6
Accuracy, Rhetoric, and Technology: The Paris-Greenwich Triangulation, 1784–88

By Sven Widmalm

In the 18th century the technology and the scope of surveying were radically transformed. There emerged a national cartography based on comprehensive triangulation measurements and a scientific discipline, geodesy, which made use of these measurements. France was in the van: Jean-Dominique Cassini, his son, grandson, and great grandson—each of whom in turn became director of the Paris Observatory—had charge of a triangulation that, in the 1730s, developed into a national survey. The influence of the Cassini methods and style had started to spread to other nations by 1750. At first, large triangulations were employed mainly to measure arcs of meridians, providing points of reference for mapmaking and also empirical material for constructing theories of the shape of the earth. Full-fledged national surveys followed, first in Denmark, next in Great Britain.

The "Trigonometrical Survey" of Britain, known since the 1820s as the "Ordnance Survey," was founded in 1791, partly as a consequence of a geodetic measurement led by Major General William Roy and by Jacques Dominique Cassini in the mid1780s in order to connect the observatories of Greenwich and Paris. The work of Roy, which will be the main subject of this chapter, was at the time

considered unsurpassed in its technical refinement and accuracy, and it supplied the model for future British geodetical surveying. The chapter begins with an overview of the development of geodesy and cartography in the 18th century and ends with a discussion of the militarization of large-scale surveying all over Europe. The story is symptomatic of a general tendency around 1800 to amass quantified data for civilian as well as military planning and control.

Geodesy and Cartography in the 18th Century

In Cassini de Thury's influential book on the measurement of the Paris meridian, published in 1744, questions relating to the shape of the earth and to the "geometrical description of the kingdom" were treated separately.^[1] The division existed only on paper. These fields had developed side by side, ever since Jean Picard surveyed a degree of the Paris meridian in the years 1668–70. Picard's triangulation prepared for a national cartographic venture, desired by Jean Baptiste Colbert; it also produced data for calculating the size of the earth, if not its shape. Throughout the 18th century, most advanced geodetical measurements had to do with mapping projects.

Cassini de Thury and Europe

The French survey was begun in 1683 and, after frequent lengthy intermissions, produced in 1718 its first major accomplishment, the triangulation of over seven degrees of a meridian line through Paris. Operations resumed after political support for the project was regained in 1730. Prompted by Pierre Louis Moreau de Maupertuis' measurement of an arc of meridian in Scandinavia in 1736–7, members of the Paris Academy of Sciences resurveyed the Paris meridian.^[2] The Cassinis had claimed that their measurements showed

[1] César François Cassini de Thury, La meridienne de l'Observatoire royale de Paris (Paris: H.L. Guerin & J. Guerin, 1744), 26, quote, and Relation des deux voyages faits en Allemagne par ordre du roi (Paris, 1765), 1–2: "le seul moyen de perfectionner la géographie, étoit de suivre pour la description d'un pays la même méthode que l'on avoit employée pour la détermination de la figure de la terre."

[2] Josef W. Konvitz, Cartography in France 1660–1848 (Chicago: University of Chicago Press, 1987), 3–13.

the earth to have an oblong shape. But Maupertuis' result suggested otherwise; the remeasurement of the Paris meridian and a survey of an arc of meridian in South America made between 1735 and 1744 confirmed that the earth has an oblate shape. Thus measurements outside of France served to calibrate the geodetic work in France. The triangulation of the whole of France now went ahead, under the direction of César-François Cassini de Thury (third in the astronomer dynasty), although it was Nicolas-Louise Lacaille who did most of the fieldwork.^[3] Between 1739 and 1744 almost 800 triangles, from Dunkerque to Perpignan, were measured, along with nineteen bases. The triangles, printed on eighteen sheets, provided a "geometrical skeleton" rather than a map. This was considered to be sufficient for their intended users, namely, engineers involved in public construction works.^[4]

In the 1750s several projects were begun or completed in Europe to complement the measurements sponsored by the French in France, Lapland, and Peru. A leading promoter of these projects was the Jesuit Roger Boscovich, who obtained the support of the pope to measure an arc of meridian between Rome and Rimini. The survey, which ran from 1750 to 1752, had the dual purpose of adding to knowledge of the shape of the earth and updating maps of the papal state. A copy of the "toise of Peru," borrowed from Paris, allowed comparison of Boscovich's geodesy with French results. Boscovich persuaded the king of Sardinia, Carlo Emanuele III, to sponsor a measurement in Piedmont, which Giovanni Battista Beccaria, a Scolopian priest and professor of physics at the University of Turin, carried out between 1760 and 1764. Beccaria's result did not confirm the oblate shape deduced by the French and so contributed to debate about gravitational irregularities and the reliability of geodesy.^[5] This

[3] Charles C. Gillispie, Science and polity in France at the end of the Old Regime (Princeton: Princeton University Press, 1980), 113–5; Lloyd A. Brown, The story of maps ([1949] New York: Dover, 1977), 252.

[4] Konvitz, Cartography in France , 15–28.

[5] Antonio Marussi, "Italian pioneers in the physics of the universe. III: Geodesy," Cahiers d'histoire mondiale, 7:2 (1963), 473–5; Elizabeth Hill, "Roger Boscovich: A biographical essay," in Lancelot Law Whyte, ed., Roger Joseph Boscovich: Studies of his life and work on the 250th anniversary of his birth (London: George Allen and Unwin, 1961), 42–6.

was true also of the first measurement of an arc of meridian in North America, for which Boscovich was also in some measure responsible. It was carried out between 1764 and 1768 by Jeremiah Dixon and Charles Mason.

Another Jesuit, Father Joseph Liesganig, director of the Observatory at the University of Vienna, began his survey of an arc of meridian between Vienna and Brün in 1759. Maria Theresa ordered this measurement following suggestions from Boscovich, and probably also from Cassini de Thury, who worked on a triangulation to connect the Paris meridian with Vienna, one purpose of which was to correct the military maps of France's ally, Austria. Cassini de Thury participated in Liesganig's work, which was calibrated with his own by means of a copy of the toise of Peru. In 1762 Maria Theresa authorized an extension of this arc and provided Liesganig with instruments and engineers from the military academy in Vienna.^[6]

Boscovich and others, including Bouguer, had supposed that irregularities in the earth's mass distribution drew plumb bobs from the perpendicular and introduced serious error into geodetic measurements. His view was widely accepted by the 1770s. In 1775 Etienne Bonnot de Condillac made public a severe critique of existing geodetic investigations, and, in agreement with d'Alembert and later also Laplace, he judged that the different measurements of arcs of meridian were too contradictory to demonstrate that the earth has a regular ellipsoid shape. In particular, measurements in France and in Piedmont around the same degree of latitude did not agree. In Condillac's view measurements should conform to theory or else theory should be modified.^[7]

[6] Cassini de Thury, Relation des deux voyages , 3–4; Ernst Bernleithner, "Oesterreichs Kartographie zur Zeit des Grafen Ferraris," La cartographie au XVIIIe siècle et l'oeuvre du comte de Ferraris (1726–1814) , Collection histoire pro civitate, no. 54 (1978), 139–42; Johannes Dörflinger, Österreichichsche Karten des 18. Jahrhunderts (Vienna: Österreichische Akademie der Wissenschaften, 1984), 61–2.

