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Contribution of the Cassinis and Maraldis

Map of the world, courtesy of NASA.

The most significant achievement of the Cassini and Maraldi families is said to have been the creation of the first, accurate, national, topographical map of France. Its production was to occupy the families’ skills over four successive generations, requiring considerable organisation skills in the design, construction, planning, acquisition and dispersal of a wide range of resources, some of them novel, all driven by the political will needed in order to achieve this end.

But, first, what’s the connection between astronomy and cartography, and how did the Cassini family become involved in these two sciences? Well, if you want to draw an accurate map, you first need to know whereabouts you are on the earth.

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Determining longitude

Illustration of longitude and latitude

It was known for a long time that latitude could be determined by observing the angle of inclination of the sun from the horizon at mid-day. However, longitude was, in the mid-seveneteenth century, still problematic. Assuming that the line of zero longitude passed through the Paris Observatory joining the north and south poles, then it would be possible to calculate exactly where you were in an east-west direction from that line if you knew the time at the same moment in those two places – each hour placing you fifteen degrees of longitude away. The chief difficulty was that it was not yet possible to tell the time accurately, and prizes were being offered to produce accurate chronographs, as they were called.

Meanwhile the middle of the seventeenth century saw France without real administrative control and with considerable corruption weakening the State.

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A little background

One of the key facts to bear in mind when looking at the work of the Cassini and Maraldi families in France – in fact, for all scientists working in France in the seventeenth and eighteenth centuries – is that their activities took place within a relatively small physical area, Paris, and within a privileged socio-cultural environment. Perhaps not so clearly understood is the extent to which this reflected the state of France at that time.

France in 1477, courtesy of Wikipedia

There’s a tendency in most of us to view history in modern terms with which we are familiar. For instance, we think of France in something like its present boundaries and with relatively coherent political, cultural and social systems. But Europe was, until relatively recently, an area in which there was considerable diversity in many of these aspects, as well as extraordinary inequalities in the distribution of its wealth. France, like many of its neighbours, was neither a coherent political nor cultural entity and the wars of the next few centuries would continue to define and redefine its borders in response to the aspirations of a number of individuals, particularly those boundaries to the east. While it is possible to follow the movement of these borders historically as discrete countries were created, fluctuated and established, development within the country we now know as France is not so easy to follow.

Illustration of population density, 1999 – left and languages – right – courtesy of Wikipedia

In fact, in the seventeenth and eighteenth centuries, not only would the majority of the population not have understood the concept of France, they did not even speak French. France was, in essence, Paris and its immediate surrounding area where the court was based, and it was mainly here that French was spoken and, to a lesser extent, written and read. The rest of France was populated, but by people with a wide variety of histories, speaking a miscellany of languages and dialects, living in relatively small cultural and economic units, and who mostly moved never more than half a day’s walk from their home, though there were some exceptions associated with seasonal movements for work and transhumance.

Because of this lack of movement and the loose pattern of settlement, there was little in the way of formal roads. The circulation system was fine-grained, poorly defined and changed with season. Those who moved through the countryside would see very few people on their journeys. Towns, such as they were, closed their gates at night and maintained border and customs posts outside them, as there were at the borders of most political entities, large and small. One of the consequences of this was that everybody feared strangers as they represented potential threats to their income, way of life or even life itself.

Beliefs were primitive and even those who were educated and came from outside the communities as teachers, doctors or ministers, had to accommodate and adapt to the local systems, learning to speak the local languages and unable to operate without local acceptance. Strangers were suspected of all kinds of things. One of Jacques Cassini’s young geometers was set upon in Les Estables, a commune in the Haute-Loire region of France, and killed because the locals feared for the strange instruments of his trade he was carrying. All over France, the structures established by the geometers from which to triangulate their mapping, were destroyed both in order to furnish building material as well as in fear of their magical significance, the latter a characteristic commonly thought imbued in many natural features.

Against this background, it slowly became apparent that maps were indeed necessary both in order to improve knowledge of the State and, with it, a rational taxation base, as well as for military purposes.

Taxation was universally hated and, in most of the country, was resisted both by evasion as well as by the development of extensive smuggling systems, some of them extremely clever in concept and effective in execution. Barter formed the natural exchange mechanism for both goods and services, creating little money to pay to the demands of the Revenue authorities, their responses often being cruel, socially divisive and ineffective.

At the same time it was becoming increasingly obvious that there were improvements needed if armies were to operate more effectively. The lack of accurate information was a continuing constraint on their success. It was common for them to fail in their endeavours due to a lack of understanding of the terrain and the ways this affected the planning of their routes of march, tactics and opportunities. Accurate mapping was an obvious solution to many of their problems.

