• In Celsius’ footsteps, by Ian Hembrow

    Retracing the route of the 1736-37 Arctic Circle expedition to establish the shape of the Earth

    A daily blog by SIS member and travel grant recipient Ian Hembrow on a research trip to Lapland for his biography of the Swedish astronomer and mathematician Anders Celsius (1701-1744).

    Figure 1. Measuring one degree of latitude in the Arctic Circle, 1736-37.1

    Thursday 5 May 2022

    The thick winter ice is just beginning to break up on the River Torne as it reaches and empties into the Baltic Sea in the Gulf of Bothnia on the border between modern Finland and Sweden. The cracks starting to snake across the surface are a reminder that we live on a dynamic planet – one that’s constantly being shaped and altered by the immense forces of gravity, magnetism, volcanism and climate.

    The river – Europe’s longest free-flowing waterway without locks, dams or any other human-made intervention – is also what brought a small but intrepid band of French and Swedish scientists here in June 1736. Their mission, decreed and bankrolled by France’s young King Louis XV, was to help settle the great scientific debate of the age – the exact shape and form of the Earth.

    The twenty-five-year-old king had already dispatched a similar expedition to Peru a year earlier. The logic was that by precisely measuring the distance of degrees latitude at the equator and as far north as possible then comparing the results, it would be possible to determine whether the planet was a perfect sphere, or as great natural philosophers like Newton and Cassini had theorised, it was slightly deformed. The big question was whether that difference was at the planet’s waistline – squeezing it into an elongated lemon shape, or at the poles making it flatter, more like an orange.

    Figures 2 and 3: Then and now – Tornio Church is little changed today from how it looked in 1736.

    My friend Mark and I arrived in Tornio at the mouth of the river in the late evening, still light of course at this time of year. In case we were in any doubt, the final stage of our journey – a two-hour propeller plane flight north from Helsinki – proved we were entering a very different realm. Far below us, Baltic pack ice stretched into the distance, with the tiny dot of an ice-breaking ship bravely battling to keep open a narrow, navigable channel.

    This is why the eighteenth-century Earth-measuring scientists had to come here in midsummer – arriving just in time to make their first astronomical observations from the elegant, birch-shingled bell-tower of Tornio Church on the longest day of 1736. The adjacent steeple became the southernmost marker on a latticework of observation and triangulation points stretching northwards up the river valley. Their objective was to survey and measure one degree of latitude – roughly 95km along the meridian running through Tornio.

    The expedition was led by the flamboyant French mathematician and royal court-favourite Pierre Louis Moreau de Maupertuis. But we’ve come to focus on another of the party, Anders Celsius – the man whose name still lives on in the one-hundred-point (‘centi-grade’) temperature scale he invented and bequeathed to the post-Enlightenment world.

    Figure 4: Period map of Tornio.

    It was good fortune and coincidence that led to Celsius being part of the study. At the time King Louis was commissioning his expeditions, the thirty-two-year-old Swede had arrived in Paris as part of his Grand Tour of Europe’s great scientific capitals. His mix of astronomical, mathematical and geodesic surveying experience was exactly what De Maupertuis needed to achieve the desired results. Plus of course it was useful that he and another member of the party – one of Celsius’ students, Anders Hellant, spoke Swedish and knew something of their Arctic destination.

    All of this is what brought us to the council chamber on the top floor of Tornio’s modern City Hall, with magnificent views of the icy river and its thickly wooded valley. Ilkka Halmkrona, head of education for the Tornio region spoke with passion and pride about not just the city’s important history, but also its unique status as a cooperative, open-border centre for business, industry, culture and tourism with its Swedish twin settlement Haparanda on the opposite riverbank. In an era of division and conflict it was refreshing to witness such enthusiasm for internationalism and clear evidence of its benefits.

    Figure 5: Early signs of thaw at Tornio – until the eighteenth century, the world’s most northerly town.

    Next we heard from Veli-Markku Korteniemi – an impressively energetic Finnish academic and entrepreneur, Chair of the Maupertuis Foundation and someone with a deeply personal reason to keep the story of the 1736-37 expedition alive. Eight generations ago, his family owned and ran a remote but well-appointed guest house where most of the scientific expedition stayed, working on their calculations during the dark and frozen months of winter.