[7] Volker Bialas, Erdgestalt, Kosmologie und Weltanschaung: Die Geschichte der Geodäsie als Teil der Kulturgeschichte der Menschheit (Stuttgart: Konrad Wittwer, 1982), 158–9, 166–7, 181–7; Condillac, Cours d'étude pour l'instruction du prince du Parme, III: De l'art de raisonner (1775; Deux-Ponts: [Bodoni], 1782), 217, 275–8. Laplace later changed his mind and advocated the view that the earth is a true ellipsoid. Pierre Simon Laplace, Oeuvres , 7 vols. (Paris: Imprimerie Royale), 5 (1846), 14–6 (text of 1823).

The conflict that Condillac and others pointed out may be characterized as one of quantification versus geometric simplicity. Possessing only a few measurements of meridianal arcs and a theoretical model authorized by the Principia , scientists could maintain that the earth had a regular shape. By the 1780s, however, it had become possible to be a Newtonian and still entertain novel shapes for the earth. The Newtonian theory flowed from the hypothesis that the earth had once been in a fluid state. With the decreasing interest in hypotheses about first causes, which characterized the late 18th-century instrumentalist attitude to science, one could choose any curve that fit the data.^[8] The work of William Roy offers an example.

Meanwhile, Cassini de Thury had created the first nationwide topographical map based on extensive triangulations. A team of draftsmen and engineers worked on the project between 1750 and its conclusion thirty-nine years later under Cassini de Thury's son, Jacques Dominique.^[9] French geodesy had a lasting influence on European cartography. As early as 1736–7, when Maupertuis visited "Lapland," the Swedish Surveying Office made an inspired but, as it happened, premature attempt to appropriate the new technology for the benefit of Swedish cartography. In Denmark, the Scientific Society of Copenhagen was commissioned to carry out a national triangulation on the French model in 1762. The Austrian military surveys by Joseph Jean Ferraris in the 1770s drew on Cassini's example in the choice of scale (1:86,400) and in the triangulation methods. Other European states and Russia did not introduce large-scale triangulations until the early 19th century.^[10]

In sum, French cartography and geodesy led European practices in both field and office. Meridianal arcs were triangulated as backbones for exact cartography; geodesists computed distances in terms of the

[8] J.L. Heilbron, Electricity in the 17th and 18th centuries: A study of early modern physics (Berkeley: University of California Press, 1979), 71–3.

[9] Gillispie, Science and polity , 480–1; Konvitz, Cartography in France , 16–21.

[10] J. Svärdson, "Lantmäteriteknik," Svenska lantmäteriet 1628–1928, 1 (Stockholm, 1928), 223; Asger Lomholt, Det Kongelige Danske Videnskabernes Selskab, 1742–1942: Samlingar til Selskabets historie, 4 (Copenhagen: E. Munksgaard, 1961), 90–104; Bernleithner, "Oesterreichs Kartographie," 132–8; Brown, Story of maps , 270.

Peruvian toise, and draftsmen used the scale of the Cassini maps, sometimes even when cartographic methods remained traditional, as in Henri Mallet's maps of Switzerland.^[11] This calibration and standardization owed much to Cassini de Thury. He envisaged a Europe geometricized to a uniform scale; to this end he extended the French triangulation to Flanders and to Austria, and tried unsuccessfully to win support for a similar extension into Italy.^[12]

Britain kept outside the sphere of Cassini de Thury's influence until 1783. Then, about a month after the end of the American war of independence, he proposed to the British government that a triangular connection should be made between London and Paris. The resulting measurement became the starting point for the Ordnance Survey, a cartographic venture undertaken by military engineers.

British Military and Scientific Engineers

British military cartography before the Ordnance Survey was poorly developed. The only important surveys outside England had been conducted in response to emergencies, like the measurements in Scotland as part of the pacification of the Highlands after the 1745 rebellion. The young draftsman William Roy led the fieldwork of the Scottish survey and later became director of the whole operation.^[13] After completing the work in 1755, he joined the corps of engineers under the Board of Ordnance and became a lieutenant in the army. Throughout his career Roy held double ranks in the engineers and in the army, the latter always being the higher.^[14] This elevated him to a higher social as well as military position than that of mere engineers, who did not acquire military rank before 1757. The status of the mere engineers rose in the 1770s, partly as a result of a new policy of

[11] M.-A. Borgeaud, "Cartographie genevoise de XVIe au XIXe siècle," Archives internationales d'histoire des sciences , no. 6 (1949), 363–74.

[12] Marussi, "Italian pioneers," 475.

[13] J.B. Harley and Yolande O'Donaghue, "Introductory notes," in The old series Ordnance Survey maps of England and Wales, 1 (Lynpne Castle: Harry Margary, 1975), xi; R.A. Skelton, "The military survey of Scotland 1747–1755," The Scottish geographical magazine, 83:1 (1967), 1–15.

[14] R.A. Gardiner, "William Roy, surveyor and antiquary," The geographical journal, 143 (1977), 441–50, on 443–4.

the Board of Ordnance that required cadets in the corps of engineers to have had some formal technical education; the requirement functioned as a social filter, favoring sons of army officers. At the same time the American war gave rise to a greater recognition of the importance of cartographic skills and to the acceptance of engineers as staff officers.^[15] By the 1780s the engineers had achieved the same social status as army officers.

Because of their specialist abilities, members of the corps of engineers (and of the artillery) saw themselves as a part of the scientific community. Some achieved membership in the Royal Society. They figured among the opposition during the so-called dissensions of 1783–4, when Sir Joseph Banks, who had been president of the Society since 1778, was attacked by practically or mathematically oriented Fellows for favoring antiquarianism and natural history—that is, "gentlemen's science."^[16] Banks' forces managed to defeat their opposition. It might therefore come as a surprise that the Banksians in the Royal Society, not the mathematical practitioners, effected the cooperation with Cassini de Thury.^[17] The key figure in their mobilization was William Roy, who belonged

[15] Douglas W. Marshall, The British military engineers 1741–1783: A study of organization, social origin, and cartography (Ph.D. dissertation, University of Michigan, Ann Arbor, 1976), 1–7, 119–24, 130, 317, 343–4.

[16] David Philip Miller, The Royal Society of London 1800–1855: A study in the cultural politics of scientific organization (Ph.D. dissertation, University of Pennsylvania, 1981), 6–14, 36–104, 115, 120, 135; W.A. Seymour, ed., A history of the Ordnance Survey (Folkestone: William Dawson, 1980), 3, 29, 67; Charles Richard Weld, A history of the Royal Society , 3 (London: J.W. Parker, 1848), 151–70; Hector C. Cameron, Sir Joseph Banks (Sydney: Angus and Robertson, 1966), 128–34; Henry Lyons, The Royal Society 1660–1940 (Cambridge: Cambridge University Press, 1944), 202–5, 211–4, 342. There is no evidence that Banks suppressed mathematically oriented science in the Philosophical transactions .

