MARIOTTE, EDME

(d. Paris, France, 12 May 1684)

experimental physics, mechanics, hydraulics, optics, plant physiology, meteorology, surveying, methodology.

Honored as the man who introduced experimental physics into France,¹ Mariotte played a central role in the work of the Paris Academy of Sciences from shortly after its formation in 1666 until his death in 1684. He became, in fact, so identified with the Academy that no trace remains of his life outside of it or before joining it. There is no documentation to support the tentative claim of most sources that he was born around 1620 in Dijon. His date of birth is entirely unknown, and his title of seigneur de Chaseüil makes the present-day Chazeuil in Burgundy (Côte-d’Or) the more likely site of his birth and childhood; several families of Mariottes are recorded for the immediate area in the early seventeenth century. Indirect evidence places him as titular abbot and prior of St.-Martin-de-Beaumont-sur-Vingeanne (Côte-d’Or), but his precise ecclesiastical standing is uncertain; contemporary sources generally do not refer to him by a clerical title.²

If not born in Dijon, Mariotte appears to have been residing there when he was named to the Academy. His letter announcing the discovery of the blind spot in the eye was sent from Dijon in 1668, as was the one extant (and perhaps only) letter he wrote to Christiaan Huygens. A letter from one Oded Louis Mathion to Huygens in 1996 suggests that Mariotte was then still in Dijon or at least that he had been there long enough to establish personal contacts.³ By the 1670’s, however, Mariotte had moved to Paris, where he spent the rest of his life.

Lack of biographical information makes it impossible to determine what drew Mariotte to the study of science and when or where he learned what he knew when named to the Academy. Seldom citing the names of others in his works, all written after joining the Academy, he left no clues about his scientific education. The circumstances surrounding his nomination, the letter to Huygens in 1668, and the nature of his scientific work combine to suggest that he was self-taught in relative isolation.⁴

It was a plant physiologist that Mariotte first attracted the attention of the Academy shortly after its founding. Engaged in discussion of Claude Perrault’s theory of the vegetation of plants, the original academicians apparently invited a contribution by Mariotte, who held the “singular doctrine”⁵ that sap circulated through plants in a manner analogous to the circulation of blood in animals. Mariotte’s verbal presentation of his theory and of the experiments on which it was based drew a rejoinder from Perrault, and the Academy charged the two men to return with written accounts and further experiments. At the same time, apparently, Mariotte was elected to membership as physicien. He carried out his charge on 27 July 1667, presenting the first draft of what was published in 1679 as De la végétation des plantes. His detailed argument from plant anatomy and from a series of ingenious experiments failed to resolve the controversy completely, and only in the early 1670’s did accumulated evidence provided by others vindicate his position.

Whatever the advanced state of his botanical learning in 1666, Mariotte’ education in other realms of science seems to have taken place in the Academy. When, for example, late in 1667 or early in 1668, he presented some of his findings on “the motion of pendulums and of heavy things that fall toward the center [of the earth]” and an account of “why the strings of the lute impress their motion on those in unison or in [the ratio of an] octave with them.” he learned from Huygens that Galileo had already achieved similar results and only then, on Huygens’ advice, read Galileo’s Two New Sciences.⁶ All of Mariotte’s works have two basic characteristics: they treat subjects discussed at length in the Academy, and they rest in large part on fundamental results achieved by others. His own strength lay in his talent for recognizing the importance of those results, for confirming them by new and careful experiments, and for drawing out their implications.

Mariotte’s career was an Academy career, which embodied the pattern of research envisaged by the founders of the institution. Although named as physicien, he soon shared in the work of the mathématiciens as well. In 1668, while continuing the debate on plant circulation, he took active part in a discussion of the comparative mechanical advantages of small and large wheels on a rocky road, read a paper containing twenty-nine propositions on the motive force of water and air (a subject to which he repeatedly returned during his career), read another paper on perspective (geometrical optics), and reviewed two recently published mathematical works.

Also in 1668 Mariotte published his first work, Nouvelle découverte touchant la veüe, which immediately embroiled him in a controversy that lasted until his death, although no one denied the discovery itself. Curious about what happened to light rays striking the base of the optic nerve, Mariotte devised a simple experiment: placing two small white spots on a dark background, one in the center and the other two feet to the right and slightly below the center line, he covered his left eye and focused his right eye on the center spot. When he backed away about nine feet, he found that the second spot disappeared completely, leaving a single spot on a completely dark surface; the slightest motion of his eye or head brought the second spot back into view. By experiments with black spots on a white background and with the spots reversed for the left eye, he determined that the spot disappeared when the light from it directly struck the base of the optic nerve, which therefore constituted a blind spot or, as he called it, defect of vision in the eye.

