Early Histories of Geodesy

How scholars who measured the size of the earth wrote about the history of that endeavor, before 1720 and the debate over the spheroidal shape of the earth

I have been rather self-indulgent as I write Maps, History, Theory and now need to reframe and rethink it in order to keep it down to size. So here’s a chunk on a subject I happen rather to like, but that I have to admit is not essential for the final work.

Note: I use “geodesy” to refer strictly to the measurement of the size and shape of the earth, as restricted by the French in the eighteenth-century (Alembert 1757); some would instead use “higher geodesy” in distinction to the simpler practices of common land surveying.

update 20 June 2021: I’ve inserted some biographical dates etc.

In The Story of Maps, Lloyd Brown (1949, 290) claimed that each early modern account of a new geodetic survey had been prefaced by a “careful review” of all previous geodetic measurements since the Ancient Greeks. Based on my early work on nineteenth-century geodesy this seemed very much to be the case (see, e.g., Airy 1845). But in researching the entry on geodetic surveying in the long eighteenth century for Cartography in the European Enlightenment, I read all the accounts by the (mostly) French and some British geodesists and found few had such introductions (all identified in Edney 2019a). Brown greatly exaggerated the historical sensibilities of practicing geodesists. Only in the accounts of the very earliest geodetic surveys, from 1617 to 1720, did geodesists seek to validate their work by appealing to the antiquity of geodesy. Thereafter, geodesists limited their introductory “historical” narratives to detailing the execution of their own particular surveys, to demonstrate the quality of their instruments and techniques, to lay out the conditions under which the work was carried out, and to explain how problems had been overcome, all to attest to the quality and validity of the survey (Delambre 1798, vi).

An initial, loose historical discourse concerning past measurements of the earth’s size developed among seventeenth-century geodesists as they sought validation both from the evident antiquity of geodesy as an endeavor and from the progress that they had made in their own work vis-à-vis that of their predecessors.

The first geodetic surveyors in the early modern era were full of the novelty of their own achievements and barely referenced Eratosthenes’ calculation of the earth’s size, in the second half of the third century BCE, or the first geodetic survey by the Caliph al-Ma’Mūn’s astronomers, in the 830s CE. Moreover, they referenced those early works only to justify their own methods of measuring the length of an arc of the meridian directly along the earth’s surface, whether with rods (Fernel 1528, sigs. B.ii recto–B.iii verso) or perambulator (Norwood 1637, [ix–xii], 1–4).

Other early geodesists, who pioneered the use of triangulation to measure arc lengths indirectly, deployed more coherent histories of geodesy to explain that their work was nonetheless part of an ancient and therefore an inherently intellectually valuable concern, one that spoke to the very nature of humanity. As Jacques Cassini [II, 1677–1756] would later explain at length:

Rien n’étoit plus important pour la Geographie que de connoître la grandeur de la Terre, & rien ne paroissoit plus difficile à entreprendre. Car comment mesurer cette vaste étenduë de continents, dont la surface est couverte d’une infinité des Montagnes qui le rendent inégale, & qui est entrecoupée en tant de manieres par les Rivieres, les Lacs & les Mers qui l’environnent de toutes partes. Aussi Pline admiroit la hardiesse de l’esprit humain d’oser tenter des choses si difficiles, & l’on n’auroit jamais pû y réüssir, si l’on n’avoit essayé de déterminer tout le circuit de la Terre par la mesure d’une de ses parties, ce qu’on a fait, en suppossant que sa figure étoit Spherique.

Nothing was more important for [ancient] Geography than to know the size of the Earth, and nothing seemed more difficult to undertake. For how is it possible to measure this vast expanse of continents, the surface of which is covered with an infinity of mountains which render it uneven, and which is intersected in so many ways by rivers and lakes and by the seas that surround it on all sides. Pliny, therefore, admired the boldness of the human spirit to dare to attempt such difficult things, and one would never have succeeded in doing so, if one had not tried to determine the whole circuit of the Earth by the measure of one of its parts, which one was able to do on the supposition that its figure was spherical. (Cassini 1720, 12; see also Cassini 1719, 245)

Jean Picard’s (1671, 22) triangulation diagram: left, main work; right, secondary checks. See Edney (2019a) for more information.

