Folkes, his diary, Freemasonry and metrology

In her discussion of early eighteenth-century arguments between materialists and anti-materialists, and of the formal foundation of modern Freemasonry with the establishment of the Grand Lodge in London in 1717, Margaret Jacob has suggested that ‘tolerant-minded Newtonians … invented a new form of ritual to worship the Grand Architect of the Universe’; Jacobs argued, in short, that Freemasonry was an innovation sprung ‘from Newtonian inspiration’.Footnote ²⁶ Garry Trompf agreed, writing, ‘The more one ponders Newton's axial principles … and then one relates this covert, Talmudically-inspired unorthodoxy to his fascination for the mysterious proportions of the Solomonic temple, the more one can sense the milieu of early Freemasonry.’Footnote ²⁷ Folkes was not only a ‘prestigious figure in the scientific and antiquarian communities’ in Britain and the Continent, but also a visible ambassador of Freemasonry's ideals of free thought and sociability, and of Newtonian scientific principles. It was rumoured, after Folkes returned from Italy, that he was the author of the scurrilous Relation Apologique (1738) for Freemasonry which applied Newtonian principles to government and communicated Masonry as a primarily scientific institution.Footnote ²⁸

Folkes was a follower of speculative Freemasonry, a non-sectarian group of freethinkers to which many fellows of the Society of Antiquaries and the Royal Society belonged; forty-five percent of the fellows of the Royal Society were Masons in the 1720s.Footnote ²⁹ Between 1719 and 1742, he proposed eleven fellow Masons of the Bedford Head and Maid's Head Lodge in Norfolk (which he founded) as fellows of the Royal Society.Footnote ³⁰ Folkes's friend and patron, Charles Lennox, was grand master of the Bedford Head Lodge (installed in 1724/5), and a fellow of the Royal Society. Folkes also provided Lennox with antiquarian documents about Freemasonry; Lennox wrote to Folkes in 1725 apologizing for missing the Masonic feast day of St John's, ‘guilty of such an omission that nobody less than the Deputy Grand Master of Masonry can make up for me’. He then proceeded, ‘I thanke you for the Old Record you sent me, it is really very curious, & a certain proof at least, of our antiquity, to the unbelievers’.Footnote ³¹

Although the precise line that divided deism, natural religion and the revealed religion of the orthodox Christian was subtle in this period, Folkes's travel diary to Italy confirmed his freethinking beliefs. He noted that he considered Catholicism and Protestantism ‘as only a tool of the state to keep the vulgar in awe’, noting that Venetian intellectuals were ‘fond of any sort of freethinking book, and with what eagerness they speak on the subject and enquire after the ways of thinking of a nation more used to liberty of thought than themselves’.Footnote ³² That said, Folkes did go on to find them wanting in the knowledge of religion:

Martin Folkes considered the Bible an authoritative historical source (one of many), and even helped Thomas Pellet edit a manuscript of Newton's Biblical Chronology of Ancient Kingdoms, ‘a truncated version of Newton's more radical manuscript’, as historian James Force has called it.Footnote ³⁴ Newton used data about the precession of the equinoxes to formulate his new chronology, and Folkes's astronomical expertise was useful in this regard. Folkes, however, unlike Newton, did not identify with the use of astronomical data to vindicate religious truths, admitting to his friend John Byrom that he was ‘a heretic about the book of Daniel’.Footnote ³⁵ Nor was Folkes a believer in natural theology, also admitting to Byrom that he thought William Derham's Astro –Theology, a corollary to the Boyle Lectures that used natural history and teleology to promote and prove a natural theology, ‘a silly book’.Footnote ³⁶ It seemed an appropriate comment for someone with such a resolutely non-teleological personal motto.

As a Freemason, Folkes was, however, interested in using biblical evidence in other ways. He wished to clarify the scripturally ambiguous dimensions of the sacred cubit of the Hebrews used to build Solomon's Temple, and to assess the dimensions of the Roman foot.Footnote ³⁷ Folkes took as his motto in the album amicorum (friendship book) for the Egyptian Society ‘omnia in mensura et numero et pondere diposuisti’, or ‘thou has ordered all things in measure and number and weight (Wisdom, 11:21)’. Folkes's interests reflected the current intellectual milieu, as Masonry emphasized a mathematical deity that, in Elliot and Daniels's phrase, ‘accorded well with the Newtonian conception of the universe, with a grand mathematician or architect at the centre’.Footnote ³⁸ Newton had previously written a dissertation upon the sacred cubit which would be republished in 1737, along with the works of John Greaves by antiquary Thomas Birch, who wrote the History of the Royal Society (1757). Moreover, as Haycock noted, in 1723, Bernard Lamy published his Apparatus Biblicus with engravings of the Tabernacle and Temple, and in 1726 William Whiston advertised ‘a small, but curious Course of Lectures’ on astronomical subjects which also included ‘Sacred Architecture past’, as well as ‘Sacred Architecture Future’.Footnote ³⁹ Freemasonry was taking off in London at this time, with prominent Newtonians playing an active role.

Therefore it is not surprising that one of Folkes's first tasks when he arrived in Venice was to measure the height of the Campanile by its shadow, concluding that it was 140 feet high. He then measured again to confirm his conclusions; to do this, Folkes figured out the conversion factor between Venetian palms and English feet. He then proceeded to measure the Rialto bridge in Venice to confirm his determination and comparison of past standards of measurement. Folkes noted on 8 July 1733 that, ‘writers not agreeing perfectly with one another’ about the Rialto's dimensions, he decided to measure it himself using ‘packthread’ and a plumb bob; he made a sketch in his diary of the bridge recording his observations.Footnote ⁴⁰ He carefully compared his own measures of the Rialto to those of it taken by Francesco Sansovino, the son of Jacopo Sansovino (1486–1570). Jacopo was the proto or chief architect of Venice who was responsible for the rebuilding of the Fabbriche Nuove di Rialto complex (seat of the magistrates in charge of customs and duty).Footnote ⁴¹ Disturbed that his measurements of the bridge were different from Sansovino's, he wrote,

