Michael S. Mahoney
Princeton University

Prepared for the Clark Library Conference on "War and Science during the Old Regime", 20-21 November 1998;
Published in Brett Steele and Tamera Dorland (eds.),
The Heirs of Archimedes: Technology, Science and the Art of Warfare through the Age of Englightenment
(Cambridge, MA: MIT Press, 2005), 221-230

The central problem of navigation and, to some extent, of cartography throughout the period under consideration was the determination of longitude. On it depended both the location of a ship at sea and the accurate mapping of the global world that Europe increasing viewed as existing for its benefit. Longitude is a matter of time. There is no fixed point of reference in the sky, but only the uniform rotation of the earth once every sidereal day. If one knows the difference in local time at two points, one knows the longitudinal distance between them. Measuring the time where one is located is relatively straightforward: when the sun is due south, it is noon. Knowing the local time elsewhere at that same moment is another matter. From the mid-sixteenth to the early twentieth century, only two methods seemed worth pursuing. One could use the clockwork of the heavens directly or one could build a model of that clock and read it indirectly. Both were perfected in the mid-eighteenth century, to be replaced only by radio signals a century and a half later.


The story of the determination of longitude has enjoyed considerable publicity over the past several years, in large part owing to a conference on the subject organized at Harvard in November 1993 to commemorate the 250th anniversary of John Harrison's marine chronometer, the clock that did the trick. That conference produced not only its own richly illustrated proceedings, The Quest for Longitude, but also provided the basis for Dava Sobel's widely read Longitude.(1) I don't want to repeat that story but rather to explore one piece of it in the context of the question at the focus of this conference, namely the relation of war and science in the early modern era, or the "possible links between the Scientific and the Military Revolutions."

1. William J.H. Andrewes, The Quest for Longitude: The Proceedings of the Longitude Symposium, Harvard University, Cambridge, Massachusetts, November 4-6, 1993 (Cambridge, Mass.: Collection of Historical Scientific Instruments, Harvard University, 1996); Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time (New York : Walker, 1995)

In The Military Revolution: Military Innovation and the Rise of the West, 1500-1800 Geoffrey Parker cites four points of revolutionary innovation: the introduction of firearms; the sudden growth in the size of armies, increasingly complex and ambitious strategies; and logistical, social, and political demands of warfare on a wholly new scale. On the sea, those innovations take the form of shipboard cannon, changes in ship design required to carry guns and to bring them to bear effectively on the enemy, new strategies of fighting at sea with large and far-flung fleets, and the burdens of paying for them. What differentiates the two aspects of the military revolution are the sites of action. For the most part, the new European armies raised havoc in Europe, while the new fleets carried war to other continents, or rather the seas around and between them.

Parker does not have much to say about the role of improved navigation and the new forms of organization its pursuit required. Yet, surely it was an essential element in the strategies and logistics of naval warfare on a global scale. War at sea was aimed at securing the commercial advantages brought by the ability to navigate on the open sea. It put the navies of some countries, including our own, into the business of astronomy and made them their nations' timekeepers.(2)

2. To this day, the United States sets its clocks to the timekeepers of the Naval Observatory in Washington. Initially conveyed to ships in port by means of a ball descending a mast at noon, the time can now be automatically downloaded via the web to any personal computer via

In the keynote address to the Longitude Conference, David Landes emphasized the contingency of the problem.(3) Clearly, knowing one's longitude precisely is not a prerequisite to travel on the open sea. The Portuguese rounded Africa and crossed the Indian Ocean without such knowledge. Columbus crossed the Atlantic, and Spanish and Portuguese ships soon followed, all without being able to determine their longitude, nor indeed knowing that of their destinations. Once one knew the approximate distance between the old and the new worlds, crossing between them was a matter of "sailing the latitudes", and the prevailing winds and currents conveniently cooperated. As early as Columbus's second voyage, in the middle of which he sent one of his captains back to Spain for more supplies, the voyage had become a matter of routine. Once the path had been opened, others could follow it. Ignorance of longitude could lead to disasters, as in the famous case of La Salle's failed and ultimately fatal attempt to reach New Orleans by sea after first approaching it by coming down the Mississippi. But knowledge of longitude was not a prerequisite to the voyages of exploration.