[17] These Banksians on the triangulation included Charles Blagden, Henry Cavendisch, John Lloyd, and John Smeaton, as well as Roy; all were members of the Royal Society Club, a center of Banksian sympathies. Letters of Blagden to Banks, 1783–4, as listed in W.R. Dawson, ed., The Banks letters: A calendar of the manuscript correspondence of Sir Joseph Banks (London: British Museum, 1958), 61–2, 64–5; Archibald Geike, Annals of the Royal Society Club (London: Macmillan, 1917), 174–5; Seymour, A history of the Ordnance Survey , 134.

socially and intellectually to both the Banksian and the mathematical camps.^[18]

In the 1760s Roy had settled in London and had become a Fellow of the Royal Society and a firm friend of Joseph Banks. Roy's strong interest in antiquities resulted in a major work on Roman Britain, published after his death; thus he qualified as a member of the "Banksian Learned Empire." By the early 1780s, Roy had also established a scientific reputation through painstaking work in the field of barometric hypsometry. As a major-general in the army and a lieutenant-colonel in the corps of engineers, he was an influential proponent of a national military survey, the realization of which was his main objective in the Paris-Greenwich triangulation.^[19]

The Paris-Greenwich Triangulation

In his mémoire submitted to the British government in October 1783, Cassini de Thury argued that a triangulation between Greenwich and Paris would give the relative position of the two observatories with more certainty than celestial observations at Greenwich had done.^[20] The mémoire made its way to the Royal Society, whose president arranged for his friend William Roy to lead the British part of the project. George III granted the Royal Society money to order a theodolite from Jesse Ramsden and the Board of Ordnance supported the project with manpower, both soldiers to undertake the manual work and officers to oversee it. The measurement required cooperation not only between the French and the

[18] Seymour, A history of the Ordnance Survey , 5–6; Yolande O'Donaghue, William Roy, 1726–1790: Pioneer of the Ordnance Survey (London: British Museum, 1977); Gardiner, "William Roy," 441–2; Theodore S. Feldman, "Applied mathematics and the quantification of experimental physics: The example of barometric hypsometry," Historical studies in the physical sciences, 15:2 (1985), 127–97, esp. 156–77.

[19] Gardiner, "William Roy," 446–7. Cf. H.B. Carter, Sir Joseph Banks (London: British Museum [Natural History], 1988).

[20] Nevil Maskelyne, "Concerning the latitude and longitude of the Royal Observatory at Greenwich; with remarks on a memorial of the late M. Cassini de Thury," PT, 77 (1787), 151–87, on 151–2. The mémoire is also printed in Charles Arden-Close, The early years of the Ordnance Survey ([1926] Newton Abbot: David and Charles, 1969), 13.

British but also between military officers and "scientists."^[21] In 1784 Roy supervised the measurement of a baseline on the outskirts of London, and three years later he led the survey from London to Dover and the cross-channel triangulation. The French part was carried out by Jacques Dominique Cassini (whose father had died in 1784), Pierre François Méchain, and Adrien-Marie Legendre.^[22] In 1788 Roy completed the survey between London and Dover. He published two elaborate reports in the Philosophical transactions , which included no fewer than sixteen finely engraved plates.^[23] In 1791 the duke of Richmond, Master General of Ordnance, decided that Roy's work should be continued under military direction. He bought a copy of the Royal Society's theodolite from Ramsden and engaged the civilian mathematician Isaac Dalby as the first employee of the Trigonometrical Survey. Dalby had participated in the triangulation of 1787–8 and was highly praised by Roy, who died in 1790.^[24] The employment of Dalby ensured continuity between Roy's work and its military sequel. The connection between the survey and the Royal Society continued until 1803, when the last report appeared in the Philosophical transactions .

It may be that Banks responded to Cassini de Thury's overture because it carried an implicit criticism of the astronomers of Greenwich. The Astronomer Royal Nevil Maskelyne belonged to the rebel camp within the Royal Society. One charge leveled against Banks during the "dissensions" was that he cared more for social status than for scientific ability; but by promoting the triangulation he showed himself to be a "very worthy President of the Royal Society,

[21] Although the term "scientist" was not in use in the 1780s, its functional equivalent, "scientific person," was. See Edward Williams, William Mudge, and Isaac Dalby, "An account of the Trigonometrical Survey carried on in the years 1791, 1792, 1793, and 1794," PT , 85 (1795), 432.

[22] Seymour, History of the Ordnance Survey , 15–7.

[23] William Roy, "An account of the measurement of a base on Hounslow Heath," PT , 75 (1785), 365–480; "An account of the trigonometrical operation whereby the distance between the meridians of the Royal Observatories of Greenwich and Paris has been determined," PT, 80 (1790), 111–270.

[24] Seymour, History of the Ordnance Survey , 21–2; Roy, "An account of the trigonometrical operation," 118–9. Dalby did practical as well as mathematical work. Ibid., 155.

ever zealous in the cause of science."^[25] Further, by turning the triangulation into an event of social significance, by bringing George III and other members of the highest stratum of society to visit the site of the baseline measurement, Banks also proved that patronage did pay off. Unlike his predecessor John Pringle, Banks was on good terms with the king, who financed a large part of the operation.

The Longitude of Greenwich and the Shape of the Earth

Jacques Dominique Cassini wrote in 1791 that the "sole aim" of the triangulation had been to ascertain the longitudinal difference between the observatories of Paris and Greenwich.^[26] On the other side, Roy had asserted in 1787 that the "chief and ultimate goal has always been considered of a still more important nature, namely, the laying the foundation of a general survey of the British Islands."^[27] But there is nothing to indicate that Roy had official support for such a scheme at this stage. Although he wished to create a national survey, the measurement he was actually conducting had a specific purpose within a scientific context.^[28] This purpose he had to defend. Consequently Roy accepted the French criticism depicting positional astronomy—or anyway British astronomy—as less accurate than geodesy. The fact that the expensive and time-consuming triangulation went forward without the cooperation of the astronomer at Greenwich suggests the strength of Roy's position within the Royal Society.

The disagreement between Roy and Maskelyne was ventilated in two papers published in 1787. Maskelyne wrote a belated reply to Cassini de Thury's mémoire ; Roy, annoyed at the delay, threatened

[25] Maskelyne, "Concerning the latitude and longitude," 151–2; Roy, "An account of the measurement of a base," 425, quote.

[26] Jacques Dominique Cassini, Pierre François Méchain, and Adrien-Marie Legendre, Exposé des opérations faites en France en 1787 pour la jonction des observatoires de Paris et de Greenwich (Paris, [1791]), 65.

[27] William Roy, "An account of the mode proposed to be followed in determining the relative situations of the royal observatories of Greenwich and Paris," PT , 77 (1787), 188–226, on 188.

[28] Seymour, History of the Ordnance Survey , 21–2. George III insisted that the financial support he gave go for "the science of astronomy"; Harley and O'Donoghue, "Introductory notes," xxi.

to publicize Maskelyne's idleness in the Philosophical transactions —thereby demonstrating that he had the official support of the Royal Society, whereas Maskelyne did not.^[29] Roy accentuated the criticism of British astronomy by adding to the uncertainty of eleven seconds of time in longitude between Greenwich and Paris, which Cassini de Thury had pointed out, an uncertainty of three seconds between Oxford and Greenwich. Geodetic methods would narrow the margin of error; Roy considered them "infallible," since they could always be controlled by verifying the bases. The planned triangulation would give a value for the longitudinal difference "sufficiently near the truth, and. . .probably considerably nearer than it will be brought for many years to come, by a mean of the best observations of the heavenly bodies."^[30]

Roy probably did not know that in 1785 Maskelyne had equipped his assistant Joseph Lindley with a number of watches and sent him on a secret "chronometer run" to Paris, to determine the time difference between the capitals. Lindley's result (9 minutes 20 seconds) verified Maskelyne's astronomically deduced value, published in 1787, which was later found to agree with the result of Roy's triangulation.^[31] Roy avoided admitting this embarrassing consistency, which he had earlier denied, by misquoting Maskelyne's data. In his final report he simply plucked from Maskelyne's paper a number about 10 seconds larger than the figure on which the astronomer finally settled, and claimed it as the astronomically deduced value.^[32] He thus demonstrated the superior accuracy of the geodetic method.