After making some enquiries after the original standard of the Venetian measures, which he found to be fruitless, he ‘took some measures of St Geminiano's Church in order to have made something out by them’. However, upon comparing the measures he had taken, Folkes found the church ‘was not built by the Venetian foot but by the Roman Architectonick palm whose length comes out very exactly by it’.Footnote ⁴³

It was a perceptive comment. St Geminiano was in the Piazza San Marco, part of the complete remodelling of the piazza and surrounding buildings by Sansovino in Renaissance Venice in the classical style; as historian Fiona Kisby has noted, the ‘effect was to superimpose an evocation of ancient Rome on the existing Byzantine elements’.Footnote ⁴⁴ St Geminiano, directly across the piazza from San Marco, was a focal point of the architectural complex designed by Jacopo Sansovino in Vitruvian proportion to evoke the ancient Roman forum (Figure 2). Hence Folkes suspected and proved that Sansovino used Roman measurements to create his building, particularly as Vitruvius in his third book of De Architectura gave a thorough description of the Roman foot or pes and palms (one-quarter of the foot).Footnote ⁴⁵ In this manner, principles of measure and geometry would ensure harmony and aesthetic appeal in the building's design. In other words, Folkes was investigating architectural metrology to provide what we would term archaeological information about architects and builders of Renaissance Venice, and, as we will see, ancient Rome.

Figure 2.

Piazza San Marco, etching by Canaletto, 1710–1758, Rijksmuseum, Amsterdam, public domain, object number RP-P-OB-35.577. St Geminiano, indicated by the arrow, was the focal point of the piazza which evoked the Roman past.

Queries about ancient metrology began in 1573 with the publication of De Mensuris et ponderibus Romanis et Graecis by Lucas Paetus. That publication spawned an active debate about the exact length of the pes. Dissatisfied with inconsistencies in textual evidence, John Greaves, professor of astronomy at Oxford, visited Rome in 1639, to ‘examine as many ancient measures, and monuments, in Italy, and other parts, as it was possible’, and to compare these ‘with as many Standards, and Originals, as I procure the sight of’.Footnote ⁴⁶ He thus measured brass measuring rods in Roman ruins, and the foot measures on the tomb of Titus Statilius Aper and the statue of Cossutius. Greaves then noted with some pleasure that these foot measures exactly corresponded with the distance between the milestones on the Appian Way.Footnote ⁴⁷ He then made comparisons between the Roman foot and the iron standard of the English foot in the London Guildhall and published his findings on Discourse on the Romane foot and denarius in 1647, concluding that the Cossutian foot was the ‘true’ Roman pes. Greaves also claimed that he thought he could find a relationship between the pes and the sacred cubit, something which Newton also noted in his own treatise on the cubit.

Folkes followed the same methodology as Greaves in his own travels. In 1736, Folkes identified the Root Canonical Greek foot as 1.0057142 times the English measure, and the Roman pes as 0.966 of the English foot, noting them as being engraved on a standards stone tablet at the Roman Capitol that might have been the actual record of the pes monetalis. His paper about the stone was subsequently published in the Philosophical Transactions of the Royal Society; Folkes recorded ‘setting the point of my Compasses’ in the lines in the stone that represented the measures, and also noted his ‘chief Attention was given to the Roman foot, as of greater Consequence than the other measures’.Footnote ⁴⁸

In making his conclusion, Folkes considered previous measurements made by Fabretti, but recorded in his diary that he also measured the height of the Trajan Pillar ‘using an exact two-foot rule brought from London’. Folkes was particularly interested in the column because the height of its shaft from the plinth of the base to the abacus of the column was said to measure exactly one hundred Roman feet, a columna centenaria.Footnote ⁴⁹ The column was thus ideal to determine the dimensions of the Roman foot.Footnote ⁵⁰ Now, of course, studies of metrology and measurement surveys of ancient buildings constitute some of the most important work in archaeology.Footnote ⁵¹ He found the column, ‘from the Ground to the Top of the Cimatium of the Capitol’, to be ‘115 feet 10 inches 5/8’; this height, divided by 120, gave nearly 966 for the quotient, thus confirming that the Roman foot was 0.966 of an English foot and used frequently in Roman architecture. Ironically, Folkes's exactitude of measurement has not been borne out in modern studies as there appear to be some slight variations in the Roman pes. Historians Soren and Soren attribute these variations to ‘the Augustan decree to standardise Roman metrology … most easily implemented by the transport of replicas of the pes monetalis at Rome to the colonies’.Footnote ⁵²

During his tour, Folkes also discussed his work on Trajan's Column in more depth with the Venetian Francesco Algarotti. Folkes was interested in measuring the figures on the column to assess and compare the Roman artist's use of visual perspective as opposed to the use of perspective in modern artistic practice.Footnote ⁵³ Their conversation comparing ancient and modern techniques was an extension of the literary quarrel of the ‘ancients and moderns’ that raged amongst French and English intellectuals in the seventeenth and early eighteenth centures. Intellectuals who sided with the ‘ancients’ argued that antique literature offered the sole models for literary excellence; the ‘moderns’, on the other hand, challenged the supposed supremacy of the classical writers. This scholarly debate was extended to assessing technological and aesthetic achievement.Footnote ⁵⁴ Folkes was particularly interested in discussing with Algarotti to what extent measurement could answer questions about the relative merits of ancient technology and artistic production.

Algarotti had associated himself with ‘radical conversazioni and early masonic lodges’ at some point during his tours of Padua and the Veneto, and subsequently in Florence and Rome of the early 1730s, where he met Folkes.Footnote ⁵⁵ Algarotti was best known for his popularization of Newton's precepts in his Il Newtonianismo per le dame, but he also wrote a number of letters and essays on aesthetics, including one in which he analysed the helical frieze on Trajan's Column. In a letter to Jean Paolucci, Algarotti recalled that he speculated with Folkes as to whether the bas relief on Trajan’s Column gave them any reason to presume that the ancients did not have any knowledge of the ‘proportions of perspective’.Footnote ⁵⁶ Folkes noted in an article he later published about the column that

It appeared from Folkes's observations of the column that the Roman artists who carved frieze on the column did not use traditional perspectival techniques in their portrayal of the Dacian Wars.