The first geodesist to use triangulation in a geodetic survey, Willibrord Snellius [Snel van Royen, 1580–1626], overtly adopted the mantle of ancient authority by calling his account, Eratosthenes Batavus (“Dutch Eratosthenes”). Snellius (1617, 1–16) and later Jean Picard [1620–1682] (1671, 3–6) emphasized their predecessors’ limitations and inaccuracies, both in measuring the length of a meridional arc directly and in not following a true north-south line. Snellius and Picard both used their historical summaries to establish how much better were their own triangulations and instruments.

The earth’s shape and size were both obviously important to geographers. Many recounted the various shapes postulated by ancient philosophers and the eventual proof of the earth’s sphericity in the fourth century (e.g., Morden 1702, 1–15; Costard 1767, 1: 205). The earth’s size was a crucial parameter in converting itinerary distances into differences of latitude and longitude, and so histories of geography also identified the various sizes proffered by ancient and medieval authorities. Jean Baptiste Bourguinon d’Anville [1697–1782] (1759, 82–100) thus undertook a detailed account of Eratosthenes’ geodetic calculations in an attempt to determine an equivalency in contemporary units for the stade, the ancient Greek unit for expressing linear extent, and the Egyptian schoenus, for use in his analytical mapping of the ancient past (also Anville 1769).

It was in this context that Giovanni Battista Riccioli SJ [1598–1671] prepared comprehensive accounts of geodetic work as part of his attempted reform of geography and charting. He identified three methodological categories of geodetic determinations: measurements of the length of an arc of a meridian, whether by calculation or by measurement; calculations that combined itineraries and marine voyages with astronomical determinations of longitude; and measurements of the geometrical relationships between widely spaced objects on the earth’s surface, the arena in which Riccioli was himself active (see Edney and Dew 2019, 435–36). He outlined the different determinations of the size of the spherical earth that had been made in each category and provided a table of linear measures in order to permit comparisons between the different results (Riccioli 1661, 136–82; Riccioli 1672, 130–75). But in reconciling historical and contemporary measures for the earth’s size, and then in defining the latitude and longitude of no less than 2,200 locations, Riccioli was not particularly critical in his assessment of early units of measure and made many assumptions (Edney 2019b, 481–82).

Riccioli’s analytical flexibility gave way before a wave of new concerns stemming from the realization that the earth is not perfectly spherical. Astronomers had of course been interested since antiquity in the earth’s size, because it provided the basic yardstick for determining distances from the earth to the moon, sun, the planets, and the fixed stars. The wide variation in the earth’s size postulated in antiquity was nonetheless of little significance. Astronomers did not need to know the earth’s size in absolute terms for the geometrical methods they employed to determine the shapes and the relative sizes of the orbits of the planets and comets (Delambre 1814, 3: 512). Cosmographers were free to make their calculations of the sizes of the spheres with whichever size of the earth they deemed most appropriate (Van Helden 1985, 4–8, 24, 30–31, 34). The early modern surveys of the earth’s size, from Fernel through Picard were all geared towards making better maps and sea charts.

This situation changed with Isaac Newton and his Philosophiæ naturalis principia mathematica (1999 [1689]). Newton argued—as several other scholars were beginning to appreciate (Edney and Dew 2019)—that the earth is not actually spherical. His calculations suggested that the earth is flattened at the poles as a consequence of gravitational attraction acting within a rotating fluid. But when Cassini II completed the triangulation of the Paris meridian in 1718 and compared the lengths of the degree at either end, he concluded that the earth is actually elongated (squeezed at the equator). In presenting these results, Cassini II used the historical introduction to justify geodetic endeavors as a singular, essential, and ancient form of scientific inquiry (Cassini 1719, 245–48; Cassini 1720, 12–21), but he went further and reassessed the seventeenth-century measurements according to how well they fit his model of an elongated earth. This reassessment entailed a detailed review of their observations and calculations, especially those by Picard, and the recalculation of those portions of the work that appeared, with hindsight, to be problematic (Cassini, 1720, 255–306). [n1]

