More on the Fetishization of Triangulation (and on the Possible Schizophrenia of Recent Map History)

Jean Picard’s “Corrected Map of France” was not by triangulation …

Today, 21 July, is the birthday of Jean Picard (1620–1682), French mathematician and astronomer, renowned in particular for two projects in support of Colbert’s plan to fix the map of France, a project that was one of the main reasons he established the Académie des sciences in 1666. Already this morning (it’s 7am here in Maine), the twitters have advertised two blogs (here and here) on Picard’s life and work that both repeat the misunderstanding that Picard’s 1693 “corrected map of France” was based on triangulation. (It was not!) This is a surprisingly common mistake that, because I am a triangulation purist, I find very annoying. It makes me wonder why the mistake is so persistent.

Here’s the map (in a 1729 re-engraving, courtesy of the Osher Map Library and Smith Center for Cartographic Education, University of Southern Maine):

Colbert’s Map Project, Picard, Triangulation, and the “Corrected Map of France”

To make better geographical maps required two new things in the late seventeenth century: knowledge of the size of the earth (still thought to be spherical) and a way to determine longitudinal differences. Latitude was already easy to determine. Given the size of the earth, geographers would be able to turn itinerary distances and bearings into accurate differences in latitude and longitude, and so could be easily fitted into a network of known lat/long control points. As the number of observed and interpolated control points increased, they could then be used to fit existing provincial maps together to make a new and correct map of France.

To determine the size of the earth, Picard was tasked in 1669–70 with measuring a chain of triangles along the meridian of the newly founded Paris Observatory, north from Paris to the Amiens near the coast of the English Channel/La Manche. He soon explained the process and the final result in a short book (Picard 1671). Because this work forms the intellectual baseline of geodetic surveying through the eighteenth century, I went into Picard’s techniques at some length in Cartography in the European Enlightenment (Edney 2019).

After this first work, Picard teamed up with Philippe de La hire and Giovanni Domenico [Jean Dominique] Cassini [I] to address the other half of Colbert’s plan. Colbert had lured Cassini from Bologna to Paris because of his work modeling the movement of the two largest moons (satellites) of Jupiter. If their motion, and more particularly the times when they eclipse (immerse) behind the body of Jupiter, could be predicted, then field observers could time such an event and then by comparing that local time with the Parisian time recorded in the predictive tables, could simply determine the difference in longitude between their location and the Paris Observatory. While the tables were still in development, in a proof of concept (as it were), Picard and La Hire made field observations around the coast of France, while Cassini continued with the observations from the observatory in Paris. On their return to Paris, Picard and La Hire could compare the times of paired (simultaneous) observations of Jupiter’s first moon and determine more accurate longitudes for the field sites. The work was complete by Picard’s death in 1682, but not published for a decade; the publication came with the above “corrected map of France” (Picard and La Hire 1693). The map contrasted the outline of France in a map by Nicolas Sanson from about 1670 (thin line) with the coastline (thick) corrected by longitude observations.

Why Do People Think that the Corrected Map Was the Result of Triangulation?

Two reasons, I think.

a) Presumed Unity of Mapping

First, there was a move by French historical geographers after 1900 to blend together the early map work of the Académie des sciences, i.e., Picard’s two projects, with its later work—both measuring the entire meridian as part of the debate over the earth’s shape (Cassini 1720) and then doing longitudinal series of triangles and infilling the chains with a mesh of triangles so as to create a dense network of fixed points that might be used to fix existing maps (Cassini de Thury [1744])—and then the private venture to undertake an entirely new survey based on that detailed triangulation to make the Carte de France (1750–1789). Earlier, map historians of all stripes had tended to see the projects as separate: one set falling into the realm of geographical mapping, the other into state-sponsored territorial surveys. But the historical geographers, following a nationalistic impulse, blended them all together into a single mapping urge (esp., Gallois 1909). This work in turn led Leo Bagrow (1951, 165) to drop the matter of longitude from the making of the corrected map of France and to attribute it solely to triangulation. Gallois influenced Perrier (1939) who in turn led Chapin (1995) to attribute the map to triangulation. Other recent scholars have echoed the argument (e.g., Iliffe 1993, 337; Branch 2014, 1–2).

b) Fetishization of the Chronometer and of Triangulation

But this morning I realized that there might be a further factor at play. Cassini I’s method of determining longitude from Jupiter’s observations was complex and strictly terrestrial in implementation. It came to be in extensive use by the end of the 1700s, with the result that the world map was “reformed” and took on its modern continental outlines (Sandler 1905a, 1905b), its importance has been overshadowed by the issue of determining longitude at sea, for which the technique cannot be used. (It needed a pendulum clock to hold local time, once determined, and pendula do not run steadily onboard a heaving ship; it needed a long and steady telescope, but the heaving deck made the image bounce around; eclipses of Jupiter’s satellites were simply too rare for the use of the mariner.) Since at least Goode (1927), map historians have focused on John Harrison’s chronometer as the solution to “the longitude problem” and the key to modern, scientific geography, a solution further championed by Dava Sobel’s Longitude (1995). In the process, map historians have quite overlooked the other marine methodology, of equal application in practice, of lunar distances! For all the early modern longitude techniques, and others, see Sandman (2019).