    Alongside us was Jarno Niskala, an affable and committed social scientist leading a project to commemorate another, even more ambitious scientific enterprise a century later. In 1842, the Torne Valley once again became the focus of international attention as a segment of the Struve Geodetic Arc – a 2,800km line of survey triangles passing through ten countries, from Norway to Ukraine’s Black Sea coast.

    Figures 6 and 7: Eighteenth and twenty-first century technologies meet at Tornio Museum.

    This UNESCO-heritage path and world-changing exercise are now brought to life through an excellent virtual reality exhibit at Tornio Museum, which we visited before heading off to see the real thing. Two hours later, a strenuous march through deep snow and stony outcrops took us to the 189m top of Mt Kaakamavaara – the next point on both the Maupertuis and Struve meridians.

    Figure 8: Jarno and Mark approaching the top of Mt Kaakamavaara.

    While we were still puffing and perspiring from a rugged climb, the incredible physical and logistical achievement of these pioneer scientists came into fresh perspective. With our modern binoculars, it was just possible to see the Tornio Church steeple to the south and another key landmark, Mt Niemivaara, a little bump on the horizon in the opposite direction.

    Maupertuis’s team had to row upstream against a strong current, lug heavy wooden and brass instruments through dense forest up to this point, fell hundreds of trees to clear the summit (all the time plagued by vicious biting mosquitoes and flies), and then be able to accurately measure angles and observe stars. It was an astonishing feat. And more astounding still is that the party – supported by a troop of tough Finnish soldiers and some local Lapps – did this for all eight of the principal measuring points in just 63 days.

    Even with modern access, equipment, machinery and communications this would be a mammoth task. And in itself, the valley route was a hastily-concocted ‘Plan B’. De Maupertuis had originally intended to use a series of islets at the mouth of the river for the survey, but these proved to be much too low and flat for the purpose. So Celsius and his companions had to draw on their collective initiative to adapt and act quickly, before the ice returned.

    Figure 9: Clearing and preparing Mt Niemivaara, with the white wooden summit marker in place.

    Friday 6 May 2022

    Our itinerary took us to two more hilltops – Aavasaksa, where the brightly-painted but crumbling ghost of the Imperial Lodge sits, patiently waiting for a Russian Tsar who never came, and Luppiovaara, overlooking a straight stretch of frozen river. This is where, after waiting for the cold and dark of winter, Celsius led his companions out onto the ice to measure a 14km baseline, from which they could then calculate all the other distances.

    Figure 10: Viewing the site of the 1736-37 baseline with the Maupertuis Foundation’s Tuomo Korteniemi.

    With just a few hours of daylight and the shimmering, ethereal Northern Lights to illuminate their work, the group split into two teams, starting from each end of the line and laying 30-foot-long, birch poles end-to-end to measure the distance. It took them ten, brutal and freezing days, vividly described by the expedition’s leader:

    Judge what it must be to walk in snow two feet deep, with heavy poles in our hands, which we must be continually laying upon the snow and lifting again; in a cold so extreme, that whenever we would take a little brandy, the only thing that could be kept liquid, our tongues and lips froze to the cup and came away bloody.’2

    But the scientists proved their mettle. When the two teams compared their results, they differed by just ten centimetres. It was a prodigious undertaking and outcome in fearsome conditions.

    For this part of our day, we met Tuomo Korteniemi: the younger brother of Veli-Markku and a journalist and publisher who first founded the Maupertuis Foundation. From Luppiovaara on the Swedish side of the river he directed us to the Arctic Circle monument at Juoksengi.

    The exact position of this line (the southern limit of continuous daylight at the summer solstice) constantly wobbles around because of the Earth’s tilt and the influence of the sun, moon and planets. But at roughly 66° 33’ it’s an eerily atmospheric place. A stainless steel depiction of the globe stands surrounded by the flags of the eight Arctic countries – with the Russian pole now conspicuously empty…

    Figures 11 and 12: Mark’s iPhone confirms our location at the Arctic Circle crossing point, Juoksengi, Sweden.
    Figure 13: The massive, heavyweight sector built by George Graham to Celsius’ specifications to observe stars in the Draco constellation and thereby pinpoint the exact latitudes at both ends of the measurement chain. The viewer lay on the bench in the centre looking directly upwards.