[29] William Roy to Nevil Maskelyne, 11 Dec 1786 (RS, DM.4.14). A copy of this letter is in PRO, O.S.3/4. Cf. Roy, "An account of the mode proposed," 213; Eric G. Forbes, "The geodetic link between the Greenwich and Paris observatories in 1787," Vistas in astronomy, 28 (1985), 173–81, on 174. Maskelyne complained that he had not been shown the mémoire until a year after preparations for the triangulation had begun. See Maskelyne, "Concerning the latitude and longitude," 153.

[30] Roy, "An account of the mode proposed," 213–4.

[31] Eric G. Forbes, Greenwich Observatory . Vol. 1: Origins and early history (1635–1835) (London: Taylor and Francis, 1975), 149–50, and "The geodetic link," 174; Maskelyne, "Concerning the latitude and longitude," 183–6; Roy, "An account of the trigonometrical operation," 231.

[32] Roy, ibid., 231. Roy's maneuvers to protect himself from the suspicion of deliberately misquoting Maskelyne are sufficiently transparent. Cf. Roy to Maskelyne, 11 Dec 1786 (PRO, O.S.3/4).

The question of the earth's shape came in as an important scientific side issue in the determination of longitude differences. Roy had developed a new technique for geodetic investigation, which involved astronomical observations of a kind different from those usually associated with longitude determinations. Nevertheless, as Isaac Dalby was to point out, it constituted perhaps the weakest link in Roy's geodetic work. By taking the angles between three mutually remote stations and at the same time observing the angles between the stations and the polestar, Roy calculated the longitudinal differences between pairs of stations by spherical trigonometry. The relationship between these differences and the distance on the ground gave a value for the length of a degree of longitude at a particular latitude. Polestar observations made at only a few stations furnished the basis for calculation of the longitude difference of the whole chain of triangles. Roy calculated the latitudes of the stations in relation to that of Greenwich from a spheroidal model of the earth devised by Pierre Bouguer.^[33]

To justify use of this spheroid, Roy computed the lengths of the arc between Greenwich and Perpignan (the southern extremity of the Paris meridian) on ten different hypotheses about the shape of the earth. In the model Roy favored, the lengths of degrees of latitude increased with the fourth power of the sine of the latitude. One of the models he rejected was an ellipsoid based on data from the six earlier arc measurements Roy thought most consistent. To achieve consistency, however, he had had to take a mean between the arcs of Cassini in France and Liesganig in Austria, since comparison between them gave an "absurd" result—that is, an oblong earth.^[34] Roy combined the six arcs into fifteen pairs and calculated the flattening for each. ("Flattening" is defined as the ratio of the equatorial axis to the difference between the equatorial and polar axes.) Values ranged from 100 to 850, but Roy did not present the extremes: he exhibited only the mean flattening of 190, well within

[33] Roy, "An account of the mode proposed," 216–20, and "An account of the trigonometrical operation," 200, 225–7.

[34] Roy, "An account of the mode proposed," 206–8.

the limits of what was considered reasonable.^[35] The same was true of the other six ellipsoids in Roy's table, resulting from other combinations of measurements or from hypothetical premises, and of the two spheroids as well.

Roy nonetheless proffered Bouguer's spheroid as the most probable alternative because, unlike the other hypotheses, it gave values sometimes above and sometimes below the lengths of the measured arcs: "a never failing proof" that it was "exceedingly near the truth."^[36] Roy hid the wide discrepancies that actually existed between different measurements behind the reassuring surface of averages. Mathematical analysis of error was then only in its infancy. Roy employed another, more visual technique for comparing the different solutions to the problem of the shape of the earth. He presented the results on the different hypotheses in tabular form so that the reader could judge, "by simple inspection only, which of the theories agrees best with actual measurement." He also gave the lengths of degrees of meridians, parallels, and oblique great circles according to Bouguer's spheroid—not only for the portion of the earth covered by his own triangulation, but for the whole earth, so that others could use these figures until, in the distant future, the shape of the earth would "ultimately" become known. Meanwhile, Roy thought, the spheroid would furnish data of "general utility."^[37]

Dalby disagreed with the use of Bouguer's spheroid and with Roy's method of finding differences in longitude. He criticized the method as too sensitive to observational errors. An error of one second of arc in the angles between the stations and the meridian would cause an error of six seconds in the longitude difference between Greenwich and Dunkerque.^[38] Roy had said that he

[35] The usual magnitude of the flattening ranged between 170 and 540—the values suggested by Maupertuis and Christian Huygens, respectively.

[36] Roy, "An account of the mode proposed," 210–1. In early mathematical analysis of observational error by Boscovich and Laplace, this condition usually came with another: that the sum of the absolute values of the errors should be minimized. See Stephen M. Stigler, The history of statistics: Measurement of uncertainty before 1900 (Cambridge, Mass.: Belknap Press, 1986), 11–61, esp. 47, 51.

[37] Roy, "An account of the mode proposed," 201, 222.

[38] Isaac Dalby, "The longitudes of Dunkirk and Paris from Greenwich, deduced from the triangular measurement in 1787, 1788, supposing the earth to be an ellipsoid," PT, 81 (1791), 236–45, on 237, and "Remarks on Major-General Roy's account of the trigonometrical operation," PT, 80 (1790), 593–614, on 607–8. Roy's method for obtaining longitudes is described in Roy, "An account of the trigonometrical operation," 206–25.

determined the longitude difference "by the instrument itself," meaning that the extreme accuracy of the theodolite guaranteed the precision of the result. Dalby challenged this assertion and rejected Roy's spheroid in favor of his own ellipsoid shape, with the flattening of 229 predicted by Newton.^[39]

As we know, the ellipsoid shape depended only on theories of gravity and mechanics and on the assumption that the earth had once been fluid. The theoretical implications of Bouguer's spheroid, on the other hand, are unclear, and probably they did not matter very much to Roy. He adopted it because it gave a good fit to existing measurements. Ramsden, not Newton, was the arbiter of exact geodesy; the theodolite could make errors "totally vanish." Dalby had no special interest in defending the elaborate technology adopted by Roy, and consequently he was happy to accept Maskelyne's value for the longitude difference between Paris and Greenwich as support for the result of the measurement in which he himself had participated.^[40] In modern terms, Roy's attitude was instrumentalist, whereas Dalby's might be called realist. Condillac, who advocated a strict empiricism, criticized both. Condillac's view eventually won out. When the concept later to be christened the geoid was developed in Germany in the early 19th century, irregularities in the earth's mass distribution ceased to be regarded as anomalies and became instead constitutive of the "real" shape of the earth.

Instruments of Competition

The technology for making accurate angular measurements under field conditions was highly refined in the second half of the 18th century, when the quality and quantity of instrument-making rose dramatically, especially in Britain. An expanding market for navigational equipment, intensified surveying, and escalating scientific

[39] Roy, "An account of the mode proposed," 219; Dalby, "The longitudes of Dunkirk and Paris," 327–8.

