican cosmos the fixed stars must have a minimum distance of approximately 7,850,000 e.r. Copernicans had no choice but to accept this, for the time, literally unbelievable distance. Tycho himself set the distance of the fixed stars in his system just beyond the orbit of Saturn at 14,000 e.r.


Up till now all of those distances had been calculated based on a combination series of dubious assumptions and rathe dodgy geometrical models, this would all change with the advent of Johannes Kepler in the game. Through out his career Kepler returned several times to the problem of the distance of the planets from the Sun expressed relative to the astronomical unit. By the time he wrote and published his Harmonices Mundi containing his all-important third law of planetary motion in 1619, the values that he had obtained were largely correct, but he still had no real measure for the astronomical unit or from the distance of the fixed stars. For his own estimate of the astronomical unit Kepler turned to a parallax argument. He argued that no solar parallax was visible, not even with the recently invented telescope, so the parallax could be, at the most, one minute i.e. one sixtieth of a degree. This would give him a minimum value for the astronomical unit of c. 3,500 e.r., three times as big as the Ptolemaic/Copernican value. As a convinced Copernican Kepler was more than prepared to accept Tycho’s argument for very distant fixed stars, his minimum value was 60,000,000 e.r.


Because the astronomical unit was essential for turning his relative values for the distances of the planets into absolute values, over the years he considered various methods for determining it. He even reconsidered Aristarchus’ half-moon method, hoping that the telescope would make it possible to accurately determine the time of half-moon and measure the angle. His own attempts failed and in his ephemeris for 1618 he appeals to Galileo and Simon Marius to make the necessary observations. However, even they would not have been able to oblige, as the telescopes were still too primitive for the task.

For once Galileo did not take part in the attempts to establish the dimensions of the solar system, accepting Copernicus’ values. He did make some measurements of the size of the planets, a parallel undertaking to determining the planetary distances. He never published a systematic list of those measurements preferring instead just to snipe at other astronomers, who published different values to his.

Kepler’s work was a major game changer in the attempts to calculate the size of the cosmos and its components. His solar system has very different dimensions to everything that preceded it and for those supporting his viewpoint it meant the necessity to find new improved ways to find a value for the astronomical unit.

*  All diagrams and tables are taken from Albert van Helden, Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley, University of Chicago Press, 1985, unless otherwise stated.

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Video-menu launched on the Marius-Portal

Regular readers of this blog will know that I am part of a group of historians of astronomy, who have, since 2014, been involved in restoring the reputation of the Franconian astronomer Simon Marius (1573-1624) .


Simon Marius Source: Wikimedia Commons

As part of our efforts we have created a Simon Marius web portal. This portal has recently acquired a new section.

There is now a short film, which in two minutes describes the career and the most important research results of the margravial court astronomer Simon Marius. The animated film visualises his discoveries with historical images and can be viewed on the Marius-Portal. This contribution was sponsored by the Nuremberger film production company 7streich.

The completion of the English language translation of the animated clip has been taken as an opportunity to install a new menu “Video – Films and Podcasts.” As well as the animated clip, there are 19 lectures, TV and Internet reports easily accessible. The majority of the films are in German but there are two English lectures, one from myself and one from Renaissance Mathematicus friend and occasional guest blogger, Professor Chris Graney. The Simon Marius Society maintains the Marius-Portal, which with 34 menu languages lists all documents by or about Simon Marius and–where possible–makes digitally available.

Marius discovered the four largest moons of Jupiter, independently of Galileo Galilei, also in January 1610. They prove that not all celestial bodies orbit the Earth. Marius propagated an interesting geo-heliocentric model, a historically important steppingstone on the route from a geo- to a heliocentric model of the cosmos.

Illustrations from the Marius short film and Marius-Portal


Montage of the first orbital presentation of the Jupiter system by Simon Marius from 1611 with a view of Ansbach from Matthäus Merian from 1648 (Town Archive Ansbach). Marius-Portal/7streich


Montage of historical illustrations of Galileo Galilei and Simon Marius Marius-Portal/7streich

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Filed under History of Astrology, History of Astronomy, Simon Marius

A book or many books?

If you count mathematics as one of the sciences, and I do, then without any doubt the most often reissued science textbook of all time has to be The Elements of Euclid. As B L van der Waerden wrote in his Encyclopaedia Britannica article on Euclid:

Almost from the time of its writing and lasting almost to the present, the Elements has exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, next to the Bible, the “Elements” may be the most translated, published, and studied of all the books produced in the Western world.

The Elements have appeared in numerous editions from their inceptions, supposedly in the fourth century BCE down to the present day. In recent years, Kronecker-Wallis issued a new luxury edition of Oliver Byrne’s wonderful nineteenth century, colour coded version of the first six books of The Elements, extending it to all thirteen books.


There are far too many different editions of this fundamental geometry textbook to be able to name them all, but this automatically raises the question, are they all the same book? If we take a random example of a book with the title The Elements of Euclid, will we always find the same content between the covers? The simple answer to this question is no. The name of the author, Euclid, and the title of the book, The Elements, are much more a mantle into which, over a period of more than two thousand years, related but varying geometrical content has been poured to fit a particular time or function, never quite the same. Sometimes with minor variations sometimes major ones. The ever-changing nature of this model of mathematical literature is the subject of Benjamin Wardhaugh’s fascination volume, The Book of WonderThe Many Lives of Euclid’s Elements.[1]


To write a detailed, complete, chronological history of The Elements, would probably produce something with the dimensions of James Frazer’s twelve volume The Golden Bough and Wardhaugh doesn’t attempt the task here. What he does do is to deliver a selective series of episodes out of the long and complex life of the book. These episodes rather than book chapters might best be described, as essays or even short stories. In total they sum up to a comprehensive, but by no means complete, overview of this fascinating mathematical tome. Wardhaugh’s essay collection is split up into four section, each of which takes a different approach to examining and presenting the history of Euclid’s opus magnum. 

The first section opens with Euclid’s Alexandria, the geometry of the period and the man himself. It clearly shows how little we actually know about the origins of this extraordinary book and its purported author. The following essays deliver a sketch of the history of the book itself. We move from the earliest surviving fragments over the first known complete manuscript from Theon in the fourth century CE. We meet The Elements in Byzantium, in Arabic, in Latin and for the first time in print. 


In the latter case I tripped over the only seriously questionable historical claim that I was aware of in the book. Wardhaugh repeats the nineteenth century claim that Erhard Ratdolt, the printer/publisher of that first printed edition, had been apprenticed to Regiomontanus. This claim is based on the fact that Ratdolt printed and published various manuscripts that had previously belonged to Regiomontanus, including the Euclid. However, there is absolutely no other evidence to support this claim. Regiomontanus was famous throughout Europe both as a mathematicus and as a printer/publisher, people were publishing books, which weren’t from him, more than one hundred years after his death, under his name. If Ratdolt had indeed learnt the printing trade from Regiomontanus he would, with certainty, have advertised the fact, he didn’t.

The first section closes with the flood of new editions that Ratdolt’s first printed edition unleashed in the Early Modern Period. 

The second section deals with the various philosophical interpretations to which The Elements were subjected over the centuries. We start with Plato, who supposedly posted the phrase, “Let no man ignorant of geometry enter” over the entrance to his school. Up next is Proclus, whose fifth century CE commentary on The Elements was the first source that names Euclid as the author. We then have one of Wardhaugh’s strengths as a Euclid chronicler, in his book he digs out a series of women, who over the centuries have in some way engaged with The Elements; here we get the nun Hroswitha (d. c. 1000CE), whose play Sapientia included sections of Euclidian number theory. Following Levi ben Gershon and his Hebrew Euclid, we get a section that particularly appealed to me. First off Christoph Clavius’ Elements, possibly the most extensively rewritten version of the book and one of the most important seventeenth century maths textbooks. This is followed by the Chinese translation of the first six books of Clavius’ Elements by Matteo Ricci and Xu Guangqi.


