Danish astronomer Tycho Brahe was among the first individuals to use this epoch-making method. In 1597, from the observatory on the island of Ven in Øresund, he completed the measurement of angles and distances across the water to Copenhagen, Malmö, Lund, Landskrona, Helsingborg, Helsingør and Kronborg. He used astronomical observations of Ven’s location and a baseline of 1,287.90 metres from the observatory to the eastern tower of St Ib’s church as his starting point, and based on his measurements was able to draw a map of the island–one of the first in the world to be based on trigonometric triangulation.
Brahe’s measurements were the first stage of a plan to publish an improved map of Denmark and Norway–King Frederick II was aware of and supported the plan, as in a letter dated 1585 he asked his librarian to provide Brahe with all the castle’s maps of the two countries. Brahe’s large-scale mapping project would never be completed, however–probably because a friend of his had similar plans.
Brahe left Ven in 1597. Christian IV, who had ascended the throne the year before, had no desire to use his funds on Brahe’s observatory, and so in 1600 Brahe left Denmark-Norway to become the official imperial astronomer to Rudolph II in Prague.
In Prague, Brahe was visited by the Dutch mathematician Willebrord Snel van Royen, known to the English-speaking world as Snell. Snell was also interested in triangulation, and just a few years later, in 1616, also put Gemma Frisius’s method into practice. Using a surveyor’s chain–a completely new invention designed to ensure more accurate survey measurements–Snell first created a baseline from north to south measuring 327.80 metres (from A to B). Using triangulation, he then measured the distance between two points to the east and west of this (C and D)–1,229 metres. He then stood at point C, and from here measured the angles to the tower of Leiden town hall and the church tower in Zoeterwoude, before doing the same from point D, creating two triangles. Using these, he was then able to calculate the distance between Leiden and Zoeterwoude: 4,118 metres.
And so on and so forth. Using his first, short baseline, Snell was able to measure increasingly greater distances, until using thirty-three triangles he had found the distance between the cities of Alkmaar and Bergen op Zoom–situated 130 kilometres apart.
For Snell, the objective of this triangulation process was to repeat the experiment performed by Greek mathematician Eratosthenes over 1,850 years earlier–to measure the Earth’s circumference. Like his predecessor, Snell started with the distance between two places located on roughly the same longitude, using Alkmaar and Bergen op Zoom where Eratosthenes had used Alexandria and Syene (Aswan). Snell also had the advantage of being able to measure the distance between his two locations with much greater accuracy than his predecessor, who had calculated the distance between Alexandria and Aswan based on how long it took to ride between the two cities by camel. In his Eratosthenes Batavus (The Dutch Eratosthenes), he explained both his method and his result: 38,639 kilometres. He was incorrect by a margin of less than 4 per cent.
CARTE DE FRANCE | France was the first country in the world to use these modern triangulation methods on a large scale. Here, the method was refined by Italian astronomer Giovanni Cassini, who arrived at the court of Louis XIV–the Sun King–in 1668. Cassini, a professor at the University of Bologna, had agreed to take part in the construction of a new observatory just outside Paris, and the Pope, for whom Cassini worked, had granted Cassini permission to travel. Both the Pope and Cassini himself believed the stay in France would be a short one, and so at first Cassini made no great effort to learn French. But Louis XIV offered a good salary, and Cassini eventually became so involved in the newly established Académie des sciences–the French Academy of Sciences–that he changed his mind. Three years later he became known as Jean-Dominique Cassini, and had taken on the role of leading the academy.
Here, Cassini worked alongside Jean Picard–priest, astronomer and surveyor–who used Snell’s method when measuring the distance between the towns of Malvoisine and Sourdon–also with the intention of finding the Earth’s circumference. Picard later built upon this triangulation method when he created a map of Paris and the surrounding areas–the Carte particulière des environs de Paris set the standard for the large-scale mapping of France, which was just around the corner.
The reasons for the establishment of the French Academy of Sciences were largely characterised by utilitarianism. Even before the academy was founded, the French Minister of Finance had ordered the creation of an updated map of the entire country, in order to obtain an overview of France’s resources and where they were located, and whether particular regions were best suited ‘to agriculture, to commerce or manufacture–and also of the state of roads and waterways, the rivers in particular, and of possible improvements to them.’
At the same time, the academy was characterised by fairly free research–not unlike the position enjoyed by the library in Alexandria in its time. The researchers’ guaranteed and generous income signalled that they were part of the governmental apparatus at the highest level. The academy was a place where information was collated, research was conducted and results were disseminated–and attracted international expertise.
In 1679, King Louis XIV ordered the academy to produce the most accurate map of France possible, and Jean Picard was chosen to lead the first stage of the process–the mapping of France’s coastline. Earlier maps of France had been based on a prime meridian that passed through the Canary Islands–a prime meridian inherited from the Greeks, who had used the outermost point of their known world. But the distance from the French coast to the Canary Islands had never been accurately measured. When over the course of three years Picard and an assistant measured latitude and longitude values from Flanders in the north to Provence in the south-east, Picard used the prime meridian that he himself had established, which passed through the observatory in Paris.