3. David S. Landes, "Finding the Point at Sea", in Andrewes, Quest, 20-30.

Exploitation was another matter. Well traveled paths can be dangerous, or at least expensive, when they mean that pirates and enemy fleets know where to look for you. The trackless ocean becomes safe ground when knowing where you are at any moment means being able to range freely. Coupled with knowing where you are, knowing exactly where you are headed means less time spent circling around, looking for your destination. It reduces the uncertainty of schedules, of provisions, of alternatives along the way. These are clearly advantages to a navy, but they are even greater advantages to commerce, whether private or mercantilist. And where commerce went, the navy would have to follow.


More than war and commerce is involved. One can write much of the history of astronomy and mechanics in the early modern era, technically and institutionally, by reference to the problem of longitude.(4) Through the clock, which it placed at the center of scientific attention, it is deeply embedded in our modern concept of the world. Through the instruments it required, it informed the development of precision toolmaking on an industrial basis.(5) It is worth taking a closer look at these connections and then stepping back to consider what light they might shed on the question before this conference.

4. See Michael S. Mahoney, "Longitude in the Context of the History of Science," in Andrewes, Quest, 64-68.

5. See, inter alia, Richard J. Sorrenson, "Scientific instrument makers at the Royal Society of London, 1720-1780" (Ph.D., Princeton, 1993), esp. Chap. 7 on Jesse Ramsden, and "The state's demand for accurate astronomical and navigational instruments in 18th-century Britain", in. The consumption of culture, 1600-1800: Image, object, text, ed. Ann Bermingham and John Brewer (London: Routledge, 1995), p.263-271.

The central figure is Christiaan Huygens, whose interest in the problem was first piqued by the challenge of clocking the pendulum.(6) I put it that way, because it was a question of automating the astronomical pendulum, the accuracy of which was compromised by the need for someone to count its beats and occasionally to keep it going with a slight push. His answer was to attach a mechanical clock, the escapement of which would count the pendulum's swings, while the driving weight provided the push. Viewed from the perspective of the clock, the pendulum provided the tautochronic regulator it had been lacking up to that time.(7) Galileo had first suggested using the pendulum, but Huygens devised how to attach it so as to keep the two mechanisms separate except at the point at which the one could regulate the other while being ever so gently driven by it.

Once Huygens made the connection, the clock became a precision mechanism it had not been before, whatever its fascination as an automaton. Accurate now to within seconds a day, it made seconds count. That had implications both for mechanics and for navigation. It made the clock an interface for theory and practice in mathematical science, an interface at which Huygens worked for his entire career from 1657 until his death in 1695.

Huygens recognized almost immediately that his pendulum clock held promise of a solution of the problem of longitude but only if he could devise a portable version capable of withstanding the rigors of travel, including first and foremost disturbances of the pendulum itself. Although Galileo had asserted, and perhaps thought he had even demonstrated, the independence of the period of a pendulum from the amplitude of its swing, others quickly determined that a simple pendulum is tautochronous only within a close neighborhood of its center. Long pendulums with heavy bobs swinging over short arcs met that condition for scientific purposes, but that would not work for a portable clock.

6. For details, see Michael S. Mahoney, "Christiaan Huygens, The Measurement of Time and Longitude at Sea", in H.J.M. Bos et al. (eds.), Studies on Christiaan Huygens (Lisse: Swets, 1980), 234-270, and "Huygens and the Pendulum: From Device to Mathematical Relation", in H. Breger and E. Grosholz (eds.), The Growth of Mathematical Knowledge (Oxford U.P., to appear), as well as J.H. Leopold, "The Longitude Timekeepers of Christiaan Huygens", in Andrewes, Quest, 101-114.