The second continues with an English stage play on geometry written for the carnival in Rome in 1635. Wardhaugh’s Euclidean research has dug very deep. Baruch Spinoza famously wrote a book on ethics in the style of Euclid’s Elements and of course it’s included here. The section closes with another woman, this time the nineteenth century landowner, Anne Lister.

The third section of the book deals with applied geometry. We start with ancient Egyptian surveyors, move onto music theory and the monochord, Roman field surveyors and the Arabic mathematician Muhammad abu al-Wafa al-Buzjani, who work on the theory of dividing up surfaces for the artisans to create those wonderful geometrical patterns so typical of Islamic ornamentation. Up next are medieval representations of the muse Geometria, which is followed by Piero della Francesca and the geometry of linear perspective. There is a brief interlude with the splendidly named seventeenth century maths teacher, Euclid Speidel before the section closes with Isaac Newton. 

The fourth section of the book traces the decline of The Elements as a textbook in the nineteenth century. We start with another woman, Mary Fairfax, later Mary Sommerville, and her battles with her parents to be allowed to read Euclid. We travel to France and François Peyrard’s attempts to create, as far as possible, a new definitive text for the Elements. Of course, Nicolai Ivanovich Lobachevsky and the beginnings of non-Euclidian geometry have to put in an appearance. Up next George Eliot’s The Mill on the Floss is brought in to illustrate the stupefying nature of Euclidian geometry teaching in English schools in the nineteenth century. We move on to teaching Euclid in Urdu in Uttar Pradesh. A survey of the decline of Euclid in the nineteenth century would no be complete without Lewis Carroll’s wonderful drama Euclid and his Modern Rivals. Carroll is followed by, in his time, one of the greatest historians of Greek mathematics, Thomas Little Heath, whose superb three volume English edition of The Elements has graced my bookshelf for several decades.


The book closes with an excursion into the arts. Max Ernst’s Euclid’s Mask morphs into a chapter on Euclidean design, including Oliver Byrne’s colour coded Elements, mentioned earlier. The final chapter is some musing on the iconic status of Euclid and his book.

There are no foot or endnotes and the book contains something that I regard as rather inadequate. Notes on Sources, which for every chapter gives a short partially annotated reading list. Not, in my opinion the most helpful of tools. There is an extensive bibliography and a good index. The book is illustrated with the now standard grey in grey prints.

Benjamin Wardhaugh is an excellent storyteller and his collected short story approach to the history of The Elements works splendidly. He traces a series of paths through the highways and byways of the history of this extraordinary mathematics book that is simultaneously educational, entertaining and illuminating. In my opinion a highly desirable read for all those, both professional and amateur, who interest themselves for the histories of mathematics, science and knowledge or the course of mostly European intellectual history over almost two and a half millennia.  

[1] Benjamin Wardhaugh, The Book of WonderThe Many Lives of Euclid’s Elements, William Collins, London, 2020


Filed under Book Reviews, History of Mathematics

The emergence of modern astronomy – a complex mosaic: Part XLVI

The discovery of stellar aberration was empirical evidence that the Earth orbits the Sun; finding empirical evidence that the Earth rotates daily on its axis proved, perhaps surprisingly, difficult. The first indirect evidence for diurnal rotation in interesting in two ways. Firstly, it is based, not on a single theory but on a chain of interdependent theories. Secondly, it is an interdisciplinary proof involving physics, astronomy, geophysics and geodesy.

That the Earth was a sphere had been accepted in educated European circles since at least the fifth century BCE. The acceptance of this knowledge automatically led to attempts to estimate or in fact measure the size of that sphere. Aristotle claimed that mathematicians had measured the circumference of the Earth to be 400,000 stadia (between 62,800 and 74,000km) which is far to large. Archimedes set an upper limit of 3,000,000 stadia (483,000km), making Aristotle look almost reasonable. One of the earliest serious attempts to measure the circumference of the Earth was that of Eratosthenes, which now has legendary status. It is reported that he calculated a figure of 250,000 stadia. What is not known is which stadium he was using so the error in his value lays somewhere between about 2% and 17%. Eratosthenes was by no means the only thinker in antiquity to give a calculated figure for the Earth’s circumference. Posidonius produced a value, which varies considerably in size in the literature in which it is quoted. Ptolemaeus gives two completely different values 252,000 stadia in his Mathēmatikē Syntaxis and later 180,000 stadia in his Geōgraphikḕ Hyphḗgēsis. In the Middle Ages, the Indian mathematician, Aryabhata, calculated a value for the Earth’s diameter of 12,500km. Islamic scholars also produced varying figures, most famously al-Khwarizmi and al-Biruni. Up till the Early Modern Period nobody could actually say, which of the various values, that were floating around in the available literature, was the correct one, Columbus famously chose the wrong value.

The basic method of determining the circumference of the Earth is to determine the length of a stretch of a meridian, a line of longitude through both poles, and then determine how many degrees of latitude this represents. From this data it is then possible to determine the circumference. This process took a major turn in accuracy with the invention, by Gemma Frisius (1508–1555), of triangulation in the sixteenth century. This meant that it was now possible to exactly measure the length of a stretch of a meridian and by taking the latitudes of the ends of the stretch to determine the length of one degree of latitude.


The Libellus de locorum describendum ratione, Gemma Frisius’ pamphlet outlining completely and in detail the technique of triangulation.

The first mathematicus to try and determine the circumference of the Earth using triangulation was the Dutchman Willebrord Snel (1580–1626), who carried out a triangulation of the Netherlands in the early part of the seventeenth century. He published the results of survey in his Eratosthenes Batavus, De Terræ ambitus vera quantitate in 1617.


The first part of the title translates as the Dutch Eratosthenes. Taking the distance between Alkmaar and Breda, which almost lie on the same meridian, he calculated one degree of latitude to be 107.37km giving a circumference of 38,653km, an error of about 3.5%.


Snel’s triangulation netwerk Source

Later in the seventeenth century the French astronomer Jean-Félix Picard (1620–1682) now triangulated a meridian arc through Paris, between 1669 and 1670, calculating a value for one degree of latitude of 110.46km producing values for the Earth’s polar radius and circumference with more than 99% accuracy.


Picard’s triangulation and his instruments

In 1672 Jean-Dominique Cassini (1625–1712) made an attempt to measure the parallax of Mars in order to determine the astronomical unit, the distance between the Earth and the Sun.


Jean-Dominique Cassini (artist unknown) Source: Wikimedia Commons

He sent his assistant Jean Richer (1630–1696) to Cayenne in French Guiana, so that he and Cassini could make simultaneous observations of Mars during its perihelic opposition. We shall return to this in a later episode, but it is another experiment or better said discovery of Richer’s, whilst in Cayenne, that is of interest here. Richer was equipped with all the latest equipment including a state-of-the-art pendulum clock with a seconds pendulum, that is a pendulum whose period is exactly two seconds, or at least it was a seconds pendulum when calibrated in Paris. Richer discovered that in Cayenne that he needed to shorten the pendulum by 2.8mm. As gravity is the driving force of a pendulum clock this meant that the Earth’s gravity was different in Cayenne to in Paris or that Cayenne was further from the Earth’s centre than Paris. The Earth was not, after all, a sphere.