    Saturday 7 May 2022

    Over to Finland again to meet Miia Kallioinen and Janne Tolvanen – two young colleagues from the Pello mayor’s office giving up their weekend to act as our guides. They took us first to the ultimate destination of Celsius and his fellow scientists, Mt Kittisvaara, at the northern end of the expedition’s survey chain.

    We crunched through snow as the rocky path wound between slender trees and a dark green carpet of bilberry and lingonberry plants just emerging to greet the spring sunshine. As we rounded a bend, a squat stone pyramid appeared – indicating the place where the scientists built a wooden observatory to house the huge sector and portable zenith custom-built for the trip by London’s master instrument maker George Graham.

    For me too, this felt like an arrival. The culmination of five years’ fascination and study of the modest young Swede with the familiar name who brought his team – and us – to this place. I left the other three and walked away into the trees for a while, listening to the breeze and birdsong. I tried to imagine the experiences and feelings of the expedition members who came here, desperately hoping that the precision of their work would satisfy their own instincts, the scientific establishment and King Louis back in the opulence of Paris.

    I paused at prominent rocks – unmoved since they were deposited by glaciers – and ran my palms across their surfaces, crusted with pink, green and white lichens. And I thought about how Celsius and his fellow scientists had probably done the same.

    Figure 14 and 15: Mark, Miia and Janne at the Maupertuis expedition pyramid on Mt Kittisvaara.
    Figure 16: Korteniemi guest house with the wooden observatory on Mt Kittisvaara top left.

    Back down from the mountain, Miia and Janne took us to two other landmarks – a memorial stone to Celsius’ student Anders Hellant, who was just 20 years old when he returned to this his hometown. He was born where another stone now stands near to the river. It marks the site of the Korteniemi guest house, where Veli-Markku and Tuomo’s ancestors sheltered the exhausted scientists and helped them to recover from their exertions.

    Some remnants of this compound might still be visible if it were not for the terrible destruction wrought by retreating Nazi forces as they left Finland in autumn 1944. In a literal application of ‘scorched earth’ tactics, they burned and obliterated everything in this part of Lapland: homes, barns, forests, bridges and crops, so that nothing remained for the Finnish population.

    The Korteniemi house was just one casualty of these events, and a sadness seemed to hang over the place as I walked down towards the riverbank. A few small buildings now dot the area – not unlike those shown in the drawing from Celsius’ time, with Mt Kittisvaara a silent, sorrowful sentinel above.

    Figures 17 and 18: Site of the Korteniemi house where Celsius stayed, with the frozen River Torne behind.
    Figure 19: Janne explains geodesic measurements – and the delights of a jug of Kalja rye beer.

    But a lovely surprise awaited us at the end of our tour around Pello – a late lunch in the town’s special Maupertuis dining room, where the walls are tastefully decorated with prints of the expedition and reproductions of seminal equations, formulae and graphs. Very tasty too was the traditional homemade dark, malted rye Kalja beer we were served – a kind of non-alcoholic-stout-meets-dandelion-and-burdock, which is almost a meal in itself.

    Sunday 8 May 2022

    A day off from the serious research as we headed further north, the scenery quickly taking on a more remote and blasted feel than any we’d encountered before. We saw our first wild reindeer – a silver- and pewter-coated adolescent grazing peacefully at the side of the road – and several sturdy-looking black-tailed capercaillies scuttling across in front of us.

    We headed for Pajala, about 60km up the valley, where the Torne is joined by the even bigger River Muonio pouring down from the far north on the border with Norway. On the way, we stopped at Kengis Bruk – a dramatic set of cascades and rapids. It’s another place with a strong connection to Celsius.

    Here, four decades before the Maupertuis expedition, Celsius’ maternal grandfather Anders Spole visited and stayed while on his own astronomical and botanical adventure to Lapland. It was partly from hearing and reading about his grandfather’s exploits that Celsius had suggested this region for the 1736 expedition. Today, Kengis is a magnet for salmon fishing, with 20kg-plus monsters more than a metre long often hauled from the dark, peaty pools beneath the waterfalls.

