La figure de la terre, déterminée par les observations de messieurs De Maupertuis, Clairaut, Camus, Le Monnier, de l’Académie royale des sciences et de M. L’Abbé Outhier, correspondant de la même académie, accompagnés de M. Celsius, professeur d’astronomie à Upsal, faites par ordre du Roy au cercle polaire.
Paris: Imprimerie Royale, 1738. First edition, a highly important presentation copy from the author to James Stirling, of this influential work detailing the 1736 expedition to Lapland to prove Isaac Newton’s theory that Earth is flattened at the poles, not elongated as the Cassini family suggested, confirming a pear-shaped (oblate spheroid) Earth through geodesic measurements. Published with contributions from Clairaut, Camus, Le Monnier, and Celsius, Maupertuis’ book became foundational in establishing Newtonian physics in France and is a key text in the history of science. James Stirling was one of the leading mathematicians of eighteenth-century Europe, cultivating relationships with Sir Isaac Newton, Colin Maclaurin, Gabriel Cramer and Leonhard Euler among others. He gives his name to the Stirling numbers and to Stirling’s formula. Stirling was a close fiend and correspondent of Newton and was considered the leading British expert on Newton’s theory of the Earth’s shape. “In 1735 France sent an expedition to Peru under the leadership of La Condamine and another to Lapland under the leadership of Maupertuis. Clairaut, Camus, and other scientists accompanied the latter. The mission of each expedition was to measure as accurately aspossible the length of a degree along the meridian of longitude. If, indeed, the earth is flattened toward the poles, as Newton had predicted, the degree of latitude should be shorter in far northern latitudes than near the equator. The voyage began on 2 May 1736 and lasted over a year. The local base for the expedition's fieldwork was Tornea, in northern Sweden – then, according to Maupertuis, a town of fifty or sixty houses and wooden cabins. On the return journey the ship was wrecked in the Baltic Sea, but without loss of life, instruments, or records. Maupertuis reached Paris on 20 August 1737, only to meet with a rather chilly reception. Envy and jealousy were already at work; he had few Newtonian supporters in France except Voltaire; and La Condamine's expedition had not yet returned from Peru … The laborious analysis of the data on the length of the arc of a meridional degree at various latitudes took much time and created much controversy” (DSB). “Maupertuis adopted and explained Newton’s propositions on attraction and on the figure of the earth; and he conducted an expedition to Lapland for the measurement of an arc of the meridian, the result of which was fatal to the Cartesian hypothesis” (Babson). Maupertuis’ results were corroborated by the findings of La Condamine’s mission to Peru, who because of various difficulties did not return to Paris until 1745. No other presentation copy listed on RBH. Provenance: Presented by Maupertuis to the Scottish mathematician James Stirling (inscribed ‘Donum Authoris’ by Stirling on the initial blank). James Stirling was born on 11 May 1692 at Garden House, near Stirling, Scotland; this book remained in the library at Garden until 2025. It was sent to him care of the astronomer John Machin (d. 1751), who informed Stirling of the gift in a surviving letter dated 22nd June 1738: “Monsr Maupertuis has sent you a present of his book which I have deliverd to Mr Watts for you. It contains a complete account of the measurement in the North. Mr Celsius likewise published two or 3 sheets on the same subject chiefly to shew that Cassini’s measurement was far inferior to this in point of exactness, and which I suppose you will need no argument to prove when you have read over M. Maupertuis's book”. On December 6, 1733, Stirling read a paper entitled “Twelve propositions concerning the figure of the Earth to the Royal Society of London. This paper could be regarded as the first major contribution by a British scientist to the theoretical study of the figure of the earth and its gravitational forces since the seminal work of Newton and Huygens. In 1735, Stirling published an extended version of his results in a paper entitled ‘Of the Figure of the Earth, and the Variation of Gravity on the Surface’, which supported Newton’s hypothesis of an oblate spheroid. Stirling was considered the leading British expert on the subject for the next few years by all, including Maclaurin and Robert Simson, who went on to make major contributions themselves. As Stirling’s unpublished manuscripts show, he did go much further than the 1735 paper, but probably the pressure of work at the mining company gave him too little time to polish the work. He explained in a letter to Maclaurin in 1738 why he had not published despite pressure to do so: “I got a letter this last summer from Mr Machin wholly relating to the figure of the Earth and the new