Category Archives: History of Astronomy

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°.

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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.

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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

Relation

Reconstruction

Actual Values

Sun’s radius in Earth radii (e.r.)

6.7

109

Earth’s radius in Moon radii

2.85

3.5

Earth/Moon distance in e.r.)

20

60.32

Earth/Sun distance in e.r.)

380

23,500

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.

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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.

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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.

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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.

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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.

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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.

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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) .

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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

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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

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

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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.

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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.

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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%.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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

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

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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.

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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).

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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.

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Portrait of Anders Celsius by Olof Arenius

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

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

and Charles Marie de La Condamine (1701–1774)

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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),

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

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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.

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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.

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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.

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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.

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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).

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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.

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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.

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John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons http://wellcomeimages.org 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 http://creativecommons.org/licenses/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)

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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).

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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).

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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.

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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.

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aberration

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.

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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.

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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.

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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.

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A scientific Dutchman

For many decades the popular narrative version of the scientific revolution started in Poland/Germany with Copernicus moving on through Tycho in Denmark, Kepler in Germany/Austria, Galileo et al in Northern Italy, Descartes, Pascal, Mersenne etc., in France and then Newton and his supporters and opponents in London. The Netherlands simply didn’t get a look in except for Christiaan Huygens, who was treated as a sort of honorary Frenchman. As I’ve tried to show over the years the Netherlands and its scholars–Gemma Frisius, Simon Stephen, Isaac Beeckman, the Snels, and the cartographers–actually played a central role in the evolution of the sciences during the Early Modern Period. In more recent years efforts have been made to increase the historical coverage of the contributions made in the Netherlands, a prominent example being Harold J Cook’s Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age.[1]

A very strange anomaly in the #histSTM coverage concerns Christiaan Huygens, who without doubt belongs to the seventeenth century scientific elite. Whereas my bookcase has an entire row of Newton biographies, and another row of Galileo biographies and in both cases there are others that I’ve read but don’t own. The Kepler collection is somewhat smaller but it is still a collection. I have no idea how many Descartes biographies exist but it is quite a large number. But for Christiaan Huygens there is almost nothing available in English. The only biography I’m aware of is the English translation of Cornelis Dirk Andriesse’s scientific biography of Christiaan Huygens, The Man Behind the Principle.[2] I read this several years ago and must admit I found it somewhat lacking. This being the case, great expectation have been raised by the announcement of a new Huygens biography by Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe.[3]

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So does Aldersey-Williams fulfil those expectations? Does he deliver the goods? Yes and no, on the whole he has researched and written what is mostly an excellent biography of the Netherland’s greatest scientist[4] of the Early Modern Period but it is in my opinion marred by sloppy history of science fact checking that probably won’t be noticed by the average reader but being the notorious #histSTM pedant that I am I simply can’t and won’t ignore.[5]

My regular readers will known that I describe myself as a narrative contextual historian of science and I personally believe that if we are to understand how science has evolved historical then we have to tell that story with its complete context. This being the case I’m very happy to report that Aldersey-Williams is very much a narrative contextual historian, who tells the complete story of Christiaan Huygens life within its wider context and not just offering up a list of his scientific achievements. In fact what the reader gets for his money is not just a biography of Christiaan but also a biography of his entire family with some members being given more space than other. In particular it is a full biography of Christiaan and his father Constantijn, who played a significant and central role in shaping Christiaan’s life.

The book opens by setting the scientific scene in the early seventeenth-century Netherlands. We get introduced to those scientists, who laid the scientific foundations on which Christiaan would later build. In particular we get introduced to Simon Steven, who shaped the very practice orientated science and technology of the Early Modern Netherlands. We also meet other important and influential figures such as Hans Lipperhey, Isaac Beeckman, Willebrord Snel, Cornelius Drebbel and others.

There now follows what might be termed a book within a book as Aldersey-Williams delivers up a very comprehensive biography of Constantijn Huygens diplomat, poet, composer, art lover and patron and all round lover of knowledge. Constantijn was interested in and fascinated by almost everything both scientific and technological. His interest was never superficial but was both theoretical and practical. For example he was not only interested in the newly invented instruments, the telescope and the microscope, but he also took instruction in how to grind lenses and that from the best in the business. Likewise his love for art extended beyond buying paintings and patronising artists, such as Rembrandt, but to developing his own skills in drawing and painting. Here Aldersey-Williams introduces us to the Dutch term ‘kenner’ (which is the same in German), which refers to someone such Constantijn Huygens, whose knowledge of a subject is both theoretical and practical. Constantijn Huygens married Suzanna von Baerle for love and they had five children over ten years, four sons and a daughter, Christiaan was the second oldest, and Suzanna died giving birth to their daughter, also named Suzanna.

Constantijn Huygens brought up his children himself educating them in his own polymathic diversity with the help of tutors. When older the boys spent brief periods at various universities but were largely home educated. We now follow the young Christiaan and his older brother, also Constantijn, through their formative young years. The two oldest boys remained close and much of Christiaan’s astronomical work was carried out in tandem with his older brother. We follow Christiaan’s early mathematical work and his introduction into the intellectual circles of Europe, especially France and England, through his father’s widespread network of acquaintances. From the beginning Christiaan was set up to become either a diplomat, like his father, grandfather and brothers, or a scientist and it is the latter course that he followed.

Aldersey-Williams devotes an entire chapter to Christiaan’s telescopic observations of Saturn, with a telescope that he and Constantijn the younger constructed and his reputation making discovery of Titan the largest of Saturn’s moons, and the first discovered, and his determination that the strange shapes first observed by Galileo around Saturn were in fact rings. These astronomical discoveries established him as one of Europe’s leading astronomers. The following chapter deals with Huygens’ invention of the pendulum clock and his excursions into the then comparatively new probability theory.