The discovery, confirmed by Mariotte’s colleagues in both Paris and London, startled him into abandoning the traditional (and correct) view that images in the eye are formed on the retina (a continuous layer of tissue) and adopting the choroid coat behind the retina (discontinuous precisely where the optic nerve passes through it to attach to the retina) as the seat of vision. Mariotte’s fellow academician, the anatomist Jean Pecquet, who with others had been investigating the eye since 1667, immediately disputed this conclusion and wrote to defend the traditional view. A series of experiments carried out before the Academy in August 1669 only widened the area of disagreement between the two men, as did Perrault’s support of Pecquet. Mariotte published a rebuttal of Pecquet’s critique in 1671, but by then the issue had become moot.⁷ As the Lettres écrites par MM. Mariotte, Pecquet et Perrault …(1676) reveals, Pecquet and Perrault could not provide a convincing explanation for a blind spot on the retina (partly because they disagreed with Mariotte over the action of nerves), and Mariotte rested part of his argument on phenomena now known to be irrelevant (such as the reflection of light from the choroid of certain animals).

Although the controversy over the seat of vision dominated Mariotte’s attention in 1669 and 1670, he continued his research in other areas. In 1669 he took part in discussions of the cause of weight (in which he supported some form of action at a distance against Huygens’ mechanical explanation) and of the nature of coagulation of liquids. The latter issue seems to lie behind a series of experiments on freezing, carried out and presented jointly with Perrault in 1670. The experiments, which concerned the pattern of formation of ice and the trapping of air bubbles in it, enabled Mariotte to construct a burning glass of ice.

In 1671 Mariotte read a portion of his Traité du nivellement (published in 1672) describing a new form of level which used the surface of free-standing water as a horizontal reference and employed reflection of a mark on the sighting stick to gain greater accuracy in sighting. In the treatise itself he gave full instructions for the instrument’s use in the field and a detailed analysis of its accuracy in comparison with that of traditional levels, in particular the chorobates of Vitruvius. In 1672 Mariotte’s activities in the Academy were restricted largely to confirmation of G. D. Cassini’s discoveries of a spot on Jupiter and a new satellite (Rhea) of Saturn.

As early as 1670 Mariotte had announced his intention to compose a major work on the impact of bodies. Completed and read to the Academy in 1671, it was published in 1673 as Traité de la percussion ou choc des corps. The first comprehensive treatment of the laws of inelastic and elastic impact and of their application to various physical problems, it long served as the standard work on the subject and went through three editions in Mariotte’s lifetime.

Part I of the two-part treatise begins with the definitions of “inelastic body,” “elastic body,” and “relative velocity” and then makes four “suppositions”: (1) the law of inertia; (2) Galileo’s theorem linking the speeds of free-falling bodies to the heights from which they fall from rest (ν² ∞ h); (3) the independence of the speed acquired from the path taken in falling; and (4) the tautochronism of simple pendulums for small oscillations. The suppositions form the basis for an experimental apparatus consisting of two simple pendulums of equal length, the replaceable bobs (the impacting bodies) of which meet at dead center. To facilitate measurement, Mariotte makes the further assumption that for small arcs the velocity of the bob varies as the arc length (rather than the versine). Repeated experiments on inelastic clay bobs of varying sizes confirm a series of propositions, most of them termed by Mariotte “principles of experience”: the additivity of motion (both directly and obliquely), the dependence of impact only on the relative velocity of the bodies (confirmed by the extent of flattening on impact), the quantity of motion (weight times speed) as the effective parameter of impact (also measured by flattening), and the laws of inelastic collision linking initial and final speeds through the conservation of quantity of motion.

The laws governing elastic collisions then follow from those of inelastic collision by means of the principle that a perfectly elastic body deformed by the impact of a “hard and inelastic” body regains its original shape and, in doing so, imparts to the impacting body its original speed. Confirmed by experiments involving the striking of a stretched string by a pendulum bob, the principle leads Mariotte to another series of experiments designed to show that such apparently “hard” bodies as ivory or glass balls in fact deform upon impact. In one test he lets ivory balls fall from varying heights onto a steel anvil coated lightly with dust; circles of varying widths show that the degree of flattening is dependent on the speed of the ball at impact, and the return of the balls to their initial heights confirms his principle of full restoration. By treating elastic bodies at the point of maximum deformation as inelastic ones, and by then distributing the added speeds acquired by restoration inversely as the weights of the bodies, Mariotte succeeds in determining the laws of elastic collision, applying them in one instance to the recoil of a cannon and directly testing the results experimentally. Part I closes with the transmission of an impulse through a chain of contiguous elastic bodies, a problem first posed by Descartes’s theory of light.