    Figures 20 and 21: Some of the rapids at Kengis Bruk, where Celsius’ grandfather Anders Spole stayed in 1695.

    Monday 9 May 2022

    Our final day of travel and investigation. We drove south, heading off the main highway onto an unmade road that took us many kilometres into the surrounding lakes and forests, to visit Mt Niemivaara.

    More reindeer lifted their heads to gaze at us from the surrounding trees. One walked straight down the track and skipped past with a barely audible clicking of its flattened hooves. There were no signs or marked paths, so when the car could go no further we just stopped and struck out for the top.

    Figure 22: A local resident.

    It was easier going than some of the other ascents, but Niemivaara has its own peculiarities: sheer stone walls cut with deep fissures and promontories that we had to negotiate our way around. And just before the summit a massive boulder field demanded careful steps and a few leaps of faith. We wondered again how Celsius and his companions had managed when this was even rougher and completely unknown territory.

    Figures 23 and 24: Boulders and smooth walls of stone near the summit of Mt Niemivaara.

    At the top of the hill we were rewarded with a stunning view of Lake Ajankijärvi – still frozen from end to end. Once again, De Maupertuis’s eighteenth-century description closely matched what we saw and felt:

    Figure 25: The frozen Lake Ajankijärvi seen from the top of Mt Niemivaara.

    ‘The beautiful lakes that surround this mountain, and the many difficulties we had to overcome in getting thither, gave it the air of an enchanted island in a romance. On one hand you see a grove of trees rise from a plain, smooth and level as the walks of a garden, and on the other you have rocks so perpendicular, so high and so smooth that you would take them for the walls of an unfinished palace rather than for the work of nature. We had been frighted with stories of bears that haunted this place, but saw none. It seemed rather a place of resort for fairies and genii than for bears.’

    Figure 26: Peeling away bark to reveal bright white wood beneath – perfect material for summit markers.

    Stopping by a towering pile of freshly cut pine and birch trunks on our way down, the air was filled with sweet, fragrant resin and sizeable black butterflies suddenly roused into busy flight by the light and warmth. I peeled back the bark of a log to uncover the pure white wood underneath. This was an important part of the expedition’s method of creating summit markers that could be easily seen from far away.

    In an unplanned instant, this simple act connected me once more to the brave and brilliant band of scientists who came here so long ago.

    Tuesday 10 May 2022

    I leave Lapland with a far greater understanding of who the members of the 1736-37 expedition were, and of what they did, why, how and where. Having followed in his footsteps, I feel closer to my subject Anders Celsius. And after standing where he stood and seeing and hearing what he saw and heard, I am even more in awe of his qualities and capabilities – both as a scientist and as a man.

    Before they even departed Finland for France in spring 1737, and years before the few survivors of the Peru expedition returned, De Maupertuis, Celsius and the rest of their team were confident that they had solved the great puzzle about the shape of the Earth.

    Figure 27: The Earth is an orange, not a lemon.

    It took some time and effort to persuade the sceptics, but their painstaking measurements conclusively showed that the planet is a slightly flattened ellipsoid – about 40 kilometres fatter than it is tall.

    The River Torne was our constant companion throughout this trip – a dominant, surging presence always in view, its colour, form and texture changing by the hour. Thanks to Celsius, his colleagues and their adventures in its majestic, snaking valley we know today that our planet is an orange not a lemon.

    [1] This and other drawings taken from Journal D’un Voyage Au Nord, En 1736 & 1737 written by expedition member Abbé Réginald Outhier. Sadly the artists’ names are not recorded.

    [2] Maupertuis P L M de, Clairaut A C, Camus C E L, Le Monnier P C, Outhier R, Celsius A. The figure of the earth, determined from observations made by order of the French king at the Polar Circle, London, 1738

  • Measuring a potato planet, by Ian Hembrow

    Research grant recipient Ian Hembrow reports on a fascinating study trip to learn about 18th century surveying methods from SIS’s Nicolàs de Hilster.