Saturn and the pendulum clock established the still comparatively young Huygens as a leading light in European science in the second half of the seventeenth century and Aldersey-Williams now takes us through ups and downs of the rest of Christiaan’s life. His contact with and election to the Royal Society in London, as its first foreign member. His appointment by Jean-Baptist Colbert, the French First Minister of State, as a founding member of the Académie des sciences with a fairy generous royal pension from Louis XIV. His sixteen years in Paris, until the death of Colbert, during which he was generally acknowledged as Europe’s leading natural philosopher. His initial dispute over light with the young and comparatively unknown Newton and his tutorship of the equally young and unknown Leibniz. His fall from grace following Colbert’s death and his reluctant return to the Netherlands. The last lonely decade of his life in the Netherlands and his desire for a return to the scientific bustle of London or Paris. His partial rapprochement with Newton following the publication of the Principia. Closing with the posthumous publication of his works on gravity and optics. This narrative is interwoven with episodes from the lives of Constantijn the father and Constantijn his elder brother, in particular the convoluted politics of the Netherlands and England created by William of Orange, whose secretary was Constantijn, the younger, taking the English throne together with his wife Mary Stewart. Christiaan’s other siblings also make occasional appearances in letters and in person.

Aldersey-Williams has written a monumental biography of two generations of the Huygens family, who played major roles in the culture, politics and science of seventeenth century Europe. With a light, excellent narrative style the book is a pleasure to read. It is illustrated with 37 small grey in grey prints and 35 colour plates, which I can’t comment on, as my review proof copy doesn’t contain them. There are informative footnotes scattered through out the text and the, by me hated, hanging endnotes referring to the sources of direct quotes in the text. Here I had the experience more than once of looking up what I took to be a direct quote only to discover that it was not listed. There is an extensive bibliography of both primary and secondary sources and I assume an extensive index given the number of blank pages in my proof copy. There were several times when I was reading when I had wished that the index were actually there.

On the whole I would be tempted to give this book a glowing recommendation were it not for a series of specific history of science errors that simple shouldn’t be there and some general tendencies that I will now detail.

Near the beginning Aldersey-Williams tells us that ‘Stevin’s recommendation to use decimals in arithmetical calculations in place of vulgar fractions which could have any denominator [was] surely the sand-yacht of accountancy … Thirty years later, the Scottish mathematician John Napier streamlined Stevin’s notation by introducing the familiar comma or point to separate off the fractional part…” As is all too often the case no mention is made of the fact that Chinese and Arabic mathematicians had been using decimal fractions literally centuries before Stevin came up with the concept. In my opinion we must get away from this Eurocentric presentation of the history of science. Also the Jesuit mathematician Christoph Clavius introduced the decimal point less than ten years after Stevin’s introduction of decimal fractions, well ahead of Napier, as was its use by Pitiscus in 1608, the probable source of Napier’s use.

We also get told when discussing the Dutch vocabulary that Stevin created for science that, “Chemistry becomes scheikunde, the art of separation, an acknowledgement of the beginnings of a shift towards an analytical science, and a useful alternative to chemie that severs the etymological connections with disreputable alchemy.” This displays a complete lack of knowledge of alchemy in which virtually all the analytical methods used in chemistry were developed. The art of separation is a perfectly good term from the alchemy that existed when Stevin was creating his Dutch scientific vocabulary. Throughout his book Aldersey-Williams makes disparaging remarks about both alchemy and astrology, neither of which was practiced by any of the Huygens family, which make very clear that he doesn’t actually know very much about either discipline or the role that they played in the evolution of western science, astrology right down to the time of Huygens and Newton and alchemy well into the eighteenth century. For example, the phlogiston theory one of the most productive chemical theories in the eighteenth century had deep roots in alchemy.

Aldersey-Williams account of the origins of the telescope is a bit mangled but acceptable except for the following: “By the following spring, spyglasses were on sale in Paris, from where one was taken to Galileo in Padua. He tweaked the design, claimed the invention as his own, and made dozens of prototypes, passing on his rejects so that very soon even more people were made aware of this instrument capable of bringing the distant close.”

Firstly Galileo claimed that he devised the principle of the telescope and constructed his own purely on verbal descriptions without having actually seen one but purely on his knowledge of optics. He never claimed the invention as his own and the following sentence is pure rubbish. Galileo and his instrument maker produced rather limited numbers of comparatively high quality telescopes that he then presented as gifts to prominent political and Church figures.

Next up we have Willebrord Snel’s use of triangulation. Aldersey-Williams tells us, “ This was the first practical survey of a significant area of land, and it soon inspired similar exercises in England, Italy and France.” It wasn’t. Mercator had previously surveyed the Duchy of Lorraine and Tycho Brahe his island of Hven before Snel began his surveying in the Netherlands. This is however not the worst, Aldersey-Williams tells us correctly that Snel’s survey stretched from Alkmaar to Bergen-op-Zoom “nearly 150 kilometres to the south along approximately the same meridian.” Then comes some incredible rubbish, “By comparing the apparent height of his survey poles observed at distance with their known height, he was able to estimate the size of the Earth!”

What Snel actually did, was having first accurately determined the length of a stretch of his meridian using triangulation, the purpose of his survey and not cartography, he determined astronomically the latitude of the end points. Having calculated the difference in latitudes it is then a fairly simple exercise to determine the length of one degree of latitude, although for a truly accurate determination one has to adjust for the curvature of the Earth.

Next up with have the obligatory Leonard reference. Why do pop history of science books always have a, usually erroneous, Leonardo reference? Here we are concerned with the camera obscura, Aldersey-Williams writes: “…Leonardo da Vinci gave one of the first accurate descriptions of such a design.” Ibn al-Haytham gave accurate descriptions of the camera obscura and its use as a scientific instrument about four hundred and fifty years before Leonardo was born in a book that was translated into Latin two hundred and fifty years before Leonardo’s birth. Add to this the fact that Leonardo’s description of the camera obscura was first published late in the eighteenth century and mentioning Leonardo in this context becomes a historical irrelevance. The first published European illustration of a camera obscura was Gemma Frisius in 1545.

When discussing Descartes, a friend of Constantijn senior and that principle natural philosophical influence on Christiaan we get a classic history of mathematics failure. Aldersey-Williams tells us, “His best known innovation, of what are now called Cartesian coordinates…” Whilst Descartes did indeed cofound, with Pierre Fermat, modern algebraic analytical geometry, Cartesian coordinates were first introduced by Frans van Schooten junior, who of course features strongly in the book as Christiaan’s mathematics teacher.