7. The central problem of the mechanical clock is converting the accelerated motion of the driving weight or spring into a uniform motion of the hands. That is accomplished through the escapement, which advances a toothed wheel by pallets or pins engaging and releasing it at regular intervals determined by an oscillating mechanism. Prior to the pendulum, none of the mechanisms employed, such as the foliot, had a natural period.

Shorter pendulums emphasize the perturbations of wide excursions, so Huygens undertook to examine the nature of tautochrony itself. Or rather, he fell upon the issue in seeking a theoretical derivation of the period of a simple pendulum, which could serve as a basis for experimental determination of the constant of gravity. To make the initial analysis mathematically tractable required an approximation. Subsequent analysis of the approximation provided an exact solution, namely that a pendulum swinging along the arc of an inverted cycloid is tautochronous over its entire trajectory. Moreover, as Huygens then quickly determined, mounting the pendulum by a flexible wire and encasing the wire between two leaves in the shape of a cycloid will constrain the pendulum's bob to follow that same cycloid. As Huygens demonstrated in opening a new area of mathematics, a cycloid is its own evolute.(8)

8. The term "evolute" derived from the technique of wrapping a string (or imagining a string wrapped) around a curve and then tracing the locus of its endpoint as the curve is unwrapped (evoluta), that is, as the string is pulled away while being held tangent to the curve. The mode of generation and hence the class of curves thus generated was new at the time, and Huygens had to develop much of his mathematical apparatus for handling them. Chapter 4, "On Evolutes", of his Horologium oscillatorium (Paris, 1673) was the first published treatise on the subject.

Tests of the cycloidal clock against the sun confirmed its accuracy to a degree that warranted investigation of the exact calibration of the pendulum. Between 1661 and 1664 Huygens attacked the outstanding problem of the center of oscillation of a compound pendulum, the solution of which led to a small weight adjustable by sliding along a scale inscribed on the rod of the pendulum. The solution itself, based on an application of the principle of conservation of mv2 (a quantity to which he gave no name), laid the groundwork for the later dynamics of rigid bodies and made extensive use of the new methods of quadrature and cubature that became the foundation of the integral calculus.

At his point, Huygens was ready to send the cycloidal pendulum clock to sea, but before following that story, let us look back to see what had transpired so far, in less than a decade of study: a successful pendulum clock, the derivation of the period of a simple pendulum, the discovery of the cycloid as tautochrone, the new theory of evolutes (later subsumed under the concept of the center of curvature), the derivation of the center of oscillation of a compound pendulum. At the risk of stating the obvious, we are looking at essential elements of the new mechanics of the Scientific Revolution, all issuing from the clock and its application to the problem of longitude.


There was more to follow. As sea trials brought out the weaknesses of the pendulum clock, Huygens became alert to alternatives. In 1675 he returned to his analysis of motion on a cycloid and determined that what made it tautochronic was the direct proportion between the effective acceleration of the body along the curve and its distance from the center at the bottom. Noting that Hooke's law of springs (ut tensio sic vis) stated essentially the same thing, Huygens determined that a coiled spring would behave exactly like a cycloidal pendulum and hence that it could replace the pendulum as a tautochronic regulator for clocks. Moreover, the spring was only one of a host of mechanisms that obeyed the basic principle of what we now refer to as simple harmonic oscillation and what has since come to be viewed as one of the most fundamental mechanisms of nature. Huygens' search for a "perfect marine balance" based on that principle continued until his death. Pace Otto Mayr, Huygens' work in this regard constitutes a study of regulation by feedback a century before Watt's invention of the steam-engine governor.(9)

9. Cf. Otto Mayr, Authority, Liberty, and Automatic Machinery in the Early Modern Era (Baltimore: Johns Hopkins University Press, 1986).