Jean Richer working in French Guiana from an engaging by Sébastien Leclerc.

Jean-Dominique Cassini and later his son Jacques (1677–1756) extended Picard’s Paris meridian northwards to Dunkirk and southwards to the Spanish border.


Jacques Cassini Source: Wikimedia Commons

They split the meridian into two and compared lengths for one degree of latitude thus obtained, combining the results with Richer’s pendulum discovery, they proposed and defended the theory that the Earth was not a sphere but a prolate spheroid or an ellipsoid created by rotating an ellipse along its major axis; put in simple terms the Earth was lemon shaped. Jacques Cassini published these results and this theory in his De la grandeur et de la figure de la terre in 1723.


Both Newton and Huygens interpreted Richer’s pendulum discovery differently. Newton arguing from an assumption of diurnal rotation and his theory of gravity theorised that the Earth was in fact flattened to the poles and a bulge at the equator. That is the Earth is an oblate spheroid or ellipsoid created by rotating an ellipse along its minor axis, put in simple terms the Earth was shaped like an orange. Huygens also arguing from an assumed diurnal rotation but Descartes’ vortex theory, rather than Newton’s theory of gravity, arrived at the same conclusion. What is important here is that the theory depended on the existence of diurnal rotation.


Given the already strident philosophical debate between the largely French supporters of Descartes and the largely English supporters of Newton, this new dispute between the Cassini, Cartesian, model of the Earth and the Newton-Huygens, Newtonian model, Huygens actually a Cartesian was here viewed as a Newtonian, rumbled on into the early decades of the eighteenth century. Finally, in the 1730s, the Académie des sciences in Paris decided to solve the issue empirically. They equipped and sent out two scientific expeditions to Lapland and to Peru, now part of Ecuador, to measure one degree of latitude.

The expedition to Meänmaa or Torne Valley in Lapland


Traditional location of Meänmaa in Norrbotten County (Sweden) and Finnish Lapland Source: Wikimedia Commons

under the leadership of Pierre Louis Maupertuis (1698–1755)


Portrait of Maupertuis wearing the costume he adopted for his Lapland expedition by Robert Le Vrac de Tournières

took place successfully in 1736-37, despite atrocious conditions, and their results combined with the results of the Paris meridian showed that the Newton-Huygens model was indeed correct.


Map of the Lapland triangulation Source

Maupertuis published his account of the expedition La Figure de la Terre, déterminée par les Observations de Messieurs Maupertuis, Clairaut, Camus, Le Monier & de M, L’Abbé Outhier accompagnés de M. Celsius. (Paris, 1738).


Jacques Cassini launched a last-ditch attempt to defend his father’s honour and wrote a scathing criticism of the expeditions work in his Méthode de déterminer si la terre est sphérique ou non (Method to determine if Earth is a sphere or not) in 1738. However, the Swedish scientist Anders Celsius (1704–1744), who had also taken part in the expedition completely demolished Cassini’s paper and the Newtonians, of whom Maupertuis although a Frenchman was one, carried the day. Celsius’ De observationibus pro figura telluris determinanda (Observations on Determining the Shape of the Earth) from 1738 made his reputation.


Portrait of Anders Celsius by Olof Arenius

The second expedition to Peru under the leadership of Pierre Bouguer (1698–1758)


Portrait of Pierre Bouguer by Jean-Baptiste Perronneau Source: Wikimedia Commons

and Charles Marie de La Condamine (1701–1774)


Portrait of La Condamine by Carmontelle 1760 Source: Wikimedia Commons

actually left Paris a year earlier that the Lapland expedition in 1735. This team had even more difficulties than their northern colleagues and only returned to Paris in 1744. Their results, however confirmed those of the Lapland expedition and the Newton-Huygens oblate spheroid. Bouguer published his account of the expedition in his La figure de la terre (1749),


La Condamine his Journal du voyage fait par ordre du roi, a l’équateur, 1751.


Through these two expeditions the Earth had acquired a new shape, it was no longer a sphere but an oblate spheroid, an important advance in the history of geodesy. However, possible more important, because the prediction of the Newton-Huygens model was based on the assumption of diurnal rotation, these results produced the first indirect empirical evidence that the Earth rotates around its own axis. This result combined with the return of Comet Halley in 1759 also led to the final general acceptance of Newtonian theory over Cartesian theory.


Filed under History of Astronomy, History of Cartography, History of Geodesy

Astrology in the age of Newton

My Annus Mythologicus blog post was recently retweeted on Twitter in response to an inane tweet from Richard Dawkins and somebody questioned the reference in it that Newton was inspired to take up mathematics upon reading a book on astrology. This was not a nasty attack but a genuine statement on interest from somebody who had difficulty believing a man, who has been called the greatest mathematician ever, should have had anything to do with an astrology book. There is a sort of naïve belief that it is impossible for the people in the age of Newton, which is touted as the birth of the age of modern science and rationalism, could have had anything to do with the so-called occult sciences. This belief led many people, who should have known better, to try and sweep Newton’s very active engagement with alchemy under the carpet. During Newton’s lifetime astrology lost its status as a university discipline but was still all pervasive and permeated all aspects and levels of society. In what follows I will sketch some of the details of the role of astrology in the age of Newton.


Newton – 1677 Source: Wikimedia Commons

The Renaissance/Early Modern Period could with justification be called the golden age of astrology in Europe. This period was actually coming to an end during Newton’s lifetime, but astrology had by no means totally disappeared. That golden age began roughly with the beginning of the fifteenth century. During the first half of the century the humanist universities of Northern Italy and Poland created the first regular, dedicated chairs for mathematics and astronomy, which were in fact chairs for astrology, created to teach astrology to medical students. Teaching astrology to medical students was one of the principle obligations of the professors for mathematics at these universities and continued to be so well down into the seventeenth century. This trend continued with the creation of the first such chair in Germany, at the University of Ingolstadt, in the early 1470s. Astrological medicine, or iatromathematics to it is formal name was just one branch of astrology that flourished in this period.

Medical astrology was along with astrological meteorology considered to be a form of natural astrology and even those, who rejected natal astrology, for example, accepted the validity of natural astrology. Opposed to natural astrology was judicial astrology collective term for a group of other forms of astrology. Natal astrology, or genethliacal astrology, is the classic birth horoscope astrology that everybody thinks of, when they first hear the term astrology.  Other forms of judicial horoscope astrology are mundane astrology concerns the fate of nations etc., horary astrology answers question by casting a horoscope when the question is presented, and electional astrology, which is used to determine the most appropriate or auspicious time to carry out a planned action.

All these forms of astrology were widespread and considered valid by the vast majority during the fifteenth and sixteenth centuries. Astrology was firmly established in the fabric of European society and almost all of the active astronomers were also active astrologers right down to those astronomers, who were responsible for the so-called astronomical revolution. Georg Peuerbach, Regiomontanus, Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers and in fact owed much of the patronage that they received to their role as astrologer rather to that of astronomer, although the terms were interchangeable in this period. The terms Astrologus, Astronomus and Mathematicus were all synonym and all had astrologer in the modern sense as their principle meaning. Following the invention of moving type printing in about 1450, by far and away, the largest number of printed articles were astrological ephemera, almanacs, prognostica, and writing and single sheet wall calendars. A trend that continued all the way down to the eighteenth century.