Along the same lines as the inaccurate camera obscura information we have the following gem, “When applied to a bisected circle (a special case of the ellipse), this yielded a new value, accurate to nine decimal places, of the mathematical constant π, which had not been improved since Archimedes” [my emphasis] There is a whole history of the improvements in the calculation of π between Archimedes and Huygens but there is one specific example that is, within the context of this book, extremely embarrassing.

Early on when dealing with Simon Stevin, Aldersey-Williams mentions that Stevin set up a school for engineering, at the request of Maurits of Nassau, at the University of Leiden in 1600. The first professor of mathematics at this institution was Ludolph van Ceulen (1540–1610), who also taught fencing, a fact that I find fascinating. Ludolph van Ceulen is famous in the history of mathematics for the fact that his greatest mathematical achievement, the Ludophine number, is inscribed on his tombstone, the accurate calculation of π to thirty-five decimal places, 3.14159265358979323846264338327950288…

Next up we have Christiaan’s correction of Descartes laws of collision. Here Aldersey-Williams writes something that is totally baffling, “The work [his new theory of collision] only appeared in a paper in the French Journal des Sçavans in 1669, a few years after Newton’s laws of motion [my emphasis]…” Newton’s laws of motion were first published in his Principia in 1687!

Having had the obligatory Leonardo reference we now have the obligatory erroneous Galileo mathematics and the laws of nature reference, “Galileo was the first to fully understand that mathematics could be used to describe certain laws of nature…” I’ve written so much on this that I’ll just say here, no he wasn’t! You can read about Robert Grosseteste’s statement of the role of mathematics in laws of nature already in the thirteenth century, here.

Writing about Christiaan’s solution of the puzzle of Saturn’s rings, Aldersey-Williams say, “Many theories had been advanced in the few years since telescopes had revealed the planet’s strange truth.” The almost five decades between Galileo’s first observation of the rings and Christiaan’s solution of the riddle is I think more than a few years.

Moving on Aldersey-Williams tells us that, “For many however, there remained powerful reasons to reject Huygens’ discovery. First of all, it challenged the accepted idea inherited from Greek philosophers that the solar system consisted exclusively of perfect spherical bodies occupying ideal circular orbits to one another.” You would have been hard put to it to find a serious astronomer ín 1660, who still ascribed to this Aristotelian cosmology.

The next historical glitch concerns, once again, Galileo. We read, “He dedicated the work [Systema Saturnium] to Prince Leopoldo de’ Medici, who was patron of the Accademia del Cimento in Florence, who had supported the work of Huygens’ most illustrious forebear, Galileo.” Ignoring the sycophantic description of Galileo, one should perhaps point out that the Accademia del Cimento was founded in 1657 that is fifteen years after Galileo’s death and so did not support his work. It was in fact founded by a group of Galileo’s disciples and was dedicated to continuing to work in his style, not quite the same thing.

Galileo crops up again, “the real power of Huygens’ interpretation was its ability to explain those times when Saturn’s ‘handles’ simply disappeared from view, as they had done in 1642, finally defeating the aged Galileo’s attempts to understand the planet…” In 1642, the year of his death, Galileo had been completely blind for four years and had actually given up his interest in astronomy several years earlier.

Moving on to Christiaan’s invention of the pendulum clock and the problem of determining longitude Aldersey-Williams tells us, “The Alkmaar surveyor Adriaan Metius, brother of the telescope pioneer Jacob, had proposed as long ago as 1614 that some sort of seagoing clock might provide the solution to this perennial problem of navigators…” I feel honour bound to point out that Adriaan Metius was slightly more than simply a surveyor, he was professor for mathematics at the University of Franeker. However the real problem here is that the clock solution to the problem of longitude was first proposed by Gemma Frisius in an appendix added in 1530, to his highly popular and widely read editions of Peter Apian’s Cosmographia. The book was the biggest selling and most widely read textbook on practical mathematics throughout the sixteenth and well into the seventeenth century so Huygens would probably have known of Frisius’ priority.

Having dealt with the factual #histSTM errors I will now turn to more general criticisms. On several occasions Aldersey-Williams, whilst acknowledging problems with using the concept in the seventeenth century, tries to present Huygens as the first ‘professional scientist’. Unfortunately, I personally can’t see that Huygens was in anyway more or less of a professional scientist than Tycho, Kepler or Galileo, for example, or quite a long list of others I could name. He also wants to sell him as the ‘first ever’ state’s scientist following his appointment to the Académie des sciences and the accompanying state pension from the king. Once again the term is equally applicable to Tycho first in Denmark and then, if you consider the Holy Roman Empire a state, again in Prague as Imperial Mathematicus, a post that Kepler inherited. Galileo was state ‘scientist’ under the de’ Medici in the Republic of Florence. One could even argue that Nicolas Kratzer was a state scientist when he was appointed to the English court under Henry VIII. There are other examples.

Aldersey-Williams’ next attempt to define Huygens’ status as a scientist left me somewhat speechless, “Yet it is surely enough that Huygens be remembered for what he was, a mere problem solver indeed: pragmatic, eclectic and synthetic and ready to settle for the most probable rather than hold out for the absolutely certain – in other words. What we expect a scientist to be today.” My ten years as a history and philosophy of science student want to scream, “Is that what we really expect?” I’m not even going to go there, as I would need a new blog post even longer than this one.

Aldersey-Williams also tries to present Huygens as some sort of new trans European savant of a type that had not previously existed. Signifying cooperation across borders, beliefs and politics. This is of course rubbish. The sort of trans European cooperation that Huygens was involved in was just as prevalent at the beginning of the seventeenth century in the era of Tycho, Kepler, Galileo, et al. Even then it was not new it was also very strong during the Renaissance with natural philosophers and mathematici corresponding, cooperating, visiting each other, and teaching at universities through out the whole of Europe. Even in the Renaissance, science in Europe knew no borders. It’s the origin of the concept, The Republic of Letters. I suspect my history of medieval science friend would say the same about their period.

In the partial rapprochement between Huygens and Newton following the Publication of the latter’s Principia leads Aldersey-Williams to claim that a new general level of reasonable discussion had entered scientific debate towards the end of the seventeenth century. Scientists, above all Newton, were still going at each other hammer and tongs in the eighteenth century, so it was all just a pipe dream.