In 1682, the corrected map of France–the Carte de France corrigée–was met with astonishment from both the academy and the king. Picard had presented the results of his survey on what had until then been the official map of France, using thick lines to highlight the differences. Suddenly, everyone was able to see that France covered an area 20 per cent smaller than previously believed. The Atlantic coast was pulled eastwards, the Mediterranean coast northwards, and it was revealed that important seaports such as Marseilles and Cherbourg had on earlier maps been situated far out to sea. ‘France has lost more territory to the Academy of Sciences than to all our enemies combined,’ Louis XIV is said to have exclaimed upon studying the map. Picard was probably well aware that his map would not necessarily prove popular–he took care to enter text on his new map that clarified it was ‘corrigée par ordre du Roy’–corrected by order of the king.
Picard’s new map showed that the academy had good reason to tear all its old maps to pieces, and plans were made for the thorough surveying of France based on Picard’s triangulations and Cassini’s new method of finding a location’s longitude by observing Jupiter’s moons.
Cassini’s method was made possible by the latest telescopes, which gave astronomers a clear view of Jupiter’s moons. By noting the times at which one of the moons came into view, disappeared behind Jupiter and then re-emerged, and comparing these times with those noted at another location, the difference in longitude between the two locations could be determined. The method was also a result of the fact that more accurate clocks with which to tell the time were now available. But the great map-making project was set aside when Jean Picard died in 1682, and France went to war with the Spanish Netherlands the following year.
Instead, work continued to extend the Paris meridian from north to south through the entire country in order to answer one of the greatest questions of the 1600s–what was the Earth’s definitive size and shape? The theory of gravitation proposed by English scientist Isaac Newton indicated that the Earth was slightly squashed in appearance, because gravity seemed to vary at the equator and the poles. But the academy disagreed, adher
ing instead to French philosopher René Descartes’ theory that the Earth was shaped like an egg. The answer to this question eventually became a matter of national honour on both sides of the English Channel.
The academy asked the king for support for expeditions to the northern regions and the equator in order to measure the distance between the lines of latitude there. If the distance between the lines of latitude was shorter in the north than in the south, then the Earth was shaped like an egg; if the distance was longer, then Newton was right.
The first expedition set out for Peru in South America in 1735; in the following year, a second journeyed to Sápmi in the border areas between Sweden and Finland. The expedition to Peru was catastrophic–the ship came ashore at a location so rife with mosquitoes that many of the crew contracted malaria. They rode on mules through jungle, forced to cut their way through the vegetation using machetes, slept in cabins on stilts when rainstorms raged, climbed mountains and slept in freezing caves at night and, finally, two years after they had at last started to take their measurements, realised they had made a mistake and had to start all over again. It was a decade before the first expedition member returned home.
Luckily, the journey to Sápmi went more smoothly. The expedition used the frozen River Torne to calculate a 14.3-kilometre-long baseline from the spire of Torne Church to Mount Kittisvaara, but the results presented to the academy in November 1737 came as a shock. The degrees of latitude had been found to be slightly longer in the northern regions, which meant that the Earth was a slightly squeezed sphere and that–perhaps worst of all–Newton and the British had been right. The French Academy of Sciences’ method had disproved the academy’s own theory–but this defeat was soon turned into a victory when the academy emphasised the excellence of its method. It was neutral, verifiable and scientific, provided an objective view of the world, and could be used by anyone, no matter their beliefs or ideology.
By 1730, France had returned to its regular cartographic activities–Philibert Orry, the country’s new controller-general of finances, had little time for philosophical discussions about the size and shape of the Earth. Orry was more concerned with the fact that the Department of Public Works lacked accurate maps that could be used in the upgrading of the country’s infrastructure, and in 1733 he asked Jacques Cassini–son of Giovanni Cassini, the man who had led the academy’s map-making project–to start the triangulation of the entire country.
Orry also took it upon himself to implement the governmental education of engineers and surveyors, with the aim of creating standardised maps that would help the navy to navigate more easily and the army to build fortresses along international borders. Later, he also asked the surveyors to prepare standardised road plans for the entire kingdom. The purpose of maps–and the words used to describe them–was starting to change. The role of the state, public benefits and standardisation were becoming increasingly more important than royal favour, merchant benefits and scientific contemplation. Geographers were in the process of becoming civil servants.
A map of Marseilles and its environs from César-François Cassini’s huge Carte de France project, started in 1748, taken over by Cassini’s son Jean-Dominique in 1784 and transferred to the Dépôt de la Guerre in 1793 in the wake of the French Revolution. The project was a great success, although technically never completed.
The surveyors had to venture out into unknown and rugged terrain. So far, triangulation had for the most part been undertaken in the Netherlands, Denmark and northern France, in areas where the terrain was relatively unchallenging, but now the surveyors were setting out for the eastern and southern mountains. Encounters with the locals were not always friendly–in the Vosges Mountains, in the border regions with Germany and Switzerland, the surveyors, with their suspicious behaviour and strange instruments pointing here, there and everywhere, were accused of being political agitators. One was even beaten to death because he was believed to be using his instruments to put a curse on the fields. Their equipment was constantly stolen, they were denied transport and nobody was willing to show them around, preferring instead to pelt them with stones.