The intense debate sparked by Cassini II’s empirical disagreement with Newton’s (and Christiaan Huygens’) mathematical models of the earth effectively ended the use of historical sentiments within further accounts of particular geodetic surveys. The new quest to establish the earth’s figure and to precisely refine its parameters engendered many innovative technological and observational improvements. Geodesists were all concerned in their published accounts to establish the value and worth of their surveys by carefully evaluating their new instruments and procedures, not by self-conscious references to ancient forebears. In 1784, William Roy [1726–1790] experimented with different technologies for baseline measurement exemplified the new rhetoric of instrumentation (Roy 1785; see Widmalm 1990; Bennett 2006). The one exception was the French account of the triangulation undertaken in the 1780s to determine the precise longitudinal difference between the observatories at Greenwich and Paris, which briefly reflected on the glorious achievements of French science by recounting the debate over the earth’s shape and the heroic geodetic surveys undertaken for its resolution (Cassini et al. 1789, ii–viii). [n2] Nor would historical commentaries be reintroduced into accounts of particular geodetic surveys in the nineteenth century.

This did not mean that histories of geodesy ceased to be written after 1720. Rather, a second effect of Newton’s Principia redirected the subject to histories of mathematics and astronomy. The issue, as Airy (1845) would explain at length, was that Newton’s celestial mechanics required the orbits of the planets to be calculated in absolute terms. (If gravitational attraction is to be defined, in part, by the inverse of the square of the distance between two objects, then that distance must be known absolutely.) Astronomers began to include historical accounts of geodetic measurements, generally ignoring the measurements made before 1670 as being hopelessly inadequate, as a preface to offering new calculations of the earth’s size and shape based on later measurements. But that is another story that remains part of Maps, History, Theory.

Notes

n1. Cassini II’s essays have also given me my band name: “Les partisans de la terre elongée.”

n2. Nationalistic pride also accounted for Jérôme Lalande’s (1789) brief account of Fernel’s pioneering measurement. This essay prompted a metrological debate in Britain over Fernel’s work half a century later (De Morgan 1841; Galloway 1842; De Morgan 1842a, 1842b).

References

Airy, George Biddell. 1845. “Figure of the Earth.” In Encyclopaedia Metropolitana, 5: 165–236, *237–*240. London. Reprinted in The Encyclopædia of Astronomy (London: John Joseph Griffin and Co., 1845), sep. pag.

Alembert, Jean Le Rond d’. 1757. “Géodésie.” In Encyclopédie, ou, Dictionnaire raisonné des sciences, des arts et des métiers, edited by Denis Diderot and Jean Le Rond d’Alembert, 7: 606–8. Paris: Briasson, David, Le Breton, Durand.

Anville, Jean Baptiste Bourguinon d’. 1759. “Dissertation sur les sources du Nil, pour prouver qu’on ne les a point encore découvertes; Mémoire concernant les rivières de l’intérieur de l’Afrique, sur les notions tirées des Anciens & des Modernes; Mémoire sur la mesure du schène Égyptien, & du stade qui servoit à le composer; Discussion de la mesure de la terre par Ératosthène, servant à confirmer la mesure du schène Égyptien, donnée dans le mémoire précédent.” Mémoires de littérature, tirés des registres de l’Académie royale des Inscriptions et Belles-Lettres 26: 46–100.

———. 1769. Traité des mesures itinéraires. Paris: Imprimerie royale.

Bennett, J. A. 2006. “Plates from Royal Society Publications: Illustrating William Roy’s Baseline on Hounslow Heath.” Notes and Records of the Royal Society of London 60, no. 2: 225–30.

Brown, Lloyd A. 1949. The Story of Maps. Boston: Little, Brown & Co.

Cassini, Jacques. 1719. “De la grandeur et de la figure de la terre.” In Mémoires de mathematique et de physique, tirés des registres de l’Académie royale des sciences, de l’année MDCCXVIII, 245–56. Paris: Imprimerie royale.