Aldersey-Williams sees Huygens lack of public profile, as a result of being in Newton’s shadow like Hooke and others. He suggests that popular perception only allows for one scientific genius in a generation citing Galileo’s ascendance over Kepler, who he correctly sees as the more important, as another example. In this, I agree with him, however he tries too hard to put Huygens on the same level as Newton as a scientist, as if scientific achievement were a pissing contest. I think we should consider a much wider range of scientists when viewing the history of science but I also seriously think that no matter how great his contributions Huygens can’t really match up with Newton. Although his Horologium oscillatorium sive de motu pendularium was a very important contribution to the debate on force and motion, it can’t be compared to Newton’s Principia. Even if Huygens did propagate a wave theory of light his Traité de la lumière is not on a level with Newton’s Opticks. He does have his Systema saturniumbut as far as telescopes are concerned Newton’s reflector was a more important contribution than any of Huygens refractor telescopes. Most significant, Newton made massive contributions to the development of mathematics, Huygens almost nothing.

Talking of Newton, in his discussion of Huygens rather heterodox religious views Aldersey-Williams discussing unorthodox religious views of other leading scientists makes the following comment, “Newton was an antitrinitarian, for which he was considered a heretic in his lifetime, as well as being interested in occultism and alchemy.” Newton was not considered a heretic in his lifetime because he kept his antitrinitarian views to himself. Alchemy yes, but occultism, Newton?

I do have one final general criticism of Aldersey-Williams’ book. My impression was that the passages on fine art, poetry and music, all very important aspects of the life of the Huygens family, are dealt with in much greater depth and detail than the science, which I found more than somewhat peculiar in a book with the subtitle, The Making of Science in Europe. I’m not suggesting that the fine art, poetry and music coverage should be less but that the science content should have been brought up to the same level.

Despite the long list of negative comments in my review I think this is basically a very good book that could in fact have been an excellent book with some changes. Summa summarum it is a flawed masterpiece. It is an absolute must read for anybody interested in the life of Christiaan Huygens or his father Constantijn or the whole Huygens clan. It is also an important read for those interested in Dutch culture and politics in the seventeenth century and for all those interested in the history of European science in the same period. It would be desirable if more works with the wide-ranging scope and vision of Aldersey-Williams volume were written but please without the #histSTM errors.

[1] Harold J Cook, Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age, Yale University Press, New Haven & London, 2007

[2] Cornelis Dirk Andriesse, The Man Behind the Principle, scientific biography of Christiaan Huygens, translated from Dutch by Sally Miedem, CUP, Cambridge, 2005

[3] Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe, Picador, London, 2020.

[4] Aldersey-Williams admits that the use of the term scientist is anachronistic but uses it for simplicity’s sake and I shall do likewise here.

[5] I have after all a reputation to uphold

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Filed under Book Reviews, History of Astronomy, History of Mathematics, History of Navigation, History of Optics, History of Physics, History of science, Newton

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

Why wasn’t Newton’s Principia the end of the gradual emergence and acceptance of a heliocentric astronomical model for the then known cosmos? There is not one simple answer to this question, but a serious of problems created in different areas all of which had still to be addressed if there was going to be an unquestioned acceptance of heliocentricity. Some of those problems were inherent in the Principia itself, which should best be viewed as a work in progress rather than a finished concept. In fact, as we will see, Newton carried on working on improving the Principia over two further editions, expanding and correcting the first edition. Other problems arose in the philosophical rejection of key aspects of Newton’s work by highly influential and knowledgeable detractors. Finally there were still massive unsolved empirical problems outside of the scope of the Principia itself. These sets of problems run chronologically parallel to each other some of them all the way into the nineteenth century and beyond so in dealing with them I will take each one in turn following it to its conclusion and then return to the starting point for the next problem but first I will sketch in a little bit more detail the problems listed above.

To begin with we need to look at the reception of the Principia when it was first published. On a very general level that reception can be viewed as very positive. Firstly there were only a comparatively small number of experts qualified to judge the Principia, as the work is highly technical and complex. There is a famous anecdote of two men observing Newton walking in the gardens of Trinity College and one says to the other, “there goes a man, who wrote a book that is so complex that even he doesn’t understand it.” However, those, who could and did understand it all, acknowledged that the Principia was a monumental piece of mathematic physics, which had no equal at that time. They also acknowledged that Newton belonged to the very highest levels both as a natural philosopher and mathematician. However, both the Cartesians and Leibnizians rejected the whole of Newton’s work on fundamental philosophical grounds and as we will see it was a long uphill struggle to overcome their objections.

Of course the biggest obstacle to the general acceptance of a heliocentric system was the fact that there was still absolutely no empirical evidence for movement of the Earth, either diurnal rotation or annual rotation around the Sun. This was of course no small issue and could not be dismissed out of hand no matter how convincing and coherent the model that Newton was presenting appeared to be.

The final set of problems were astronomical ones that Newton had failed to solve whilst writing the Principia, open questions that still needed to be answered. There were two major ones the succeeding history of which we will examine, comets and the orbit of the Moon. As we will see showing that the orbit of the Moon obeys the law of gravity proved to be one of the biggest astronomical problems of most of the next century. In the 1680s Newton had only managed to show that the comet of 1680/81 had rounded the Sun on a parabolic orbit and extrapolated from this one result that the orbits of all comets obeyed the law of gravity. This was an unsatisfactory situation for Newton and it was here that he first began his programme to revise the Principia.

For what might be termed project comet flight path, Newton engaged Edmond Halley, who following his efforts as copyeditor, publisher, financier and midwife of the Principia became Newton’s lieutenant and most loyal supporter and one of the few fellow savants, whom Newton apparently never fell out with. Halley willingly took on the task of trying to determine the flight path of comets other than the 1680/81 comet, already included in the 1st edition of Principia.