[40] Roy, "An account of the mode proposed," 219, quote; Dalby, "The longitudes of Dunkirk and Paris," 245.

demands for accuracy all pushed development. The accuracy of angular measurements increased from about 2 seconds to about 0.5 seconds, verniers and microscopes for reading off the scales became common equipment, and the achromatic lens and the dividing engine set new standards for precision.^[41]

The level of accuracy of surveying technology was raised significantly through the Paris-Greenwich triangulation, which for a while turned the coast of the English Channel into an arena for technological rivalry between Britain and France. The competitive spirit no doubt helped both the French and the British parties to gain financial support from their respective monarchs. George III financed the Ramsden theodolite, and Louis XVI paid for a repeating circle by Etienne Lenoir. William Roy wrote that "The honour of the nation is concerned in having at least as good a map of this as there is of any other country."^[42] Governments and the military knew that geodesy yielded accurate maps that could facilitate the exercise of political power and the waging of war. The French astronomers were directed not from the Académie des sciences but from Versailles. Cassini was to report on everything concerning the operations to the minister De Breteuil in Paris, who acted as intermediary with the court. Cassini and Méchain were instructed to undertake a little industrial espionage while in London for the triangulation, paying special attention to the telescopes of Herschel and the instruments of Dollond and Ramsden.^[43] They were also to try to talk Ramsden into

[41] Maurice Daumas, Scientific instruments of the seventeenth and eighteenth centuries and their makers (London: Batsford, 1972), 53–5, 153–6, 176, 189–204; Allan Chapman, "The accuracy of angular measuring instruments used in astronomy between 1500 and 1800," Journal for the history of astronomy, 14 (1983), 133–7; Willem D. Hackman, "Instrumentation in the theory and practice of science: Scientific instruments as evidence and as an aid to discovery," Istituto e museo di storia della scienza di Firenze, Annali, 10 (1985), 103–6.

[42] Breteuil to J.D. Cassini, 9 Jun 1787 (BOP, D5–7); Roy, "An account of the trigonometrical operation," 162–3. Cf. Daumas, Scientific instruments , 184.

[43] Breteuil to J.D. Cassini, 9 Jun and 30 Aug 1787 (BOP, D5–7). Cf. J.D. Cassini, "De la jonction des observatoires de Paris & de Greenwich, & précis des travaux géographiques exécutés en France qui y ont donné lieu," Académie des Sciences, Paris, Mémoires , 1788 (1791), 706–54, esp. 714–7.

joining the staff at the Paris observatory or taking French apprentices.^[44]

The French repeating circle (fig. 6.1) and the British theodolite (figs. 6.2, 6.3) were vastly improved versions of older instruments. They soon replaced the quadrant as the preferred instrument in large surveys. They also represented two attitudes to precision measurement that henceforth would prevail. The theodolite represented the very best in British instrument-making.^[45] The circle was also well constructed, and in that sense signified a breakthrough for French instrument-making. Equally important, however, its accuracy depended on a new principle—a method of averaging errors mechanically—which paralleled the theoretical notions of error under way in the 1780s and fully developed after 1800.^[46]

Everybody involved in the Paris-Greenwich triangulation recognized that it set new standards for surveying. Elaborate descriptions of the new instruments were published, although, in the case of the theodolite, not all the details, which (as Roy indelicately put it) would have been "a disgusting labour." Cassini and his coworkers expatiated on the merits of their repeating circle in their book on the triangulation.^[47] The circle made possible high precision by repeating the angular observations an arbitrary number of times over the whole of its limb, so that irregularities in its construction would eventually even out. The circle offered advantages of cost and size over the theodolite: it weighed only about 20 pounds; the British instrument, over 200 pounds. The cross-channel triangulation (fig. 6.4) served as an important check on the accuracy of the French method; Cassini wrote that the information about the relative merits of the circle and the theodolite would perhaps be its most interesting result. Triangles

[44] Konvitz, Cartography in France , 27.

[45] Cassini called the theodolite the "chef-d'oeuvre du plus habile Artiste qu'il y ait en Europe." Cassini, Méchain, and Legendre, Exposé des opérations faites en France , 58. Cf. Daumas, Scientific instruments , 129, 174, 186–7.

[46] Gillispie suggests a direct connection between Legendre's work on the theory of the repeating circle and his development of the method of least squares. Gillispie, Science and polity , 127.

[47] Roy, "An account of the trigonometrical operation," 135–6; Cassini, Méchain, and Legendre, Exposé des opérations faites en France , 23–7.

were closed to within a few seconds using either the circle or the theodolite.^[48] The measurement therefore served as a kind of calibration as well as demonstration of the new instruments. The size and cost of the theodolite had at least one advantage. Roy argued that it would be a great waste not to use it for a national survey toward a good map of Britain, on which, as he put it, the country's honor depended.

The Rhetoric of Accuracy

The Paris-Greenwich triangulation increased the efficiency and reliability of surveying. At the same time the praises and promises of accuracy that surrounded it served as rhetorical devices, upholding the close relationship between scientific and technological applications of precision measurement. William Roy's accomplishment depended on his command of both the rhetorical and technological resources of accuracy.

The eminent metrologist Jean André Deluc had stated: "We are obliged to take up with probability in Nature in so many respects, that it is perhaps of more importance to us to investigate the physical rules of probability than to attend to its mathematical rules upon hypotheses." Deluc advocated that research be directed toward precision measurement rather than mathematical analysis of error, and he predicted that "we shall be led to seek for exactness in every thing."^[49] Roy, who knew Deluc's work well, acted on this metrological precept. He treated every measurement with extreme care, but as an isolated event, and he did not take the accumulation of possible errors into account even when estimates of the precision of individual measurements might have been made. Like his contemporaries, Roy did not think in terms of significant figures; for example, he might add figures with five and two decimals, and give the sum to four.^[50]

[48] Cassini, Méchain, and Legendre, Exposé des opérations faites en France , 57–65. Cf. J.D. Cassini, "De la jonction des observatoires," 713.

[49] Jean André Deluc, "An essay on pyrometry and aerometry, and on physical measures in general," PT, 68 (1778), 493, 545–6. Cf. Feldman, "Applied mathematics and the quantification of experimental physics," 150–6.

[50] Roy, "An account of the measurement of a base," 401–2, 441–61, 476–8. Roy wrote: "The hypotenuse length of the base, as measured by 1369.925521 glass rods of twenty feet each + 4.31 feet. . .has been shewn to be 27402.8204." This figure was rounded off to one decimal, because "the most accurate measurement imaginable is still more liable to err in excess than in defect." Ibid., 478. Cf. Seymour, A history of the Ordnance Survey , 35.

In fact, he loved decimals, which abound in his writings far beyond practical, but perhaps within rhetorical, efficacy.^[51]

In Britain the rhetoric of accuracy extended to the prestige of the instrument-maker. Unlike their French colleagues, British instrument-makers could be highly respected members of the scientific community. Jesse Ramsden became a Fellow of the Royal Society (FRS) in 1786 and won the Copley medal in 1795. Ramsden's name was synonymous with accurate measurement, and his instruments assured the quality of the British triangulation.^[52] The implicit reasoning went like this: because Ramsden was such an "ingenious artist" (although "dilatory"), his instruments were "rendered extremely perfect," hence the measurements showed a "wonderful degree of accuracy."^[53] Most of the devices manufactured for Roy existed in one copy only; not even specialist readers were likely to get their hands on a Ramsden theodolite, but had to be convinced of its excellence verbally. Besides the theodolite, Ramsden constructed a surveying chain "which would measure distances much more accurately than anything of that kind had ever done before," a pyrometer "of such accurate construction that it seems not easy to improve it," and other smaller instruments. Furthermore, Ramsden himself sometimes took part in especially important measurements; he was called upon for advice during the Paris-Greenwich triangulation and later in the Ordnance Survey.^[54]

The commendation of Ramsden's achievements, like the long rows of decimals and the frequent references in the work of Maskelyne,

[51] Cf. Heilbron, Electricity in the 17th and 18th centuries , 76, 83; see Theodore S. Feldman, chap. 5 in this volume.