Part II opens with a treatment of oblique collision, in which Mariotte employs (without citing his source) Huygens’ model of impact in a moving boat. In Mariotte’s use of the model, the boat is traveling at right angles to the plane of the impacting pendulums, allowing the application of the parallelogram of motion to derive the laws of oblique collision from those of direct impact. Mariotte then turns to some problems in hydrodynamics, in which he combines the hydrostatic paradox and the results thus far obtained to argue that the speed of efflux of water from a filled tank varies as the square root of the height of the surface above the opening. Examining next the force of that efflux, he determines by use of a balance beam that the force is to the weight of the water in the reservoir as the cross-sectional area of the tube (or opening) is to that of the reservoir. Combining these results, he concludes that the force of impact of a moving stream against a quiescent body varies as the cross-sectional area of the stream and the square of its speed. In a particularly suggestive passage Mariotte argues that a body moved by a steady stream of fluid striking it (that is, by a succession of uniform impulses) accelerates in the same manner as a falling body, that is, according to Galileo’s law of S oc t².In contradiction to Galileo, however, he insists that bodies falling through air must have a finite first speed of motion.

The use of a balance beam as apparatus and model leads to a treatment of the center of percussion, or center of agitation, of a compound pendulum, that is, the point on the pendulum that strikes an object with the greatest force. In one of the earliest published applications of algebraic analysis to physical problems, Mariotte obtains a solution by determining the point that divides a rigid bar rotating about one endpoint into two segments having equal quantities of motion. His attempt then to equate the center of percussion with the center of oscillation (he calls it the center of vibration) makes his treatment of the latter far less successful than that of Huygens in his Horologium oscillatorium, also published in 1673. A few experiments on the fall of bodies through various media, performed in 1682 with Philippe de La Hire, bring the final version of the Traité de la percussion to a close.

Taken as a whole, the treatise reveals Mariotte as a gifted experimenter, learned enough in mathematics to link experiment and theory and to draw the theoretical implications of his work. He made full use of the results obtained by his predecessors and contemporaries, but his experimental mode of analysis and presentation differed markedly from their approaches to the problem. Clearly he knew of the work of Wallis, Wren, and Huygens published in the Philosophical Transactions of the Royal Society in 1668; and there are enough striking similarities between Mariotte’s treatise and Huygens’ then unpublished paper on impact (De motu corporum ex percussione, in Oeuvres, XVI) to suggest that he knew the content of the latter, perhaps verbally from Huygens himself. Certainly his colleagues in the Academy recognized Mariotte’s debt to others while they praised the clarity of his presentation. And yet Galileo’s name alone appears in the treatise; Huygens’ in particular is conspicuously absent.

Some seventeen years later, in 1690, when Mariotte was dead, Huygens responded to this slight (whether intentional or not) by accusing Mariotte of plagiarism. “Mariotte took everything from me,” he protested in a sketch of an introduction to a treatise on impact never completed,

… as can attest those of the Academy, M. du Hamel, M. Gallois, and the registers. [He took] the machine, the experiment on the rebound of glass balls, the experiment of one or more balls pushed together against of line a equal balls, the theorems that I had published [in the philosophical Transactions (1668) and the Journal des sçavans (1669)]. He should have mentioned me. I told him that one day, and he could not respond.⁸

Except for the published theorems, if Mariotte took the other ideas from Huygens, he could have done so only when Huygens offered them in the course of Academy discussions. Mariotte may well have considered the content of those discussions the common property of all academicians and have felt no need to record their specific sources when publishing them under his own name.

Certainly in 1671 and 1673 Huygens made no proprietary claims in the Academy. His response to Mariotte’s treatise consisted of a critique of the theory of elasticity on which parts of it were based. His commitment on cosmological grounds to the existence in nature of perfectly hard bodies that rebound from one another and transmit impulses placed him at odds with Mariotte’s empirically based rejection of them.⁹ Later that same theory of elastic rebound formed an integral part of Huygens’ Traité de la lumière (1690). Huygens also later denied Mariotte any role in the determination of the center of oscillation, claiming (despite the evidence of Mariotte’s treatise) that he had discussed only the center of percussion and had failed to demonstrate that it was the same as the center of oscillation.

Following the presentation of the Traité de la percussion, Mariotte seems largely to have withdrawn from Academy activities until 1675. Scattered evidence, particularly a striking demonstration of the hydrostatic paradox performed before a large audience at the Collège de Bourgogne in Paris in 1674 and reported in the Journal des sçavans in 1678 (p. 214), suggests that he was at work on the pneumatic experiments that form the basis of his De la nature de l’air (1679). Like his other works, Nature de l’air combines a review and reconfirmation of what was already known about its subject with some original contributions. Like the Traité de la percussion, it also omits the name of the author on whom Mariotte clearly had relied most heavily, in this case Robert Boyle, while acknowledging its debt to a more distant source, Blaise Pascal’s équilibre des liqueurs.

