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. 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
British but also between military officers and "scientists." 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. 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. 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. 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,
ever zealous in the cause of science." 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. 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." 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. 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
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. 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."
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. 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. He thus demonstrated the superior accuracy of the geodetic method.
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.
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. 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
the limits of what was considered reasonable. 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." 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."
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. Roy had said that he
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.
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. 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
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.
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." 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. They were also to try to talk Ramsden into
joining the staff at the Paris observatory or taking French apprentices.
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. 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.
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. 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
were closed to within a few seconds using either the circle or the theodolite. 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." 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.
In fact, he loved decimals, which abound in his writings far beyond practical, but perhaps within rhetorical, efficacy.
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. 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." 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.
The commendation of Ramsden's achievements, like the long rows of decimals and the frequent references in the work of Maskelyne,
Cassini, and Roy to measurements made to "the last exactness" or to "mathematical exactness," may be considered the rhetoric of exact science. 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." 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.
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," and
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.
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. 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. 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.
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. 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. 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.
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. 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. Roy used the glass tubes to control
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. 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. 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. 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.