Edmund_Halley-2

Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons

Starting around 1695 Halley began searching for and collecting observation data on all of the comets throughout history that he could find. Having acquired enough raw data to make a start he set about analysing it in order to try and determine flight paths. In the 1680s Newton had been the first astronomer to develop a technique for determining the flight path of a comet given three accurate observations at equal or nearly equal time differences. However, the method that he devised was anything but simple or practicable. Using his data he created a geometrical, semi-graphical plot of the flight path that he then iterated time and again, interpolating and extrapolating producing ever more accurate versions of the flight path. This method was both difficult and time consuming. Halley improved on this method, as he wrote to Newton, that having obtained the first three observations he had devised a purely numerical method for the determination of the flight path.

Halley started with the comet of 1683 and found a good fit for a parabolic orbit. This was followed by the comet of 1664, recognising some errors in Hevelius’ observations, and once again found a good fit for a parabolic orbit.

Komet_Flugschrift

The Great Comet of 1664: Johann Thomas Theyner (Frankfurt 1665) Source: Wikimedia Commons

At this point he first began to suspect that the comet of 1682,

which he had observed, was the same as the comet of 1607, observed by Thomas Harriot, William Lower and Johannes Kepler,

herlitz-von-dem-cometen_1-2

David Berlitz, Von dem Cometen oder geschwentzten newen Stern, welcher sich im September dieses 1607. Source

and the comet of 1531 observed Peter Apian amongst others.

SS2567834

Halley’s Comet 1531 Peter Apian Source

He also in his correspondence with Newton on the topic began to consider the problem of perturbation, that is deviation from the flight path caused by the gravitational attraction of Saturn and Jupiter, as a comet flew passed them. Neither Halley nor Newton succeeded in solving the problem of perturbation. In 1696 Halley held talks at the Royal Society in which he presented the results of his cometary research including his belief that the comets of 1607 and 1682 were one and the same comet on an elliptical orbit, which would return in 1757 or 1758.

Over a period of ten years Halley calculated the orbits of a further twenty comets presenting the results of his researches to the Royal society in 1702. Following his appointment as Savilian Professor for Astronomy at Oxford in 1705 he published the results of his work in the Philosophical Transactions of the Royal Society, Astronomiae cometicae synopsis, and also as a separate broadsheet, with the same title, from the Sheldonian Theatre in Oxford.

halley+sinopsys

An English translation, A synopsis of the astronomy of comets, was published in London in the same year. This work contained a table of results for twenty-four comets in total. Over the years Halley continued to work on comets and a final updated version of Astronomiae cometicae synopsis in 1726.

synopsisofastron00hall

In his work Halley emphasised the problem inherent in working with inaccurate historical observations. Newton used some of Halley’s results in both the second and third editions of Principia.

PSM_V76_D021_Orbit_of_the_planets_and_halley_comet

Diagram of Halley’s orbit in the Solar System Popular Science Monthly Volume 76 Source: Wikimedia Commons

Halley would have been one hundred and one years old in 1757 meaning he had little chance of seeing whether he had been correct in his assumptions concerning the comet from 1682; in fact he died at the ripe old age of eight-five in 1742. A team of three French mathematicians–Alexis Clairaut (1713–1765), Joseph Lalande (1732–1807) and Nicole-Reine Lepaute (1723–1788)–recalculated the orbit of the comet making adjustments to Halley’s results.

clairaut

Alexis Claude Clairaut Source: MacTutor

Jérôme_Lalande

Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons

lepaute001

Taken from Winterburn The Quite Revolution of Caroline Herschel see footnote 1

The comet returned as predicted and was first observed on Christmas Day 1758 by the German farmer and amateur astronomer Johann Georg Palitzsch (1723–1788).This was a spectacular confirmation of Newton’s theory of gravity and Halley’s work. The comet was named after Halley and is officially designated 1P/Halley. It is now know that it is the comet that appeared in 1066 and is depicted on the Bayeux tapestry

Tapisserie de Bayeux - Scène 32 : des hommes observent la comète de Halley

Bayeux Tapestry depiction of Comet Halley in 1066

PSM_V76_D015_Halley_comet_in_1066_after_emergence_from_the_sun_rays

Halley comet in 1066 after emergence from the sun rays artist unknown Source: Wikimedia Commons

and it was also the comet observed by Peuerbach and Regiomontanus in 1456.

PSM_V76_D015_Halley_comet_in_1456

Comet Halley 1456 artist unknown Source: Wikimedia Commons

SS2567833

Comet Halley 1456 a prognostication!

It still caused a sensation in 1910

Halley's_Comet,_1910

An image of Halley’s Comet taken June 6, 1910. The Yerkes Observatory – Purchased by The New York Times for publication. Source: Wikimedia Commons

 

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Filed under History of Astronomy, History of Mathematics, Newton

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

 

Newton’s Principia is one of the most original and epoch making works in the history of science. There is absolutely nothing original in Newton’s Principia. These two seemingly contradictory judgements of Isaac Newton’s Philosophiæ Naturalis Principia Mathematica are slightly exaggerated versions of real judgements that have been made at various points in the past. The first was the general hagiographical view that was prevalent for much of the eighteenth, nineteenth and twentieth centuries. The second began to appear in the later part of the twentieth century as some historian of science thought that Newton, or better his reputation, needed to be cut down a bit in size. So, which, if either of them, is correct? The surprising answer is, in a way, both of them.

Royal_Society_-_Isaac_Newton’s_Philosophiae_Naturalis_Principia_Mathematica_manuscript_1

Isaac Newton’s Philosophiae Naturalis Principia Mathematica manuscript volume from which the first edition was printed. Written in the hand of Humphrey Newton, Isaac Newton’s assistant. Source: Royal Society Library via Wikimedia Commons

The Principia is a work of synthesis; it synthesises all of the developments in astronomy and physics that had taken place since the beginning of the fifteenth century. All of the elements that make up Newton’s work were, so to speak, laid out for him to integrate into the book. This is what is meant when we say that there is nothing original in the Principia, however the way that Newton integrated them and what he succeeded in creating was at the time unique and totally original. The Principia was truly a case of the whole being greater than the parts. Before we take a brief look at the contents of the Principia there are a couple of anomalies in its construction that need to be addressed.