Nature de l’air focuses on three main properties of air: its weight, its elasticity, and its solubility in water. To show that air has weight, Mariotte points out the behavior of the mercury barometer and the common interpretation that the weight of the column of mercury counterbalances the weight of the column of air standing on the reservoir. Turning to the elasticity of air, he presents a series of experiments in which air is trapped in the mercury tube before it is immersed in the reservoir, thus depressing the height at which the mercury settles. He thereby establishes that

…the ratio of the expanded air to the volume of that left above the mercury before the experiment is the same as that of twenty-eight inches of mercury, which is the whole weight of the atmosphere, to the excess of twenty-eight inches over the height at which [the mercury] remains after the experiment. This makes known sufficiently for one to take it as a certain rule of nature that air is condensed in proportion to the weight with which it is charged.¹⁰

This last statement, further confirmed by experiments with a double-column barometer and extended to the expansion of air through experiments in a vacuum receiver, has gained Mariotte a share of Boyle’s credit for the discovery and formulation of the volume-pressure law; indeed, it is called “Mariotte’s law” in France. If, however, in the essay Mariotte gives no credit to Boyle, neither does he make any claims of originality; rather, he treats the law as one of a series of well-known properties of air.

Interested in the barometer more as a meteorological tool than as an experimental apparatus, Mariotte turns next to a discussion of the relation between barometric pressure and winds and weather (a subject to which he returned at greater length in his Traité du mouvement des eaux), and then to the solubility of air in water. The determination through experiment that water does absorb air in amounts dependent on pressure and temperature leads him, in one of his rare excursions into the theory of matter, to posit the existence of a matière aérienne, a highly condensed form of matter into which air is forced under high pressure and low temperature. His discussion, which includes the work on freezing done with Perrault in 1670, rests in part, however, on a lack of distinction between the air dissolved in water and the water vapor produced by high temperature and low pressure.

Despite his commitment to a special form of matter to explain solubility, Mariotte rejects any attempt to reduce the elasticity of air to a more fundamental mechanism. Explicitly denying the existence of an expansive subtle matter among the particles of air, he prefers to rely heuristically on Boyle’s analogy (without citing the source) of a ball of cotton or wool fibers. A similar analogy of sponges piled on top of one another, together with the volume-pressure law, suggests to him a means for determining the height of the atmosphere. On the initial assumption that a given volume of air at sea level would expand some 4,000 times without the pressure of the air above it and that the pressure drops uniformly with increasing altitude, he divides the atmosphere into 4,032 strata, each stratum corresponding to a drop of 1/12 line (1/144 inch) in pressure from a height of twenty-eight inches of mercury at sea level. Comparing measurements made by Toinard and Rohault with ones made by himself with Cassini and Picard, he estimates that at sea level a rise of five feet in altitude corresponds to a drop of 1/12 line in pressure; hence the first stratum is five feet in height. By the volume-pressure law, the 2,016th stratum is ten feet thick, the 3,024th is twenty feet thick, and so on.

As a simplifying arithmetical approximation to the resulting geometric progression, Mariotte assumes an average stratum of 7.5 feet for the first 2,016 strata, an average of fifteen feet for the next 1,008, and so on. Each group of strata then has a thickness of 15,120 feet, or 5/4 league, and a total of twelve groups has a total height of fifteen leagues (sixty kilometers). As Mariotte notes, varying estimates of the full expansibility of air lead to different values for the height of the atmosphere; but even a factor of 8 million produces a height of less than thirty leagues by his method, which he further confirms by theoretical calculation of the known heights of mountains.

Mariotte’s essay closes with some random observations, one of which, an assertion that air is not colorless but blue, forecasts his next major investigation. Involved in 1675–1676 in the Academy’s (never completed) project to meet Louis XIV’s request for a complete inventory of the machines in use in France, which was to be prefaced by a short theoretical introduction,¹¹ and in 1677 in a series of varied experiments, by 1678 he had begun a fairly continuous series of reports to the Academy on the rainbow and the refraction of light by lenses and small apertures. A proposal by Carcavi in March 1679 for a complete treatise on optics by Mariotte, Picard, and La Hire resulted in Mariotte’s presentation in July and August of his De la nature des couleurs. He worked further on the essay over the next two years, reporting frequently to the Academy. In 1681 he read the final version, which then appeared as the fourth of the Essays de physique.

Perhaps the best example of Mariotte’s experimental finesse, the essay on colors also illustrates well his scientific eclecticism, combining Cartesian epistemology, Baconian methodology, and Aristotelian modes of explanation. He begins:

Among our sensations it is difficult not to confuse what comes from the part of objects with what comes from the part of our senses…Supposing this, one clearly sees that it is not easy to say much about colors,…and that all one can expect in such a difficult subject is to give some general rules and to derive from them consequences that can be of some use in the arts and satisfy somewhat the natural desire we have to render account of everything that appears to us.¹²

On the basis, then, of four suppositions (the geometric structure of the light cone and of a sunbeam passing through an aperture; the gross phenomenon of refraction, including partial reflection; the refraction of light toward the normal in the denser medium, and conversely; and the focusing of the human eye), ¹³ Mariotte presents a comprehensive catalog of experimental results concerning refraction, emphasizing the precise order and intensity of the colors produced and the angles of the rays producing them.