During the fifteenth and sixteenth century efforts to give astrology a solid empirical footing were central to the activities of the astronomer-astrologers. Starting with Regiomontanus several astronomers believed that the inaccuracies in astrological forecasting were due to inaccuracies in the astronomy on which it was based. The reform of astronomy, for exactly this reason, was a principle motivation for the research programmes of Regiomontanus, Tycho Brahe and Wilhelm IV, Landgrave of Hessen-Kassel. Another approach was through astro-meteorology, with astronomer keeping weather diaries in which they noted the horoscope for the day and the actual weather on that day. They were looking for correlations, which they failed to find, but the practice led to the beginnings of modern weather forecasting. Notable weather diarists were Tycho Brahe and Johannes Werner. There were also attempts to find genuine correlations between birth charts and biographies of prominent people. Such biographical horoscope collections existed in manuscript before the invention of movable type printing. One of the largest, still extant, such manuscript collections is that of Erasmus Reinhold, a professor of mathematics at Wittenberg. The first such printed collection was that of Gerolamo Cardano, Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, printed and published by Johannes Petreius, specialist for astrological literature, in Nürnberg in 1543; the same year as he published Copernicus’ De revolutionibus.


During the first half of the seventeenth century the failures to find empirical evidence for astrology, a change in the philosophy underpinning science, astrology was justified with Aristotelian metaphysics, and changes in the ruling methodologies of mainstream medicine led to a decline in the academic status of astrology. Although a few universities continued teaching astrology for medical students into the eighteenth century, astrology as a university discipline largely ceased to exist by 1660. However, astrology was still very much woven into the fabric of European society.

Newton was born in 1642, which meant he grew up during the Civil War and the Interregnum. Astrology was used by both sides as propaganda during Civil War. Most famously William Lilly (1602–1681) publishing powerful pamphlets on behalf of the parliamentary side.


Portrait of Lilly, aged 45, now housed in the Ashmolean Museum at Oxford Source: Wikimedia Commons

This caused him major problem following the restitution. Lilly’s Christian Astrology (1647) was a highly influential book in the genre. Lilly was friends with many important figures of the age including Elias Ashmole (1617–1692) an antiquary who gave his name to the Ashmolean Museum of Art and Archaeology in Oxford, which was founded on his collection of books, manuscripts many objects. Ashmole was a passionate astrologer and a founding member of the London Society of Astrologers, which included many prominent intellectuals and existed from 1649 to 1658 and was briefly revived in 1682 by the astronomer, astrologer, printer and globemaker Joseph Moxon (1627–1691).


Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source: Wikimedia Commons

Moxon successfully sold Ptolemaic globes in the last quarter of the seventeenth century, which were intended for astrologers not astronomers. Moxon’s Ptolemaic globes reflect an actual fashion in astrological praxis that could be described as back to the roots. In the middle of the seventeenth century many astrologers decide that astrology wasn’t working, as it should, because the methodology used had drifted to far from that described by Ptolemaeus in his Tetrabiblos. This movement was led by the Italian P. Placido de Titis (1603 – 1668) whose Physiomathematica sive coelestis philosophia published in 1650 with an improved 2nd edition, 1675.



Alongside Moxon another English supporter of this back to the roots movement was John Partridge (1644–c. 1714), who published the first ever English translation of Ptolemaeus’ Tetrabiblos in 1704. Partridge was one of the most well-known astrologers of the age until he got skewered by Jonathan Swift in his infamous Isaac Bickerstaff letters beginning in 1708.

V0004503ER John Partridge. Line engraving by R. White, 1682, after hims

John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons John Partridge. Line engraving by R. White, 1682, after himself. 1682 By: Robert WhitePublished: – Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

We always talk about the big names in the histories of astronomy and mathematics, but it is often more insignificant practitioners, who teach the next generation. In this Newton’s education in astronomy followed the norm and he learnt his astronomy from the books of Vincent Wing (1619–1668) Astronomia Britannica (1669)


Author portrait of Vincent Wing engraved by T. Cross (Frontispiece to the “Astronomia Britannica” of 1669) Source: Wikimedia Commons

and Thomas Streete (1621–1689) Astronomia Carolina, a new theorie of Coelestial Motions (1661).


They were the two leading astronomers in England during Newton’s youth and were both practicing astrologers. The two men were rivals and wrote polemics criticising the errors in the others work. Streete was friends with several other astronomers such as Flamsteed, who also used the Astronomia Carolina as his textbook, or Halley together with whom Streete made observation. Streete was Keplerian and it’s Kepler’s astronomy that he presents in his Astronomia Carolina , although he rejected Kepler’s second law and presented the theories of Boulliau and Ward instead. It is very probable that reading Streete was Newton’s introduction to Kepler’s theories.

Flamsteed, as already said, like Newton, a student of Steete, actually cast an electional horoscope for the laying of the foundation stone of the Royal Observatory in 1675 although he didn’t actually believe in astrology but was maintaining a well-established tradition.


Another example of this sort of half belief can be found in the attitude of Newton and Halley to comets. The two of them did far more than anybody else to establish comets as real celestial bodies affected by the same physical laws as all other celestial bodies and not some sort of message from the heavens. However, whilst neither of them believed in the truth of astrology both retained a belief that comets were indeed harbingers of doom.

As I said at the beginning Newton grew up and lived all of his life in a culture permeated with a belief in astrology. At the end of the seventeenth century astrological ephemera–almanacs, prognostica, etc.–were still a mass market phenomenon.


Zodiac man in EPB/61971/A: Goldsmith, 1679. An almanack for the year of our Lord God, 1679 (London: Printed by Mary Clark, for the Company of Stationers, 1679), leaf B2 recto. Image credit: Elma Brenner. Source:

A large annual fair such as Sturbridge in 1663, the largest annual fair in Europe, would have had a large selection of astrological literature on offer for the visitors; a public many of whose yearly almanac was the only printed book that they bought and read.


It is perfectly reasonable that a twenty-one year old Newton, just entering his second year at Cambridge university, stumbled across an astrological publication that awakened his mathematical curiosity as reported separately by both John Conduitt and Abraham DeMoirvre, in their memoirs based on conversations with Newton.


Filed under History of Astrology, History of Astronomy, Newton, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part XLV

The problem of an empirical proof of heliocentricity would occupy astronomers for the next couple of centuries following the publication of Newton’s Principia; the general acceptance of heliocentricity had now been achieved, but people very much wanted concrete assurance of its truth. The Principia actually contained a theoretical proof. Newton showed, assuming the law of gravity and Kepler’s laws of planetary motion, that given the mass of the Sun, the mass of the Earth and the distance between them then it was only possible that the Earth orbited the Sun and not vice versa. This proof was very technical, relied on a heap of assumptions and intelligent estimates, nobody actually knew the real masses of the Sun and Earth or the distance between them, so very few people at the time considered it totally convincing.

What people were looking for was empirical evidence that the Earth was actually moving, both revolving on its own axis and orbiting the Sun; it was providing those proofs that would prove difficult. Many thought that the most likely evidence consisted of the detection of stellar parallax, which should have been visible if the Earth really was orbiting the Sun.

I think most people will have encountered the concept of parallax during their education but just in case, for those who might have forgotten. Parallax is the apparent displacement of an object, due to an actual displacement of the observer. The demonstration you learn at school is to hold a finger up in front of your nose aligned with some point in the background. If you close your right eye your finger appears to move to the right and if you close your left eye to the left. This phenomenon of our binocular vision is how our brain estimates distance, comparing the two offset views that our eyes deliver. Because the distance between out eyes is vey small this only works for fairly close objects, a couple of hundred metres or so. Using technical instruments, we can increase the visual base line and measure greater distances. This is actually the basis of triangulation in surveying.