But let's go back to the clock at sea. Before it could serve to determine longitude, Huygens had to deal with an old question to which the accuracy of his clock now gave new importance. Ignoring precession, it seems at first a matter of indifference whether one sets the clock to the sun or to the stars. However, owing to the declination of the sun's orbit (as navigators do to this day, we shall assume a Ptolemaic solar system for ease of calculation), the length of the solar day in fact varies over the year. A clock set to noon on February 10 and calibrated to a mean solar day will fall almost twenty minutes behind the sun by May 14, catching up to within nine minutes on July 25, but then falling more than thirty minutes behind again by November 1.(10) It will catch up fully only after a year. Those discrepancies add up to serious errors in longitude unless one has a table of daily values and instructions on how to use them. Here the clock as astronomical instrument became the means of making those values precise, while the precise values in turn made the clock accurate as a navigational instrument. In the process a problem of astronomy had been elucidated.

10. The dates of the turning points are Huygens' and differ from the modern values, which according to the 1964 English edition of Flammarion's Astronomy are 11 February, 15 May, 27 July, and 4 November.

Once underway, Huygens' clocks met with only mixed success under the rigors of travel by sea. A design arrived at in collaboration with Alexander Bruce (later Lord Kincardine) went along with Captain Robert Holmes on voyages in 1663 and '64 from London to Lisbon and Guinea and then out into the Atlantic. The encouraging data of the first voyage were heightened by the drama of the second, when Holmes, relying on the clocks, overrode the advice of his fellow masters concerning their distance from the Cape Verde Islands and proved to be correct.(11) Trials in the Mediterranean in 1668-69 seemed equally promising. But, eager now to claim suitable reward and recognition from official bodies in England and France, Huygens withheld publication of his treatise on the clock pending long-range tests on an expedition to the West Indies commissioned by the Paris Academy of Sciences in 1670. It was a disaster for the clocks, largely, Huygens believed, owing to the negligence of Jean Richer, the élève deputed to care for them. Wherever the fault lay, the clocks remained unproved, and Huygens proceeded with publication of his masterpiece, the Horologium oscillatorium of 1673, unable to claim a working solution to the problem of longitude.

11. Sir Robert Moray (Murray) to Christiaan Huygens, 23 January 1665, in Huygens, Oeuvres complètes, Vol. V, 205ff. There was some delay in confirming Holmes's report, because he had been thrown in the Tower for attacking and capturing without declaration of war several Dutch fortresses in the CapeVerde Islands and Guinea (Ibid, 168, n.6).

After a hiatus of some fifteen years, during which he experimented with a variety of new regulating mechanics described in part above, Huygens again sent his pendulum clock to sea in 1686-87, this time to the Cape of Good Hope on board the Dutch East India Company ship Alkmaar. The clocks responded badly to heavy seas on the way out, but on the return worked well enough for Huygens to plot a course that could be compared with the ship's logs and with sightings of land. According to the clocks, the Alkmaar had sailed right through Ireland and Scotland rather than around them.

Far from invalidating the clocks, that result tied the determination of longitude back to fundamental questions of mechanics. On an Academy of Sciences expedition to Cayenne in 1672-73, Jean Richer carried out instructions to determine the length of a 1-second pendulum and found that it was shorter by 1-3/4 lignes than a 1-second pendulum in Paris. Huygens immediately drew the horological conclusion: a clock set in Paris to mean solar time would run behind by 2m 10-s owing to the apparent lengthening of its pendulum.(12) The deviation was of the order of the solar inequality and hence affected the calculation of longitude. Subsequently others reported a variation in the length of a seconds pendulum at various locations on the globe. At issue, of course, was the value of g, as measured through the weight of a body. While some scientists, such as Jean Picard, insisted on its constant value everywhere, the data from the Alkmaar voyage decided Huygens in favor of its variation, a conclusion he had reached in the late 1660s in a study of the cause of weight and its application to the period of a pendulum.(13) Then he had reasoned that the rotation of the earth exerted a centrifugal force that decreased the weights of bodies by a factor dependent on the latitude. At the pole, it had no effect; at the equator it caused the greatest decrease, about 1/289. Applied to the data of the voyage, that adjustment brought the course determined by the clocks into line with that of the logs, once allowance was made for the incorrect longitude used by the pilots for the Cape of Good Hope. Reassured by this empirical evidence, which also gave him grounds for rejecting Newton's theory of universal gravity, he now moved to publish the earlier treatise on the subject.(14)