Mariotte’s review of various mechanisms proposed for explaining these results finds fundamental weaknesses in all of them. In particular Descartes’s notion of a rotatory tendency to motion, besides being inherently unclear, implies constantly alternating patterns of color contrary to observation; and Newton’s proposal of white light as a composite of monochromatic colors, although it explains much, fails on the crucial test. That is, repeating Newton’s refraction of violet rays through a prism, Mariotte finds further separation in the form of red and yellow fringes about the image. ¹⁴ In the absence of an adequate theory, he retreats in the essay to eight “principles of experience,” which are essentially generalizations of the behavior of refracted light as observed in the preceding experiments. Using these principles, Mariotte then undertakes to explain a long series of observed phenomena, including the chromaticism of lenses, the shape of the spectrum, and diffraction about thin objects. The explanations are merely a prelude, however, to his main concern, a complete account of the rainbow.

Reviewing previous accounts from Aristotle to Descartes, Mariotte states his basic agreement with that of Descartes but points to its lack of complete correspondence with observation. In particular Descartes failed to explain the upper and lower boundaries (40° and 44°) of the primary rainbow. Mariotte’s own full account applies to Descartes’s basic mechanism the precise measurements made in the preceding experiments but ends with a small divergence between the calculated and the observed height of the rainbow. The divergence, a matter of forty-six minutes of arc, led Mariotte to carry out with La Hire a protracted series of refraction experiments using water-filled glass spheres. Employing the techniques established in his essay on air, he made adjustments for the different densities of air (and hence different indexes of the sun on the water in the spheres. 500 feet, where the rainbow is formed, and for the heating effects of the sun on the water in the spheres. This work brings theory and observation into closer alignment. Similar but less extensive use of the “principles” offers satisfying explanations of stellar coronas (explained by refraction through water vapor in the clouds), solar and lunar coronas, and parhelia and false moons (all explained by refraction through small filaments of snow in the shape of equilateral prisms.)

In contrast with the precision and clarity of the treatment of refraction in part I of the essay, Mariott’s attempt in part II to explain the color of directly observed bodies seems vague and undirected, perhaps because there was little for him to build on. A mass of undigested empirical phenomena forces him ultimately to retreat to an essentialist stance and to argue, for example, that “the weak and discontinuous light of the ignited fumes of brandy, sulfur, and other subtle and rarefied exhalations is disposed with respect to the organs of vision in a manner suited to make blue appear.”¹⁵

For all its apparent diversity, Mariotte’s research reflects a continuing concern with the motion of bodies in a resisting medium. The subject forms the core of the letter to Huygens in 1668 and of part II of the Traité de la percussion in 1673. Moreover, it was the subject of a full Academy investigation in 1669. A report in 1676 on the reflection and refraction of cannon balls striking water, and one in 1677 on the resistance of air to projectile motion, pursued the issue further. It was, however, only in 1678 that Mariotte broached the topic that would unite this research in a common theme: natural springs, artificial fountains, and the flow of water through pipes. His long report formed the basis for his Traité du mouvement des eaux at des autres corps fluides, published posthumosuly by La Hire in 1686. Mariotte was still working on the treatise at his death; his last two reports to the Academy dealt with the dispersion of water fires from a cannon and with the origin of the winds.

The Mouvement des eaux, a treatise in five parts, represents Mariott’s grand synthesis. Part I, section 1, reviews the basic properties of air and water as presented in the Nature de l’air and the paper on freezing. Section 2 uses these properties, together with meteorological and geological data, to argue that natural springs and rivers derive their water exclusively from rainfall (an extension of a theory first proposed by Pierre Perrault in 1674); the discussion includes an original estimate of the average total rainfall in France and of the content of its total rainfall in France and of the content of its major rivers. Section 3 carrier the meteorological discussion into the topic of the winds and their origin. Having met with some success in establishing a chain of weather stations across Europe, ¹⁶ Mariotte uses their reports and those of others to give a full account of the world’s and Europe’s major winds, basing it on the daily eastward rotation of the earth, the rarefaction and condensation of air due to heating and cooling, and changes in the distance of the moon from apogee to perigee. The account is particularly striking for the extent of detailed geographical and meteorological information from around the world.

Part II deals with the balancing forces of fluids due to weight, elasticity, and impact. Beginning with a treatment of statics based on a “universal principle of mechanics” akin to that of virtual velocities and illustrated by the solution of what is known as “Mariotte’s paradox,”¹⁷ the treatise moves to experimental and theoretical demonstrations of the hydrostatic paradox and the Archimedean principle of floating bodies. Turning from the force of weight to that of elasticity, it recapitulates in some detail the discussion of the volume-pressure law in the Nature de l’air, asserting of water only that it is practically incompressible and hence has no elastice force. It does, however, have a force of impact, which Mariotte had already begun to explore in part II of the Traité de la percussion and which he continues to study here in the form of the speed of efflux of water through a small hole at the base of a reservoir. Five “rules of jets of water” relate the speed and force of the flow to the height of the reservoir and the cross-sectional area of the opening. The rules are then adapted to the impact of flowing water against the paddles of mills; direct measurement tends to confirm the applicability of the laws of inelastic collision to he situation.