    At the start of 2022 I was thrilled to receive a grant from the Society to support my project to write a biography of the Swedish scientist Anders Celsius (1701-44). Best known of course for his centigrade temperature scale, Celsius made an array of other discoveries and breakthroughs in a stellar career cut tragically short by his death from tuberculosis aged just forty two.

    Figure 1. Measuring one degree of latitude in the Arctic Circle, 1736-37.

    In particular, he played a vital role in settling the great scientific debate of his age about the shape of the Earth, taking part in a perilous winter expedition to the Arctic Circle in 1736-37 to measure the exact distance of one degree of latitude (see figure 1). Comparing the results with a parallel expedition to the equator proved Newton’s theory that the planet is an oblate ellipsoid, slightly flattened at its poles by the centripetal force of its spin. The Earth, they showed, is shaped like an orange – roughly 43km broader than it is tall.

    Keen to find out how Celsius and his companions made their measurements I reached out to the SIS network for help to understand the methods and equipment they used in the frozen north. Surveyor and collector Nicolàs de Hilster answered my call, inviting me to visit him in the Netherlands to do some hands-on study. It turned out to be an enthralling and memorable trip.

    Figure 2: Nicolàs lines up for a viewing of the sun.

    When I entered Nicolàs’ home, a short train ride west from Amsterdam, I noticed a laptop with what appeared to be an image of the sun surrounded by tables of flickering data. Some sort of astronomical website I thought. But no, this was actually the live-feed from Nicolàs’s own observatory perched on top of the house! I followed my host up the spiral stairs to discover his amazing creation: a cluster of powerful telescopes mounted within a beautiful wooden dome – all hand-crafted from scratch by Nicolàs (see figure 2). The instruments included a custom-made Galilean-type refractor intentionally made to replicate the imperfections of 17th century lenses.

    Nicolàs attached a special filter to one of telescopes and invited me to look directly at the sun. Unsurprisingly, I saw a bright, fiery orange ball. “Now adjust that knob and you’ll be able to see some solar flares,” he advised. And sure enough, as I fine-tuned the focus, little looping swirls appeared around the edge of the image, clearly moving in real time.

    “Wow!” I said. “How big are they?” “About five times the size of Earth,” replied Nicolàs. I was stunned and nearly moved to tears by the magnificence of what I was seeing.

    The observatory though was simply the tip of a very big iceberg. I went on to admire an astounding collection of surveying instruments and devices – from the simplest sighting sticks to massive, high-specification theodolites, an enormous library and two gorgeous bespoke ‘de Hilster’ sun-dials mounted on the walls outside.

    Figure 3: ‘Touring the horizon’ with a modern theodolite.

    After a fine lunch kindly prepared and served by Nicolàs’s wife Ria, we loaded up the truck with a collection of sextants and measuring rods and headed out into the polder nearby – flat countryside criss-crossed by drainage ditches giving way to sand dunes up towards the nearby North Sea coast. Ever prepared, Nicolàs had found a spot where we could ‘tour the horizon’, first using a modern ‘total station’ instrument (see figure 3) and then a handheld, brass sextant.

    Figure 4: Back to older technology with a sextant.

    My heart sank when it was explained to me that geodetic sextants use the 400-point Gradian system, rather than the more familiar (to me at least) 360 degrees of geometry. But I needn’t have worried, because once I’d got the hang of how to use the heavy brass device – merging the direct and mirrored images of adjacent sighting points like church spires and telephone masts – I managed to take and call out full-circle readings from our location (see figure 4). Nicolàs noted down the numbers at each point and then pulled out his phone to check their accuracy against the digital results.

    Figure 5: Student and teacher: Ian (L) and Nicolàs (R).

    Thanks to the expert tuition and supervision, my readings added up to 399.49 grad – just 0.51 of a grad out. Nicolàs smiled and declared this was “acceptable for a first attempt,” before going on to explain how even a small difference like this soon multiplies up to a huge margin of error when applied over the sorts of distances Celsius had to measure.