Algarotti also recalled discussing with Folkes the arguments of Charles Perrault, who rose in the French Academy to champion modern authors in the quarrel between the ancients and moderns. Folkes and Algarotti noted that Perrault was of the opinion that while the ancients excelled in sculpture (a genre that in Perrault's eyes demanded little ‘reflection’ and abstract thought), bas-reliefs and painting required a deeper understanding of perspective and spatial relations which the ancients did not have. Perrault thought his opinion was supported by the ‘casts of the Trajan Column’ he saw in Paris, which to him were naive in their understanding of perspective space.Footnote ⁵⁸ However, Folkes and Algarotti were sceptical about Perrault's claim, Algarotti writing that ‘the defects which are believed to been seen in the ancient bas-reliefs, and especially in the Trajan Column, prove nothing against the knowledge of the ancients in regard to perspective’. Rather, Algarotti and Folkes realized the artists who carved the column used fewer emblematic forms to represent the events of the war rather than hundreds of individual participants; perspectival tricks could not assist the artist in highlighting ‘certain figures, groups, or parts of the composition’. Indeed, the composition in the frieze is characterized by diagonals so that the ‘figure of the emperor is emphasized along with the direction of gazes and actions of the figures surrounding him’.Footnote ⁵⁹ To make the figures and iconography intelligible to a spectator who was at a great distance, the composition required a multiperspectival approach and simple converging and diverging orthogonals were not appropriate. Trajan's Column was in fact designed so that viewers could comprehend the story of the Dacian Wars from bottom to top standing in one place rather than circling the column twenty-three times as the carved spiral frieze does. A viewer could see key events of the war from two main vantage points.Footnote ⁶⁰ Folkes and Algarotti thus concluded that far from being naive, the designer of the column's frieze was more like a great captain employing a stratagem of sophistication.

Folkes, Venice and Newtonianism

Folkes's conversation with Algarotti reflected his pervasive interest in optics, optical illusion and perception, topics which came to the fore when he was in Venice. Although the Venetians were aware of the theories of Newtonian optics, in the 1730s there was a degree of scepticism among natural philosophers there about the validity of the refrangibility of light in the visible spectrum. As a result, when he was in the Veneto, Folkes cultivated fellow mathematicians and astronomers to gain adherents of the Newtonian research programme in the Royal Society.

Before he left for his journey and during his time on the Council of the Royal Society, Folkes was exposed to a constant stream of accounts ‘of the present state of Learning and Experimental Philosophy in Italy’, from the English Jacobite Thomas Dereham, the Royal Society's contact in Florence. Dereham was the translator into Italian of Astro-Theology, a five-volume set of the Philosophical Transactions of the Royal Society (published by Felice Mosca between 1729 and 1734), as well as a work by Newtonian physician George Cheyne.Footnote ⁶¹ Dereham relied on luminaries such as Eustachio Manfredi, the chair of mathematics in Bologna, discoverer of a comet and asteroid, and observer of the transit of Mercury, for natural-philosophical news to pass on to the Royal Society; Manfredi was a correspondent of Algarotti and also passed along news of Venetian natural philosophy.Footnote ⁶²

Venice, in particular, was also a favourite haunt of Newtonian mathematicians and their intellectual circles, and Folkes went there to convince their virtuosi of the truth of Newton's work in optics. Twenty years previously Newtonians had fought a campaign against Italian supporters of Leibniz in the calculus dispute. In Padua and Venice, after 1710, Jakob Hermann and Nicolas Bernoulli were ‘promoters of a fierce campaign against Newton's methods of fluxions in the calculus’.Footnote ⁶³ Hermann had taught differential and integral calculus using Leibniz's method at Padua from 1707 to 1713. However, Newton had friends as well, and hoped to diminish the prestige of Leibniz through the offices of Abbé Antonio Schinella Conti, who was born and educated in the Veneto but spent several years abroad before returning to Venice in 1726. Conti was in London between 1715 and 1718 to become part of Newton's intellectual circle, where he met Folkes. In his travel diary of 1733 Folkes noted, ‘I had known the Abbé very well in England above 16 years ago, I had a very agreeable conversation with him as he is a Gentleman of great knowledg and politeness, and indeed the most knowing man of all the Italians of his side the country’.Footnote ⁶⁴ Conti would also serve as a go-between for Leibniz and Newton in the calculus affair, and, through Conti's offices, Newton thought he could lessen Leibniz's prestige in Italy, which had grown during the calculus dispute.Footnote ⁶⁵

Folkes had also been tutored by Abraham De Moivre (1667–1754), his correspondence showing that he and Edward Montagu dined with their former teacher on de Moivre's eightieth birthday in 1747.Footnote ⁶⁶ De Moivre would subsequently be an intermediary in a mathematical dispute between Newton and Bernoulli, so Folkes was intimately au fait with the history of the Newton Wars.