Part III derives directly from Mariotte’s work at the fountains of Chantilly in 1678 and is devoted to the experimental determination of the constants required for applying his theoretical rules to actual fountains. Of particular interest here is his report on the variation of the period of a pendulum with respect to latitude, a consideration made necessary by the use of the pendulum as a timing device for measuring rate of flow. Part IV continues in a practical vein, discussing the deviation from the ideal in real fountains. The discussion provides an opportunity to introduce Mariott’s findings on the effect of air resistance on the path and speed of projectiles, both solid and fluid, and leads directly to the subject of friction in conduit pipes, the opening topic of part V, again treated with reference to experiments performed at Chantilly.

Part V and the treatise conclude with a study of the strength of materials, in which Mariotte disputes Galileo’s analysis and solution of the problem of the breaking strength of a loaded beam. ¹⁸ His solution, based largely on experimental results, is then applied to water pipes, relating the height of the reservoir to the necessary cross-sectional thickness of the pipes.

Mariotte’s treatise attracted widespread attention and was the only one of his major works to be translated into English (by J. T. Desaguliers in 1718). Although eventually superseded in its theoretical portions by Daniel Bernoulli’s Hydrodynamica (1738), it remained a standard practical guide to the construction of fountains for some time thereafter.

According to the testimony of La Hire and his colleagues, Mariotte was also the author of an unsigned Essay de logique that appeared in 1678. B. Rochot has shown that this work closely resembles in content and structure, and frequently quotes verbatim, an unpublished manuscript by Roberval.¹⁹ According to Rochot, however, Mariotte did not plagiarize Roberval but, rather, succeeded him at his death in 1675 as recording secretary for an Academy project on scientific method, whence the absence of an author’s name upon publication. The work bears Mariotte’s unmistakable stamp, however, both in the fit between its proposed methodology and his actual research procedures and in the use of his own research as examples (in particular the argument for the choroid as the seat of vision).

Like all treatises on method in the seventeenth century, Mariotte’s rests on the conviction that divergence of scientific opinion derives from faults in procedure—that is, from faulty deduction or induction, from inadequate experimentation, or from failure to observe procedure arising out of ulterior motives. Because the last is beyond his control, and because the rules of proper deduction are well known, Mariotte concentrates on the rules of induction, especially induction based on experiment. Following Descartes, he accepts both a distinction between reality and perception and also the existence of self-evident propositions that are true of reality. For the most part, however, those propositions are of a mathematical nature, abstracted from the contingencies of the natural world, which are known only through sense data. Since those data do not allow the distinction between the perception and what is perceived, they make extremely difficult, perhaps even impossible, any reliable transition from knowing the world as it appears to us to knowing the world as its really is. Hence, for Mariotte induction and analysis must stop at general principles that are directly verifiable by the senses. Although hypothetical systems that go beyond this point can have immense heuristic and organizational value (he gives as examples both the Ptolemaic and the Copernican systems), they generally can claim no epistemological status other than convenience.

In general Mariotte brought to his Essay de logique the precepts and procedures that characterize his actual research. Concerned more with the articulation and application of experimentally determined generalizations than with their reduction to more fundamental (and unverifiable) mechanisms or principles, Mariotte treated subjects in piecemeal fashion, relying on common sense and good judgment based on intimate familiarity with the physical situation to guide his reasoning. His essay seldom delves beyond this level of analysis, and his fifty-three general principles do little more than recapitulate what had been the common methodological stock of experimentalists since Aristotle. His distrust of theoretical systems extended to methodology itself and led him at one point in the essay to assert that there are no sure rules of method, other than constant experimentation in the study of nature.

As an active member of the Academy for over twenty-five years, Mariotte exerted influence over scientific colleagues both within and without that institution. His closest associate seems to have been La Hire, but during his tenure he carried out joint investigations with most of the other members, including Huygens. His work was known to the Royal Society and was cited by Newton in the Principia. Mariotte conducted an extensive correspondence (as yet unpublished) with Leibniz, for whom he was a source of information about the work of the Academy in the early and mid-1670’s and who in turn cooperated with Mariotte’s meteorological survey. Huygens’ accusation of plagiarism in 1690 seems to have done little to dim the reputation Mariotte had earned during his career. In speaking of his death in 1684, J.-B. du Hamel summed up that career as follows:

The mind of this man was highly capable of all learning, and the works published by him attest to the highest erudition. In 1667, on the strength of a singular doctrine, he was elected to the Academy. In him, sharp inventiveness always shone forth combined with the industry to carry through, as the works referred to in the course of this treatise will testify. His cleverness in the design of experiments was almost incredible, and he carried them out with minimal expense.²⁰

NOTES

1. Condorcet, “Éloge de Mariotte,” in Éloges des académicines de l’ Académie royale des sciences, morts depuis 1666, jusqu’en 1699 (Paris, 1773), 49; Oeuvres complètes de Christiaan Huygens, VI (Amsterdam, 1895), 177, n. 1.