12. Angered by what he considered Richer's negligence on the earlier voyage, Huygens had refused to commit his clocks a second time to the young man's care and so had passed up another opportunity to test them on a long journey.

13. Huygens, "Calcul de la période d'une oscillation (cycloïdale)en un endroit déterminé de la terre en tenant compte de la force centrifuge due à la rotation du globe terrestre," Oeuvres complètes, XVII, 285-6.

14. On the role of the voyage in Huygens' critique of Newton's theory, see George E. Smith, "Huygens's 1688 report to the directors of the Dutch East India Company on the measurement of longitude at sea and its implications for the non-uniformity of gravity," De Zeventiende Eeuw 12, 1(1996), 198-214.

More is involved in this story than Huygens' personal, serendipitous quest. When Colbert decided at the end of 1666 to bring together the French mathematicians and natural philosophers receiving stipends from Louis XIV and incorporate them as a Royal Academy of Sciences, he included Huygens and indeed looked to him for leadership and guidance. In response to Colbert's inquiry about what such an Academy might undertake, preferably to the benefit of its sponsor, Huygens proposed several agendas, one of which included the following group of projects:

10. Observe the motion of the companions of Jupiter and make tables of them.

11. With the aid of these tables, observe here and in other places in the world, such as in Madagascar, the occultation of each of the said companions behind or in front of Jupiter, to find thereby the true longitude of the said places and to rectify [current] maps.

11,1. Observe the declination of the magnet and the change that it undergoes.

12. Send pendulum clocks to sea with the necessary instructions and a person to take care of them, to carry out [pratiquer] the determination of longitudes, which has already succeeded so well in the experiments thus far made.

13. Measure the times and ratios of the fall of heavy bodies in air.

14. Measure the size of the earth. Advise on the means of making geographical charts with greater exactitude than hitherto.

15. Establish once for all the universal measure of sizes [i.e. a universal standard of measure] by means of pendulums, and in consequence [the universal measure] of weight.(15)

15. Christiaan Huygens, Oeuvres complètes, Vol. XIX, 255-6.
Evidently, Huygens was thinking well beyond his clocks and the problem of longitude, or rather he was thinking of the problem of longitude in the context of a much larger program of mechanical and astronomical research. His own experience of the previous decade had shown him the promise of the pendulum as an instrument linking celestial and terrestrial phenomena through its own mechanics

The research agendas that Huygens proposed for the Academy of Sciences reveal an important aspect of the relation of science and the state at the beginning of the latter's institutionalization of the former. Colbert's ministry stands as the historical embodiment of the mercanilist state. To page through his administrative correspondence and the Comptes des bâtiments (which kept accounts of much more than the king's buildings) is to watch a man dedicated to the organization and expansion of the commercial, industrial, and military infrastructure of Louis XIV's realm. Yet, he himself had no program of research in mind for the Academy of Sciences when he founded it, nor is there much evidence that he brought the resources of the Academy to bear on the projects described in the administrative documents just mentioned. He had a general idea of what he needed, but he could not translate that into an agenda for the mathematicians and natural philosophers he was ostensibly enlisting in the service of the state. He knew he needed their expertise, but he did not know just what that expertise was or how it applied to the problems he was facing. Rather, he left it to the scientists themselves, foremost among them Huygens, to tell him what he needed from them. It is hardly surprising that what he needed is what they happened to be doing, or rather what they wanted to do.(16)

16. One can see a parallel in the research agenda that J.C.R. Licklider and other members of the computer community laid out for the Defense Department's Advanced Research Projects Agency in the early 1960s in response to the Agency's expressed need for "command and control systems"; see Arthur L. Norberg and Judy E.O'Neill, Transforming Computer Technology: Information Processing for the Pentagon, 1962-1986 (Baltimore: The Johns Hopkins University Press, 1996).