I am now wondering whether the separate fetishizations of the chronometer and of triangulation has created some kind of schizophrenia in map history. A divide in how historians perceive past mapping practices. On the one side is the sea, where longitude is significant and the chronometer is the technological fix. On the other, is the land, where triangulation appears as the fix for systematic observation and measurement without reference to longitude. In actual practice, there was no such divide. But with the post-1980 rise of the (common but false) argument that modern cartography arose with the implementation of geometry to map making in the Renaissance, the practices of terrestrial geometry seem to preclude longitude and promote triangulation. In such an intellectual system, the corrected map of France cannot involve longitude. It’s a land map, it must have been based on improved techniques of land measurement, i.e., triangulation.

This seems to be an interesting byproduct of another historiographical trend that I have only just put my finger on (having been struggling with it for years). Specifically, even as sociocultural map history has since 1980 challenged the old ideas of “the map,” that same kind of map history has only reinforced the idealization of “the map” created by the ideal of cartography … which is why I’m trying to push for some other approach to maps and mapping. For more on this point, though, you’ll have to stay tuned for the next book, now entitled "The Map: Concepts and Histories.

Now I need my breakfast.

Update 7/24/21. The desire for breakfast led me to omit a final point when I write this the other day. The special status accorded the Pucard-La Hire corrected map of France is rather undermined by the fact that there are actually several other maps produced during the 1650–1800 era, showing old and corrected coastlines/boundaries, none even remotely associated with a triangulation. Only occasionally mentioned by map historians, at least three have been reproduced in Cartography in the European Enlightenment, volume four of The History of Cartography (Chicago, 2019), edited by myself and Mary Pedley:

fig. 11: John Cowley’s Coasting Lines of…North Britain i.e. Scotland (1734)

fig. 281: J B B d’Anville’s Parallele du contur de l’Italie (1744)

fig. 532: Tobias Mayer’s Germaniae…mappa criticia (1750) - this one fairly well-known

References

Bagrow, Leo. 1951. Die Geschichte der Kartographie. Berlin: Safari-Verlag.

Branch, Jordan. 2014. The Cartographic State: Maps, Territory, and the Origins of Sovereignty. Cambridge: Cambridge University Press.

Cassini, Jacques. 1720. De la grandeur et de la figure de la terre. Suite des mémoires de l’Académie royale des sciences, année MDCCXVIII. 2 vols. Paris: Imprimerie royale.

Cassini de Thury, César François. [1744]. “La description geometrique de la France.” Bibliothèque nationale de France, GE EE-1322 (RES).

Chapin, Seymour L. 1994. “Geodesy.” In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, edited by Ivor Grattan–Guinness, 2: 1089–100. 2 vols. London: Routledge.

Edney, Matthew H. 2019. “Geodetic Surveying in the Enlightenment.” In Cartography in the European Enlightenment, edited by Matthew H. Edney and Mary S. Pedley, 439–50. Vol. 4 of The History of Cartography. Chicago: University of Chicago Press.

Gallois, Lucien. 1909. “L’Académie des sciences et les origines de la carte de Cassini.” Annales de géographie 18, no. 99-100: 193–204 and 289–310.

Goode, J. Paul. 1927. “The Map as a Record of Progress in Geography.” Annals of the Association of American Geographers 17, no. 1: 1–14.

Iliffe, Rob. 1993. “Aplatisseur du monde et de Cassini: Maupertuis, Precision Measurement, and the Shape of the Earth in the 1730s.” History of Science 31, no. 94: 335–75.

Perrier, Georges. 1939. Petite histoire de la géodesie: Comment l’homme a mesuré et pesé la Terre. Paris: Presses Universitaires de France.

Picard, Jean. 1671. Mesure de la terre. Paris: Imprimerie royale.

Picard, Jean, and Philippe de La Hire. 1693. “Pour la carte de France corigée sur les observations de MM Picard & de la Hire.” In Recueil d’observations faites en plusieurs voyages par ordre de sa Majesté, pour perfectionner l’astronomie et la géographie, pt.3, 91–92. Paris.

Sandler, Christian. 1905a. Die Reformation der Kartographie um 1700. Munich: R. Oldenbourg. Reprinted Bad Langensalza: Verlag Rockstuhl, 2003.

Sandman, Alison. 2019. “Longitude and Latitude.” In Cartography in the European Enlightenment, edited by Matthew H. Edney and Mary S. Pedley, 735–50. Vol. 4 of The History of Cartography. Chicago: University of Chicago Press.

Sandler, Christian. 1905b. Die Reformation der Kartographie um 1700. Karten–Mappe. Munich: R. Oldenbourg.

Sobel, Dava. 1995. Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. New York: Walker & Co.