2. C. Oursel reviews previous accounts and the available documentation regarding Mariott’s birthdate and birthplace in Annales de Bourgogne, III (1931), 72–74.

3. Huygens, Oeuvres, VI, 536.

4. According to J. A. Vollgraf in Huygens, Oeuvres, XXII (1950), 6321, Huygens knew nothing of Mariotte until the latter joined the Academy in 1666.

5. J.-B. du Hamel, Regiae scientiarum academiae historia, 2nd ed. (Paris, 1701), 223. For the full context of the remark, see the quotation at the end of the present article.

6. Huygens, Oeuvers, VI, 177–178.

7. Huygens, for one, thought Marottte’s to be the stronger argument; see Huygens, Oeuvres, XIII (1916), 795. William Molyneux in his Dipotrica nova (London, 1692) opted for the retina but acknowledged the strength of Mariotte’s argument and felt the choice was immaterial.

8. Huygens, Oeuvers, XVI (1929), 209.

9. Mariotte’s theory of elastic bodies is also a major theme of the review of the Treatié de la percussion that appeared in the Journal des sçavans,4 (1676), 122–125.

10. Mariotte, Oeuvres (1717), 152.

11. On this project see the full account in du Hamel, Historia, 150–155.

12. Mariotte, Oeuvres, 196–197.

13. Interestingly, Mariotte mentions the sine law of refraction only in passing and nowhere treats it as a phenomenon to be explained.

14. See in this regard the letter from Leibniz to Huygens, 26 Apr. 1694, in Huygens, Oeuvers, X (1905), 602. In it Leibniz refers to Mariotte’s experiment and asks if Huygens has had the opportunity to investigate it further.

15. Mariotte, Oeuvres, 285.

16. According to Wolf, History of Science, Technology, and Philosophy in the 16th and 17th Centuries, 2nd ed. (New York, 1950), I, 312–314, Mariotte’s effort was not the first, having been preceded most notably by that of the Accademia del Cimento in 1667.

17. The paradox is the reversal of the normal law of a bent-arm balance in the following situation: one arm of the balance is parallel to the horizon, the other inclined downward, the weights are placed at equal distances from the fulcrum along the arms, and the free-rolling weight on the inclined arm in held in place by a frictionless vertical wall. See Pierre Costabel, “Le paradox de Mariotte,” in Archives internationales de l’histoire des sciences,2 (1949), 864–881.

18. For details see Wolf, II, 474–477.

19. B. Rochot, “Roberval, Mariotte et la logique,” in Archives internationales de l’histoire des sciences,6 (1953), 38–43.

20. Du Hamel, Historia, p. 233.

BIBLIOGRAPHY

I. Original Works. Oeuvres de Mariotte, 2 vols. in one (Leiden, 1717; 2nd ed., The Hague, 1740), contains all of Mariotte’s published works and one unpublished paper; most of the articles that appeared under his name in vols. I, II, and X of the Historie de l’s Académie depuis 1666 jusq’en 1699 (Paris, 1733) are reports made to the Academy prior to their inclusion in the published works. The 1717 Oeuvres includes the following:

1. (I, 1–116) Traité de la percussion on choc des corps, 3rd ed.(Paris, 1684)—the Oeuvres dates in 1679, but the concluding experiments were not carried out until 1682); 1st ed., Paris, 1673; 2nd ed. in Recueil de plusieurs traitez de mathématique de l’ Académie royale des sciences (Paris, 1676). Reviewed in Journal des sçavans,4 (1676), 122–125.

2. (I, 117–320) Essays de physique, pour servir à; la science des choses naturelles:

a. (I, 119–147) De la végétation des plantes (Paris 1679); reviewed in Journal des sçavans,7 (1679), 245–250. G. Bugler, in Revue d’histoire des sciences …, 3 (1950), 242–250, reports a 1676 version under the title Lettre sur le sujet des plantes; the report is confirmed by the “Avis” of the Oeuvers but not by other sources.

b. (I, 148–182) De la nature de l’air (Paris, 1679); reviewed in Journal des sçavans,7 (1679), 300–304.

c. (I, 183–194) Du chaud et du froid (Paris, 1679); reviewed in Journal des sçavans,7 (1679), 297–299.

d. (I, 195–320) De la nature des couleurs (Paris, 1681); reviewed in Journal des sçavans,9 (1681), 369–374.