His request for guidance from Huygens came as Huygens was looking to follow up on the first English test of his clocks. Placing his research agenda at the heart of that of the new Academy placed the resources of the Academy at his disposal, not only for testing the clocks themselves but also for confirming the astronomical and mechanical theories on which their design was based. Colbert's administrative correspondence reveals the extent of those resources. A letter to Colbert de Terron, Intendant at Rochefort, dated 10 March 1670, informs him that:

M. Richer, having been chosen by the Academy of Sciences to go to the East [sic] Indies in order there to carry out astronomical observations that may be related to those being carried out here and to test the clock and pendulums that have been constructed for determining longitude at sea, the King has deemed it proper for him to travel with the squadron of his vessels that is headed to that land. As the said Mr. Richer is a person of merit who must apply himself to quite abstruse (curieuses) matters, I ask you to require the captain of the vessel on board which he shall embark to give him a place at his table and a place at the common table for the man he will be taking with him, seeing to it above all that he [Richer] shall find all the accommodations he will need, both for adjusting the said clocks and for transporting his baggage and instruments, which left six days ago. I am sure you will attend to this most exactly.(17)
The larger research program required a different sort of facility, realized in the Observatory built to the Academy's specifications in 1671 and dedicated to the advancement of astronomy, "that noble science which deals with matters that are obscure but which is thought so useful to public interests, primarily to navigation and geography, as well as to the propagation of the Christian religion."(18) It was on the floor of the west tower that Sedileau and Chazelle, under the direction of Cassini, laid out planispheric projection of the earth on which researchers placed locations of which the longitude and latitude had been accurately determined by measurement of lunar eclipses.(19)

17. Jean Baptiste Colbert, Lettres, instructions et mémoires de Colbert, ed. Pierre Clément (7 vols., Paris, Imprimerie impériale, 1861-1873), Vol. V, 294-95. The following year, Colbert wrote to the French ambassador in Denmark, ordering that he smooth the way there for astronomical observations to be carried out by Picard. Colbert prefaced his order by noting that "entre les grandes choses auxquelles le Roy, nostre maistre, s'applique, celle des sciences n'occupe pas moins son esprit que toutes les autres qui regardent la guerre...." Later, Colbert put the resources of both the navy and the army at the disposal of Cassini to move large lenses from Rome to Paris.

18. Jean-Baptiste du Hamel, Regiae scientiarum academiae historia, 2nd ed. Paris, 1701, Book I, Sect. 8, Chap. 1, p. 103.

19. Du Hamel, Historia, II, 11, 4, v., p. 217. The original was effaced but a copy was published by Jean Baptiste Nolin in 1696 and is reproduced in The Quest for Longitude, p. 56.

As several recent studies have described in detail, the Observatory became the center of an extensive effort to map the globe and to measure its surface.(20) That meant establishing and maintaining tables of lunar distances and lunar eclipses (both of our moon and those of Jupiter) used for the determination of longitude of points on land even after Harrison's clock, measurement of the length of the meridian and of the constant of gravity at various places, and the application of those data to the question of the shape of the earth. Along with such theoretical matters went the practical issues of tables, instruments, and instructions for those who had the task of navigating a ship through unknown waters and of mapping the world they were exploring. A similar story may be told of the Greenwich Observatory. It is at such institutions that science became part of the infrastructure of the modern state.

20. See most recently Jordan Kellman, "Discovery and Enlightenment at Sea: Maritime Exploration and Observation in the 18th-Century French Scientific Community" (Ph.D., Princeton, 1998).