———. 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, Jean-Dominique, Pierre F. A. Méchain, and Adrien-Marie Legendre. 1789. Exposé des opérations faites en France, en 1787, pour la jonction des observatoires de Paris et de Greenwich. Paris: Imprimerie de l’Institution des sourds-muets.

Costard, George. 1767. The History of Astronomy, with Its Application to Geography, History, and Chronology. London.

Delambre, Jean Baptiste Joseph. 1798. Méthodes analytiques pour la détermination d’un arc du méridien; précédées d’un mémoire sur le même sujet par A. M. Legendre. Paris: Duprat.

———. 1814. Astronomie théorique et pratique. 3 vols. Paris: Mme. Ve. Courcier.

De Morgan, Augustus. 1841. “On the History of Fernel’s Measure of a Degree.” Philosophical Magazine and Journal of Science 19, no. 126: 445–47.

———. 1842a. “On Fernel’s Measure of a Degree, in Reply to Mr. Galloway’s Remarks.” Philosophical Magazine and Journal of Science 20, no. 130: 230–33.

———. 1842b. “On Fernel’s Measure of a Degree.” Philosophical Magazine and Journal of Science 20, no. 132: 408–11.

Edney, Matthew H. 2019a. “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 History and Cartography. Chicago: University of Chicago Press.

———. 2019b. “Geographical Mapping in the Enlightenment.” In Cartography in the European Enlightenment, edited by Matthew H. Edney, and Mary S. Pedley, 474–89. Vol. 4 of History and Cartography. Chicago: University of Chicago Press.

Edney, Matthew H., and Nicholas Dew. 2019. “Geodesy and the Size and Shape of the Earth.” In Cartography in the European Enlightenment, edited by Matthew H. Edney, and Mary S. Pedley, 433–39. Vol. 4 of History and Cartography. Chicago: University of Chicago Press.

Fernel, Jean. 1528. Cosmotheoria. Paris: Simonis Colinæi.

Galloway, T. 1842. “Remarks on Fernel’s Measure of a Degree.” Philosophical Magazine and Journal of Science 20, no. 129: 90–98.

Lalande, Jérôme. 1789. “Sur la mesure de la terre, que Fernel publia en 1528.” In Histoire de l’Académie royale des sciences, année M.DCCLXXXVII. Avec les mémoires de mathématique & de physique, pour le même année, 216–22. Paris: Imprimerie royale.

Morden, Robert. 1702. “Geography and Navigation Made Easy: Or, A Plain Description and Use of the Terrestrial Globe.” In An Introduction to Astronomy, Geography, Navigation, and Other Mathematical Sciences Made Easie by the Description and Uses of the Coelestial and Terrestrial Globes, separately paginated. London.

Newton, Isaac. 1999 [1689]. The Principia: Mathematical Principles of Natural Philosophy. Translated by I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press.

Norwood, Richard. 1637. The Sea-Mans Practice, Contayning a Fvndamentall Probleme in Navigation, Experimentally Verified: Namely, Touching the Compasse of the Earth and Sea, and the Quantity of a Degree in our English Measures. Also an Exact Method or Forme of Keeping a Reckoning at Sea, in Any Kinde or Manner of Sayling. London: George Hurlock.

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

Riccioli, Johannes Baptista. 1661. Geographiae et hydrographiae reformatae libri duodecim. Bologna: Benatius.

———. 1672. Geographiae et hydrographiae reformatae, nuper recognitae et auctae, libri XII. Venice: Joannes La Nou.

Roy, William. 1785. “An Account of the Measurement of a Base on Hounslow-Heath.” Philosophical Transactions of the Royal Society 75: 385–480.

Snellius [Snel van Royen], Willebrord. 1617. Eratosthenes Batavus, de Terrae ambitus vera quantitate. Leiden: Jodocus van Colster.

Van Helden, Albert. 1985. Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. Chicago: University of Chicago Press.

Widmalm, Sven. 1990. “Accuracy, Rhetoric, and Technology: The Paris-Greenwich Triangulation, 1784–88.” In The Quantifying Spirit in the 18th Century, edited by Tore Frängsmyr, J. L. Heilbron, and Robin E. Rider, 179–206. Berkeley: University of California Press.