Before his journey, Folkes had attended a series of Royal Society meetings in which the society responded to the refutation of Newton's optical work by Giovanni Rizzetti (1675–1751), a Paduan nobleman who belonged to the circle of the mathematician Jacopo Riccati (1676–1754) of Castlefranco Veneto. The Royal Society journal book for 27 June 1728 reported that the society received Rizzetti's De Luminis Affectionibus Specimen Physico Mathematicum; the tract was referred ‘to Dr Desaguliers which he promised to make an extract of’.Footnote ⁶⁷ In De Luminis, Rizzetti discussed refrangibility, the degree to which light refracts passing from one medium into another, or, as Newton wrote, a ‘predisposition, which every particular Ray hath to suffer a particular degree of Refraction’.Footnote ⁶⁸ In particular, Rizzetti claimed he could not replicate the experiments in Book 1 of the Opticks, in which Newton used a candle to illuminate a two-coloured card with black silk threads wrapped around it, thus supposedly demonstrating the principle of chromatic aberration.Footnote ⁶⁹

Newton had placed a glass lens at a distance of six feet from the card, and used it to project the light coming from the illuminated card onto a piece of white paper which was at the same distance from the lens on the other side. He moved the piece of white paper back and forth, taking note where and when the red and blue parts of the image were most distinct. The black threads indicated distinctness of the image (when the lines created by the thread were sharpest). Newton found it ‘impossible to focus the image of black silk-thread lines upon a blue background at the same distance as when the same lines are placed against a red background; the distance between the two positions of sharp focus was as much as one and half inches’.Footnote ⁷⁰ In other words, to get a distinct red image, the paper had to be held 1.5 inches further away than to obtain a distinct blue image. Newton thus concluded that the blue light was refracted more by the lens than the red, and was more refrangible.Footnote ⁷¹

Red and blue light were not strictly homogeneous, and so not all the blue light was more refrangible than all the red light, something Newton admitted. However, he indicated that this experiment demonstrated a general effect: ‘But these Rays, in proportion to the whole Light, are but few, and serve to diminish the Event of the Experiment, but are not able to destroy it’.Footnote ⁷² Newton thus described an ideal experiment.

The inability to create these ideal conditions was the point upon which Rizzetti had seized. The popular lecturer John Theophilus Desaguliers (1683–1744) refuted Rizzetti's claims in a series of optical experiments performed at the Royal Society in 1728 in response to Rizzetti's De Luminis Affectionibus. In his article published in Philosophical Transactions, Desaguliers noted that ‘we hear indeed in a letter from Sir Thomas Dereham to Sir Hans Sloane, President of the Royal Society, that now Signior Rizzetti alledges, that he was deceived in his experiments by reason of the badness of his prisms which he had from Venice’.Footnote ⁷³ In other words, Rizzetti claimed he did not have ideal experimental conditions due to the quality of his prisms.

As Simon Schaffer has shown in his essay ‘Glass works’, the quality of the prisms was important; Francesco Algarotti's attempts in Bologna in 1726 to replicate the experimentum crucis were described by Rizzetti as failures since he could not isolate a single red ray of light; Algarotti eventually realized that his prisms were defective, and he had success at replicating the experimentum crucis when he tried again with some top-quality English prisms.Footnote ⁷⁴ Schaffer shows us how and why acceptance or denial of the specific experimental apparatus became a flashpoint in disputes over knowledge and method; we see the beginnings of the establishment of standards for professional instrumentation, or what has been termed the sociology of calibration.

Schaffer did not analyse as much the debate over Newton's Opticks in Italy, which continued long after Desaguliers's 1728 demonstrations in the Royal Society.Footnote ⁷⁵ Long after Isaac Newton's fame was recognized, Venetian natural philosophers had an attitude of ‘critical acceptance, if not open aversion’, towards Newtonianism.Footnote ⁷⁶ Part of the reason for Folkes's travels in Venice was so that he could serve in Desaguliers's stead as a Newtonian demonstrator, and the quality of Folkes's prisms was still the focus of inquiry for Venetian intellectuals. It seemed particularly important that Folkes prove the truth of Newtonian optics in the city whose glass had been the ‘standard against which other glass was to be compared’.Footnote ⁷⁷ Folkes's status as a protégé of Newton and a vice president of the Royal Society (his office conferred by Sloane six weeks before his travels), and his fluency in Italian and French, were also helpful assets.

On 9 July 1733, Folkes received a letter from Abbé Conti, who began, ‘I beg you to bring these Italian manners to an end and to treat me as a friend, that is the first favour I am asking you’.Footnote ⁷⁸ Conti related that his colleague, Giovan Bernardo Pisenti (d. 1742), having heard of the success of past demonstrations of Newtonian optics, requested ‘to see demonstrated geometrically the order of the colours of the image’.Footnote ⁷⁹ Pisenti was a Somasco cleric educated by the Jesuits who also studied with Eustachio Manfredi in Bologna, and he himself served as a personal tutor to Girolamo Ascanio Giustiniani; Folkes's diary shows that he spent much of his time in Venice at the Giustiniani Palace with Girolamo's family, so it is likely that he met Pisenti there.Footnote ⁸⁰ Pisenti was also the translator of George Berkeley's An Essay towards a New Theory of Vision (1709) into Italian, and dedicated his translation to Berkeley's friend Sir John Percival, with whom he was also acquainted.Footnote ⁸¹ In scholar Antonella Barzazi's opinion, the initiative to publish Berkeley's work was probably born in the wake of the Newtonian optics controversy aroused in the Venetian world by the attacks of Rizzetti; Berkeley refuted an account of distance vision of Malebranche and Descartes which required tacit geometrical calculations, that we perceive space by lines and angles.

Malebranche and Descartes argued that distance was judged by the geometry of angles between the eyes and the perceived object, or via the angles of light rays that fall upon the eye.Footnote ⁸² One thus judges distances by the optic axes of the eyes which form an angle at the object; whether that angle is great or small, we judge if the object is far or near. Berkeley rejected those accounts and was quite negative about using Euclidean geometry of the visual world as the sole basis for visual perception. Berkeley argued against the classical scholars of optics by claiming that space is perceived by experience. As Berkeley later stated in his Philosophical Commentaries, ‘The common Errour of the Opticians, that we judge of Distance by Angles strengthens men in their prejudice that they see things without and distant from their mind’.Footnote ⁸³ In Berkeley's view, the visual perception of distance was explained by the association of ideas of both sight and touch, and this associative approach challenged appeals to geometric calculation that profess to explain completely monocular vision and the moon illusion, ‘anomalies that had plagued the geometric account’.Footnote ⁸⁴