Although there was a small amount of two-dimensional mapping carried out, mostly as records by those who owned land, there was no national understanding of the way in which the communities linked due, in most part, to the difficulty described above in moving around the country. Strangely, many of the natural features of the country were not named, even by those who lived near them.

This, then, was the setting in which Cassini began the process of assembling teams of geometers, designing their instrumentation and rationalising recording, that was to lead to the first accurate map of France.

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Jean-Baptiste Colbert, a protégé of Cardinal Mazarin, fed King Louis XIV’s animosity to the increasingly powerful and corrupt Nicolas Fouquet and was, in 1661, appointed Minister of Finance in his place by the King to begin the process of administrative reform, economic consolidation and reorganisation necessary for managing France. One outcome of this was that it permitted Louis XIV to expand his personal interests in spending on his court as well as entertaining foreign expansion.

Colbert, the son of a draper from Reims, was an unpopular figure but oversaw considerable change, beneficial to France. He occupied a series of important positions of State and, under his patronage, a number of key organisations were instituted and initiatives begun. Among them Colbert founded the Académie des sciences in 1666 and, in 1667, l’Observatoire de Paris.

The Abbé Picard, Prior of Rillé in Anjou was the successor to Gassendi in the Chair of Astronomy at the College de France. He recommended Giovanni Domenico Cassini to Colbert as the potential head of the Observatory and, in 1668, Colbert invited Cassini to Paris. Pope Clement IX, for whom Cassini was working at the time, agreed – perhaps hesitantly – to lend Cassini, who arrived in Paris on the 4th April 1669 to begin work.

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The introduction of Cassini to France

A detail of the 1668 map of Paris from

The maps of France at that time were unco-ordinated and often inaccurate. At the first meeting of the Académie it was decided that the maps of France should be improved using the method of triangulation first introduced by Tycho Brahe and later developed in Holland and England. The Académie led the work which resulted in the publication, in 1674, of a map – in nine sheets of three by three array – of Paris and its surrounding area. The above detail is a part of the central sheet.

Triangulation map of France 1792-1799 by courtesy of Ken Alder

The use of the principle of triangulation was an important innovation in that it brought greater accuracy in the surveying of land through the inherent characteristic of the triangle not to distort. But this accuracy was also dependent upon the quality of the surveying instruments measuring the distance and angles between measuring stations.

The illustration of triangulation to the right is taken from a site dealing with the fascinating French initiative between 1792 and 1799 to set the length of the metre. The exercise was made by Jean Baptiste Joseph Delambre and Pierre Méchain along the line of the meridian running through the Observatory in Paris from Dunkirk on the Channel in the north to Barcelona on the Mediterranean in the south, but illustrates the same principle used in the earlier Cassini and Maraldi mapping. Earlier, measurements based on the triangulation of base points were made right across the Kingdom. From this, Cassini and Maraldi were able to produce their map shown below.

One difficulty at this period of the Cassini’s work was the difference of opinion between father and son. Jacques believed that the Earth was elonogated along its axis, whereas César François sided with the Newtonian view that it was flattened at its poles. Within the Académie the scientists were split into two opposing camps and a number of expeditions were made with a view to settling the matter. Regrettably, the results of their instrumentation were not sufficiently accurate for a decision to be made for elongation or flattening.

A map of France drawn by Giovanni Domenico Cassini

So, the early eighteenth century saw Jacques Cassini – Cassini II, and later with his son, César François Cassini – Cassini III, beginning the process of developing the principles of triangulation and accuracy in order to produce more accurate mapping, specifically a more accurate map of France.

The resulting map, shown to the right here, was produced in 1746 and 1747 and was considerably more accurate than anything which had preceded it. It comprised eighteen sheets at a scale of 1:86,400.

Part of a map drawn by Jean Dominique Cassini based on triangulation

One of their findings was that France was approximately ten per cent larger than had previously been thought. Just as important, the Cassinis accurately located the geographical relationship between the observatories in Paris, France and Greenwich, England, establishing the basis for greater accuracy in making astronomical observations. For those with an interest in reading the maps, there is another site which sets out the legends used on the maps by the various features which go to making the maps readable.

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What is interesting to us nowadays is the accuracy obtained with the instruments available to them at the time, as well as the methods of recording. This is particularly so bearing in mind the fact that, in the middle of the eighteenth century there were over eight hundred different measures operating round France, there being centuries of resistance by nobility to royalty’s attempts to standardise them.

But it was not just the French who were concerned about cartography and the related field of instrumentation. The British were also attempting to produce more accurate instrumentation in order that longitude could be more accurately determined at sea.