The first concerns the general methodological structure of the book. Medieval science was dominated, not exclusively, by the theories of Aristotle and Aristotelian methodology. The developments in astronomy, physics and mathematics that we have covered up to now in this series have seen a gradual but steady deconstruction of the Aristotelian structures and theories. In this situation it comes as a bit of surprise that the methodology of the Principia is classically Aristotelian. Aristotle stated that true episteme (Greek) or scientia (Latin), what we would term scientific knowledge, is achieved by setting out a set of first principles or axioms that are perceived as being true and not in need proof and then logically deducing new knowledge from them. Ironically the most famous example of this methodology is the Elements of Euclid, ironically because Aristotle regarded mathematics as not being real knowledge because it doesn’t deal with objects in the real world. This is the methodology that Newton uses in the Principia, setting out his three laws of motion as his basic principles, which we will come back to later, and not the modern methodologies of Francis Bacon or René Descartes, which were developed in the seventeenth century to replace Aristotle.

The second anomaly concerns the mathematics that Newton uses throughout the Principia. Ancient Greek mathematics in astronomy consisted of Euclidian geometry and trigonometry and this was also the mathematics used in the discipline in both the Islamic and European Middle Ages. The sixteenth and seventeenth centuries in Europe saw the development of analytical mathematics, first algebra and then infinitesimal calculus. In fact, Newton made major contributions to this development, in particular he, together with but independently of Gottfried William Leibniz, pulled together the developments in the infinitesimal calculus extended and codified them into a coherent system, although Newton unlike Leibniz had at this point not published his version of the calculus. The infinitesimal calculus was the perfect tool for doing the type of mathematics required in the Principia, which makes it all the more strange that Newton didn’t use it, using the much less suitable Euclidian geometry instead. This raises a very big question, why?

In the past numerous people have suggested, or even claimed as fact, that Newton first worked through the entire content of the Principia using the calculus and then to make it more acceptable to a traditional readership translated all of his results into the more conventional Euclidian geometry. There is only one problem with this theory. With have a vast convolute of Newton’s papers and whilst we have numerous drafts of various section of the Principia there is absolutely no evidence that he ever wrote it in any other mathematical form than the one it was published in. In reality, since developing his own work on the calculus Newton had lost faith in the philosophical underpinnings of the new analytical methods and turned back to what he saw as the preferable synthetic approach of the Greek Euclidian geometry. Interestingly, however, the mark of the great mathematician can be found in this retrograde step in that he translated some of the new analytical methods into a geometrical form for use in the Principia. Newton’s use of the seemingly archaic Euclidian geometry throughout the Principia makes it difficult to read for the modern reader educated in modern physics based on analysis.

When referencing Newton’s infamous, “If I have seen further it is by standing on the sholders [sic] of Giants”, originally written to Robert Hooke in a letter in 1676, with respect to the Principia people today tend to automatically think of Copernicus and Galileo but this is a misconception. You can often read that Newton completed the Copernican Revolution by describing the mechanism of Copernicus’ heliocentric system, however, neither Copernicus nor his system are mentioned anywhere in the Principia. Newton was a Keplerian, but that as we will see with reservations, and we should remember that in the first third of the seventeenth century the Copernican system and the Keplerian system were viewed as different, competing heliocentric models. Galileo gets just five very brief, all identical, references to the fact that he proved the parabola law of motion, otherwise he and his work doesn’t feature at all in the book. The real giants on whose shoulders the Principia was built are Kepler, obviously, Descartes, whose role we will discuss below, Huygens, who gets far to little credit in most accounts, John Flamsteed, Astronomer Royal, who supplied much of the empirical data for Book III, and possibly/probably Robert Hooke (see episode XXXIX).

We now turn to the contents of the book; I am, however, not going to give a detailed account of the contents. I Bernard Cohen’s A Guide to Newton’s Principia, which I recommend runs to 370-large-format-pages in the paperback edition and they is a whole library of literature covering aspects that Cohen doesn’t. What follows is merely an outline sketch with some comments.

As already stated the book consists of three books or volumes. In Book I Newton creates the mathematical science of dynamics that he requires for the rest of the book. Although elements of a science of dynamics existed before Newton a complete systematic treatment didn’t. This is the first of Newton’s achievement, effectively the creation of a new branch of physics. Having created his toolbox he then goes on to apply it in Book II to the motion of objects in fluids, at first glance a strange diversion in a book about astronomy, and in Book III to the cosmos. Book III is what people who have never actually read Principia assume it is about, Newton’s heliocentric model of the then known cosmos.

Mirroring The Elements of Euclid, following Edmond Halley’s dedicatory ode and Newton’s preface, Book I opens with a list of definitions of terms used. In his scholium to the definitions Newton states that he only defines those terms that are less familiar to the reader. He gives quantity of matter and quantity of motion as his first two definitions. His third and fourth definitions are rather puzzling as they are a slightly different formulation of his first law the principle of inertia. This is puzzling because his laws are dependent on the definitions. His fifth definition introduces the concept of centripetal force, a term coined by Newton in analogy to Huygens’ centrifugal force. In circular motion centrifugal is the tendency to fly outwards and centripetal in the force drawing to the centre. As examples of centripetal force Newton names magnetism and gravity. The last three definitions are the three different quantities of centripetal force: absolute, accelerative and motive. These are followed by a long scholium explicating in greater detail his definitions.

We now arrive at the Axioms, or The Laws of Motions:

1) Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.

This is the principle of inertia that Newton had taken from Descartes, who in turn had taken it from Isaac Beeckman.

2) A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

Somewhat different from the modern formulation of F=ma, this principle has its origin in the work of Huygens although there is not a one to one correspondence.

3) To any action there is always an opposite and equal reaction, in other words, the actions of two bodies upon each other are always equal and always opposite in direction.

This law originates with Newton and its source is not absolutely clear. It seems to have been inspired by Newton’s examination of Descartes laws of inelastic collision but it might also have been inspired by a similar principle in alchemy of which Newton was an ardent disciple.

Most people are aware of the three laws of motion, the bedrock of Newton’s system, in their modern formulations and having learnt them, think that they are so simple and obvious that Newton just pulled them out of his hat, so to speak. This is far from being the case. Newton actually struggled for months to find the axioms that eventually found their way into the Principia. He tried numerous different combinations of different laws before finally distilling the three that he settled on.