Visual perception of distance was also of great interest to Folkes. We recall his conversations with Algarotti about the friezes on Trajan's Column. Folkes also gave advice to Robert Smith FRS, Plumian Professor of Astronomy at Cambridge University, in his A Compleat System of Opticks in Four Books (1738). Cantor has judged that the work was the most ‘famous book dealing with the subject’ after Newton's own Opticks (1704).Footnote ⁸⁵ Smith acknowledged Folkes for his ‘curious remarks’ on fallacies in vision, applying optics to explain phenomena such as ‘the sun's apparent distance, on the apparent figure of the sky, on the apparent curvity of the sides of long walks and ploughed lands, and the changes of curvity by the observer's motion’.Footnote ⁸⁶

Folkes had also spoken to Algarotti about Molyneux's problem in some depth.Footnote ⁸⁷ The Irish natural philosopher William Molyneux (1656–1698) had asked John Locke whether, if a blind person could suddenly see, he or she would be able to recognize by sight an object's shape they previously only knew by touch. Presented with a globe and a cube, could such a person determine which was which just by looking? An affirmative answer meant that one believed in a rationalist and innate conception of space common to touch and sight. A negative answer indicated an empiricist view, that this was a relationship that we learn only through experience. Locke responded in his Essay Concerning Human Understanding that the formerly blind person would not be able to say with certainty ‘which was the globe, which the cube … though he could unerringly name them by his touch’; the connection between the senses was learned.Footnote ⁸⁸ Berkeley also offered a negative response, that a perception of distance was an ‘act of judgment grounded on experience’.Footnote ⁸⁹

However, well before Diderot's famous essay Letter on the Blind (1749), Folkes spoke to Algarotti about Molyneux's problem in reference to the case of Nicholas Saunderson (1682–1739), the blind Lucasian Professor at Cambridge and fervent Newtonian who lost his sight at twelve months from smallpox and who could purportedly judge the size of a room and his distance from the wall by sound. Saunderson made Newton's Opticks the basis of several lectures that he made at Cambridge, including some on the theory of vision.Footnote ⁹⁰ Folkes was a close colleague of Saunderson and commissioned a painting of him. Saunderson affirmed he could have distinguished the objects with his sight restored, namely because he innately understood the mathematical definition of a sphere and cube and could identify them from the number of vertices they would present to him, as well as the shape of their cast shadows. This was an argument drawn out of Saunderson's Elements of Algebra, in which he proved that the cube could be divided into six equal pyramids having their vertices at the centre of the cube and the six faces as their bases; ‘this is used for an elegant proof that a pyramid is one-third of a prism having the same base and height’.Footnote ⁹¹ Folkes, as a Newtonian mathematician, believed there was an innate geometrical quality to vision and was a very supportive subscriber to Saunderson's Elements of Algebra, putting money in for eight books, ‘4 Royal and 4 common paper’.Footnote ⁹²

In order to create a demonstration to counter directly Rizzetti's disavowal of Newtonian optics and tacitly Berkeley's caution about using optics as the sole means of explaining vision, Conti wrote to Folkes for advice. Conti indicated to Folkes that he made a figure ‘to show visibly the different relative refrangibility’, showing ‘the different perpendiculars with which are made the angles of the refraction of the exiting rays; these angles are as small as the others that are made with the internal perpendicular are large’.Footnote ⁹³ He then indicated to Folkes,

Conti was right. Newton had only conjectured in the Opticks about these issues rather sparsely; for instance, although Newton analogized about the behaviour of light and matter, he really did not even assert the materiality of light. As Geoffrey Cantor has shown, later popularizers of Newton, such as Desaguliers, Smith and later Willem Jacob ’s Gravesande (1688–1742), interpreted Newton's Opticks as if, in Cantor's phrase, it were ‘an appendix to the Principia’, in which forces ‘were employed to explain all those phenomena in which light deviated from its natural rectilinear path’.Footnote ⁹⁵ In this form of projectile optics, light was postulated to travel in a straight line with finite velocity, and refraction was explained by the influence of attractive forces. One could say, for instance, that refractive dispersion was due to a particulate model of light, the rays or bodies being of different sizes, the violet-making rays the smallest and the red-making ones the largest and heaviest.Footnote ⁹⁶

Conti then went on to mention the work of Paris lawyer and Anglophile Nicolas Gauger, who in 1727 produced a long account defending Newtonian optics. In July 1727, Gauger had written Conti a twenty-page letter which was publicly printed, addressing the danger of Rizzetti's attacks on the Newtonian system, with particular mention of the two-colour-card experiment.Footnote ⁹⁷ But five years later, Conti lamented to Folkes that ‘although Mr Gauger has given it quite amply … I don't know if his book is still being printed’. He went on, ‘It is certain that if the ray was not divided into several threads, so they made different angles, you would see the image differently from how we see it … I am waiting for your decisions on this’.Footnote ⁹⁸ But such pedagogically clear, if sometimes superficial, explanations by Newtonian pedagogues had not reached or convinced all Venetian ears; hence Conti's plea to Folkes for a proper diagram and clarification of refrangibility.

Shortly after this exchange, on 5 August 1733, Folkes met Rizzetti himself, recording that Father Giovanni Crivelli ‘calld on me with Sigr. Rizzetti author of a book which he gave me of the nature of light and colours against Sir Isaac Newton’.Footnote ⁹⁹ Crivelli had written Elementi de fisica in 1731, a textbook which was a reinterpretation of recent discoveries in natural philosophy within an Aristotelian framework. Historian Vincenzo Ferrone considered Crivelli's work as reflecting the attitude of a large segment of Venetian society towards Newton's works.Footnote ¹⁰⁰ While the first volume offered the most complete, if dispassionate, explanation of Newtonian gravity that has appeared in Italy (for example, he rejects Newton's concept of a vacuum in space), the explanation of the Opticks is equally neutral. Crivelli presented both Newtonian optics and the objections of Rizzetti in a manner that subtlely neutralized them, doing the same thing in his coverage of astronomy, noncommittally describing Copernican, Tychonic and Ptolemaic hypotheses with little comment.Footnote ¹⁰¹ Although one receives the impression from reading his manual that there was wide-ranging knowledge of Newtonian theory in the Veneto, one also receives the impression that there was a rejection of any sort of Newtonian orthodoxy.Footnote ¹⁰² In this light, Crivelli's visit with the antagonistic Rizzetti in tow may be interpreted as a challenge to the Newtonian Folkes.