A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from “Viewpoint A”, the object appears to be in front of the blue square. When the viewpoint is changed to “Viewpoint B”, the object appears to have moved in front of the red square. Source: Wikimedia Commons

The ancient Greeks already realised that one could use parallax to determine the distance of celestial objects. If you view the same object simultaneously from two points on the Earth relatively far apart then they it will appear to align with different stars in the background sphere of fixed star. If you know the distance between the two observation points you can create a triangle and determine the distance of the observed object using a bit of simple trigonometry. Using this method Hipparchus succeeded in determining the distance between the Earth and the Moon. However, despite numerous attempts nobody succeeded in determining the distance to any other celestial object. The distances were too great and the resulting acute angle in the measuring triangle was far too small to determine accurately. This was the case even if one used the entire width of the earth’s sphere (about 13,000km), measuring the position of the desired object from the same point twelve hours apart. This is of course dependent on the daily rotation of the planet but is also valid if one assumes that it is the sphere of the fixed stars that rotate every twenty-four hours rather than the Earth.

With heliocentricity the length of the possible base grows to distance between the aphelion and perihelion of the Earths orbit, its nearest and furthest points from the Sun in its orbit, a distance of about 300 million km, although the exact size of this distance was not known in the Early Modern Period. It was assumed that given this base line it should be possible to measure the parallax and thus the distance of a star.


Stellar Parallax Source: Wikimedia Commons

In fact, in the pre-telescope age all attempts to measure the parallax of a star failed. Even the attempts to measure the parallax of any of the planets failed.


Tycho Brahe depicted sitting in his large mural quadrant at Uraniborg Source: Wikimedia Commons

Tycho Brahe believed he had determined the parallax of Mars, but he was mistaken. Tycho was the best astronomical observer of the sixteenth century with the most accurate instruments, he argued that is the parallax was too small for him to measure this implied for the heliocentric model a distance to the stars that was for him simply unimaginable. He couldn’t conceive a reason why there should be so much empty space between the orbit of Saturn and the nearest stars and so his dismissed the heliocentric model as a fantasy. Little did he realise that the distances involved were much, much larger even than those he had imagined in his wildest speculations. Tycho’s argumentation appeared reasonable to most of the other contemporary astronomers. The invention of the telescope in 1608 appeared, to those trying to measure stellar parallax, to be a game changer but this proved to be an illusion, at least for the next three hundred years.


Justus Sustermans – Portrait of Galileo Galilei, 1636 Source: Wikimedia Commons

Galileo, of course, saw the telescope as a possibility to finally detect and measure the stellar parallax that should be present in a heliocentric model. In his Dialogo (1632) he presents and describes two schemes for measuring parallax with a telescope. The first consists of fixing a telescope to a post, wall, whatever permanently direct at a point in the heavens and taking regular readings of the position of the stars visible through it, over an extended period of time. As we will see a variation of this method was actually utilised at the end of the century and again at the beginning of the eighteenth century with interesting results. The second method introduced the concept of differential parallax. Instead of viewing just one star against the background of the fixed stars, the astronomer observes a so-called binary star, i.e. two stars that appear to be comparatively close to each other, over a period of time looking for systematic variations in the observed distance between them.

Of interest, in particular with reference to the second method, is that in the Dialogo, Galileo presents these methods as something that astronomers could attempt in the future. This is interesting because Galileo actually made extensive efforts to apply the binary star method on various double star with very inconclusive results. In his published works, including the Dialogo, he makes no mention whatsoever of these failed attempts to detect parallax and his observation logs of these attempts remained unknown until discovered in 2004.

Throughout the seventeenth century various astronomers attempted to detect parallax with telescopes and failed. Although, some claimed to have actually observed parallax, all such claims proving to be false. At the end of the century Robert Hooke announced plans to apply Galileo’s first method with a vertical or zenith telescope, arguing, correctly, that this would remove the problem of atmospheric refraction in his observations and measurements. He constructed a large, somewhat ramshackle zenith telescope in his quarters in Gresham College, cutting holes in the roof and intervening floors to accommodate the instrument, which he christened his Archimedean Engine.


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

As his observation object he chose Gamma Draconis, a not particularly prominent star, but one that is almost directly overhead in London. Hooke only made a total of four observation of Gamma Draconis with his new telescope, the fourth one of which showed the star to be further from the true zenith than the previous three. Hook broke off his observations and claimed that he had detected parallax. Why he broke off after only four observation, he never explained and the value that he claimed to have to observed was fairly obviously false and was not accepted by other astronomers.


Draco constellation map Gamma Draconis on the left at the bottom Source: Wikimedia Commons

As we shall see, to have any hope of success, this type of observational series has to be carried out systematically over a long period of time and all observation carefully controlled for accuracy and possible errors. The men, who realised this and carried out such a programme were the amateur astronomers Samuel Molyneux (1689–1728) and James Bradley ((1692–1762).


James Bradley by Thomas Hudson c. 1744 Source: Wikimedia Commons

Molyneux, a wealthy MP, decided to take up Hooke’s proposed method of detecting stellar parallax. He had a state of the art, precision, zenith telescope constructed by George Graham (1673–1751), London’s leading instrument maker, which he attached the chimney in his mansion in Kew, cutting holes in the roof and between floors to accommodate it.


George Graham artist unknown Source: Wikimedia Commons

He engaged James Bradley, who already had an excellent reputation as an observational astronomer, as his expert advisor and partner. Like Hooke the two started observing Gamma Draconis. Bradley had in advance calculated the expected movement of the star caused by parallax. The star displayed no movement during the first four observation during the first two weeks of December 1725. However, when Bradley observed on 17 December Gamma Draconis had perceptively changed its apparent position but the opposite direction to that expected from parallax. The two men stopped and thoroughly checked their entire technical set up and calculations to eliminate any possible error; they found none.



The two men continued to observe well into 1727 recording 80 observation during which Gamma Draconis appeared to journey south stopped turned and journey back northwards. During an entire year the star travelled a systematic route unrelated to parallax. Puzzled by their observation, Bradley acquired a second smaller zenith telescope with a wider field of view from Graham, which he installed in his deceased uncles house in Wanstead. Bradley’s uncle, James Pound (1669–1724), had also been an astronomer, who had introduced his nephew to the science. With his new telescope Bradley observed a total of about 200 relatively bright stars and confirmed the same behaviour in all of them. He was at a loss to explain the results of his observations.

Molyneux died in 1728 before Bradley solved the puzzle. The solution is said to have come to Bradley during a boat trip on the Thames. When the boat changed direction, he noticed that the windvane on the mast also changed direction. This appeared to Bradley to be irrational, as the direction of the wind had not changed. He discussed the phenomenon with one of the sailors, who confirmed that this was always the case. The explanation is that the direction of the wind vane is a combination of the prevailing wind and the headwind created by the movement of the boat, so when the direction of the headwind changes the direction of the windvane also changes. Bradley realised that the direction of the light coming from the stars was affected in the same way by the movement of the Earth orbiting the Sun. He and Molyneux had discovered stellar aberration and the first empirical evidence of the Earth’s orbit around the Sun. The more common phenomenon used to explain aberration uses rain. When one is standing still the rain appears to fall vertically but when one in walking the rain appears to slant into one’s face at an angle. The same happens to starlight falling onto the moving Earth.



Stellar Aberration: Stars at the ecliptic poles appear to move in circles, stars exactly in the ecliptic plane move in lines, and stars at intermediate angles move in ellipses. Shown here are the apparent motions of stars with the ecliptic latitudes corresponding to these cases, and with ecliptic longitude of 270°. Source: Wikimedia Commons

Bradley wrote up the results of his observations and his interpretation of them in a letter to Edmond Halley, the Astronomer Royal, in 1729, who had the letter published in the Philosophical Transactions of the Royal Society.