[52] Daumas, Scientific instruments , 102–6, 241–3; E.G.R. Taylor, The mathematical practitioners of Hanoverian England, 1714–1840 (Cambridge: Cambridge University Press, 1966), 43; Gillispie, Science and polity , 113; R.S. Webster, s.v. "Ramsden, Jesse," DSB, 11 , 285.

[53] Roy, "An account of the mode proposed," 189, and "An account of the trigonometrical operation," 136, 149.

[54] Roy, "An account of the measurement of a base," 394, 402, 416–7, 435, 462; Williams, Mudge, and Dalby, "An account of the Trigonometrical Survey," 432, 435, 438.

Cassini, and Roy to measurements made to "the last exactness" or to "mathematical exactness," may be considered the rhetoric of exact science.^[55] This rhetoric papered over a serious rift between Roy and Ramsden, which is worth uncovering for its illumination of underlying social realities. Roy criticized Ramsden severely for his dilatoriness in the draft of the last report on the project. Most of the complaints did not reach print because Ramsden filed countercomplaints with the Royal Society and Roy's death allowed some freedom with his text. Ramsden's complaint gives an unusual glimpse of the working relationship between a scientist and an instrument-maker during the late 18th century. He claimed the credit for the high precision achieved in the triangulation, and was sorry that Roy—a gentleman —treated him with such disrespect: it was not "consistent with common sense, that a Tradesman or Mechanic, should suffer his professional character in particular to be publicly traduced in so respectable a place as at [a] meeting of the Royal Society."^[56] Ramsden could get no satisfaction from Banks (who threatened to defend Roy's position "with every drop of my blood") and therefore appealed directly to the Council.^[57]

Ramsden asserted that Roy was not a competent judge of the technological aspect of the work; that he, Ramsden, had decided what kind of instrument should be made for the triangulation; that he, Ramsden, had written the description of the theodolite for the Philosophical transactions ; that he had constructed every single piece of apparatus used in the measurements; and that Roy had not given him full credit. He claimed further that Banks and Roy had granted him a free hand to construct a theodolite that was "superior in point of accuracy to any thing of whatever radius yet made,"^[58] and

[55] Maskelyne, "Concerning the latitude and longitude," 186, "the last exactness"; Roy, "An account of the trigonometrical operation," 165, "mathematical exactness." Cf. Roy, ibid., 149, 154, 166, 244, 161; and Cassini, Méchain, and Legendre, Exposé des opérations faites en France , 23, 34, 58–9.

[56] Seymour, A history of the Ordnance Survey , 17; Roy to Banks, 3 May 1790, The Banks letters , 721; Jesse Ramsden to the Council of the Royal Society, 30 May 1790 (RS, MM.3.30).

[57] Banks to Roy, 30 Jan 1790, The Banks letters , 720–1.

[58] Jesse Ramsden to the Council of the Royal Society, 30 May 1790 (RS, MM 3.30); cf. RS, MM.DM.4.44, an unsigned statement by Ramsden about his technical work for Roy. Roy did indeed fail to give Ramsden credit for the technical description of the theodolite; he mentioned Ramsden's name only a few times, one of them libelously, in his last report. See Roy, "An account of the trigonometrical operation," 135–60.

complained when the innovations took time to perfect. These complaints showed that Roy did not understand the character of precision technology.

If we credit any of this, Roy's dependence on Ramsden's abilities was even closer than the official reports suggested. It does seem clear that Roy controlled the successful achievement of his goal—to make a measurement and create a technology of unprecedented accuracy—not so much by mastery of the necessary technique or technology, but rather by command of the social situation through his influence in the Royal Society and in the Ordnance. Roy could purchase Ramsden's and Dalby's know-how and employ them to write the difficult technological and mathematical passages in his reports. Like Ramsden, Dalby complained that Roy could not judge his work competently, and he had to append a long list of corrections to Roy's final paper in 1790.^[59]

The rhetoric of accuracy that helped to cover up those disputes was meant to inspire faith in a vast and costly undertaking like a national survey.^[60] When Roy invited the citizens of London to confirm the accuracy of his measurements by stepping out on their rooftops and sighting the angles between buildings that had been used as triangulation stations, the cartographic entrepreneur was speaking.^[61] When the state or the public supported the geodetic and cartographic sciences, they were offered accuracy in return for their money. When they were promised "absolute" or "mathematical" accuracy, they no doubt expected new and superior technology.

[59] Roy, "An account of the trigonometrical operation," 118–9, 193; Blagden to Banks, 31 Aug, and 23 and 26 Sep 1790, The Banks letters , 76–7; Dalby, "Remarks on Major-General Roy's account."

[60] In September 1783 Roy wrote to Banks that the government would probably grant a sum of £ 1000 toward the triangulation, "if they are assured that it shall be frugally and faithfully applyed to the above, or any other scientific operation." Roy to Banks, 28 Sep 1783 (RS, DM.4.4).

[61] Roy, "An account of the trigonometrical operation," 258–9.

Accuracy and Technology

Another of Roy's rhetorical devices was his repeated use of the word "truth" in describing the intended goal of exact measurement.^[62] The quest for "truth" meant a quest for accuracy; and in surveying it covered all the steps of the operation, not just the final result. Since everything had to be superior to previous surveys, everything had to be new . Because of their novelty, the methods and instruments had to be meticulously described so that the public could affirm their value.^[63] Hence the many pages of technical description and numerous plates that made Roy's reports a résumé of the state of the art of trigonometrical surveying. Delambre's account of the methods used in the metric survey would play the same part ten years later.^[64]

The high precision of Roy's work made it possible to calibrate simpler and more convenient methods. His measurement of the baseline on Hounslow Heath is a case in point. At first Roy used the traditional wooden rods as measuring sticks. He rejected these because their contraction and expansion varied erratically with humidity, and replaced them with glass tubes, whose lengths depended only on the temperature in a way accurately determinable by Ramsden's pyrometer.^[65] Roy knew about the properties of glass from his work with the barometer: the use of glass tubes for the baseline measurement was an imaginative piece of technology transfer from barometry to geodesy.^[66] Roy used the glass tubes to control

[62] Roy, "An account of the mode proposed," 214, "sufficiently near the truth," 219, "differ very little from the truth"; cf. Roy, "An account of the trigonometrical operation," 128–9, 186, 230–1, 247.

[63] Roy, "An account of the trigonometrical operation," 247; Roy, "An account of the measurement of a base," 406, 461. Cf. A.W. Richeson, English land measuring to 1800 (London: Cambridge, Mass.: MIT Press, 1966), 180–1.

[64] J.-B.-J. Delambre, Rapport historique sur les progrès des sciences mathématiques depuis 1789, et sur leur état actuel (Paris: Imprimerie Press, 1810), 66.

[65] Roy, "An account of the measurement of a base," 434–5, 461–6. Cf. Seymour, A history of the Ordnance Survey , 34.