After Rizzetti's visit and a short period of illness (Folkes and his wife contracted a kind of heat rash termed scotture), Folkes met Conti on 23 July. The latter had just come to town and upon hearing about Rizzetti's visit to Folkes proposed that he and Folkes act and publicly ‘make some of Sir I[saac] Newton's experiments on fryday next’. Folkes subsequently indicated in his travel diary on Friday 27 August 1733:

Clearly on the hunt for apparatus, Folkes had three days earlier indicated, ‘I was also at another person who is a practical Mathematician to see some instruments but nothing was particular what he had best were some English things’.Footnote ¹⁰⁴

On 28 August 1733, Folkes recorded triumphantly, ‘I was again at the Guistinian Palace and made most of the Experiments of the first book of Opticks with very good success and to the satisfaction of all that were here which were … men of the first people of Venice’.Footnote ¹⁰⁵ Folkes was rewarded by Giustiniani with a present of ‘spanish Chocolate’.Footnote ¹⁰⁶ On 2 and 7 September, Folkes then indicated,

Considering Crivelli's neutral stance in presenting Newton's optics in his Elementi, his obstinate behaviour during the demonstration was not surprising. Rizzetti also continued his anti-Newtonian campaign until the 1740s, with diminishing success.

Nonetheless, Folkes's performance had the required effect. When he left Venice, Folkes noted that his experimental success showed that he had ‘conversd with many of them [the Venetians] in a manner no English man almost has done before me’.Footnote ¹⁰⁸ In a letter from the physician Pietro Michelotti to John Machin, secretary of the Royal Society, Michelotti indeed indicated that Folkes had spent several days staying with him in Venice, indicating close familiarity.Footnote ¹⁰⁹ Several of the Newtonian adherents in Venice that Folkes indicated in his diary that he met in Venice, including Ludovico Riva (1698–1746), professor of astronomy at Padua, were subsequently put forward for election in the Royal Society and became fellows.Footnote ¹¹⁰ Although Folkes worried about his apparatus, his use of Conti's ‘very good’ English prisms and his expertise in his demonstrations vindicated, or so he was told, Newtonian optics in the Veneto.

Folkes continued his Newtonian campaign when he travelled to Florence, but he still worried about the quality of his equipment. In a letter of c.1734 to Sir Philip Stanhope (who was on his own Grand Tour at the time) Folkes wrote,

Folkes's son, also named Martin, was sent to take Earl Stanhope to the house of Antonio Cocchi, a well-known physician and defender of Newton whom Folkes met in 1723, where the experiments were performed.Footnote ¹¹² It does not seem that Folkes's comments about his equipment were the result of a false modesty, as the presentation of the optical experiments was important due to the importance of the participants in the audience. Folkes invited ‘Mr Rhodes’, secretary to Charles Fane, the British minister in Tuscany, and ‘Mr Mann’ or Sir Horace Mann, 1st Baronet (1706–1786), the long-standing British resident in Florence. (Folkes and Mann had been at Clare College, Cambridge, together, where they initially met.)Footnote ¹¹³

The presentation was much less public, probably because outside the safety of the Venetian Republic, the Inquisition was active and dangerous; it placed Locke's Essay on Human Understanding on the Index in 1734. Algarotti's Il Newtonianismo per le dame had also been condemned as Masonic, and the Inquisition denounced Newtonian Antonio Conti, whom Folkes had met in Venice. Open acceptance of Newtonian gravitation was impeded because the Catholic Church still banned belief in the Earth's motion, and the refutation of Newtonian colour theory in itself was an implicit opposition to a moving Earth.Footnote ¹¹⁴ Although we do not know the specific outcome, we do know that upon Folkes's return, when he informed Cocchi of his intention to visit Italy again, Cocchi replied that he was ‘overjoy'd’ at Folkes's decisions. Conti offered to make domestic arrangements for Folkes during his planned visit, and reminded him to bring a telescope and microscope from England. Conti added, ‘I should very proud if you would habilitate my Terrace with Some of your Astronomical Observations … and other Phisical experiments will be very much admired here’.Footnote ¹¹⁵ Folkes in his correspondence in subsequent years also successfully cultivated Stanhope as a fellow mathematician working on problems of series and probability, so his demonstration was probably convincing.Footnote ¹¹⁶ When Folkes was in Venice, he was questioned by several virtuosi, such as Cristino Martinelli, about the probability problems and the odds of winning the Pope's Lottery, so he was known for his expertise in this area.Footnote ¹¹⁷ In Venice and Florence, Folkes thus successfully demonstrated Newtonian optics, cultivated fellow natural philosophers, and fashioned himself as a ambassador of Newtonianism.

Folkes, Venice and Celsius

Not only did Folkes demonstrate the primacy of Newtonian optics as well as awareness of standards of professional equipment during his journey, but he also had another encounter that would contribute to the primacy of Newtonianism and English instruments. On 18 September 1734, while he was in Venice, Folkes recorded in his diary a meeting with

‘Schelsius’ was, of course, Anders Celsius, his work on the aurora borealis the Nova Methodus distantiam solis a terra determinandi (New Method for Determining the Distance from the Earth to the Sun), which was first read to the Royal Society on 8 April 1736, and printed in Philosophical Transactions. Celsius was also one of the first to suggest a connection between aurorae and changes in the Earth's magnetic fields, and he would also make observations of sightings in England.Footnote ¹¹⁹ Folkes would have been very interested to talk to Celsius as Folkes himself made some of the earliest sightings of aurorae from King's Lynn, Norfolk, not too far from his country seat, Hillington Hall. The early part of the century saw the end of the Maunder minimum, and London, Plymouth and King's Lynn were ideally situated to observe aurorae (Figure 3).Footnote ¹²⁰

Figure 3.