Two men set out to measure stellar parallax and failed but instead discovered the till then unknown phenomenon of stellar aberration. The heliocentric theory had acquired its first empirical evidence for the annual orbit of the Earth around the Sun 186 years after Copernicus first published his hypothesis. The world would have to wait somewhat longer for the first indirect evidence of diurnal rotation, one hundred years for the first detection of stellar parallax and somewhat longer than that for the first direct evidence of diurnal rotation. However, after 1729 no serious scientist doubted that the solar system was heliocentric.


Filed under History of Astronomy

It was forty years ago today…

As I don’t keep a diary, I don’t know the actual date in 1980 when I stuck my thumb out, at the beginning of the M4 motorway, on the Newport roundabout starting a holiday trip that would take me away from the UK forever. It was, however, sometime in the middle of a mild September. I had intended a trip of a few weeks maybe a couple of months but I have now lived outside of the land of my birth for forty years.

As I look back I wonder where the time went. What follows is a brief survey of some of the things that have filled out those forty years. The astute reader will note that they add up to more than forty years because many of them took place concurrently. 

I started out by going down the Orwell route and worked for six months as a dishwasher in a luxury hotel. If you don’t speak the language! That ended when I walked out after calling the manager a racist, because he was. I could never keep my mouth shut. This was followed by a period of working as a freelance gardener; growing up in the country, in a house with half a hectare of garden had to pay off sometime. Gardening brings meagre pickings in winter, so I got a job as an industrial cleaner, the man for special jobs, for the next four years. I got around quite a bit and got to see the inside of quite a lot of leading German companies. If you keep your ears and eyes open you can learn an awful lot, nobody takes any notice of cleaners, so you get to see and hear things that are supposed to be kept secret! 

The language thing was the most important problem and right from the beginning I started going to evening classes to learn German. This was too slow so I looked around for something better and started a German as a foreign language course at the local university. German lessons in the morning, cleaning factories and office blocks in the afternoon, the high life. This was the start of twelve years spent at university as a mature student. The first three years studying mathematics and philosophy, with an emphasis on history and philosophy of science. Then I shifted to philosophy, same emphasis, with English philology and history. For nearly all of those years at the university I worked as a research assistant in a major research project into the social history, read external history, of formal logic, my real apprenticeship as a historian of science.

Before I quit the cleaning firm I had already started working in a local cultural and youth centre that would become my home from home for fourteen years. Here I managed a jazz club for ten years and worked for a couple of years, as a fly poster. I spent two afternoons a week, for many years, working in a self help bicycle workshop, where people could maintain and repair their own bicycles, with assistance from people like me if required. For ten years I was one of the centres evening shift managers responsible for the running of the whole building. With up to three thousand guests on a Friday or Saturday night and a shift from six in the evening until four in the morning a more than somewhat strenuous task. In the same building when I wasn’t being evening manager I also worked as a live concert lighting and sound technician. I had been lighting and sound technician for theatre groups earlier in the UK.

In the middle of the 1990s I was studying full time working a paid thirty to forty-hour week and an average thirty-hour unpaid week, whilst basically living on drugs and alcohol. What inevitably had to happen, happened. As I have documented elsewhere the wheels fell off and I discovered the joys of German heath care for the mentally ill. I spent several months in the loony bin followed by several years as a very active member of the AA and even more years in outpatient therapy. These days I’m reasonably healthy, mentally that is, fairly stable but I am very much aware that I will never be cured; there is no cure for my afflictions.

In Germany I also became a dog owner for the first time in my life. I have owned loved, cared for and lost four wonderful dogs over the last thirty years. They have been my constant, loving and true companions through thick and thin. My dogs helped me to cope with and overcome my mental illnesses and I owe them big time.

When I was reasonably sober and stable, being aware that I was never going to become a professional academic, I quit my studies shortly before my master’s exams and left the research project. I was the most sensible way of reducing the stress in my life. A few years later the cultural centre dispensed with my services. After a period of unemployment, during which I was official classified as unfit for work, a judgement that is still formally valid, I spent a year working for a mail order company selling Apple computers and accessories. As a result, I acquired my first iMac a cute, Bondi Blue G3. There is a certain irony here, during my research project I had become an expert on the history of the computer but unlike many of my contemporaries I had never previously owned a computer. 

The computer company was bought up by a larger rival and moved to Stuttgart about 240 km from where I live and I became unemployed again. I then ran into the problem of agism, a concept which up till then I had found mildly amusing. I was only around fifty but apparently too old to be employable. A typical telephone conversation from this period:

Me: Good Morning, my name is Christie and I ringing about your job advert

Them: How old are you?

Me: fifty something

Them: Thank you for your call.

Some didn’t even bother to say thank you before ringing off, so I became self-employed.

Since then I have tutored school kids in maths and English, taught, mostly business, English to adults, copyedited a very wide range of English texts written by non-native English speakers and translated an equally wide range of German texts into English. It has never made me rich, but I have over the years mostly managed to pay my bills. Four years ago, I officially retired.

Somewhere down the line I got back into the history of science and seventeen years ago began holding public lectures on a diverse range of topics. Eleven years ago, I started this blog, having previously discovered the world of #histSTM blogging and having been encouraged by other #histSTM bloggers to do so. It still feels kind of weird but somehow late in life I seem to have carved out a rather strange career as a historian of science. 

I suppose the final consequence of my forty years of living, working, studying, loving, and suffering in Germany is that last year I became a German citizen. As should be obvious from this very brief sketch, my life has followed anything but the normal life and career path, or at least what is considered normal for a white, male Northern European, but has meandered over a wide terrain, taking quite a few detours along the way. I wonder what the future will bring, knowing me and looking back over the last forty years it probably won’t be anything normal or conventional.


Filed under Autobiographical

A Different Royal Society

What do the Penny Post, the Great Exhibition of 1851, the Albert & Victoria Museum, GCSEs, the iMac and the art works on the fourth plinth in Trafalgar Square all have in common? Their origins are all in someway connected to the Royal Society for the Encouragement of Arts, Manufactures and Commerce. The Royal Society for what, I hear you ask, or at least that was my reaction when I first read the name.

Few people have heard of the Royal Society for the Encouragement of Arts, Manufactures and Commerce. Even fewer know what it does. Many assume, as its name is usually abbreviated to the Royal Society of Arts, that it is all about art. It has certainly done a lot to promote art, but it has also done much more than that. In fact, the Society is by its very nature difficult to define. There is no other organisation quite like it, and nor has there ever been. It is in a category of its own.

The quoted paragraph is the opening paragraph to the introduction to Anton Howes’ Arts and MindsHow the Royal Society of Arts Changed a Nation[1], which is the fourth official history of the Society and the first written by an independent, professional historian. The first three were written by society secretaries. Howes’ book will answer any and all question that you might have about the Royal Society of Arts. In little more than three hundred pages he takes his readers on a whirl wind tour of three centuries of British political, social, cultural and economic history and the at times complex and influential role that the Society played in it. To describe Howes’ work as a tour de force barely does this superb piece of interdisciplinary history justice. 

One would be forgiven for assuming that the Royal Society of Arts (RSA) had nothing to do with the Royal Society that more usually features on this blog, but you would be mistaken. The RSA owes its existence very directly to its Royal cousin and not just in the sense of a society for the arts modelled on the one for science. The Royal Society of London was modelled on the natural philosophical concepts of Francis Bacon. A very central element of Bacon’s utopian vision of natural philosophy was that advances in the discipline would and should serve the improvement of human society, i.e. science in the service of humanity. This ideal got lost, pushed aside, forgotten fairly rapidly as the Royal Society evolved and in the eighteenth century various people discussed revitalising this Baconian utopian aim and after much discussion the result was the founding of the RSA, whose aims were to support efforts to improve human society. As a side note the Royal Society became royal on the day it was founded, whereas the RSA only acquired its royalty in the nineteenth century and didn’t actually call itself Royal until the early twentieth century.