mensuration, he seems to think this a proper time for me to publish my proposition on that subject when everybody is making a noise about it; but I choose rather to stay till the French arrive from the south[i.e., La Condamine’s expedition], which I hear will be very soon. And hitherto I have not been able to reconcile the measurements made in the north to the theory.” “The origins of the eighteenth-century dispute [about the shape of the earth] go back to Isaac Newton and Christiaan Huygens, both of whom calculated the earth to be slightly flattened at the poles, though they were working from different theories of gravity. The only empirical support available to them came from pendulum measurements taken near the equator that showed the effect of gravity to be less there than at higher latitudes. By the early eighteenth-century French astronomers had produced another set of data: measurements of celestial arcs and terrestrial distances made in the course of an ambitious project to map the kingdom of France. In 1718 Jacques Cassini announced that these measurements implied an elongated rather than a flattened earth. Virtually uncontested for fifteen years, his claim attracted renewed attention in the early 1730s, when a contingent of Paris Academy mathematicians questioned the adequacy of local measures for settling the matter … “In the early 1730s a great deal of academic attention focused on the shape of the earth, for a variety of reasons. For one thing, in 1730 the new finance minister, Philibert Orry, decided to fund a new round of fieldwork for mapping purposes, to be led by Cassini II. In 1733 the first of many surveying expeditions left Paris to measure a line perpendicular to the Paris meridian. In addition, work by the Italian mathematician Giovanni Poleni prompted consideration in the academy of new methods of determining the earth's shape using differences in longitude rather than in latitude. As the question came to occupy more and more academicians, both as a theoretical and as an observational problem, discussion centered on the decisive value of measurements obtained at distant latitudes, measurements that would require considerable financial and political backing. Selling their plans to the Comte de Maurepas, Minister of the Navy, the academicians promised improved methods of navigation, playing to the Crown's growing interest in the commercial possibilities of colonial expansion. In the end the king approved funding for two expeditions, the first headed for Peru under the direction of Louis Godin and the second, organized by Maupertuis, to the arctic circle. “In emphasizing long-distance navigation, the new geographers replaced the insular vision of France represented by the Royal Observatory mapmakers with the promise of extending the Crown’s reach to distant corners of the globe. Once determining the shape of the earth became a primary investigative goal, rather than the by-product of local cartography, the observers directed their gaze outward from France and implied that they would enable the king to do likewise. Enlisting the cooperation of the king of Spain, Louis XV stressed the utility of the academicians' efforts ‘not only for the progress of the sciences, but also for commerce, in making navigation more exact and easier.’ The expenditures approved for the geodetical expeditions must be understood in this global setting, a context distinct from that of the observatory’s mapmaking, which originated in an earlier reign concerned with the consolidation and centralization of royal power. “Though Maupertuis came to the problem of the earth's shape from mathematics, he selected it as the core of his program for an analytic astronomy because of the possibilities for exploring it empirically. In spite of the difficulty of procuring sufficiently accurate observations, these held the potential for considerable propaganda payoff. The academy heard several substantial memoirs on geodesy by Maupertuis in the period from 1732 to 1736. Some of these papers stressed the transparency of observational data, while others developed mathematical apparatus for deriving the earth’s shape from these measurements. Maupertuis’s philosophical stance alternated between defending Newton’s theory and claiming theoretical agnosticism. Given the current status of the question, observations themselves appeared problematic, as ‘observations seem to give the earth the shape of an elongated spheroid, and solid reasoning seems to give it the opposite shape.’ The resolution of this discrepancy must lie in procuring better observations rather than revision of ‘solid reasoning.’ Knowing very well that some members of the academy objected strenuously to the assumptions behind this ‘reasoning,’ Maupertuis shifted attention to measurements, thereby deflecting objections to contested categories like attraction. In claiming that the problem was no more than ‘a question of fact which ought to be decided by actual measurements,’ he could distance himself from causal arguments about the origin of the earth’s ellipsoidal shape, even as he positioned himself and his allies to undertake the crucial measurements. “In the period from 1733 to 1735, algebraic analysis of complex problems in solid geometry appeared frequently in the memoirs of Maupertuis, Alexis-Claude Clairaut, Louis Godin, and Pierre Bouguer, all of whom later joined one or the other of the geodetic expeditions. Characteristic of this work was an eagerness to explore alternative methods of observation and calculation, using a kind of mathematical analysis foreign to Cassini and his collaborators. Cassini’s 1720 volume [????] contained some geometrical diagrams and demonstrations and many tables of observations, but no equations. Maupertuis and Clairaut directed much of their work toward showcasing mathematical methods, often in the context of weighing the merits of various observational programs. A common expository device was to work out the ratio of the earth’s axis to its diameter assuming various hypothetical ‘theories’ of gravity. In this usage, theory meant no more than a mathematical description whose consequences could be explored analytically. Or an equation could be formulated to give the ratio between the axis and the diameter that would contain only observable terms and hence remain ‘independent of any system.’ In yet another example of this kind of exploration of mathematical possibilities, Maupertuis derived an expression for the error accruing in a standard series of triangulations used in surveying distances. To find the optimum number of triangles for such a series, he differentiated to minimize observational error analytically. Using a simple application of the calculus, Maupertuis effectively shifted the terms of discussion away from the observational and plane-geometrical terrain familiar to Cassini. “Maupertuis made it clear from the start that his expedition to Lapland would not be modeled on the French surveying efforts. Rather than calling on individuals trained apprentice-style at the observatory, Maupertuis assembled a group of men with a range of expertise. Although he recognized the necessity of including accomplished observers, mathematical experience and interest in Newtonian physics took precedence over practical astronomical skills. Neither Maupertuis nor Clairaut had any real experience as observers, yet they proposed to carry out a series of precision measurements under extremely difficult conditions. They apparently assumed that they could learn the necessary astronomical skills quickly, and even enlisted the help of Cassini in doing so. The most experienced astronomer of the Lapland team, Anders Celsius, was a Swede with strong ties to the English astronomical community. The remaining scientific members were Pierre-Charles Le Monnier, a twenty-one-year-old trained at the Royal Observatory; Charles Etienne Camus, who was especially knowledgeable about clocks and other instruments; and the Abbé Réginald Outhier, secretary to a provincial bishop and a corresponding member of the academy who had experience in surveying and mapmaking. “If Maupertuis bypassed the local astronomical establishment in assembling his team, he did so further in equipping it, procuring a transit telescope, a pendulum, a clock, and a zenith sector from the English instrument maker George Graham. Although he also took several French quadrants made by Claude Langlois and several clocks by Julien Le Roy, Maupertuis repeatedly called attention to the new design and the consequent precision of the nine-foot English sector, to be used for observing stars close to the zenith. The zenith sector, designed by Graham for Newtonian astronomers in England, represented yet another implicit challenge to Cassini and his French instruments, and indeed became the focal point of the controversy later. “Even the specific plans for the Lapland measurements, while using the same basic combination of surveying and stellar observation, contradicted the standard cartographical procedure of measuring as many triangles as possible. Having shown analytically that limiting measurements to an arc of 1 degree of latitude would actually reduce the potential for overall error, Maupertuis proposed to measure a single series of triangles, with the stipulation that all three angles of every triangle be observed directly. This made an advantage of the difficulties of working in the arctic terrain and drew attention to the shortcomings of the common French practice of extrapolating some angles when direct observations proved impossible. “Although they adopted some features of French cartography, the Peru and Lapland expeditions inaugurated a new kind of geodetical practice, incorporating methods, techniques, and instruments from other, often foreign, sources. For example, simply because they planned to travel beyond French borders, the academicians embroiled themselves in international