Having set up his definitions and laws Newton now goes on to produce a systematic analysis of forces on and motion of objects in Book I. It is this tour de force that established Newton’s reputation as one of the greatest physicist of all time. However, what interests us is of course the law of gravity and its relationship to Kepler’s laws of planetary motion. The following is ‘plagiarised’ from my blog post on the 400th anniversary of Kepler’s third law.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[1], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[2] he then shows that, If several bodies revolve about a commo[3]n center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name. Newton would go one to claim the rights to laws one and two as he had, in his opinion, provided their first real proof. He acknowledges, however, Kepler’s claim to the third law.

Book II as already mentioned appears to go off a tangent in that it deals with motion in a fluid medium, as a result it tends to get ignored, although it is as much a tour de force as Book I. Why this detour? The answer can be found in the theories of René Descartes and Newton’s personal relationship to Descartes and his works in general. As a young man Newton undertook an extensive programme of self-study in mathematics and physics and there is no doubt that amongst the numerous sources that he consulted Descartes stand out as his initial primary influence. At the time Descartes was highly fashionable and Cambridge University was a centre for interest in Descartes philosophy. At some point in the future he then turned totally against Descartes in what could almost be describe as a sort of religious conversion and it is here that we can find the explanation for Book II.

Descartes was a strong supporter of the mechanical philosophy that he had learnt from Isaac Beeckman, something that he would later deny. Strangely, rather like Aristotle, objects could only be moved by some form of direct contact. Descartes also rejected the existence of a vacuum despite Torricelli’s and Pascal’s proof of its existence. In his Le Monde, written between 1629 and 1633 but only published posthumously in 1664 and later in his Principia philosophiae, published in 1644, Descartes suggested that the cosmos was filled with very, very fine particles or corpuscles and that the planets were swept around their orbits on vortexes in the corpuscles. Like any ‘religious’ convert, Newton set about demolishing Descartes theories. Firstly, the title of his volume is a play upon Descartes title, whereas Descartes work is purely philosophical speculation, Newton’s work is proved mathematically. The whole of Book II exists to show that Descartes’ vortex model, his cosmos full of corpuscles is a fluid, can’t and doesn’t work.

Book III, entitled The System of the World, is as already said that which people who haven’t actually read it think that the Principia is actually about, a description of the cosmos. In this book Newton applies the mathematical physics that he has developed in Book I to the available empirical data of the planets and satellites much of it supplied by the Astronomer Royal, John Flamsteed, who probably suffered doing this phase of the writing as Newton tended to be more than somewhat irascible when he needed something from somebody else for his work. We now get the astronomical crowning glory of Newton’ endeavours, an empirical proof of the law of gravity.

Having, in Book I, established the equivalence of the law of gravity and Kepler’s third law, in Book III of The PrincipiaThe System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[4] Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 2: The circumsaturnian planets, by radii drawn to the center of Saturn, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 3: The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun. Phenomena 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun—the fixed stars being at rest—are as the 3/2 powers of their mean distances from the sun. “This proportion, which was found by Kepler, is accepted by everyone.”

Proposition 1: The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the center of Jupiter and are inversely as the squares of the distances of their places from that center. “The same is to be understood for the planets that are Saturn’s companions.” As proof he references the respective phenomena from Book I. Proposition 2: The forces by which the primary planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the sun and are inversely as the squares of the distances of their places from its center. As proof he references the respective phenomenon from Book I.

In the 1st edition of Principia Newton referenced the solar system itself and the moons of Jupiter as system that could be shown empirically to Kepler’s third law and added the moons of Saturn in the 3rd edition.

Book III in the first edition closes with Newton’s study of the comet of 1680/81 and his proof that its flight path was also determined by the inverse square law of gravity showing that this law was truly a law of universal gravity.

I have gone into far more detain describing Newton’s Principia than any other work I have looked out in this series because all the various streams run together. Here we have Copernicus’s initial concept of a heliocentric cosmos, Kepler’s improved elliptical version of a heliocentric cosmos with it three laws of planetary motion and all of the physics that was developed over a period of more than one hundred and fifty years woven together in one complete synthesis. Newton had produced the driving force of the heliocentric cosmos and shown that it resulted in Kepler’s elliptical system. One might consider that the story we have been telling was now complete and that we have reached an endpoint. In fact, in many popular version of the emergence of modern astronomy, usually termed the astronomical revolution, they do just that. It starts with Copernicus’ De revolutionibus and end with Newton’s Principia but as we shall see this was not the case. There still remained many problems to solve and we will begin to look at them in the next segment of our story.

[1]  Isaac Newton, The PrincipiaMathematical Principles of Natural Philosophy, A New Translation by I: Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen, University of California Press, Berkley, Los Angeles, London, 1999 p. 462

[2] Newton, Principia, 1999 p. 467

[3] Newton, Principia, 1999 p. 468

[4] Newton, Principia, 1999 pp. 797–802

 

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

The event that would eventually lead to Isaac Newton writing and publishing his magnum opus, the Philosophiæ Naturalis Principia Mathematica (the Mathematical Principles of Natural Philosophy), took place in a London coffee house.

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Title page of ‘Principia’, first edition (1687). Source: Wikimedia Commons

This is not quite as strange as it might at first appear, shortly after their first appearance in England around 1650 coffee houses became the favourite meeting places of the English scientific intelligentsia, the astronomers, mathematicians and natural philosophers. Here, these savants would meet up to exchange ideas, discuss the latest scientific theories and pose challenges to each other. These institutions also earned the appellation Penny Universities, as some of those savants, such as William Whiston, Francis Hauksbee and Abraham de Moivre, bettered their incomes by holding lectures or demonstrating experiments to willing audiences, who paid the price of a cup of coffee, a penny, for their intellectual entertainment. Later, after he had become Europe’s most famous living natural philosopher, Isaac Newton would come to hold court in a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny. However, all that still lay in the future.

One day in January 1684 Christopher Wren, Robert Hooke and Edmond Halley were discussing the actual astronomical theories over a cup of coffee. Wren, today better known as one of England most famous architects, was a leading mathematician and astronomers, who had served both as Gresham and Savilian professor of astronomy. Newton would name him along with John Wallis and William Oughtred as one of the three leading English mathematicians of the seventeenth century.