But in 1744 the work was finally completed, the surveyors having measured 800 triangles and nineteen baselines. The Nouvelle carte qui comprend les principaux triangles qui servent de fondement à la description géométrique de la France (New Map Including the Principal Triangles that Form the Basis for the Geometric Description of France) was published as a collection of eighteen sheets that same year, but the work was incomplete. Large areas, such as the Pyrenees, Jura Mountains and the Alps, were only outlined, and the map said little about the country’s topography, being only a network of triangles–a geometric skeleton–featuring a broad range of points that followed the country’s coastlines, rivers and roads. But the map fulfilled the controller-general of finance’s wish for an overview that could be used in planning activities.
During the survey, a third generation Cassini–César-François Cassini de Thury–had taken over responsibility for the work and felt it was now complete, although he admitted that the surveyors had not visited every farm nor measured the course of every river. But public or private institutions could now fill in the details on regional maps.
But history would not turn out as Cassini had planned–France went to war with Austria before the map was finished, and in 1746 battles with the Austrian Netherlands raged. Cassini was sent away to help the military engineers to map the battlegrounds. After France had won the war, Louis XV visited the engineers and Cassini, comparing Cassini’s map with the terrain. He was impressed: ‘I want the map of my kingdom to be done in the same way, and I charge you [Cassini] with doing it.’
Both the king and Cassini knew that mapping France in detail would be an enormous project, and although Cassini had his doubts about what it would be possible to achieve, the opportunity to undertake an even greater survey, this time including every river, village, mountaintop and copse of trees, was an offer he couldn’t possibly refuse. He estimated that it would take him eighteen years and 180 maps to cover the entire country–placed side by side, they would create a map of France measuring twelve by eleven metres. Ten maps would be produced each year, each of them with a budget of 4,000 livres to cover equipment, triangulation and printing costs. The first print run would comprise 2,500 copies, with maps each costing four livres–significantly more than other maps at the time. If all the maps sold, they would bring in a total of 1,800,000 livres for the national treasury, which had been seriously depleted by the latest war. The controller-general thought the project sounded like an excellent idea.
But the project’s execution proved more difficult than expected. Cassini was an exceptionally thorough person, obsessed by details and accuracy. He inspected and controlled all aspects of the work, from the survey itself to the printing of the maps, checking and double-checking every last detail. Local residents were also consulted to a greater extent now that every little stream and place name had to be included. The skeletal map from 1744 was fleshed out; given muscles, arteries and skin. It would become the body of Marianne, goddess of liberty–the symbol of the French Republic.
After eight of Cassini’s estimated eighteen years had passed, only two maps had been completed. In the summer of 1756, when Cassini was granted an audience with the king to show him the second map, Louis XV dropped a bombshell: ‘My poor Cassini,’ said the king, ‘I am terribly sorry, I have bad news for you: my controller-general doesn’t want me to go on with the map. There’s no more money for it.’ And the king had a point–the map wouldn’t be finished before the next century if work on it continued at the present pace. Undeterred, Cassini responded: ‘The map will be made.’
Cassini changed tactics. With the king’s approval, he established the Société de la carte de France, its fifty members requested to contribute 1,600 livres per year. This doubled Cassini’s budget, meaning that the project would be able to be completed within ten years. In return, the society’s members w
ould receive a share of the profits, in addition to two copies of each map. It was a brilliant move–the shares sold like hot cakes, and leading members of the nobility, eminent politicians and even the king’s mistress, Madame de Pompadour, purchased subscriptions. Cassini acquired more money than he needed, and was able to employ more surveyors, cartographers and engravers.
Over the next three years, Cassini published as many as thirty-nine maps, each in a print run of 500 copies. The maps sold well, and in 1760 a total of 8,000 copies of the first forty-five maps had been sold. Maps were circulated as never before and, for many, Cassini’s map production became a symbol of the French nation. Farmers with large holdings and members of the bourgeoisie were also interested in purchasing shares to invest in a little piece of France. Cassini set up a public subscription, which could be purchased for a third of the Société price.
Much of the project’s success and popularity was a result of what had previously threatened to derail it–Cassini’s pedantic nature. It was obvious to anyone who viewed them that these maps were more beautiful and more detailed than any of those previously published. They were printed using the best inks on the best paper, and characterised by simplicity, clarity and a great number of details reproduced using modern typography and standardised symbols for everything from monasteries to mines.
But at the same time, what was actually deemed to constitute the French nation was becoming a politically charged question. France was characterised by regional autonomy and the fact that the country’s inhabitants spoke a broad range of languages from Italian and German to Breton and Catalan, but Cassini mapped all the regions in the same way and used the same Parisian French to write the various place names, contributing to the standardisation and uniting of the entire nation. The project collapsed in a wave of democratisation at the end of the 1700s, with an increasing number of individuals arguing that it was the nation itself, and not the monarchy and nobility, who should hold political power.
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