3. (II, 321–481) Traité du mouvement des eaux et des autres corps fluides (Paris, 1686; 2nd ed., Paris, 1690; 3rd ed., Paris, 1700), trans. into English by J. T. Desaguliers as The Motion of Water and Other Fluids, Being a Treatise of Hydrostaticks … (London, 1718).

4. (II, 482–494) “Ràgles pour les jets d’eau,” in Divers ouvrages de mathématique et physique par MM. de l’ Académie royale des sciences (Paris, 1693), English tran. by Desaguliers as addendum to Traité … des eaux.

5. (II, 495–534) “Letters écrites par MM. Mariotte, Pecquet et Perrault sur le sujet d’une nouvelle décoverte touchant la veüe par M. Mariotte,” in Recueil de plusieurs traitez de mathématique… (Paris, 1676), and then separately (Paris, 1682). Mariotte’s first letter was originally published, along with Peacuquet’s response, as Nouvelle découvert touchant la veüe (Paris, 1668) and was reviewed in Journal des sçavans,2 (1668), 401–409. Mariotte’s reply was published as Seconde lettre de M . Mariotte à M. Pecquet pour montrer que la choroīde est le principal organe de la veüe (Paris, 1671).

6. (II, 535–556) Traité du nivellement, avec la description de quelques niveaux nouvellement inventez (Paris, 1672), repub. in Recueil… (Paris, 1676); reviewed in Journal des sçavans,3 (1672), 130–131).

7. (II, 557–566) “Traité du mouvement des pendules,” from MS letter to Huygnes repub. from Leiden MS i Huygens, Oeuvres, VI, 178–186.

[The Pagination of the 1717 Oeuvres jumps form 566 to 600; the table of contents and the index show no work omitted.]

8. (II, 600–608) Expériences touchant les couleurs et la congélation de l’eau. Both taken from Academy records as later published in the Hisotrie de l’Acadeémie depuis 1666 jusqu’en 1699, X, 507–513; the paper on freezing appeared earlier in Journal des sçavans,3 (1672), 28–32.

9. (II, 609–701) Essay de logique, contenant les principes des sciences et la mainère de s’en servir pour faire des bons raisonnments (Pairs, 1678), unsigned.

Of these works only three have been republished in a modern ed.: Discours de la nature de l’air, de la végétation des plantes. Nouvelle découverte touchant la vue, in the series Maītres de la Pensée Scientifique (Paris, 1923).

Few original papers remain, the most important of which are 28 letters from Mariotte to Leibniz and 10 from Leibniz to Mariotte. According to P. Costabel, Archives internationales d’histoire des sciences,2 (1949), 882, n. 1, they are among the Leibniz papers in Hannover.

II Secondary Literature. There is no biography or secondary account of Mariotte’s work. The above account has been culled largely from references to him in Huygens’ correspondence and papers (Huygens, Oeuvres, passim) and in J.-B. du Hamel’s Historia, passim. Condorcet’s éloge gives only the broadest outline of Mariotte’s career, as do other general French biographical reference works. The fullest catalog of his positive achievements remains Abraham Wolf’s scattered references in the 2 vols. of his History of Science, Technology and Philosophy in the 16th and 17th Centuries, 2nd ed. (New York, 1950), which have the added virtue of placing those achievements in their contemporary context. For specific aspects of Mariotte’s career, see Pierre Brunet, “La méthodologie de Mariotte,” in Archives internationales d’hisotrie des sciences,1 (1947), 26–59; G. Bugler, “Un précurseut de la biologie expérimentale: Edme Mariotte,” in Revue d’histoire des sciences …,3 (1950), 242–250; Pierre Costabel, “Le paradoxe de Mariotte,” in Archives internationales d’histoire des sciences,2 (1949), 864–881; and “Mariotte et le phénomène élastique,” in 84e Congrès des socieété savantes (Paris, 1960), 67–69; Douglas McKie, “Boyle’s Law,” in Endeavour,7 (1948), 148–151; Jean Pelseneer, “Petite contribution à; la connaissance de Mariotte,” in Isis, 42 (1951), 299–301; Bernard Rochot, “Roberval, Mariotte et la logique,” in Archives internationales d’shisotrie des sciences,6 (1953), 38–43; Maurice Solovine, “à; propos d’un tricentenaire oublié: Edme Mariotte (1620–1920),” in Revue scientifique (24 Dec. 1921), 708–709; and E. Williams, “Some Observations of Leonardo, Galileo, Mariotte, and Others Relative of Size Effect,” in Annals of Science,13 (1957), 23–29.

On the blind-spot controversy, see John M. Hirschfield, “The Académie Royale des Sciences (1666–1683): Inauguration and Initial Problems of Method” (diss., Univeristy of Chicago, 1957), ch. 8.

Michael S. Mahoney