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Wren, portrait c.1690 by John Closterman Source: Wikimedia Commons

Hooke was at the time considered to be the country’s leading experimental natural philosopher and Halley enjoyed an excellent reputation as a mathematician and astronomer.

NPG 4393; Edmond Halley by Richard Phillips

Portrait by Richard Phillips, before 1722 Source: Wikimedia Commons

The topic of discussion was Kepler’s elliptical, heliocentric astronomy and an inverse, squared law of gravity. All three men had arrived separately and independently at an inverse, squared law of gravity probably derived from Huygens’ formula for centrifugal force. Wren posed the question to the other two, whether they could demonstrate that such a law would lead to Kepler’s elliptical planetary orbits.

Hooke asserted that he already had such a demonstration but he would first reveal it to the others after they had admitted that they couldn’t solve the problem. Wren was sceptical of Hooke’s claim and offered a prize of a book worth forty shillings to the first to produce such a demonstration.  Hooke maintained his claim but didn’t deliver. It is worth noting that Hooke never did deliver such a demonstration. Halley, as already said no mean mathematician, tried and failed to solve the problem.

In August 1684 Halley was visiting Cambridge and went to see Newton in his chambers in Trinity College, who, as we know, he had met in 1682.

Trinity_College_Cambridge_1690

Trinity College Cambridge, David Loggan’s print of 1690 Source: Wikimedia Commons

According the Newton’s account as told to Abraham DeMoivre, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…” Newton acted out the charade of looking for the supposed solution but couldn’t find it. However he promised Halley that he would send him the solution.

In November Edward Paget, a fellow of Trinity College, brought Halley a nine page thesis entitled De motu corporum in gyrum (On the Motion of Bodies in an Orbit).

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Page of the De motu corporum in gyrum

When Halley read Newton’s little booklet he was immediately aware that he held something truly epoch making in the history of astronomy and physics in his hand. Newton had delivered up a mathematical proof that an elliptical orbit would be produced by an inverse square force situated at one of the foci of the ellipse, thus combining the inverse square law of gravity with Kepler’s first law. He went on to also derive Kepler’s second and third laws as well as laying down the beginnings of a mathematical theory of dynamics. Halley reported details of this extraordinary work to the Royal Society on 10 December 1684:

Mr Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De motu: which, upon Mr. Halley’s desire, was he said promised to be sent to the Society to be entered upon their register.

Mr. Halley was desired to put Mr. Newton in mind of his promise for securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.

The interest in and the demand to read Newton’s new production was very high but the author decided to improve and rewrite his first offering, triggering one of the most extraordinary episodes in his life.

Although he was Lucasian Professor and would turn forty-two on 25 December 1684, Newton remained a largely unknown figure in the intellectual world of the late seventeenth century. Following the minor debacle that resulted from the publication of his work in optics in the 1670s he had withdrawn into his shell, living in isolation within the walls of Cambridge University. He carried out his duties as Lucasian Professor but had almost no students to speak of and definitely no disciples. Thanks to the word of mouth propaganda of people like his predecessor as Lucasian Professor, Isaac Barrow, and above all the assiduous mathematics groupie, John Collins, it was rumoured that a mathematical monster slumbered in his chambers in Trinity College but he had done nothing to justify this bruited reputation. His chambers were littered with numerous unfinished scientific manuscripts, mostly mathematical but also natural philosophical and an even larger number of alchemical and theological manuscripts but none of them was in a fit state to publish and Newton showed no indication of putting them into a suitable state. Things now changed, Newton had found his vocation and his muse and the next two and a half years of his life were dedicated to creating the work that would make him into a history of science legend, the reworking of De motu into his Principia.

Over those two and a half years Newton turned his nine-page booklet into a major three-volume work of science. The modern English translation by I B Cohen runs to just over 560 large format pages, although this contains all the additions and alterations made in the second and third editions, so the original would have been somewhat shorter. Halley took over the editorship of the work, copyediting it and seeing it through the press. In 1685 the Royal Society had voted to take over the costs of printing and publishing Newton’s masterpiece, so everything seemed to be going smoothly and then disaster struck twice, firstly in the form of Robert Hooke and secondly in the form of a financial problem.

Hooke never slow to claim his priority in any matter of scientific discovery or invention stated that he alone had first discovered the inverse square law of gravity and that this fact should, indeed must, be acknowledged in full in the preface to Newton’s book. Halley, realising at once the potential danger of the situation, was the first to write to Newton outlining Hooke’s claim to priority, stating it, of course, as diplomatically as possible. Halley’s diplomacy did not work, Newton went ballistic. At first his reaction was comparatively mild, merely pointing out that he had had the inverse square law well before his exchanges with Hook in 1679 and had, in fact, discussed the matter with Wren in 1677, go ask him, Newton said. Then with more time to think about the matter and building up a head of steam, Newton wrote a new letter to Halley tearing into Hooke and his claim like a rabid dog. All of this ended with Newton declaring that he would no longer write volume three of his work. Halley didn’t know this at the time but this was in fact, as we shall see, the most important part of the entire work in which Newton presented his mathematical model of a Keplerian cosmos held together by the law of gravity. Halley remained calm and used all of his diplomatic skills to coax, flatter, persuade and cajole the prickly mathematician into delivering the book as finished. In the end Newton acquiesced and delivered but acknowledgements to Hooke were keep to a minimum and offered at the lowest level of civility.

The financial problem was of a completely different nature. In 1685 the Royal Society had taken over the cost of printing and publishing the deceased Francis Willughby’s Historia piscium as edited by John Ray.

This was an expensive project due to the large number plates that the book contained and the book was, at the time, a flop. This meant when it came time to print and publish Newton’s work the Royal Society was effectively bankrupt. One should note here that the popular ridicule poured out over Willughby’s volume, it having almost prevented Newton’s masterpiece appearing, is not justified. Historia piscium is an important volume in the history of zoology. Halley once again jumped into the breach and took over the costs of printing the volumes; on the 5 July 1687 Halley could write to Newton to inform him that the printing of his Philosophiæ Naturalis Principia Mathematica had been completed.

 

 

 

 

 

 

 

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Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of science, Newton