[66] Roy, "An account of the measurement of a base," 435. Roy's papers at the Public Record Office contain several documents relating to investigations of the behavior of rods and tubes of glass at different temperatures (PRO, O.S.3/3). Cf. Feldman, "Applied mathematics and the quantification of experimental physics," 172–4.

measurements with a surveyor's chain, also from Ramsden's workshop. The chain did well, and since it was easier to handle than glass tubes or metal bars, Roy recommended it for surveying. The chain would be good enough for the national survey, for which, as Roy put it, "there would not be any necessity for that wonderful exactness" requisite in the Paris-Greenwich triangulation.^[67] Thus "scientific" exactness became a benchmark in the creation of a solid and efficient surveying technology.

Simplifications of surveying practices were not an accidental spinoff from scientific work: Roy had identified the development of more efficient surveying techniques as an explicit goal of the triangulation.^[68] Cassini de Thury had likewise pointed out that instruments had to be simplified and made portable in order to make practical the technology of surveying.^[69] The repeating circle accomplished both objectives. The British theodolite did not meet the needs of the ordinary surveyor, but was practical in an organization that could maintain a work force to transport it, erect solid stations, operate cranes, and so forth. In short, British technology was serviceable in a military organization.

The Militarization of Cartography

In 1762, in the course of extending the French triangulation into Austria, Cassini de Thury and the Heidelberg professor Christian Mayer measured a baseline in an unusual location. They used the alley, almost three leagues long, leading up to the new observatory in the main building of the Palatine Elector Karl Theodor's summer residence, situated between Mannheim and Heidelberg. Karl Theodor was delighted: "the position of the new base and [that] of the

[67] Roy, "An account of the measurement of a base," 394, 449–50; Roy, "An account of the trigonometrical operation," 268.

[68] Roy, "On the advantages that are likely to rise from the operations on Hounslow Heath" (RS, DM.4.6).

[69] Cassini de Thury, Relation des deux voyages , 1–2.

observatory were two monuments that should coincide."^[70] The base was a monument to the scientific patronage of the creator of the Mannheim Academy of Sciences and to Cassini's knack for fraternizing with nobility and royalty. It symbolized the union of political power and science, so important in the fields of geodesy and cartography at this time and in the next century when national cartography in Europe was militarized. With the technology of triangulation, the geometrical grid—formerly present only in the mind, on maps, or in architecture—was imposed on the landscape itself. Geodetic surveying quantified geographical information, which became atomized and readily presentable in tabular form. This kind of extensive, yet compressed, knowledge was an attractive resource for centralized governmental and military planning. In the terminology of Michel Foucault, the Ordnance Survey and similar organizations brought an expansion of military surveillance from the limited disciplinary units of the garrison and the fortress to the full physical extent of a nation.^[71]

The social ascent of engineers and artillery men was a major ingredient in the genesis of national triangulation as a military operation in Britain, where it first occurred. The new strategy of the Revolutionary and Napoleonic wars also promoted the fusion of military and national cartography. Larger and more mobile armies now appeared, and the battle conquered the siege as the decisive element in war. That made every place a potential theater of war and created a demand for knowledge of the whole geography, making comprehensive and accurate cartography an essential preparation for warfare.^[72]

[70] Ibid., xxiii, xxxiii, 94–5; Adolf Kistner, Die Pflege der Naturwissenschaften in Mannheim zur Zeit Karl Theodors (Mannheim: Selbstverlag des mannheimer Altertumsverein, 1930), 52–3.

[71] Michel Foucault, Discipline and punish: The birth of the prison (Harmondsworth: Penguin Books, 1977), 184–9, 195–203.

[72] William H. McNeill, The pursuit of power: Technology, armed forces, and society since A.D. 1000 (Oxford: Basil Blackwell, 1982), 161–3, 170–1; Richard A. Preston and Sydney F. Wise, Men in arms: A history of warfare and its interrelationships with Western society , 4th ed. (New York and London: Holt, Rinehart and Winston, 1979), 133–48, 173–80; Alfred Vagts, A history of militarism: Civilian and military , 2d rev. ed. (London: Hollis & Carter, 1959; 1st. edn. 1938), 58, 75–91, 114; N.H. Gibbs, "Armed forces and the art of war," The new Cambridge modern history (Cambridge: Cambridge University Press, 1965), 10 , 62–9, 74–5; Henning Eichberg, "Geometrie als Barocke Verhaltensnorm: Fortification und Exerzitien," Zeitschrift für Historische Forschung, 1 (1977), 40–50.

In Britain, fortifications were not a major part of the defense system, which relied mainly on the navy. When William Roy proposed in 1766 that a "General Military Map of England" be drawn on the French model, he pointed out that should an enemy reach the British Isles, engagement would necessarily take place in the field, about which detailed geographical knowledge would be required.^[73] In the 1780s the question as to whether Britain should embark on a program of extensive fortification brought heated debate.^[74] The Duke of Richmond advocated defense works for the docks of Plymouth and Portsmouth; he was supported by Pitt, and vehemently opposed by others, who carried Parliament in 1786 by one vote. Richmond's opponents argued that large fortifications would lead to an "unconstitutional" militarization of British society.^[75] Thousands of men living in barracks would foster and spread a militarism, which might become a stronghold for royalist and other anti-Parliament sympathies. The agitation included some jibes at engineers:^[76]

If this Military projector [Richmond] was not checked in his career, none could know what consequences might ensue. A Master General, with his Committee of Engineers, like the Laputan philosophers in their flying island might hover over the kingdom in an Ordnance balloon, descend in a moment, and seize on any man's house and domain. . ., draw out their scales and compasses, or sketch out their works. The country Gentlemen would find their terraces converted into bastions, their slopes into glacis,

[73] George III, The correspondence of King George the Third, from 1760 to December 1784 , John Fortescue, ed. (London: Macmillan and Co., 1927), 1 , 328–9.

[74] [James Glenie], A short essay on the modes of defence best adopted to the situation and circumstances of this island , 2d ed. (London, 1785); [Charles Lennox, Duke of Richmond] An answer to "A short essay. . ." (London, 1785); [James Glenie], A reply to the answer to a short essay . . . (London, 1785), and Observations on the Duke of Richmond's extensive plans of fortification (London, 1794). Cf. Alison Gilbert Olson, The radical Duke: Career and correspondence of Charles Lennox third Duke of Richmond (London: Oxford University Press, 1961), 81–6.

[75] An authentic account of the Debates in the House of Commons, on Monday, February 27, and Tuesday, February 28, 1786, on the proposed Plan for Fortifications, by His Grace the Duke of Richmond (London, 1786), 1–2, 20, 34, 56–7.

[76] An authentic account , 48.

their pleasure grounds into horn works and crown works to which they have hitherto borne an irreconcilable aversion.

Richmond returned from his defeat five years later with a new, subtler, and more successful scheme for militarization: the Ordnance Survey. In the words of one of Richmond's critics, the survey would provide essential information to "a resistance, which is not confined to particular spots, but is capable of operating every where."^[77] It also provided the British public with detailed information about their land: in 1801 the first one-inch map, of Kent, was published.

The work of Roy and of the Ordnance Survey won acclaim outside of Britain as a model of scientific accuracy, for example in India, where military surveying using Roy's methods began in 1802.^[78] It was above all the French who exported geodetically founded military cartography to the rest of Europe, by force as well as by example. Napoleonic military cartography was founded on the methods developed by Delambre and Méchain during the metric survey of 1792–8, and therefore also on the French experiences during the Paris-Greenwich triangulation. Delambre's formulas and Lenoir's repeating circle came to dominate French military cartography, and by 1810 "an army of astronomers armed with chronometers, telescopes, and sextants" had invaded Europe.^[79]

[77] [Glenie], A short essay , 30–1.