diplomacy. Without the endorsement of the Swedish king and the physical assistance of Finnish soldiers, the Lapland expedition could not have proceeded. In shopping for instruments they also looked abroad; in the case of the Graham zenith sector, Maupertuis imported an instrument previously used not for mapmaking but for precision stellar observations. Once they extracted the question of the earth’s shape from its cartographical context, Maupertuis and his colleagues changed the rules of the geodetical game. When they argued for a northbound expedition to mirror the original proposal for measurements at the equator, the Paris mathematicians hoped to make Cassini’s local measures largely irrelevant. If both groups returned to France armed with new numbers from distant latitudes, they assumed, the difference between their results would be enough to decide the question with only passing reference to the observatory work. As it turned out, the travelers needed to mobilize a range of resources once they returned to Paris, in order to achieve consensus about the shape of the earth. “The expedition to Peru ran into innumerable problems, including a vicious quarrel between Charles-Marie de La Condamine and Bouguer, civil war, colonial bureaucracy, earthquakes, and volcanic eruptions. The astronomers only returned to France, separately, in the mid 1740s. Things went better for Maupertuis and his colleagues. Arriving in Lapland in the summer of 1736, they were able to conduct their terrestrial measurements before the arrival of winter made celestial observation possible. They spent the spring verifying their measurements, and they returned to Paris, after only a fifteen-month absence, in August 1737. “On his return Maupertuis reported his results to the academy, in the presence of several royal ministers; the next day he and his companions were presented to the king. He apparently expected consensus and accolades to follow, but Cassini challenged the Lapland measurements immediately, voicing doubts in particular about measurements made with the vaunted Graham sector. Maupertuis reported to Celsius, ‘[Cassini’s] main quibble concerns the fact that we did not turn the sector in both directions to assure against any disturbance which could have arisen in moving it.’ This technical objection referred to the standard practice for meridian observations of verifying the placement of the instrument by aligning it with the meridian first in one direction and then physically turning the instrument to check its alignment in the opposite direction. This remained the core of Cassini’s challenge throughout the dispute that flowered over the next two years, as he pointed to deficiencies in the observational techniques of the Lapland team. In response, Maupertuis and his collaborators recounted the precautions they had taken to ensure reliable observations … “In its published form, Maupertuis’s book included a history of the problem of the earth’s shape, the story of his expedition, the data collected, and the calculations leading to his final results. The narrative invited the reader into the familiar terrain of travel literature. Tales of hardships and adventures imbued the results with added credibility by gaining the sympathy of the reader for the hero-philosopher, ready to risk his comfort and well-being for the truth. As the Mercure de France reported, ‘one cannot think of all these obstacles and difficulties without admiring the courage of those who subjected themselves to and surmounted them.’ Maupertuis described the terrain, climate, and interactions with local inhabitants alongside instruments, verification procedures, and corrections to the raw data. The numbers, displayed like prizes won by heroic effort, included tables of stellar observations, angles used in the triangulation, observations of the sun for determining the meridian, the linear measurement of the baseline, observations by all five observers for verifying the division of the sector, measurements of gravity with a pendulum, and so on. He included the necessary corrections to the raw observations and described his method for calculating the earth’s shape from the results. The zenith sector played a prominent role in the account; Cassini’s challenge to its accuracy, common knowledge to the reading public, was never mentioned. Through their variety and quantity, the numbers – representing the process of observing, measuring, and calculating – implicitly reduced that challenge to pettiness” (Terrall). Babson 94; Macclesfield 1337; Norman 1458; Sabin 46946 (English ed.); Wellcome IV, p. 175. Terrall, ‘Representing the Earth’s Shape: The Polemics Surrounding Maupertuis's Expedition to Lapland,’ Isis 83 (1992), pp. 218-237.
8vo (195 x 123 mm), pp. xiv, [4] ,184, with engraved folding map, 9 engraved folding plates. Contemporary tan calf (extremities slightly rubbed, joints starting, spine-label perished). A clean, crisp copy.
Item #6606
Price: $15,000.00