Aurora borealis observed by William Rastrick, one of Folkes's neighbours in Norfolk. Letter from Rastrick to Folkes, 20 March 1726/7, EL/R1/61. © The Royal Society.

Folkes then noted the next day,

More importantly, Folkes indeed would be involved with the scientific work of Celsius, assisting him with his geodesic expedition with Maupertuis to measure the shape of the Earth. The argument over the Earth's shape involved predictive calculations by Newton, and thus its outcome was crucial to the primacy of Newtonianism. When Celsius came to London to procure scientific instrumention for the expedition, was he introduced by Folkes not only to key members of the Royal Society, but also to fellows of the Society of Antiquaries, as Folkes promoted close ties between the two organizations, which had common interests in metrology.

When he met Folkes, Celsius had just been to Paris on a grand tour of European observatories and had met Algarotti in Italy.Footnote ¹²¹ And when they arrived in Paris together at the end of the summer of 1734, Algarotti introduced Celsius to Maupertuis and his colleagues. Here the idea for the Lapland expedition to measure the true shape of the Earth was born and given a royal warrant five months later to find and provision a ship to take the travellers to Stockholm.Footnote ¹²² The expedition would help settle a dispute that Maupertuis had with French cartographer Jacques Cassini over whether the Earth was prolate (longer along its axis from north to south), or oblate (broader along its diameter at the equator). Cassini believed that the Earth was prolate. Maupertuis in his expedition, and Newton with predictive calculation, proved it was oblate. The expedition to Lapland, lasting from July 1736 to March 1737, measured an arc of the meridian from Tornea to Kittis. The scientific party consisted of Maupertuis, Clairaut, Camus, Le Monnier, the Abbé Outhier and of course Celsius, who would measure the meridian arc near the North Pole. Another expedition organized by the French to South America (1735–43) near the equator to measure the meridian arc would eventually demonstrate that Newton was correct about the Earth's shape.

The travellers would use a fixed-length pendulum clock, a theodolite and a zenith sector that could the measure the shape of the Earth in tropical, temperate and Arctic latitudes. The first method depended on the comparison of the periods of pendulum clocks at different latitudes, eliminating the temperature-dependent variable (clocks went a second a day slower for every two divisions of temperature rise on the thermometer).Footnote ¹²³ Newton in his Principia noted that astronomers found that pendulum clocks moved slower near the equator, thus supporting his prediction that their increase in weight from the equator to the poles was as the square of the sine of the latitude.Footnote ¹²⁴ Other than comparing the period of pendulum clocks, one could use a theodolite and surveyors’ rods to measure out a large distance (sixty to seventy miles) and, using a zenith sector, measure the degree of arc that distance covered, a more direct means of measuring the Earth's surface.

As Celsius was on his way to London, Maupertuis asked him to obtain several instruments made by George Graham.Footnote ¹²⁵ Maupertuis desired a model of Graham's portable zenith sector, for observing the transits of fixed stars that allowed for the calculations of latitude; it was this sector with which in 1728 James Bradley had also discovered the aberration of starlight measuring Gamma Draconis. Gamma Draconis has a high northerly position of 51.5 degrees north of the celestial equator, which takes it through the zenith, as seen from London. The atmosphere of the Earth causes refraction of light, which makes stars appear higher than they really are, but using a star that passes directly overhead like Draconis solves such problems. Draconis was thus used to measure stellar parallax. However, in his work with Samuel Molyneux, Bradley detected a small apparent motion of Draconis not due to parallax (the annual timetable for Draco's parallax was different), but instead due to what is termed stellar aberration resulting from the finite speed of light and the orbital motion of the Earth.Footnote ¹²⁶

Maupertuis and Folkes had become friends in 1728 during the Frenchman's own Grand Tour. Folkes was a chief patron of Graham, having nominated him to the fellowship of the Royal Society on 8 December 1720.Footnote ¹²⁷ Folkes also appended to his ‘memoranda’ a list of prices for Graham's watches, often securing them as gifts for his scientific correspondents. Folkes and Graham were close friends, recorded in John Byrom's diary as often socializing in various coffeehouses or taverns such as the Sun after Royal Society meetings (Figure 4).Footnote ¹²⁸ When Celsius was in London in 1735, he observed a lunar eclipse from Graham's house using some of Bradley's new telescopes.

Figure 4.

William Hogarth's sketch of Folkes examining a watch, c.1720s, Button's Coffeehouse, British Museum, image 1861.0413.508, Creative Commons BY-NC-SA 4.0 license.

Celsius was also invited to attend meetings at both the Royal Society (where he discussed aurora borealis he had seen in Sweden), and to meetings of the Society of Antiquaries, showing his deep connections between the two organizations. For instance, on 13 November 1735 Celsius presented at Antiquaries ‘a draught of two kinds of Runic Characters, namely the Vulgar and Helsingic together with some remarks on them’, found on the Malsta stone in Rogsta, Hälsingland, Sweden (Figure 5).Footnote ¹²⁹ This paper on runes was published by the Philosophical Transactions of the Royal Society in 1737 with an attempt to date the stone by examining the genealogy of the family it described and applying the rationale used to date events in Newton's biblical Chronology of Ancient Kingdoms.Footnote ¹³⁰ In Folkes's presence, Celsius attended the Society of Antiquaries again on 9 March 1735/6 and on 18 March 1735/6, where Celsius ‘delivered an account of an ancient Alabaster vase found in Sweden … at the Antiquarian College of Stockholm … which was read’; Celsius also presented the Society of Antiquaries ‘with a wooden print of the said vase’.Footnote ¹³¹ As Celsius received his instruments, Folkes's friends received an antiquarian gift, part of a time-honoured exchange characteristic of the Republic of Letters. The ties between the Royal Society, the Antiquaries and Newtonianism were strengthened.

Figure 5.