    Back at the house, Nicolàs then showed me the inherent difficulties of using measuring rods to gauge accurate distances. The 1736-37 expedition members used thirty-foot-long wooden poles laid continuously end-to-end on a frozen river surface. But even on the flat floor of a modern building the kinks and dips of a twelve-foot sectioned rod were obvious to the naked eye. Our planet is of course not entirely smooth, so surveyors have to take account of all the slumps and bumps in their way. “Remember Ian,” said Nicolàs, “the Earth is not a true ellipsoid – it’s a potato!”

    The key to surveying accuracy, I learned, is to measure, measure and measure again – using multiple base lines and repeated calculations to obtain the best possible answer. And, Nicolàs reminded me, measuring the linear distance was only the start of the job – Celsius then had to do some complex astronomical sightings to determine their precise latitude.

    That will have to wait for another time and visit…

    My sincere thanks to Nicolàs and Ria for making me so welcome and treating me to such an extraordinary day.

    In early May 2022 Ian is retracing the route of the 1736-37 expedition in Swedish and Finnish Lapland. Watch out for his report of that trip.

  • A Measurement of the Weight of the World: Then and Now, by Carolyn Kennett, FRAS

    Descending ladders into the mine to seek a suitable sub-surface location to run the experiment to measure the density of the Earth. Photograph credit: © Carolyn Kennett, 2021

    How did we weigh the Earth (and why did this go beyond simple curiosity)? This may be a question people asked themselves during childhood, and have not considered since. Yet it is a question a small group of scientists, including myself, have returned to as we research experiments conducted in the 1820s in a Cornish mine to measure the acceleration due to gravity of the Earth.

    In 2022 it is our intention to re-create the mine experiments by building a replica Kater invariable pendulum and taking it down a Victorian mine in west Cornwall to make measurements of gravity. We will set the pendulum in two locations, one overground and one underground, and time the swing of the pendulum in both locations. The difference in the rate allows us to calculate the amount of gravitational pull on the pendulum, as the underground pendulum will swing at a slower rate. The original experiment was conducted by George Biddell Airy and William Whewell in the deepest mine in England, Dolcoath. This has unfortunately closed and the lower recesses are flooded, so we are using a mine named Rosevale, which gives us a difference of 250 metres between the overground and underground stations. Although Rosevale is not as deep as Dolcoath (700 metres at the time of the original experiment), it gives the opportunity to explore how the experiment was conducted in what can only be described as less than ideal conditions. Mines are dirty places which can be excessively damp and hot. During the original experiment the scientists would have had to contend with vibrations and noise from the working environment, making their achievements all the more significant.

    Why is this all important now you may ask? Yes, simple curiosity does play into this but we find ourselves in a time when the power of gravity is something we have learnt to manipulate and overcome. There are frequent launches into space and discussions of journeys to far-flung destinations such as Mars. Without the arduous and at times dangerous early experimentations into measuring the gravity of the Earth untaken by Airy, Whewell and others we could still be stuck without the knowledge to reach beyond our own planet. Therefore we think it is the perfect time to highlight the work they undertook and their achievements in what was an important building block for us to travel into space. Details of the actual experiment itself, and the results obtained, will be published in a forthcoming issue of the Society’s Bulletin.

    For more information see: https://archaeoastronomycornwall.com/

    This experiment has been part-funded by a SIS grant. For more information on the grants we offer, click here.

    Carolyn Kennett’s recorded Fireside Chat can be found in the Video-section of this website.

  • Abbot and Inventor: Giovanni Caselli, the Pantelegraph, and Catholic Science in the 19th Century, by Carlo Bovolo, Università di Torino

    Figure 1. Giovanni Caselli’s Pantelegraph (image courtesy of Biblioteca di Fisica e Astronomia of the University of Padua)

    In 1860 the famous composer Gioacchino Rossini sent an autographed text from Paris to Amiens, a distance of about 140 km, in only a few minutes. To celebrate such an important event, the musician wrote a piece for piano, the ‘Allegretto del pantelegrafo’. What made the incredibly fast transmission possible was the invention of an Italian priest: in the middle of the nineteenth century, the abbot Giovanni Caselli (1815–1891) had created the pantelegraph (a portmanteau of the words pantograph and telegraph – Figure 1), which, anticipating the facsimile machine, was able to send handwritten texts and pictures by telegraph.