The Society was founded as a subscription and premium society. Membership was open to all and members paid a yearly subscription. This money and other donations were then used to pay premiums to help people to develop ideas that were seen as improvements. From the beginning the whole concept of improvement and what could or should be improved was left very vague, so over the three centuries of its existence the Society has launched a bewildering assortment of projects over a very wide range of disciplines. A standard procedure was to select an area where improvement was thought necessary and then to write out a call for suggestions. The suggestions were then examined and those thought to be the best were awarded a premium. The areas chosen for improvement varied wildly and were mostly determined by powerful individuals or pressure groups, who managed to persuade the membership to follow their suggestions. Often those pressure groups, brought together by common aims within the RSA, moved on to found their own separate societies; one of the earliest was the Royal Society of Chemistry. Over the three centuries many other societies were born within the RSA.

Howes guides he readers skilfully through the meandering course that the Society took over the decades and centuries. Presenting the dominant figures, who succeeded in controlling the course of the Society for a period of time and the various schemes both successful and unsuccessful that they launched. One area that played a central role throughout the history of the RSA was art, but predominantly in the form of art applied to industrial design. However, the Society also encouraged the development of art as art putting on popular exhibitions of the art submitted for premiums. 

We follow the society through its highs and lows, through its periods of stagnation and its periods of rejuvenation. As the well-known cliché goes, times change and the society had to change with them. Howes in an excellent guide to those changes taking his readers into the depth of the societies’ problems and their solutions. Here one of his strengths is his analysis of the various attempts by the society to define a new role for itself since World War II and up to the present.

Having grown up in the second half of the twentieth century, I was pleasantly surprised to be reminded of two important socio-cultural developments from my youth, where I was not aware of the strong involvement of the RSA. The first was the beginning of the movement to conserve and preserve historical building and protect them from the rapacious post-war property developers. The Society was active in arranging the purchase of such buildings to place them out of harm’s way, even at one point buying an entire village. The second was the birth and establishment of environmentalism and the environmental protection movement in the UK, which was led by Peter Scott, of the Wildfowl Trust, and Prince Philip, who was President of the Society. It was for me a timely reminder that Phil the Greek, who these days has a well-earned bad reputation amongst left wing social warriors, actually spent many decades fighting for the preservation of wildlife and the environment. I was aware of this activity at the time but had largely forgotten it. I was, however, not aware that he had used his position as President of the RSA, and the Society itself, to launch his environmental campaigns. 

To go into great detail in this review would produce something longer than the book itself, so I’ll just add some notes to the list in my opening question. The Penny Post was a scheme launched by the society to make affordable and reliable written communication available to the general public. The Great Exhibition of 1851, the first ever world fair, was set in motion by the Society in imitation of and to overtrump the industrial fairs already fairly common in various cities on the continent. Howes takes us through the genesis of the original idea, the initial failure to make this idea a reality and then the creation of the Great Exhibition itself. This probably counts as the Societies greatest success. Two things I didn’t know is one that the Societies’ committee played a significant role in setting up and promoting later world fairs other countries in the nineteenth century and was responsible for the British contributions to those fairs. Secondly the desire to preserve much of the content of the Great Exhibition led to the setting up of the museums in South Kensington, including the V&A. 

To help working people acquire qualifications in a wide range of subjects and disciplines that they could then use to improve their positions, the Society set up public examinations, in the nineteenth century. As they became popular and widespread Oxford and Cambridge universities took over responsibility for those in academic disciplines and these are the distant ancestors of todays GCSEs. Jonathan Ive was Apple’s chief designer and the man behind the iMac, as a polytechnic student he won the RSA Student Design Award, which afforded him a small stipend and a travel expense account to use on a trip to the United States, which took him to Palo Alto and his first contact with the people, who would design for Apple. I was surprised to discover that the, at time controversial, scheme to present art works on the empty fourth plinth in Trafalgar Square also originated at the RSA.

This is just a small selection of the projects and schemes launched by the RSA and I found it fascinating whilst reading to discover more and more things that are attributable to the RSA’s efforts. Howes’ book is a historical and intellectual adventure story with many surprising discoveries waiting to be made by the reader. Despite being densely packed with details the book is highly readable and I found it a pleasure to read. It has extensive endnotes, which are both references to the very extensive bibliography, as well containing extra details to passages in the text. The whole is rounded out by a good index. As one would expect of a book about the greatest active supporter of design in UK history the book is stylishly presented. A pleasant and easy to read type face, a good selection of grey in grey illustrations and a good collection of colour plates. 

If you like good, stimulating and highly informative history books or just good books in general, then do yourself a favour and acquire Aton Howes’ excellent tome. No matter how much you think you might know about the last three centuries of British political, social, cultural and economic history, I guarantee that you will discover lots that you didn’t know. 

[1] Anton Howes, Arts and MindsHow the Royal Society of Arts Changed a Nation, Princeton University Press, Princeton & Oxford, 2020.


Filed under Book Reviews, Uncategorized

The emergence of modern astronomy – a complex mosaic: Part XLIV

Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.  

Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.

Sir Francis Bacon, c. 1618

You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.

Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting. 

Source: Wikimedia Commons

The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century. 

Hans Sloane by Stephen Slaughter Source: Wikimedia Commons

This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.

The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity. 

Frans Hals – Portrait of René Descartes Source: Wikimedia Commons

The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz. 

What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.  

The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck between 1684 and 1687. Source: Wikimedia Commons

Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.


I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; 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.

Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.

Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.

Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.

Engraving of Gottfried Wilhelm Leibniz Source: Wikimedia Commons

In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.

In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote: 

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. 

Relative, apparent, and common time […] is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…

Newton is saying that space and time have a separate existence and all objects exists within them.

In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects. 

 In his third letter to Clarke he wrote:

As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.

Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton. 

Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.


Filed under History of Astronomy, History of Physics, History of science, Newton

Microscopes & Submarines

The development of #histSTM in the early decades of the Dutch Republic, or Republic of the Seven United Netherlands, to give it its correct name, was quite extraordinary. Alongside the development of cartography and globe making, the most advanced in the whole of Europe, there were important figures such as the engineer, mathematician and physicist, Simon Stevin, the inventors of the telescope Hans Lipperhey and Jacob Metius, the mathematical father and son Rudolph and Willebrord Snel van Royan and Isaac Beeckman one of the founders of the mechanical philosophy in physics amongst others. However, one of the most strange and wonderful figures in the Netherlands during this period was, without doubt, the engineer, inventor, (al)chemist, optician and showman Cornelis Jacobszoon Drebbel (1571–1631).


Source: Wikimedia Commons

Drebbel is one of those larger than life historical figures, where it becomes difficult to separate the legends and the myths from the known facts, but I will try to keep to the latter. He was born to Jacob Drebbel an Anabaptist in Alkmaar in the province of North Holland. He seems not to have received much formal education but in about 1587 he started attending the Academy of the printmaker, draftsman and painter Hendrick Goltzius (1558–1617) in Haarlem also in North Holland.