In the early part of the eighteenth century the British Parliament had offered a large prize to anybody who could calculate longitude to a half degree on a voyage between London and the West Indies. Between 1735 and 1762 John Harrison, a clock maker, developed the concepts worked on by Christian Huygens in the middle of the previous century. The essential difference was in Harrison’s developing a mechanism which, working much more quickly than Huygens’ slow pendulum, was able to counter the movement of waves more effectively. Harrison built four different chronometers in order to win the prize. Although his fourth chronometer achieved the task, political manoeuvering and alternative methods of determining longitude – such as Tobias Mayer’s lunar tables – delayed his receiving the prize until 1773.

In 1783, Jean Dominique Cassini – Comte de Cassini and Director of the Paris Observatory – proposed that the differences in measurement of longitude between the Paris and Greenwich observatories should be resolved by triangulating the south-east of England and extending the measurements to France.

Joseph Banks, President of the Royal Society, suggested that Major General William Roy, who had begun his professional engineering creating maps of the Scottish mainland for the Duke of Cumberland, should carry out this task. Roy commissioned Jesse Ramsden, the most prominent scientific instrument maker of his day, to make a number of instruments to enable him to carry out his work. In 1784 Ramsden produced for Roy a one hundred foot steel chain, six glass rods each one metre long, and a three foot theodolite. The original distance was measured with deal rods and iron bars as 27,404 ft. Re-measured with 1,370 placements of glass rods this became 27,406 ft. and, following correction for temperature and to mean sea-level, the value was determined to be 27,404.2 ft. or 8.352800 kilometres.

In September 1787 cross-channel measurements were taken linking France and England. While this work was proceeding, triangulation survey work continued within England, forming the basis of the Ordnance Survey.

In September 1784 Jean Dominique Cassini, Comte de Thury, had written to Charles Blagden, the recently elected Secretary of the Royal Society suggesting that he could better carry on his father’s work by becoming a member of the Royal Society and asking Blagden to support him. He was elected 30th April 1789. His father had been elected 17th January 1750.

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Since the middle of the seventeenth century there had been recommendations as to how standardisation of distance might be effected, but it was not until 1790 that the National Assembly passed a resolution regarding it. Charles Maurice de Talleyrand-Périgord took a proposal of Marie-Jean-Antoine-Nicolas de Caritat, Marquis de Condorcet, to the Assembly recommending that a measure of length should be adopted from nature, that it should be decimal in character, and that other measures of area, weight, volume and the like should be related to it.

It was intended that this should be an international exercise but England, the United States and France were unable to agree the basis for the measure. In fact there was a suspicion that the French were not so much interested in the measure itself but on fixing the curvature of Earth, this having been a preoccupation of French scientists for some time.

In 1793 the Revolution disbanded the Académie des Sciences but, before they did so, Jean-Charles de Borda had produced a tentative measurement of a metre based on the work of Cassini in 1740. Work continued on making a more precise measure for a metre, and this was commpleted in 1799 with the direction it should be used throughout France. However, not only was there reluctance in France to its adoption, England, Germany and the United States refused to accept it for a variety of reasons.

Napoleon returned France to the old system of measurement in 1812 but, ironically, his successes in wars abroad had taken the metric system with him and, on his defeat, they were retained by the Low Countries.

A detail of the map of Paris from A detail of the above map from

So, it can be seen that the work of scientists in the eighteenth century – particularly in cartography and astronomy – was constrained by significant difficulties, not just in the basis for measuring their sciences, but also in the effects on them of the Revolution.

Here, to the right, are two details at different scales of a part of the map relating to Paris.

Cassini carried out his work without the benefit of being able to use the Borda repeating circle, a device for measuring angles, which was only introduced by Borda in 1785. Its benefit was that it was more accurate than its predecessors through the use of a process which essentially halved inaccuracies at each re-registration of the equipment’s sightings.

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Borda’s repeating circle

Borda Repeating Circle method

Borda’s repeating circle consisted of two separate horizontal rings, each with its own telescope attached to, and capable of being read against, a single circular scale. The improved accuracy was obtained by sighting the two telescopes on separate, fixed points, then locking them together and moving them so that one telescope was sighted on the other point. They were then uncoupled and that telescope moved back to sight its initial point, the other being locked stationary. At that stage the angle subtended by the two telescopes would be twice the actual angle to be measured. This process could be repeated, each time the angle increasing by a factor of one, and the required angle being calculated by dividing the subtended angle by the number of readings which had been made. Essentially, the process refined the actual angle with each measurement.

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