    Caselli, a priest from Siena devoted to physics, realized a prototype of the pantelegraph in Florence in 1856, a technology which mixed telegraphy and electrochemistry and whose operation was based on a regulating clock. Searching for funding, he then moved to Paris, where he improved his instrument thanks to Paule-Gustave Froment and attracted the attention of the public and of Napoleon III.

    The French government funded further research and experiments, including Rossini’s transmission in 1860. The experiments were successful: in 1864 the French government officially adopted the pantelegraph, establishing lines between Paris, Lyon, and Marseille. Other short lines were built in England, Russia, and China.

    At the Italian national exhibition in Florence in 1861 and, above all, at the Universal Exhibition in Paris in 1867, the pantelegraph reached the pinnacle of its success: public demonstrations were made, newspapers described its functioning and extolled its advantages, and Caselli was celebrated as a brilliant inventor. However, its success – though intense – was short. Due to the complexity of the technology, its costs, and an incomplete understanding of its potential, the pantelegraphic network remained very limited and was dismantled in subsequent years. Caselli (inventor also of a cinemograph for measuring the speed of trains, a nautical electric torpedo, and a hydromagnetic rudder) returned to Italy, where he died in Florence in 1891.

    Despite the parable of the pantelegraph, Caselli became a hero of the Catholic apologetics of science: in the apologetical and propagandistic discourse about science and technology proposed by the Catholic press in the second half of nineteenth century, the inventor-priest was a symbol of the Catholic contribution to scientific and technological progress, represented a rebuttal to accusations of obscurantism against the Church, and laid claim to a public role for Catholicism in science.

    Carlo’s research was funded by a 2020 SIS Grant. A longer piece on this subject will feature in a future SIS Bulletin.

  • Poleni’s geometrical instruments to trace transcendental curves, by Pietro Milici, University of Insubria (Italy)

    Figure 1. Poleni’s machines for the tractrix (left) and the logarithmic curve (right) in the Letter to Hermann.

    During the 17th century, mathematicians radically modified their idea of a curve, transitioning from the trace of a geometrical mechanism to the solution of an equation. With that in mind, Descartes and Leibniz introduced theoretical machines (i.e., sketches to be considered mentally but not practically realized) to legitimate the geometrical status of algebraic and transcendental curves obtained as solutions of analytical equations. In the first half of the 18th century, a few scholars converted some theoretical machines for transcendental curves into material instruments. We focus on the geometric instruments designed by Giovanni Poleni (1683-1761), a polymath and Professor at the University of Padua in Italy. These instruments had been described with an engineer’s precision both in textual and graphical representations (as visible in Figure 1) in a letter to Jacob Hermann who was Poleni’s predecessor in the chair of Mathematics. The letter was included in Poleni’s Epistolarum Mathematicarum Fasciculus of 1729.

    In 1739, Poleni inaugurated a unanimously praised laboratory of experimental physics (“Teatro di Filosofia Sperimentale“) that grew also with his successors. Such a Paduan museum still exists and is dedicated to its founder (today it’s named “Giovanni Poleni museum”). Between the machines present in the collection, Poleni listed the ones for the tractrix and the logarithmic curve: also the modern catalogue (Gian Antonio Salandin & Maria Pancino, Il “teatro” di filosofia sperimentale di Giovanni Poleni, LINT, 1987) confirms that there is a sample of a geometrical machine for our transcendental curves. Thanks to an SIS grant, I got the opportunity to observe, manipulate and film such a machine (see Figure 2).

    Figure 2. The machine of the Giovanni Poleni Museum classified as the one for the tractrix and the logarithmic curve.

    Indeed, differences between the artefact in the collection and the designs of the Letter are visible at the first glance. Furthermore, reading the description in Poleni’s index, the machine also differs in materials. In any case, also because of missing pieces, we have no idea of the purposes of such an artefact.

    To our knowledge, no copy of Poleni’s geometrical machines is available: therefore, together with Frédérique Plantevin (University of Brest, France), we decided to reconstruct the machines meticulously described in the Letter to Hermann. After a 3D digital modelling of the machine, we contacted the artisan Uri Tuchman to realize a working model in the materials described by Poleni. We are still working to complete an informative video and a paper on these topics.

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