Sketch of Celsius's discovery of runes on the Malsta stone in Rogsta, Hälsingland, Sweden, which was engraved and published in the Philosophical Transactions, CLP/16/51, © The Royal Society

Folkes also gave advice to Celsius while he was on expedition. In December 1736, Celsius wrote to Folkes stating that he was ‘one thousand times grateful for the courtesies you did for me during my stay in London’. He continued, ‘We have observed the difference of latitude between Torne and Pello with Mr Graham's instrument. The observations were made in September in Pello, having not found any suitable star other than the Dragon. We then observed it in October here in Torne’.Footnote ¹³²

In other words, Graham's sector measured the angle at which a particular star, in this case Draco or the Dragon, near the zenith passed the meridian (the star's altitude). The expedition moved then to another mountaintop at Pello and repeated the same measurement. The difference between the star's altitudes was due to the party's having travelled south. As Sorrenson stated, they then had to ‘establish the distance between the two mountains by surveying a series of triangles and measuring several of the baselines with wooden poles’.Footnote ¹³³ Once they had the distance between the two points and the difference in angles, they ‘calculated that the length of one degree of arc near the polar circle was longer than at Paris’, and concluded that the Earth was oblate, vindicating Newton. However, there was one problem. As Celsius continued,

As mentioned, Bradley's observations of the motion of Draco led to his discovery of stellar aberration. As Celsius was using Draco as a reference point for his triangulation measurement, he was concerned that this aberration would affect his measurements. Folkes's reply to Celsius's query is not extant, but we know that Bradley's calculations regarding stellar aberration were communicated. Maupertuis, in his publications about the exhibition, incorporated Bradley's data about declination, and used Bradley's precision in measuring stellar positions as an example of new standards of astronomical practice only possible with the best instruments. Maupertuis stated, ‘Mr Bradley very kindly shared with me his latest discoveries on the motions of the stars, and communicated to me the necessary correction to the arcs we observed’. As Terrall has shown, this precision of English instruments was used as a weapon against Cassini's claims for a prolate Earth. When Maupertuis's book finally did appear about the shape of the Earth (Le figure de terre) in 1738, he wrote to Folkes,

He then continued, ‘It has been very sweet to me, Sir, to find myself still in the honour of your memory after such a long time … I [send my book] to you as one of the first scholars in Europe’.Footnote ¹⁴¹

Folkes's interest in stellar parallax, aberration and the modification of the constellations over time was demonstrated by a model he had made of the globe which he demonstrated to the Society of Antiquaries on 7 July 1736 when he returned to England. It was a plaster of Paris copy of the Farnese Globe, the oldest surviving depiction of this set of Western constellations; Folkes recorded in his travel diary, ‘Diam of the Farnesian Globe. 2f. 5 inch. 1/10 English Measure’, likely indicating that he saw and measured in it Rome.Footnote ¹⁴² The globe puts the celestial figures against a grid of circles comprising the celestial equator, the colures, the ecliptic, the tropics and the Arctic and Antarctic Circles. This allows for the constellations to be positioned accurately. It was noted at the Antiquaries meeting that ‘the colure of this globe passes by those parts of the asterism by which it is said to have past in the days of Hipparchus but the intersection of the Equator and Eccliptic is not at the Colure’. This was a reference to the 26,000-year precession or axial wobble on the Earth which Newton discovered shifts the positions of the celestial circles over time, so that the observed positions on the Farnese Atlas can be traced to a particular date in celestial time. ‘The declination of the Arctic and Antarctic Circles will correspond to a particular latitude for the observer whose observations were adopted by the sculptor … a detailed analysis of the globe will reveal the latitude and epoch for the observations incorporated in the globe’.Footnote ¹⁴³ The Society of Antiquaries’ entry in their Minute Book about Folkes's presentation about the globe noted that its age could be determined to be during the time of the Antonine emperors.

Geodesy also continued to be a preoccupation of Folkes when he eventually realized his goal of being appointed president of the Royal Society, and then of the Society of Antiquaries, nearly a decade after his initial Italian visit. Folkes became one of the strongest supporters in the Royal Society of John Harrison and his longitude clock, convinced of Harrison's ‘strong impulses of a natural and uncommon genius’.Footnote ¹⁴⁴ And in 1745 Folkes intervened when Antonio de Ulloa, who went on the Peruvian expedition to measure the meridian arc near the equator, was captured by the English as he sailed home when the expedition was completed. Spain and Britain were at the time at war. Ulloa's calculations were confiscated and he languished in prison in Portsmouth, until he was granted leave to travel to London at the request of the Royal Society. Folkes mediated, and on 8 May 1746 he used his knowledge of Spanish to summarize the details of Ulloa's expedition in thirty-three pages of manuscript which he presented to the society later that month.Footnote ¹⁴⁵ Folkes reproduced Ulloa's triangulation and its results, which confirmed Newton's predictions of the shape of the Earth. Folkes noted that the ‘proportion resulting of the Axis of the Earth’ from the Maupertuis expedition ‘to its Equatorial Diameter’ of Ulloa's measurements ‘will be nearly 223 to 222 surprizingly near to that given from calculation only, by the great Sir Isaac Newton, of 229 to 230, in the last edition of his Principia’.Footnote ¹⁴⁶ Rather ironically, Folkes noted that ‘Dr Bradley's aberration of the fixed stars from the successive propagation of light is not brought into the account’.

Folkes also recorded their barometric observations made in the Andes, as well as the heights of the mountains, and included Ulloa's ethnographic information about the Peruvians and descriptions of the flora and fauna, including the deadly coral snake. Folkes noted that he did not want the material to be made public, as Ulloa intended to publish a book about his exploits when he returned to Spain (accomplished in 1748 with twelve subsequent editions in French, English, Dutch and German); Folkes noted that he was unwilling to publicize Ulloa's findings because of the pleasure the public would ‘without doubt receive’ from Ulloa's book.Footnote ¹⁴⁷ Apart from the evident esteem Ulloa and Folkes developed for each other, vindication of Newtonianism was all the more powerful from an outside entity. Ulloa was made an FRS, his papers were returned to him by order of the Lords Commissioners of the Admiralty, and it was arranged that he would get passage to Portugal, which was a neutral in the war, so he could get back to Spain.