[78] Clements R. Markham, A Memoir on the Indian Surveys (London, 1878; reprinted Amsterdam: Meridian, 1968), 60–6; [Franz Xaver von Zach], "Ost-Indische Gradmessung, der Länge und Breite," Monatliche Correspondenz zur Beförderung der Erd- und Himmelskunde, 12 (1805), 485–94. Roy's measurement was praised by Delambre, for example, although at the Dépôt de la Guerre it appeared "dégénère en science purement spéculative." J.-B.-J. Delambre, Grandeur et figure de la terre (Paris: Gauthier-Villars, 1912), 334–9; Delambre, Rapport historique , 74–5; "Des opérations géodesiques de détail," Mémorial topographique et militaire , an XI (1803), 1–56, 126.

[79] Delambre, Rapport historique , 77–8 ("une armée d'astronomes munis de chronomètres, de lunettes et de sextans"). General Nicolas Sanson, director of the Dépôt de la Guerre , prescribed the use of the repeating circle as well as the use of Delambre's mathematical methods. See Berthaud, Les ingénieurs géographes , 307; review of Sanson's "Instruction sur la disposition et la tenue des régistres de calculs géodesiques," Monatliche Correspondenz zur Beförderung der Erd- und Himmelskunde, 11 (1805), 49–66; Delambre, Rapport historique , 66. Cf. J.L. Heilbron, chap. 7 in this volume.

The French government had taken control of cartography in 1793 by expropriating the Cassini map; a quarter century later, it initiated a new survey, supervised by the general staff. The map of the Étatmajor (published 1833–81) deployed information and expertise assembled in the French army after more than a decade of military cartographic expansion.^[80] In 1801 Napoleon had started local Topographical Bureaus to extend the Carte de Cassini to the areas conquered by the French army; soon bureaus existed in Hanover, the Rhineland, Bavaria, Switzerland, Savoy, and Italy.^[81]

Austria set up similar services in 1806, and the Netherlands followed suit in 1816.^[82] In the same year, in response to its experience of French warfare, Russia founded a military cartographic organization that was to become the largest in Europe.^[83] The leader of the Franco-Italian Topographical Corps in Milano, the Swede Gustaf Wilhelm Tibell, founded a similar corps in Sweden in 1805, which made use of the technology imported from France for the remeasurement of Maupertuis' arc of meridian in Lapland in 1801–3.^[84] We see in Sweden the same interplay between military cartography and science-related geodesy that occurred earlier in Britain, and which recurred in Hanover in 1821–5 when a military survey took over Carl Friedrich Gauss' measurements.^[85]

Major Johann Jacob Baeyer, of the Prussian Army, was co-leader on Friedrich Wilhelm Bessel's famous survey of East Prussia in 1831–6; and Friedrich Georg Wilhelm Struve and general C. de

[80] Konvitz, Cartography in France , 59–61.

[81] Henri Marie Auguste Berthaut, Les ingénieurs géographes militaires 1624–1831: Étude historique (Paris: Service Géographique de l'Armée, 1902), 1 , 239–40, 305–431.

[82] See the collection La cartographie au XVIIIe siècle ; Frans Depuydt, "The large scale mapping of Belgium, 1800–1850," Imago mundi, 27 (1975), 21–4; Brown, The story of maps , 274–5.

[83] George M. Wheeler, Report upon the Third International Geographic Congress and Exhibition at Venice, Italy, 1881, accompanied by data concerning the principal government land and marine surveys of the world (Washington, D.C.: Government Printing Office, 1885), 365–79.

[84] Ulla Ehrensvärd, "Fortifikationsofficeren som kartograf," in Bertil Runnberg, ed., Fortifikationen 350 år, 1635–1985 (Stockholm: Fortifikationskåren, 1986), 115–9.

[85] W. Grossmann, "Gauss' geodätische Tätigkeit im Rahmen zeitgenössischer Arbeiten," Zeitschrift für Vermessungswesen, 80 (1955), 371–84.

Tenner found what they called "the problem of their lives" in their measurement of a meridian of more than 25° (1816–55).^[86] Baeyer subsequently founded the Europäische Gradmessung , which met seventeen times between 1864 and 1912; it brought together astronomers, military cartographers, and civilian administrators to coordinate and promote geodetic measurements all over continental Europe.^[87] The twenty national cartographic organizations that existed in Europe and its colonies in 1885 were all under military direction.^[88] The cartographic situation paralleled the use of military manpower, technology, and administrative expertise in the construction of railroads and canals and in the development of mechanized industrial production.^[89]

As the store of geodetic data increased, the notion of a regular shape of the earth came into general doubt. The long-disputed ellipsoid had been put out of court by Delambre and Méchain, whose demonstration that meridians are irregular was corroborated by the Ordnance Survey in 1803.^[90] As more surveys comparable in

[86] Friedrich Wilhelm Bessel, Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten (Berlin, 1838), iv, ix–x; Friedrich Georg Wilhelm Struve, Arc du méridien de 25 × 20' entre le Danube et la Mer Glaciale (St. Petersburg, 1860), 1 , xv ("problème de leur vie").

[87] Of those participating in the meeting in 1867, twenty-four were directors of observatories or academics, eleven were military officers, and five were civilian administrators. See C. Bruhns, W. Foerster, and A. Hirsch, eds., Bericht über die Verhandlung der vom 30. September bis 7. October 1867 zu Berlin abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung (Berlin, 1868), 3–4. Bialas, Erdgestalt , 242–6.

[88] Brown, The story of maps , 280–1.

[89] See, e.g., Merritt Roe Smith, "Introduction," in Merritt Roe Smith, ed., Military enterprise and technological change: Perspectives on the American experience (Cambridge, Mass.: The MIT Press, 1985), 1–37; and Barton C. Hacker and Sally L. Hacker, "Military institutions and the labor process: Noneconomic sources of technological change, women's subordination, and the organization of work," Technology and culture, 24:4 (1987), 743–75. Cf. Svante Lindqvist's and Robin Rider's contributions in this volume (chaps. 10 and 4, resp.).

[90] For example, see the report of the international commission that investigated the metric survey. Jan Hendrik van Swinden, "Rapport sur la mesure de la méridienne de France, et les résultats qui en ont été déduits pour déterminer les bases du nouveau systéme métrique," Institut national des sciences et arts, Mémoires , Sciences mathématiques et physiques, 2 (an VII), 47, 49–52. Several contributions from the heated debate concerning the British meridian are reprinted in Olinthus Gregory, Dissertations and letters. . .tending either to impugn or defend the Trigonometrical Survey of England and Wales (London, 1815). Delambre defended the British results; see Delambre, Grandeur et figure , 363–72.

magnitude to Delambre's and Méchain's were carried out and interconnected, the ellipsoid came to be viewed as a convenient fiction. The notion of the geoid, developed by Friedrich Wilhelm Bessel and Gauss around 1830 but not christened thus until 1873, became the preferred theoretical tool to describe the physical shape of the earth (or rather of the geopotential surface).^[91] The shape of the geoid could not be predicted; it had to be measured, over and over again, whenever instrumental improvements promised refinements. Increased data caused geometrical simplicity to give way to dynamic complexity, which could be managed only by the systematic work of well organized institutions like the military.

[91] Irene Fischer, "The figure of the earth—changes in concepts," Geophysical surveys, 2:1 (1975), 3–54, esp. 20–8; Bialas, Erdgestalt , 234–5.