Hendrick Goltzius – Self-Portrait, c. 1593-1594 – Google Art Project Source: Wikimedia Commons

Goltzius was regarded as the leading engraver in the Netherlands during the period and he was also an active alchemist. Drebbel became a skilled engraver under Goltzius’ instruction and also acquired an interest in alchemy. In 1595 he married Sophia Jansdochter Goltzius, Hendrick’s younger sister. They had at least six children of which four survived into adulthood. The legend says that Sophia’s prodigal life style drove Drebbel’s continual need to find better sources for earning money.


Drebbel’s town plan of Alkmaar 1597 Source: Wikimedia Commons

Drebbel initially worked as an engraver, cartographer and painter but somewhere down the line he began to work as an inventor and engineer.


Astronomy [from the series The Seven Liberal Arts]. Engraving by Drebbel Source: Wikimedia Commons

Not surprisingly, for a Netherlander, he a turned to hydraulic engineering receiving a patent for a water supply system in 1598. In 1600 he built a fountain at the Noorderpoort in Middelburg and at the end of his life living in England he was involved in a plan to drain the Fens. At some point, possibly when he was living in Middelburg, he learnt the craft of lens grinding, which would play a central roll in his life.

Also in 1598 he acquired a patent for Perpetuum mobile but which he, however, had not invented. The so-called Perpetuum mobile was a sort of clock, which was in reality powered in changes by the air temperature and air pressure had actually been invented by Jakob Dircksz de Graeff (1571–1638), an influential politician and natural philosopher, who was a friend of both Constantijn Huygens and René Descartes, and Dr Pieter Jansz Hooft (1574/5–1636) a politician, physician and schoolteacher.


Jakob Dircksz de Graeff Source: Wikimedia Commons


Pieter Jansz Hooft (1619), Attributed to Michiel van Mierevelt Source: Wikimedia Commons

Drebbel not only patented the Perpetuum mobile but also claimed to have invented it. His increasing reputation driven by this wonder machine earned his an invitation to the court of King James VI &I in London as the guest of the crown prince Henry in 1604. When on the court in London the Queen accidentally broke the Perpetuum mobile, Drebbel was unable to repair it.


The barometric clock of Cornelis Drebbel patented in 1598 and then known as “perpetuum mobile”. Print by Hiesserle von Choda (1557-1665) Source: Wikimedia Commons

At the court in London he was responsible for staging masques, a type of play with poetry, music, dance, and songs that was popular in the sixteenth and seventeenth centuries. He designed and built the stage sets and wonderful machines to enchant the audiences. Drebbel was by no means the only scientist-engineer to be employed to stage such entertainments during the Early Modern Period but he appears to have been very good at it. It was almost certainly Drebbel, who through his contacts imported from the Netherlands the first ever telescope to be seen in England, which was presented to James at the high point of a masque in 1609. He also built a magic lantern and a camera obscura with which he also entertained the members of the court.

Drebbel’s reputation grew to the point where he received an invitation to the court of the Holly Roman Empire, Rudolf II, in Prague in October 1610. Rudolf liked to surround himself with what might be termed wonder workers. Amongst those who had served in this capacity in Prague were Tycho Brahe, John Dee, Edward Kelley, Johannes Kepler and Jost Bürgi. There are no reports of any interactions between Drebbel and either Kepler or Bürgi, who were all on the court of Rudolf at the same time. In Prague he once again functioned as a court entertainer or showman.


AACHEN, Hans von – Portrait of Emperor Rudolf II Source: Wikimedia Commons

Rudolf was deposed by his brother Archduke Mathias in 1611and Drebbel was imprisoned for about a year. Following the death of Rudolf in 1612, Drebbel was released from prison and returned to London. Here, however, his situation was not as good as previously because Henry, his patron, had died in 1612. He kept his head above water as a lens grinder and instrument maker.

As a chemist Drebbel published his best-known written work Een kort Tractaet van de Natuere der Elemente (A short treatise of the nature of the elements) (Haarlem, 1621).


He was supposedly involved in the invention of the explosive mercury fulminate, Hg(CNO)2, but this is disputed. He also developed other explosive mixtures. He invented a chicken incubator with a mercury thermostat to keep it at a constant, stable temperature. This is one of the earliest feedback controlled devices ever created. He also developed and demonstrated a functioning air conditioning system.


Error-controlled regulator using negative feedback, depicting Cornelius Drebbel’s thermostat-controlled incubator of circa 1600. Source: Wikimedia Commons

He didn’t himself exploit one of his most successful discoveries, one that he made purely by accident. He dropped a flask of aqua regia (a mixture of nitric and hydrochloric acid, normally used to dissolve gold) onto a tin windowsill and discovered that stannous chloride (SnCl2) makes the colour of carmine (the red dye obtained from the cochineal insect) much brighter and more durable. Although Drebbel didn’t exploit this discovery his daughters Anna and Catherina and their husbands the brothers, Abraham and Johannes Sibertus Kuffler (a German inventor and chemist) did, setting up dye works originally in Leiden and then later in Bow in London. The colour was known as Colour Kuffler of Bow Dye and was very successful. Kuffler later continued his father-in-law’s development of self-regulating ovens that he demonstrated to the Royal Society.

In the early 1620s Constantijn Huygens, the father of Christiaan, came to London on a diplomatic mission. He made the acquaintance of Drebbel, who demonstrated his magic lantern and his camera obscura for the Dutch diplomat. Huygens was much impressed by his landsman and for a time became his pupil learning how to grind lenses, a skill that he might have passed onto his sons.


Constantijn Huygens (1596-1687), by Michiel Jansz van Mierevelt. Source: Wikimedia Commons

It is not known, who actually invented the microscope and it’s more than likely that the principle of the microscope was discovered by several people, all around the same time, who like Galileo looked through their Galilean or Dutch telescope the wrong way round. What, however, seems to be certain is that Drebbel is the first person known to have constructed a Keplerian telescope, that is with two convex lenses rather than a concave and a convex lens. As with all of his other optical instruments, Drebbel put on microscope demonstration introducing people to the microscopic world, as always the inventor as showman.

Drebbel’s most famous invention was without doubt his submarine. This is claimed to be the first-ever navigable submarine but has become the stuff of legends, how much of story is fact is difficult to assess. His submarine consisted of a wooden frame covered in leather, and one assumes waterproofed in someway; it was powered by oar.


Artistic representation of Drebbel’s submarine, artist unknown Source: Wikimedia Commons

It had bladders inside that were filled with water to enable the submarine to submerge; the bladders were emptied when the vessel was required to surface. In total between 1620 and 1624 Drebbel built three different vessels increasing in size. The final submarine had six oars and could carry up to sixteen passengers. Drebbel gave public demonstrations with this vessel on the river Thames. According to reports the vessel dived to a depth of four to five metres and remained submerged for three hours traveling from Westminster and Greenwich and back again. Assuming the reports to be true, there has been much speculation as to how fresh air was supplied inside the closed vessel. These speculations include a mechanical solution with some form of snorkel as well as chemical solutions with some sort of chemical apparatus to generate oxygen. It is also reported that Drebbel took King James on a dive under the Thames. Despite all of this Drebbel failed to find anybody, who would be prepared to finance a serious use of his submarine.

In the later 1620s Drebbel served the Duke of Buckingham as a military advisor but his various suggestions for weapons proved impractical and failed, the British blaming  the inventor and Drebbel blaming the English soldiers, finally ruining whatever reputation he still had. As already stated above towards the end of his life he was supposedly involved in a scheme to drain the Fens but the exact nature of his involvement remains obscure. Drebbel died in financial straights in 1633 in London, where he was scraping a living running a tavern on the banks of the Thames.

















Filed under History of Alchemy, History of Cartography, History of Chemistry, History of Optics, History of Technology, Renaissance Science